Tutorials—Materials Science · Cerius2 Tutorials—Materials Science Release 3.0 April 1997 9685 Scranton Road San Diego, CA 92121-3752 619/458-9990 Fax: 619/458-0136

Cerius2Tutorials—Materials Science

Release 3.0April 1997

9685 Scranton RoadSan Diego, CA 92121-3752

619/458-9990 Fax: 619/458-0136

Copyright*

This document is copyright © 1997, Molecular Simulations Incorporated. All rights reserved.Except as permitted under the United States Copyright Act of 1976, no part of this publica-tion may be reproduced or distributed in any form or by any means or stored in a databaseretrieval system without the prior written permission of Molecular Simulations Inc.The software described in this document is furnished under a license and may be used orcopied only in accordance with the terms of such license.

Restricted Rights LegendUse, duplication, or disclosure by the Government is subject to restrictions as in subpara-graph (c)(1)(ii) of the Rights in Technical Data and Computer Software clause at DFAR252.227–7013 or subparagraphs (c)(1) and (2) of the Commercial Computer Software—Restricted Rights clause at FAR 52.227-19, as applicable, and any successor rules and regula-tions.

Trademark AcknowledgmentsCatalyst, Cerius2, Discover, Insight II, and QUANTA are registered trademarks of MolecularSimulations Inc. Biograf, Biosym, Cerius, CHARMm, Open Force Field, NMRgraf, Polygraf,QMW, Quantum Mechanics Workbench, WebLab, and the Biosym, MSI, and Molecular Sim-ulations marks are trademarks of Molecular Simulations Inc.IRIS, IRIX, and Silicon Graphics are trademarks of Silicon Graphics, Inc. AIX, Risc System/6000, and IBM are registered trademarks of International Business Machines, Inc. UNIX is aregistered trademark, licensed exclusively by X/Open Company, Ltd. PostScript is a trade-mark of Adobe Systems, Inc. The X-Window system is a trademark of the MassachusettsInstitute of Technology. NSF is a trademark of Sun Microsystems, Inc. FLEXlm is a trademarkof Highland Software, Inc.

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Reprinted with permission from Cerius2 Tutorials—Materials Science, April 1997,Molecular Simulations Inc., San Diego.

Requests should be submitted to MSI Scientific Support, either through electronic mail [email protected] or in writing to:

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To print photographs or files of computational results (figures and/or data) obtained usingMolecular Simulations software, acknowledge the source in the format:

Computational results obtained using software programs from Molecular Simu-lations Inc.—dynamics calculations were done with the Discover® program,using the CFF91 forcefield, ab initio calculations were done with the DMol pro-gram, and graphical displays were printed out from the Cerius2 molecular mod-eling system.

To reference a Molecular Simulations publication in another publication, no author should bespecified and Molecular Simulations Inc. should be considered the publisher. For example:

Cerius2 Tutorials—Materials Science, April 1997. San Diego: Molecular Simula-tions Inc., 1997.

Cerius2 Tutorials—Materials Science/April 1997 v

Contents

How to Use This Book xi

Who should use this book . . . . . . . . . . . . . . . . . . . . . . . . . . xiiThings you need . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiUsing other Cerius2 books. . . . . . . . . . . . . . . . . . . . . . . . . . . xiv

Drug Discovery Workbench . . . . . . . . . . . . . . . . . . . . . . . xvOther Cerius2 books of possible interest . . . . . . . . . . . . xv

Typographical conventions . . . . . . . . . . . . . . . . . . . . . . . . xvi

1. Anisotropic Line Broadening inX-ray Powder Patterns 3

Before you begin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Step-by-step instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Reviewing the solution . . . . . . . . . . . . . . . . . . . . . . . . . . . .13What to do next . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

2. Effect of Changing Site Occupancies onX-ray Powder Patterns 15

Before you begin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15Step-by-step lesson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

What to do next. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21

3. Refinement of Semiconductor Dopant SiteStructure Against EXAFS Data 23

What to do next . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34

4. Examining a Defect in a Ceramic StructureUsing HRTEM 35

Before you begin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35Step-by-step procedure . . . . . . . . . . . . . . . . . . . . . . . . .36

A. Load a model of the BISCO superconductingBi2Sr2CuO6 oxide . . . . . . . . . . . . . . . . . . . . . . .36

vi Cerius2 Tutorials—Materials Science/April 1997

.

5. Rietveld Refinement of Inorganics 45

Before you begin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Solving the problem step-by-step . . . . . . . . . . . . . . . . . . . . 46

First refinement stage: background, intensity factor,and cell dimensions . . . . . . . . . . . . . . . . . . . . . . . . 56

Second refinement stage: peak profile refinement . . . . 60Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

What to do next . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6. Screening of Zeolites: Gas SeparationProperties 67

Before you begin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Solving the problem step-by-step . . . . . . . . . . . . . . . . . . . . 69

Load the zeolite, Li-X . . . . . . . . . . . . . . . . . . . . . . . . . . 69Create a zeolite model from a published paper . . . . . . 73Incorporate cations and alter the Si:Al ratio. . . . . . . . . 79Calculate Connolly surface . . . . . . . . . . . . . . . . . . . . . 84Load the adsorbate molecules . . . . . . . . . . . . . . . . . . . 89Load the forcefield . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Set up the Monte Carlo simulation . . . . . . . . . . . . . . . 95Analyze the adsorption results . . . . . . . . . . . . . . . . . 102Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

7. Vibrational Frequency and ElectronicProperty Calculation of Aspirin 113

Before you begin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113A. Building an atomistic model of aspirin . . . . . . . . . . . . 114B. Initial optimization of the structure using molecular

mechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116C. Modeling aspirin using quantum mechanics . . . . . . . . 117D. Analyzing the quantum mechanics model to obtain

predictions of structural and electronic properties . . 119E. Predicting vibrational spectra and normal modes . . . . 123

8. Studying a Ziegler-Natta PolymerizationCatalyst 125

Before you begin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Solving the problem step-by-step . . . . . . . . . . . . . . . . . . . 127

A. Sketching in the ansa-zirconium catalyst . . . . . . . 129

Cerius2 Tutorials—Materials Science/April 1997 vii

B. Creating the syndiotactic transition state . . . . . . . .139C. Optimizing the transition state . . . . . . . . . . . . . . . .145D. Creating and optimizing the isotactic

transition state . . . . . . . . . . . . . . . . . . . . . . . . . . .150E. Comparing energies and rationalizing tacticity . . .152

Reviewing the solution . . . . . . . . . . . . . . . . . . . . . . . . . . .154In this tutorial you learned or reviewed… . . . . . . . . .155

What to do next . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155References and related material . . . . . . . . . . . . . . . . . . . .156

9. Predicting an Ab-initio Crystal Structurefor Urea 159

Before you begin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159Solving the problem step-by-step . . . . . . . . . . . . . . . . . . .163

A. Creating a urea molecule . . . . . . . . . . . . . . . . . . . .163B. Prediction sequence setup. . . . . . . . . . . . . . . . . . . .167C. Running prediction sequence . . . . . . . . . . . . . . . . .171D. Evaluating the results. . . . . . . . . . . . . . . . . . . . . . .172

Reviewing the solution . . . . . . . . . . . . . . . . . . . . . . . . . . .181Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .182What to do next . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .182References and related material . . . . . . . . . . . . . . . . . . . .182

10. Investigating the Inhibition of InorganicScales 185


A. Loading a model of barium sulphate. . . . . . . .189B. Predicting the crystal morphology of barium

sulphate . . . . . . . . . . . . . . . . . . . . . . . . . . . . .190C. Creating a surface model from the barium

sulphate (2 0 0) crystal face . . . . . . . . . . . . . .193D. Viewing and saving the (2 0 0) surface . . . . . .196E. Measuring the sulphate ion spacings on

the (2 0 0) crystal face . . . . . . . . . . . . . . . . . . .197F. Creating and measuring surfaces for the other

barytes faces. . . . . . . . . . . . . . . . . . . . . . . . . .200G. Sketching the potential inhibitor, a

diphosphonate molecule . . . . . . . . . . . . . . . .203H. Optimizing the potential inhibitor. . . . . . . . . .204I. Comparing the inhibitor molecule spacings

with surface ion spacings. . . . . . . . . . . . . . . .207J. Visualizing the surface/inhibitor interaction . .210

viii Cerius2 Tutorials—Materials Science/April 1997

.

Reviewing the solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 216Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217What to do next . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218References and related material . . . . . . . . . . . . . . . . . . . . 219

11. Density and Bandstructure ofAluminum Arsenide 223

12. Optimizing the Geometry of Stishovite 233Before you begin . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233Running the tutorial lesson . . . . . . . . . . . . . . . . . . . . 233

13. Optical Properties of Diamond 245Before you begin . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245Running the tutorial lesson . . . . . . . . . . . . . . . . . . . . 245

14. Calculating the Density of States ofFerromagnetic Gd 253

Analyzing the result of a self-consistent calculation . 257

15. Calculating the Dielectric Constant of GaP 265

16. Structure of Quartz 275

Further study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

17. Estimating Polymer Properties UsingQSPR Methods 285

Before you begin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285Solving the problem step-by-step . . . . . . . . . . . . . . . . . . . 288

Example 1: Designing a polyimide for use in thedielectric base of high performancecomputer chips . . . . . . . . . . . . . . . . . . . . . . . . . . 288A. Building structures and optimizing the

candidate polyimide repeat units . . . . . . . . . 288B. Predicting properties of the candidate

polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295Example 2: designing a mixed acrylate

copolymer to be compatible with PVC . . . . . . . . 298A. Predicting properties for pure PVC. . . . . . . . . 298B. Building a new repeat unit . . . . . . . . . . . . . . . 300C. Calculating properties for a mixed acrylate

copolymer . . . . . . . . . . . . . . . . . . . . . . . . . . . 304

Cerius2 Tutorials—Materials Science/April 1997 ix

Reviewing the solution . . . . . . . . . . . . . . . . . . . . . . . . . . .308Poly A/poly B phase diagram from

solubility parameters . . . . . . . . . . . . . . . . . . . . . .309Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .310

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .310

18. Evaluating the Miscibility of a Polymer/SolventSystem 311


A. Building a model of the polymer fragment . . . . . .315B. Sketching a model of the solvent molecule . . . . . . .318C. Setting up the blends calculation . . . . . . . . . . . . . .321D. Running the blends calculation . . . . . . . . . . . . . . .325E. Computing interaction parameters. . . . . . . . . . . . .329

Reviewing the solution . . . . . . . . . . . . . . . . . . . . . . . . . . .337In this tutorial you learned or reviewed… . . . . . . . . .338

What to do next . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .338References and related material . . . . . . . . . . . . . . . . . . . .338

19. Predicting Permeability of AmorphousPolymers 341

Before you begin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .341 Solving the problem step-by-step . . . . . . . . . . . . . . . . . . .344

A. Building a model of bulk amorphous PDMS . .344B. Equilibrate using energy minimization and

molecular dynamics. . . . . . . . . . . . . . . . . . . .350C. Calculate the mean squared displacement

(MSD) of the oxygen molecules anddetermine their diffusion coefficient . . . . . . .354

Reviewing the Solution . . . . . . . . . . . . . . . . . . . . . . . . . . .358 What to do next . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .359References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .360

x Cerius2 Tutorials—Materials Science/April 1997

.

Cerius2 Tutorials—Materials Science/April 1997 xi

How to Use This Book

The Cerius2 Tutorials—Materials Science presents a series of tutorialexercises that introduce you to the materials science applications.Doing these tutorials will quickly make you familiar with both theCerius2™ program and with strategies for using Cerius2 to solveproblems in materials science.

This book is intended to supplement the other Cerius2 core andmaterials science documentation:

♦ Cerius2 Modeling Environment

♦ Cerius2 Builders

♦ Cerius2 Simulation Tools

♦ Cerius2 Forcefield-based Simulations

♦ Cerius2 Quantum Mechanics — Chemistry

♦ Cerius2 Quantum Mechanics — Physics

♦ Cerius2 Computational Instruments: Property Prediction

♦ Cerius2 Analytical Instruments

While these guides discuss each module separately and in greatdetail, the Cerius2 tutorial books, Basics and Materials Science, giveyou an overview of program capabilities by working through anumber of typical real-life problems. The tutorials teach youimportant features of each module and show how you can use sev-eral modules in conjunction to solve challenging scientific prob-lems. There is also a collection of life science lessons in the Cerius2

Tutorials — Life Science.

This book is divided into five parts, based on application area:

♦ Part One: Analytical Instrumentation

♦ Part Two: Catalysis and Sorption

♦ Part Three: Chemical Reactions

xii Cerius2 Tutorials—Materials Science/April 1997

. How to Use This Book

♦ Part Four: Electronic, Optical, and Magnetic Properties

♦ Part Five: Polymer Modeling and Property Prediciton

Who should use this book

♦ If you are a materials scientist who is new to Cerius2, youshould go through the lessons in Cerius2 Tutorials — Basics andthose chapters in this book that are of interest to you.

♦ If you are a materials scientist who is already familiar with theCerius2 user interface, you should read those chapters in thisbook that are of interest to you.

Things you need

You should be familiar with a few things before you start workingwith Cerius2:

♦ The windowing software on your workstation

♦ How to use the mouse on your workstation

♦ Basic UNIX® commands

You should have the following things on your workstation beforeyou start:

♦ A licensed copy of Cerius2 installed

♦ A home directory in which files and subdirectories can be cre-ated

Modules you will need The exercises that you can do in this book depend upon whichCerius2 modules you have licensed. Before you begin one of theselessons, check that you have all the modules needed to complete it.

Things you need

Cerius2 Tutorials—Materials Science/April 1997 xiii

Lesson These modules are required

1:Anisotropic Line Broadeningin X-ray Powder Patterns

Diffraction-Crystal, Graphs

2: Effect of Changing SiteOccupancies on X-rayPowder Patterns

Crystal Builder, Diffraction Crystal, Graphs

3: Refinement ofSemiconductor Dopant SiteStructure Against EXAFS Data

Crystal Builder, EXAFS

4: Examining a Defect in aCeramic Structure UsingHRTEM

Crystal Builder, HRTEM

5: Rietveld Refinement ofInorganics

Diffraction-Crystal, Rietveld (DBWS)

6: Screening of Zeolites: GasSeparation Properties

Crystal Builder, Open Forcefield, Sorption

7:FastStructure: Structure ofQuartz

FastStructure, Crystal Builder,

8: Castep: Density andBandstructure of AluminumArsenide

CASTEP

9: Castep: Optimizing theGeometry of Stishovite

Crystal Builder, CASTEP, Open Force Field

10: Castep: Optical Propertiesof Diamond

CASTEP

11: ESOCS: Calculating theDielectric Constant of GaP

ESOCS, Graphs

12: ESOCS: Calculating theDensity of States ofFerromagnetic Gd

ESOCS

13: Vibrational Frequencyand Electronic PropertyCalculation of Aspirin

Open Force Field, Minimizer, MOPAC

14: Studying a Ziegler-NattaPolymerization Catalyst

Open Force Field, Minimizer, Dynamics

xiv Cerius2 Tutorials—Materials Science/April 1997


Using other Cerius2 books

You may want to keep the Cerius2 manuals at hand as you followthe tutorials. These Cerius2 books provide detailed informationabout the modules that you will be using in the tutorials.

♦ Cerius2 Modeling Environment—Basic modeling using theCerius2 Visualizer.

♦ Cerius2 Builders—Using the various Builders to create crystal,surface, interface, polymer, amorphous, and analog models.

♦ Cerius2 Simulation Tools—Open Force Field, Force Field Editor,Charges, Minimizer, Dynamics Simulation, Analysis, andMMFF modules.

♦ Cerius2 Computational Instruments: Property Prediction— instru-ments that rely on forcefield energy calculations: PolymerProperties, Blends, Crystal Packer, Polymorph Predictor, Mor-phology, Sorption, Synthia, and MesoDyn.

♦ Cerius2 Analytical Instruments—Diffraction-related Cerius2

materials science modules: Diffraction-Crystal, Diffraction-Amorphous, Diffraction-Faulted, Rietveld, DLS, PowderIndexing, LEED/RHEED, EXAFS, and HRTEM.

♦ Cerius2 Quantum Mechanics—Chemistry—Quantum MechanicsWorkbench™, a suite of applications that include Cerius2 inter-faces to the ADF, Gaussian, and MOPAC programs.

15: Predicting an Ab-initioCrystal Structure for Urea

Crystal Builder, Polymorph, Open Force Field, Minimizer,Diffraction-Crystal

16; Investigating the Inhibitionof Inorganic Scales

Morphology, Surface Builder, Open Force Field, Minimizer

17: Estimating PolymerProperties Using QSPRMethods

Synthia, Open Force Field, Minimizer

18: Evaluating the Miscibility ofa Polymer/Solvent System

Blends, Polymer Builder, Open Force Field, Minimizer

19: Predicting Permeability ofAmorphous Polymers

Polymer Builder, Amorphous Builder, Open Force Field,Minimizer, Dynamics, Dynamics Analysis

Lesson These modules are required

Using other Cerius2 books

Cerius2 Tutorials—Materials Science/April 1997 xv

♦ Cerius2 Quantum Mechanics—Physics—More QuantumMechanics Workbench™, including CASTEP, ESOCS, and Fast-Structure.

Drug Discovery Workbench

These books discuss the Cerius2 Drug Discovery Workbench,which do not relate to any of the tutorials in this book.

♦ Cerius2 Drug Discovery Workbench, QSAR+ and Diversity—con-tains information about the QSAR+ and Diversity drug discov-ery tools.

♦ Cerius2 Drug Discovery Workbench, Hypothesis and ReceptorModels—contains information about Receptor, Alignment, DBAccess, Systematic Search, and Catshape.

♦ Cerius2 Drug Discovery Workbench, Conformer Search and Analy-sis—information about Conformational Search and Analysisdrug discovery tools.

♦ Cerius2 Forcefield-Based Simulations: General Theory and Methodol-ogy—collects scientific and task-oriented information aboutforcefields into one book.

Other Cerius2 books of possible interest

Other Cerius2 books that you should have in your documentationset are:

♦ Cerius2 Software Developer’s Kit—a collection of developmentresources and tools that enable you to design, build, and inte-grate your own scientific applications to run in the Cerius2modeling environment.

♦ Cerius2 Command Scripts Guide—Capturing and replaying ascript of Cerius2 commands; enhancing command scripts withthe Tool Command Language (Tcl).

♦ Cerius2 Installation and Administration Guide—Instructions forinstalling and administering Cerius2 in your operating envi-ronment.

xvi Cerius2 Tutorials—Materials Science/April 1997


Typographical conventions

Unless otherwise noted in the text, this book uses the typographi-cal conventions described below:

♦ Instructions that you are to follow are presented in boxes. Forexample:

♦ Words that you type are in a bold font. For example:

Enter cerius2 to run the program.

♦ Comments and optional steps are italicized. For example:

A light blue cross representing the zirconium atom appears.

♦ The names of keys on your keyboard are enclosed in anglebrackets:

Press the <Enter> key on your keyboard.

♦ Text window output and file samples are represented incourier font. For example:

3 H3 .999 99.82 O1 O24 H4 .999 99.81 -180.0 O2 O1 H3

Click near the center of the model window.

Part 1Analytical Instrumentation

Cerius2 Tutorials—Materials Science/April 1997 3

1 Anisotropic Line Broadening inX-ray Powder Patterns

This tutorial shows how to model the effects of morphology onX-ray powder patterns. By following this tutorial, you will learnhow to calculate an X-ray powder pattern of a crystal model, andhow to simulate the effect of crystallite size and shape on the calcu-lated powder pattern.

Before you begin

Prerequisites To complete this tutorial, you will need a licensed copy of Cerius2

that includes the Diffraction-Crystal module.

Overview of the prob-lem

Morphology effects are particularly important in certain types oforganic molecular crystals, especially dyes and pigments where par-ticle size is small and powder peaks are often close together due tolarge unit cells. Morphology effects can lead to confusion as towhether or not new polymorphic forms have been discovered.

See, for example, Potts et al. (1994), which discusses the case of γ–quinacridone and suggests that the γ and γ' forms, previouslythought to be distinct polymorphs, are, in fact, the same structureand that the two forms are the manifestations of differences in crys-tallite size and shape.

Overview of the solu-tion

In this tutorial, you will study the blue pigment indanthrone. Youwill use the Diffraction-Crystal module and the Graphs module tostudy how variation in crystallite size and shape can lead to signifi-cant variation in the observed X-ray powder pattern of indanthrone.

Summary of proce-dure

The method is summarized as follows:

♦ Load the indanthrone model. (page 4)

4 Cerius2 Tutorials—Materials Science/April 1997

1. Anisotropic Line Broadening in X-ray Powder Patterns

♦ Calculate the X-ray powder pattern of crystalline indanthrone.(page 5)

♦ Modify Graphs settings (page 7)

♦ Recalculate the powder pattern for a smaller crystallite. (page 9)

♦ Recalculate the powder pattern for a different crystallite shape.(page 10)

Step-by-step instructions

This section takes you through the procedure outlined above.

You will see how Cerius2 might be used to help you discern whetherX-ray patterns of two indanthrone samples differ because the sam-ples are polymorphs of each other or because the samples have dif-ferent crystal morphologies.

1. Load the indanthrone model.

The crystal structure of indanthrone is loaded into the first model space,and some basic information about the crystal structure is written to thetext window.)

If Cerius2 is not already running, start it by typing cerius2in a UNIX window.

Select File/Load Model… from the pulldown menu.

Load the file Cerius2-Models/molecular-crystals/pig-ments/indanthrone.msi.



The model that you see is a representation of one monoclinic unit cellcontaining two molecules of indanthrone. The unit cell is approximately30.8 x 3.8 x 7.8 Å.

2. Calculate the X-ray powder pattern of crystalline indanthrone.

You may need to wait a moment for Cerius2 to open the Calculate Crys-tal Diffraction control panel.

Close the Load Model control panel.

View the model from all angles: rotate it by holding downthe right mouse button and dragging the mouse over themodel window.

Find the Diffraction-Crystal card (on the Analytical 1stack.)

Choose Calculate Diffraction on the Diffraction-Crystalcard.

Click the Preferences… button that is next to the Powderradio button.



This opens the Display Powder Diffraction control panel.

In this example, you do not want reflection labels obscuring the detailsof the final pattern.

In subsequent calculations, you will vary this size, but leave it as it isfor now.

A diffraction pattern like the one shown below should appear in the

Uncheck the Label Reflections? box.

Note that the Crystallite Size, listed under the Peak broad-ening factors heading, is 500.0 x 500.0 x 500.0 Å.

Close the Display Powder Diffracton control panel.

In the Calculate Crystal Diffraction control panel, edit theMin and Max values for 2 Theta to 5˚ and 45˚.

Click the Calculate button on the Calculate Crystal Diffrac-tion control panel.



graph window.

3. Modify Graphs settings

This opens the Graphs Expert Functions control panel.

Note the sharpness of the lines.

Enlarge the graph window by clicking and dragging on anedge or corner of the window.

Find the Graphs card on the Tables & Graphs stack.

If the card is not already at the front of the stack, click on itstitle to bring it to the front.

Choose Gallery —> Expert Functions from the Graphscard.



This will cause the next powder patterns calculated to be plotted on thesame graph as the current powder pattern.

This opens the Graph Manager control panel, which is used to controlwhich data-sets are visible and which can be edited.

Now only the Powder/simulated data-set can be edited.

Change the Data Placement popup from Replace Existingto Combine With Existing.

Choose Graph —> Manager from the Graphs card.

Uncheck the Edit box for the Powder/ticks data-set.

Click the Plotting Attributes… button, which is at the footof the Graph Manager control panel.



This opens the Plotting Attributes control panel, which you use tochange the color and labeling of the data-set.

You see that the color update of the graph window takes place right awayand that only the color of the Powder/simulated data-set (not the ticks)changes.

These label and color changes to the graph will allow this simulation tobe easily distinguished from the powder pattern simulation that youwill do in the next section.

4. Recalculate the powder pattern for a smaller crystallite.

100 x 100 x 100 Å is a more realistic size for a pigment crystal.

The diffraction pattern of the smaller crystallite is displayed over the

Use the Color popup on the Graph Manager control panelto change the color from yellow to blue.

Change the text in the Label entry box from simulated to500 x 500 x 500.

Return to the Display Powder Diffraction control panel, andchange the Crystallite size to a=b=c=100 Å.

Click the Redisplay button.



blue 500 x 500 x 500 pattern.

Compare the two patterns: note that the lines in the 100 x 100 x 100 pat-tern are much broader and that the line positions are unchanged. Thisis isotropic line broadening — each peak has been broadened to the sameextent. In the next section, you will simulate the diffraction pattern fora more realistic crystallite shape.

5. Recalculate the powder pattern for a different crystallite shape.

Re-initialization returns all Graphs controls to their default state anddeletes all data-sets from the system. The words “Gallery Empty”

Zoom into the graph by dragging in the graph windowusing the middle mouse button and holding down the<Shift> key.

Scroll horizontally or vertically along the graph by drag-ging in the graph window using the middle mouse button(without the <Shift> key).

Reset the Graphs module by clicking Reset on the Graphscard and confirming that you want to Re-initialize Graphs.



should now have replaced the powder patterns in the graph window.

100 x 100 x 500 Å is a more realistic shape for a pigment crystal.

The diffraction pattern for a 100 x 100 x 500 Å crystallite is displayedin the graph window.

Note how some of the peaks are more broadened than others. Peak inten-sity ratios are changed from the previous isotropic crystallites; here, thecrystals are much elongated along the crystallographic c-axis. Note alsothat this is not a true texture (preferred orientation) effect.

Return to the Display Powder Diffraction control panel, andchange the c parameter for the Crystallite size to 500 Å.


Repeat the Graphs/Gallery Expert Functions and Graphs/Graph Manager actions from step 3 on page 7 to set theData Placement to Combine With Existing. As you did instep 3, restrict the data-set to be edited to Powder/simu-lated v1, then change the labeling and coloring for thatdata-set.

In the Display Powder Diffraction control panel, change thec parameter for the Crystallite size back to 100 Å andchange the a parameter to 500 Å.



Next, you will simulate the powder pattern for a 500 x 100 x 100-Åcrystallite.

This calculates the powder pattern for a crystallite elongated along thea-axis and displays it over the blue 100 x 100 x 500 pattern.

Note how different the patterns appear — and that the difference isentirely due to the difference in crystal morphology.

There appears to be peak shift of about 0.2˚ between the two morpholo-gies. This is because there are, in fact, two peaks in both patterns; a dif-ferent one of which is broadened in each pattern. (You can spot theshoulder on the low angle side in the 500 x 100 x 100 pattern.) This sortof effect can lead to the mislabeling of patterns and misinterpreting dif-fering patterns as being from different polymorphs whereas, in reality,they are from the same structure but with different crystal morpholo-gies.


Use the mouse, as on page 10, to zoom into and scroll alongthe graph.

Zoom in to examine the peak at about 11.5˚.

Reviewing the solution


6. Finishing up


This tutorial has illustrated how crystallite size and shape effects canlead to significant differences in powder pattern structure and howCerius2 diffraction simulations can be used to help you recognizethese morphology effects.

In this tutorial you learned or reviewed:

❏ Loading a structure from a file into Cerius2 (Load the indan-throne model., page 4)

To end the Cerius2 session, close all open panels and selectFile/Exit from the Visualizer menu bar.

If you want to go on to another tutorial, or use Cerius2 torun an experiment, first close all panels and select File/NewSession from the menu bar.

shoulder



❏ Calculating X-ray powder patterns (Calculate the X-ray powderpattern of crystalline indanthrone., page 5)

❏ Working with Graphs (Modify Graphs settings, page 7)

What to do next

To learn more about the Diffraction-Crystal module, read the chap-ter about this module in the Cerius2 Computational Instruments: Dif-fraction and Microscopy.

You can learn more about working with Graphs in the Cerius2 Mod-elling Environment and in the Graphs tutorial in Cerius2 Tutorials—Basics.

You may want to read a published account of how Potts et al. (1994)used Cerius2 to solve a similar problem for the pigment quinacri-done.

Reference

Potts, G. D.; Jones, W.; Bullock, J. F.; Andrews, S. J.; Maginn, S. J.;J.Chem. Soc. Commun., 2565–2566 (1994).


2 Effect of Changing SiteOccupancies on X-ray PowderPatterns

This tutorial describes modeling and visualization of the effects ofchanging relative and fractional site occupancies on a powder X-raydiffraction pattern.

Before you begin

You need these mod-ules

To complete this tutorial lesson, you need a licensed copy of Cerius2

that includes these modules:

♦ Crystal Builder

♦ Diffraction-Crystal


Atomic sites within a lattice may be occupied by atoms of differenttypes in different unit cells, or may be vacant in some cells and occu-pied in others. Many physical and electronic properties of materialsdepend on site occupancies, and thus their derivation is of impor-tance.

Overview of the solu-tion

This simple example shows how Diffraction-Crystal may be used tovisualize the effect of site occupancy. Such analysis is of value inplanning experimental approaches aimed at rationalizing observedoccupancy effects.


2. Effect of Changing Site Occupancies on X-ray Powder Patterns

Step-by-step lesson

1. Calculate and compare X-ray powder patterns for puregrossular and uvarovite structures.

These two are different forms of the garnet structure — the differenceis that grossular has 100% Al on one site on which uvarovite has 100%Cr.

Enter cerius2 in a UNIX window to start the program.

Load the models Cerius2-Models/minerals//9A-Orthosili-cates/grossular.msi and uvarovite.msi.

Hold down the <Shift> key whileholding down the middlemouse button and dragging to zoom in on either one of thestructures. Label by element to show this. Flick between onestructure and the other using the Models Manager.

Step-by-step lesson


You can see there is a consequent small change in unit cell dimensionsbetween the compounds, and a small change in geometry around the Al/Cr site.

Go to Analytical-1 and select Diffraction-Crystal/CalculateDiffraction.

Switch on the Monitor Diffraction flag, and change theDisplay Range for 2 theta to 5 - 45. Select Calculate.



The pattern is autoamtically recalculated and a graph appears.

Notice that the patterns differ slightly in peak positions (because of thedifferent unit cell dimensions), but more greatly in relative peak inten-sities. Note in particular the (220) peak at around 21˚—it is quite prom-inent in the uvarovite pattern, but virtually absent in the grossularpattern.

This overlays the next graph onto the current one.

Switch between models again, using the Models Manager.

Finish with the uvarovite pattern, and uncheck the MonitorDiffraction option.

Locate the GRAPHS card (usually on the Tables andGraphs card deck). In Graphs/Gallery/Expert Functions,change from Replace Existing to Combine with Existing.

Make the grossular model current and calculate the powderpattern.

Step-by-step lesson


The two diffraction patterns should now be overlaid.

Note the substantial differences in relative peak intensities.

Note also that the (220) peak is in fact present in the grossular pattern,but of very low relative intensity.

2. Predict X-ray powder pattern for a mixed material.

This changes the selection criterion to select by element, so that whenyou select a particular atom in the structure with the right-hand mousebutton, then all atoms of that element in the structure are selected.

In the Graphs Manager, switch off the editing of all but thesimulated data, v2.

Then select Plotting Attributes and change the color tosomething different, say, blue. Change the labelling to gros-sular.

Then, in the Graphs Manager, switch off the editing of allbut the simulated data, v1, and the labelling to uvarovite.

Zoom in on the pattern.

On the toolbar, change the right-hand yellow Atom box toEl.

Pick one aluminum atom in the grossular model



This highlights all aluminums.

This changes all selected atoms— in this case all the aluminum atoms—in the model to that newly-defined element type.

Note the color and labelling change on the model.

The model now represents a material with 60% grossular and 40%uvarovite structure.

If you were performing an experiment where samples were removed atdifferent times from a system where, say, a trapped molecule was beingremoved from a clathrate lattice, or a system component was diffusingin and taking up ordered lattice positions, then this procedure would tellyou which parts of the X-ray powder pattern to scan to follow the pro-cess most easily and quickly.

For example, if a sample is unstable it is important to know this so a

From the toolbar, select Build/Element Defaults/Mixturesand set Mixture Element to MM. Enter Mixture Composi-tion as Al Cr and the Mixture Proportions as 0.6 and 0.4.

In Build/Edit Atoms, type MM in the element box.

In Diffraction-Crystal, calculate the diffraction.

The pattern is overlaid on the two already present, so goback into the Graphs Manager and edit this version of sim-ulated data (v3) to red and label it intermediate.

In the Graphs Manager box, click off the display of the sim-ulated data, v1, the uvarovite pattern (this has slightly dif-ferent peak positions than the other two), by clicking off theflag at the left-hand end of the uvarovite line.

Zoom in on the pattern and note which peaks show thegreatest change in intensity between the two.

Step-by-step lesson


quick, informative scan can be made.

3. Finishing up

What to do next

Site occupancies may be refined against experimental data usingCerius2•Rietveld.






3 Refinement of SemiconductorDopant Site Structure AgainstEXAFS Data

Prerequisites To complete this tutorial, you will need a licensed copy of Cerius2,including these modules:

♦ Crystal Builder

♦ EXAFS


The electronic properties of semiconductors depend on the natureand structure of defects present within their lattices. In the case ofdopant atoms, which are often present in extremely small concentra-tions, it is impossible to study the structure of the dopant sites byconventional X-ray diffraction. Hence Extended X-ray AdsorptionFine Structure (EXAFS), a structural probe of the immediate envi-ronment around an atom, is used.

In this tutorial, which is based on data and work from the DaresburyLaboratory, UK (in collaboration with whom the EXAFS modulewas developed), the structure of an arsenic dopant site within a sil-icon crystal lattice is studied and refined.

1. Build a model system.

If Cerius2 is not already started, type cerius2 in a UNIX win-dow.

Use the File/Load Models menu item to open the filebrowser and load the model Cerius2-Models / semiconduc-tors / Si.msi.


3. Refinement of Semiconductor Dopant Site Structure Against EXAFS Data

The atom's color changes from orange to yellow.

Select the Visualization item on the Crystal Builder cardand set the Crystal Cell Display Range to 2 x 2 x 2 and clickEnter to increase the display range of the lattice. On theCrystal Builder card, select the Crystal Building menu itemand press the Run Crystalline Superlattice button to makea crystalline superlattice (larger unit cell).

Open the Build / Edit Atoms box from the top tool bar.

Pick the central Si atom in the lattice to select it, and thentype As in the Element field and press <Enter> to change itinto an arsenic atom.


2. Read in experimental data.

The data will not be plotted until display options are selected.

This enhances the EXAFS spectrum emphasizing long-range features.

You see that the Fourier transform shows three peaks of varying inten-sities.

Close the Edit Selected Atoms and Crystal Building panels.

Now go to the EXAFS card in the Analytical 2 deck. Openthe Experimental Data control panel, and load the dataCerius2-Resources/EXAMPLES/data /SiAs_cryst.dat.

Select the Options button from the EXAFS ExperimentalData control panel and check on the Display both spectrumand FT. Then in the Run EXAFS control panel (Run on theEXAFS card) change the weighting factor to k^3.

You can now close the EXAFS Plot Options control paneland select the Plot Spectra button on the EXAFS Experi-mental Data panel.



3. Define the model parameters for spectra calculation andrefinement.

You are offered a choice of how many arsenic atoms to calculate for—either all in the model, or just selected ones. There is also a choice ofmaximum shell radius.

The parameters are shown in the boxes at the top of the Parameters con-trol panel. N is the coordination number (number of atoms in thatshell), R is the radius of the shell, A is a Debye-Waller factor (a measure

First, change the X-Ray Edge atom in the Run EXAFS con-trol panel from Cu to As.

Now go to the EXAFS card and open the EXAFS Parameterscontrol panel by selecting Parameters from the EXAFS card.Press the Calculate from Model... button.


of thermal vibration), and B is a measure of anisotropy in the Debye-Waller factor.

When you press the Run button here, the program automatically looksat the environment around the arsenic atom and defines it in terms ofshells of atoms out to a 6-Å distance.

4. Calculate potentials and phase shifts for the atoms in thesystem.

When calculating the potentials for the atom pairs you must ensure thatthe interstitial or background potential is the same for each. This meansthat you must employ an iterative procedure.

The default is Hedin-Lundquist, which you will use here, but the alter-native is X alpha, which will in some circumstances give a betterrefinement. The atom type is automatically As, and is recognized asbeing the central atom.

The calculated Fermi energy is reported in the textport, as is the inter-

Leave the Maximum radius set to the default of 6Å. Pressthe Run button for Calculate for All As centers.

Open the EXAFS Potentials control panel by choosingPotentials from the Potentials & Phaseshifts item on theEXAFS panel.

First choose the Hedin-Lundquist potential set.

Now change the Neighbor type to Si on the EXAFS Poten-tials control panel and press Calculate.



stitial potential for the default As muffin-tin radius.

You only need calculate potentials for each element in the system once,using the most common neighbor for that element.

Note the interstitial potential produced. If it is within 2 eV of that forAs, then it is acceptable.

If not, then you can iterate the muffin-tin radii of the elements on cal-culating the potentials, to give a consistent interstitial potential.

5. Optional: Recalculate each element’s potentials.

In this example, it is not strictly necessary to perform the above iterativeprocedure, but it is recommended that you try it.

6. Calculate and compare the EXAFS spectrum.

Now change the atom type to Si and leave the Neighbortype as Si.

Press the Calculate button to calculate the Si potential.

Click the Use target interstitial potential box on, and recal-culating the potentials for each element iteratively. The tar-get value is automatically set to the average of thosecalculated formerly, but you can change it.

Once suitable potentials have been calculated for each ele-ment, calculate the phaseshift for each by simply pressingthe Calculate all phaseshifts button in the EXAFS/Poten-tials & Phaseshifts/EXAFS Phaseshifts control panel.


You are now ready to calculate the EXAFS spectrum for your model,and compare it with the experimental data.

This ensures that the phaseshifts you have just calculated are used. It ispossible, of course, to simply press the Calculate button and obtain anEXAFS spectrum, but the iterative procedure described above is not fol-lowed in that case.

The EXAFS spectrum matches only very approximately with the exper-imental one, but the Fourier transform looks much better. The peakintensities are wrong, and there is a small shift in peak positions.

Select the EXAFS/Run menu item to open the Run EXAFScontrol panel and press the Preferences... button next toCalculate EXAFS spectrum, and uncheck all the toggles tooff in the EXAFS Calculate Preferences panel.

Now press Calculate EXAFS spectrum on the Run EXAFSpanel.



7. Refine the model.

Now you can refine your model against the experimental data. Allrefinement flags may be found in the EXAFS Parameters dialog box.

For the first round of refinement, go to the EXAFS/Parame-ters control panel and check refinement of the Fermi Energyand the Resolution Factor only, then in the Run EXAFScontrol panel, press Refine EXAFS parameters.


The difference made is small but significant.

This makes a clear difference to the fit, as the peak positions look muchbetter.

By now, the peak positions in the FT are fine, but the intensities are stillwrong.

For the next round, checkmark the first three shell radii (R)in the EXAFS Parameters panel and toggle off the refine-ment of the Resolution Factor. Again select Refine EXAFSparameters from the Run EXAFS menu.

Now include the remaining shell radii for the next round ofrefinement: in the EXAFS Parameters control panel, checkthe checkboxes for the remaining shell radii. Again selectRefine EXAFS parameters from the Run EXAFS menu.

In the EXAFS Parameters panel, add checkmarks (as shownbelow) for the refinement of the first two shells' Debye-Waller factors (A and B) and select Refine EXAFS parame-ters from the Run EXAFS menu.



This makes a dramatic difference, as the intensity of the left-hand peakin the FT increases and now matches much better. Including the refine-ment of the other three shells' Debye-Waller factors will make a final,small improvement.


Refinement has now proceeded as far as it can. Although the differencesare small geometrically, they have vastly improved the fit to the experi-mental EXAFS spectrum, and have been fed back to the parameters dis-played in the Parameters dialog box, and are listed in the textport.

It is possible to constrain values to refine as the same value, althoughthis will not make any improvement in this example. This is often donefor Debye-Waller factors, particularly in outer shells.

8. Finishing up





What to do next

To learn more about the ESAFS module, read Cerius2 ComputationalInstruments: Diffraction and Microscopy.

You can learn more about working with Graphs in the Cerius2 Mod-elling Environment and in the Graphs tutorial in Cerius2 Tutorials—Basics.

Acknowledgments

Acknowledgment is due to A.J. Dent and J.F.W. Mosselmans of theDaresbury Laboratory, on whose EXCURV tutorial and data this isbased.


4 Examining a Defect in a CeramicStructure Using HRTEM

This tutorial describes how to use the HRTEM module in Cerius2

to visualize the effect of a defect in a crystal structure. First, theimage for a perfect crystal will be calculated. Then, a defect will beintroduced to the model and the image will be recalculated andcompared with the original, defect-free crystal image.

Before you begin

You need these modules To complete this tutorial lesson, you need a licensed copy ofCerius2 that includes these modules:

♦ Crystal Builder

♦ HRTEM

Overview of the problem High Resolution Transmission Electron Microscopy (HRTEM) is apowerful method for studying structures where details in the sub-micron size range are important. However, images are often diffi-cult to interpret due to factors such as multiple scattering effectsand sensitivity to microscope parameters. As may be suggested bythe name, it differs from the related scanning Electron Microscopytechnique in that the electron beams that create the image areallowed to pass through the sample, rather than being scatteredback from it, and therefore undergo diffraction, allowing somemolecular level detail to be seen.

Overview of the solution HRTEM simulations are usually carried out by the multi-slicemethod. This involves defining the crystal sample as a series of“slices”, which in turn may be defined from one crystal unit cell,or from different crystals. The slice sequence is thus defined to pro-vide a representative model of the crystal. The diffraction of theelectron beam through each slices is calculated in sequence andthen propagated through the microscope to arrive at the simulated


4. Examining a Defect in a Ceramic Structure Using HRTEM

HRTEM image. The purpose of producing simulated HRTEMimages is to compare them with real ones, to test the validity of themodel used to calculate them. This model may be produced bysimply building it, or by some other molecular modeling proce-dure such as quantum mechanics or molecular mechanics.

Run logfile If we provide a logfile that reproduces or parallels the tutorial,mention it here, with brief instructions on how to run it:

To get an overview of the application of the HRTEM module, youmay want to run the Cerius2 example file ANL_htrem_parti-cle.log, which displays an example similar to the one in this lesson.

1. Enter Cerius2 in a UNIX window to start the program.

2. Choose Playback Script... from the Utilities menu to open thePlayback Script control panel.

3. Check the Re-initialize checkbox and double-click the ANL_htrem_Particle.log script file located in the Cerius2-Resources/EXAMPLES/demos directory.

The logfile leads you through the example, explaining each stepperformed in the HRTEM simulation.

Step-by-step procedure

This section takes you through the procedure outline earlier. Youwill see how Cerius2 can be used to study defects in solids.

A. Load a model of the BISCO superconducting Bi2Sr2CuO6oxide

In the following steps, you will load an msi model for the BISCOsuperconducting oxide Bi2Sr2CuO6 and display it in the polyhe-dral style structural representation.


1. Load the model.

2. Change the display style.

This shows the oxygen tetrahedra, face centered on the bismuth atoms,and the four-fold copper centered copper-oxygen planes typical of hightemperature superconductors.

If Cerius2 is not currently running, enter cerius2 in a UNIXwindow.

From the main menu bar, select File/Load Model... and usethe file browser to load Cerius2-Models / ceramics /Bi2Sr2CuO6.msi.


On the Visualizer tool bar, change the model viewing con-trol from Stick to Polyhedra.



3. Define the number of slices through the cell and thepropagating electron beam direction.

To simulate the HRTEM image, we first need to define the direction ofthe propagating electron beam and the number of slices to create alongthe beam direction.

This sets the direction of the incident electron beams on the crystal asthe a-axis, or equivalently the b-axis, as the current model is body-centered tetragonal.

This means that the electron beam will be propagated through 100unit cells. The HRTEM module uses the multi-slice method to simu-late images, but we have defined the whole unit cell as one slice here,so all slices are identical.

4. Calculate the projected electrostatic potential for each slice.

This makes sure that the defaults within the HRTEM module are rel-

From the ANALYTICAL2 deck, bring the HRTEM card tothe front and open the Create Slices control panel.

Set the zone-axis, as indicated by the Zone uvw label, to 1 00. Then change the Seed File name to pure.

On the HRTEM card, select Crystal Propagation. In thecontrol panel, set the Slice Sequence to 100(1).

In the Create Slices panel, click the button that says Initial-ize Scattering Geometry.


evant to the current crystal structure.

The program has now calculated the potential that will be experiencedby the electron beam as it traverses each cell or slice using the electronscattering factors for the elements in the compound and has calculatedhow this will affect the phase of the beams.

5. Calculate the phase transfer function for each slice andpropagate through the sequence.

This calculates the phase transfer, or transmission, function for eachslice. This is done using the projected potential and the incident beamenergy, and represents the effect of the slice on the electron beam (thatis, absorption, phase change), thus defining what amplitude and phaseis passed on to the next slice in the sequence.

6. Propagate the diffracted beams through the simulated opticsof the microscope.

An image (one unit cell's worth) is plotted in the Graph window. Thecalculation here has brought the scattered beams back together usingthe particular optics of the microscope to form the image.

Then click the Create Projected Potential file button andfinally the Create ptf button.

Back in the Crystal Propagation control panel, click theStart propagation... button.

To open the Microscope Propagation panel, select Micro-scope Propagation from the HRTEM card. Toggle on theSave .PIC as button, to ensure that the calculated image issaved. Then click the Start propagation... button.



One can compare this view of the BISCO model to that seen in theHRTEM simulated image.

7. Create a defect in the lattice and calculate the HRTEM imageand compare.

Now go back to the model displayed in the model window.Rotate (depress the right mouse button and drag) it so thatyou are looking down the crystallographic a-axis.

Open the Crystal Builder card in the BUILDERS 1 deck.Select Visualization to bring up the Crystal Visualizationcontrol panel. In the Crystal Cell Display Range, enter thevalues 1, 1, 2 and press the ENTER button. Select CrystalBuilding on the Crystal Building card. In the Crystal Build-ing control panel, press the Crystalline Superlattice button.


This doubles the number of unit cells along the direction of the c-axisand then makes the two unit cells into one large unit cell with P1 sym-metry.

This should line up two of the Bi-O groups in the lattice, which in theunaltered structure alternate in position by half a unit cell. What youhave just done is to produce a geometrical model of a slip defect.

If we now use this altered model as the basis for an HRTEM calcula-tion, using the same parameters as above, we will be able to see theeffect of a slip of half a unit cell for the bottom half of the cell, in everysecond cell in the crystal. That is, a regular array of defects. If the slicesequence were set up differently, it would be possible to define a calcu-lation to show the effect of just one slip defect in an otherwise purecrystal. This may be a useful exercise to try once this tutorial is com-pleted, but first attempt the regular array of defects.

The image plot you obtain is “longer” than before, because you haveused a unit cell of twice the size. As previously mentioned, the imageis just one unit cell's worth.

Select the bottom one-fourth of the new, doubled unit cell(by holding down the <Shift> key and the left mouse buttonwhile dragging a bounding box). Move its contents by one-half unit cell along the positive b-direction. To move it, pressthe <Control> key down and hold the right mouse buttondown as you drag the selected atoms.

In the HRTEM Create Slice box, change the seed name todefect and then repeat steps 4 through 6, above.

Go to the TABLES & GRAPHS deck. Select the GRAPHS /Graph Manager menu item. In the Graph Manager controlpanel, click Graph Scaling... and set both the Max x andMax y values to 50.



This enables you to view a larger portion of the image, as you wouldsee in a real HRTEM machine. Zoom out further using the mouse ifyou wish (hold down the <Shift> key and press the middle mouse but-ton while dragging to the left). You should be able to see that everyfourth bright layer in the image is defected.

This redisplays the pure pattern you calculated earlier. Again, this isonly one unit cell's worth.

You should now have the defected image and the pure crystal's imagenext to each other. Compare the two — see how easy it is to tell themapart?

HRTEM is routinely used to examine and characterize the defects instructures of interest in the electronics industry, such as this one, orin the oil and gas industries, such as zeolite structures. Some organo-metallic pigments are also investigated using the technique.

Select GRAPHS/Gallery Manager and in the control panelselect Expert Functions. Set Data Placement to ADDI-TIONAL GRAPH.

In the HRTEM/Display panel, enter pure100.pic in the PICfile box and click the Run button for plot PIC file.

As before, use the GRAPHS/Graph Manager/Graph Scal-ing functionality to look at the same area of image as youalready have displayed for the defected image.


8. Finishing up






5 Rietveld Refinement of Inorganics

This tutorial shows how the Cerius2 Rietveld (DBWS) module canbe used to refine a trial crystal structure. Rietveld refinement iter-atively improves an approximate (trial) structure to maximize theagreement between simulated and experimental diffraction pat-terns.

In this tutorial, you will use the experimental X-ray diffractiondata provided to refine a suggested trial structure for the mineralAkermanite.

Before you begin

Prerequisites To complete this tutorial, you will need a licensed copy of Cerius2



♦ Rietveld (DBWS)

Overview of the problem Rietveld refinement is a popular and versatile computational tech-nique for crystal structure refinement and sample analysis usingX-ray or neutron powder diffraction data.

In research, Rietveld refinement gives valuable insight into thestructure-property relationships of materials, allowing furtherrefinement of structural modeling against experimental data. Inmore routine analysis, Rietveld refinement accurately determinesstructural parameters and relative phase proportions in mixedsamples.

Overview of the solution In this particular tutorial problem, you will use the Cerius2 inter-face to the DBWS-9006 program to Rietveld-refine a trial crystalstructure of the mineral Akermanite towards its experimentalpowder pattern. Akermanite is a simple silicate clay mineral(Ca2MgSi2O7).


5. Rietveld Refinement of Inorganics

In the case of this tutorial, the akermanite “trial” structure hasactually been fabricated by applying some modification/distor-tion to the real crystal structure. However, in practice, you wouldobtain the trial crystal structure in some other way. For example,you might obtain a starting structure by editing the known crystalstructure of a similar mineral. Or, you might use a trial structureproduced by a modeling procedure such as Cerius2 Crystal Packeror Polymorph calculations, or some other molecular mechanics orquantum chemistry program.

First you will determine if the akermanite trial crystal structure isvalid, and then you will use Rietveld refinement to improve thecrystal structure against the experimental data.

Summary of procedure The steps you follow carrying out this tutorial are as follows:

♦ Load the trial structure of akermanite. (page 46)

♦ Load the experimental powder pattern. (page 48)

♦ Calculate the Rietveld R-factor. (page 52)

♦ First refinement stage: background, intensity factor, and celldimensions (page 56)

♦ Second refinement stage: peak profile refinement (page 60)

♦ Examine the result. (page 63)

Solving the problem step-by-step

This section takes you through the procedure outlined above. Youwill see how Cerius2 might be used to help you discern whetherthe trial crystal structure is plausible and, if so, then to refine thetrial structure.

First, you will refine those parameters that have the greatest effecton the powder pattern such as scale factor and cell dimensions.Next, you will include the more subtle parameters such as peakprofile parameters and atomic positions.

1. Load the trial structure of akermanite.



In this section, you will load in the trial structure of the akermanitecrystal that has been provided in the Cerius2-Resources/EXAM-PLES directory.

The trial crystal structure of akermanite is loaded into the first modelspace, and some basic information about the crystal structure is writ-ten to the text window.

Begin with a new or reinstalled session of Cerius2.

Open the Load Model control panel by choosing File/LoadModel… from the Visualizer menu bar.

Load the file Cerius2-Resources/EXAMPLES/data/ak100.msi



Elemental labels appear on all the atoms in the model window.

2. Examine different views of the model.

The polyhedra style highlights the tetrahedral coordination of the sil-icate.

Troubleshooting

3. Load the experimental powder pattern.


Label the atoms in the model by changing the Atom Label-ing popup on the toolbar from NO LABEL to ELEMENTS.

View the model from all angles: rotate it by holding downthe right mouse button and dragging the mouse over themodel window.

Change the display style: select the POLYHEDRA stylefrom the toolbar.

If some of the model remains in stick form, you may haveselected some of the atoms in the model window. If any atomsare selected, then only those selected will be displayed in thenew style. To correct this, you should click the Deselect Allbutton in the toolbar, and then choose the POLYHEDRA styleonce more.

(The Deselect All button looks like this .)

Rotate the view and then change the style back to STICK.



In this section, you will load an experimental X-ray powder pat-tern of an akermanite sample (Dove 1992). You will also use theDiffraction-Crystal module to simulate the diffraction pattern ofthe akermanite trial structure and compare it to the experimentaldata.

This opens the 1-D Experimental Data control panel.

The experimental data file is written in the Cambridge 3cam format.When the file is loaded, the experimental data-set is plotted in thegraph window.

4. Simulate the diffraction pattern.

This opens the Calculate Crystal Diffraction control panel.

Find the Diffraction-Crystal card. (It is most likely to be onthe Analytical 1 stack.)

Choose Diffraction-Crystal/Use Experimental Data —>1-D Experimental Data.

Use the 1-D Experimental Data control panel to load the fileCerius2-Resources/DIFF-EXP/ak100.3cam.

Choose Calculate Diffraction on the Diffraction-Crystalcard.



You want to calculate the pattern in same range as the experimental

In the Calculate Crystal Diffraction control panel, edit theMin and Max values for 2 Theta to 10˚ and 90˚.



data.


You do not want reflection labels to obscure details of the pattern.

The simulated diffraction pattern for the akermanite model structureis overlaid on the experimental data.

5. Compare the experimental and simulated diffractionpatterns.

Press the Preferences… button that is next to the Powderradio button.

Uncheck the Label Reflections? box.

Click the Calculate button on the Calculate Crystal Diffrac-tion control panel.

Place the mouse in the graph window and press the <F2>key.



This enlarges the graph window to fill the screen.

Examine the fit in detail. Note how that, although the calculated pat-tern clearly matches the experimental one, there is an offset betweenthe two. The trial structure needs some, but not too much, refinement.

6. Calculate the Rietveld R-factor.

In this section, you will set up and run a Rietveld calculation with-out refinement. This way, you will obtain starting values for theR-P and R-WP fit factors.

You may need to wait a moment for Cerius2 to open the Rietveld(DBWS) Run control panel.

Zoom into the graph by dragging in the graph windowwhile holding down the middle and right mouse button.

Scroll horizontally or vertically along the graph by drag-ging in the graph window using the middle mouse button.

Return to the normal-sized graph window by pressing the<F2> key again. Close all open control panels by clicking theclose all windows tool on the Visualizer toolbar:

Select the Rietveld (DBWS) card (also on the Analytical 1stack) to the front.

Choose Run on the card.



This opens the DBWS Radiation control panel.

Click the Radiation… button under the Simulation Setupheading.

Be sure that the radiation wavelength is correct. For a cop-per source, the default values (shown on the panel above)are correct. Close the DBWS control panel.

Click the Range… button under the Simulation Setupheading.



This opens the DBWS Range control panel.

Although it is quite possible to use the whole range of the experimentaldata for the refinement, in this example, you will only use a portion ofit.

Note the R-factor values, R-P and R-WP.

You may want to increase the size of the graph window to see thesebetter. (P is for pattern and W is for weighted.) An R-factor may also

Set the 2theta range to 10˚ to 50˚; this is the default range.

Click the Run button on the Rietveld (DBWS) Run controlpanel.

R-P and R-WPR-factors



be referred to as a figure of merit. For more detail, please see yourDBWS manual.

Where, Iobs i is the observed (experimental) intensity; Icalc i is the cal-culated intensity with all the refined parameters; and n is the numberof data points in the range.

The R-WP factor is much the same except that a weighting, wi, isapplied to give more importance to the fit at higher angles.

R 100

Iobsi Icalci–

1

n

∑Iobsi

1

n

∑------------------------------------------

=

R 100

wi Iobsi Icalci–( ) 2

1

n

∑wiIobsi

2

1

n

∑------------------------------------------------------

1 2⁄

=

R-P and R-WPR-factors



First refinement stage: background, intensity factor, andcell dimensions

In this section, you will begin the Rietveld refinement by fitting asloped background, adjusting the scale factor, and modifying theunit cell dimensions.

7. Adjust Rietveld refinement settings.

Ten refinement cycles will be performed each time you click the Runbutton on the Rietveld (DBWS) Run control panel. This should beenough to ensure that each refinement stage converges before you goon to the next stage.

Open the Rietveld (DBWS) Refinement control panel usingthe Preferences... button on the Rietveld (DBWS) Run con-trol panel.

Change the Number of Cycles from 1 to 10.

Click the Background… button on the Rietveld (DBWS)Run control panel.



This opens the DBWS Background control panel.

In DBWS, the X-ray or neutron background is refined as a polynomialof whatever order you choose. Here, by selecting to refine the first andsecond coefficients, you have specified that a first-order polynomial (alinearly sloped background) will be fitted.

In the DBWS Background control panel, check the Coeffi-cient 1 and the Coefficient 2 boxes.



Note In this case, you are not going to adjust the 2θ zero point. Anerror in zeropoint leads to a systematic peak shift such as yousee in this example (the Zoom into the graph... step on page 52).However, the peak shift may also be due to inaccurate celldimensions. For this reason, careful practitioners of the art ofpowder diffraction always ensure that their diffractometers arealigned to within 0.05˚, so zeropoints greater than that shouldbe regarded with suspicion. Here you give the data the benefitof the doubt and omit the zeropoint refinement. In any case,zeropoint refinement should always be carried out after celldimension refinement.

Click the Model… button on the Rietveld (DBWS) Run con-trol panel.



This opens the DBWS Model Variables control panel.

Check the Scale Factor box.



This will adjust the overall intensity of the calculated pattern.

Note that the b parameter is tied to the a parameter and also that youcannot select the angles. This is because of the tetragonal symmetry ofthe structure.

By now, you have set up five independent parameters for refinement:background (2), intensity scaling factor (1), and cell dimensions (2).In the next step, you execute the first stage of the refinement.

Note that the R-P drops to 11.5%. And the R-WP is at about 17.8%;if this were an organic compound, such a figure of merit would alreadybe considered a very good fit, but it is not yet good enough for thismineral.

Second refinement stage: peak profile refinement

In this section, you will refine the peak profile shape. DBWS givesyou a choice of seven profile types: Gaussian, Lorentzian, twoforms of modified Lorentzian, pseudo-Voigt, Pearson, andThompson. Pseudo-Voigt is the default form and the one you willuse in this example.

Also in the DBWS Model Variables control panel, check thea and c parameters for refinement.

Click the Run button on the Rietveld (DBWS) Run controlpanel to refine ten cycles.



Pseudo-Voigt (pV) peak is a mixture of the Gaussian (G) andLorentzian (L) peak forms:

Where , and and are refinable “mixing”parameters.

8. Refine peak profile shape.

The R-PW value should now be down to 10–11%.

Note how narrow the peaks are. The W width parameter has droppedfrom 0.1 (default) to less than 0.02. This indicates that the sample is

Press the Models... button in the Refinable Variables sec-tion of the Rietveld (DBMS) Run control panel to open theDBWS Model Variables control panel. Add a checkmark tothe W width checkbox for the Pseudo-Voigt width.

Click the Run button on the Rietveld (DBWS) Run controlpanel to refine ten cycles.

Expand the graph window as you did earlier, using the<F2> key and the mouse to scroll and zoom.

pV ηL 1 η–( ) G+=

η A B 2θ( )+= A B



highly crystalline.

The fit is good, but there are more improvements to be made.

The width parameters define how the profiles vary with diffractionangle, and the mixing parameter defines the relative Lorentzian/Gaussian character of the profiles.

Refining the orientation parameter will account for some of the tex-ture in the sample, which, when present, can grossly alter the relativeintensities of peaks. The direction of the texture may be chosen usingthe Direction boxes, but the default of (0 0 1) is fine in this case.

Check the U, V width parameters and the A mixing param-eter in the DBWS Model Variables control panel.

Add a checkmark to the G1 Orientation checkbox.

Click the Run button to refine ten cycles.

Review


Again there is a good improvement in the fit quality. The R-WP valueshould now be about 8 – 9%.

9. Examine the result.

The low R-factor indicates conclusively that this is the correct crys-tal structure of akermanite. In this section, you will examine theresults of your refinement.

Carefully examine the fit of the simulated pattern to the experimentalone.

10.Finishing up

Review

This tutorial has illustrated how the Rietveld DBWS method canbe used to refine a trial crystal structure against experimental pow-der diffraction data.

In this tutorial you learned or reviewed...

❏ Loading a crystal structure from file into Cerius2 (Load the trialstructure of akermanite., page 46)

❏ Loading an experimental X-ray data (Load the experimental pow-der pattern., page 48)

Expand the graph window as you did earlier, using the<F2> key and the mouse to scroll and zoom.





❏ Calculating a diffraction pattern (page 49)

❏ Performing a Rietveld refinement (page 52 – 63)

What to do next

To learn more about the Rietveld module, read the chapter aboutthis module in Cerius2 Analytical Instruments. You may also want tolook at some of the references cited in that chapter.

Reference

Experimental data courtesy of Dr. M. T. Dove, Department ofEarth Sciences, University of Cambridge (1992).

Part 2Catalysis and Sorption


6 Screening of Zeolites: GasSeparation Properties

This chapter presents a classic gas separations problem and showshow a zeolite may be screened to ascertain its viability in separat-ing two industrially important gases. The tutorial guides youthrough a series of steps to a solution. Along the way, you willlearn about setting up the zeolite and adsorbate models, runninga Monte Carlo simulation to predict adsorption isotherms, andanalyzing the results.

This chapter is divided into four parts:

♦ Before you begin — provides some background informationabout the problems and an overview of the solution.

♦ Solving the problem step-by-step — gives you specific instructionsto follow in order to solve the problem.

♦ Review — discusses the scientific significance of the solutionand gives a checklist of the Cerius2 skills you have learned andpoints you to relevant MSI documentation and to publishedwork.

Before you begin

You need these modules To complete this tutorial you will need a licensed copy of Cerius2


♦ Crystal Builder

♦ Open Force Field

♦ Sorption

Overview of the problem Gas separations is an area of great industrial importance. Forexample, utility gas producers wish to supply pure methane


6. Screening of Zeolites: Gas Separation Properties

which has a much higher calorific value than typical gas mixturesfound in gas fields. Specialty gas producers need purified gases foranesthetics, laboratory research and industrial processes such aswelding and metallurgy. Zeolites provide the ideal 3D frameworkin which gas separations can take place. The factors determiningthe viability of a zeolite for a separation are the physical pore sizeof the zeolite and the location, size, and charge of any cationspresent. Hence there are a virtually infinite number of possiblestructures which can be screened for a particular adsorption prop-erties.

Traditionally solutions have been experimental and have involvedrunning samples in large rigs. They are expensive in manpowerand materials and often take days to produce an isotherm. Aboveall there is the problem that only a limited number of zeolites areavailable from off the shelf commercial zeolite suppliers and thereported structures of these are often incomplete due to the pres-ence of cation impurities.

Overview of the solution Researchers at British Gas plc have been among the first to realizethe potential of computer modeling for the screening of zeolitestructures, both theoretical and published, for gas separations. Inthe example presented, the lithium form of the zeolite faujasite, Li-X, is investigated as a possible medium to separate mixtures ofoxygen and nitrogen gases. Experimental information was alreadyavailable suggesting that Li-X was suitable for this purpose. Com-puter modeling was not only able to reproduce the experimentaladsorption isotherms, but was additionally able to yield informa-tion as to the binding sites involved—explaining why this zeoliteis suited for this particular application.

In this tutorial you will explore some of the tools used for carryingout such work within the Cerius2 modeling environment—build-ing crystal structures, running Monte Carlo simulations, and ana-lyzing the output.

Run the logfile To get an overview of the tutorial, you may want to run the Cerius2

logfile CAT_sorp_LiX.log, which illustrates the procedure. To runthis logfile:

1. Enter cerius2 at the UNIX prompt.

2. Open the Examples control panel from the Help pulldown.

3. Double-click CAT_sorp_LiX.log to run the logfile.



The logfile shows the methodology that you will follow in thisexample. The plan is to investigate the adsorption of nitrogen andoxygen in Li-X. You will see how the framework atoms and adsor-bates are constructed, the Monte Carlo simulations performed andhow the results may be analyzed to show not only the predictedadsorption isotherms but also the localization of nitrogen to cat-ions which is important in this system.

This method is summarized thus:

1. Load the zeolite, Li-X

2. Create a zeolite model from a published paper

3. Incorporate cations and alter the Si:Al ratio

4. Calculate Connolly surface

5. Load the adsorbate molecules

6. Load the forcefield

7. Set up the Monte Carlo simulation

8. Analyze the adsorption results


This section takes you through the procedure outlined above. Youwill see how Cerius2 has been used to predict the adsorption prop-erties in Li-X.

Begin with a new session of Cerius2. See Cerius2 Tutorials— Basicsfor information on running Cerius2 or beginning a new Cerius2

session from within the program.

Load the zeolite, Li-X

The zeolite, Li-X, is saved in the file Cerius2-Resources/EXAM-PLES/ data/sep_LiX_CAT03.msi. However, for most applicationsyou would probably either have to load a model from the molecu-lar sieves database (Cerius2-Models/zeolites) or construct a crys-tal structure by inputting coordinates directly from a publishedpaper. In this section you will be shown how to load and view a



Alter Si:Al ratio andadd cations

Calculate Connollysurface

Add blockingatoms?

Build adsorbates

Load zeolite framework(either from database orinput via Crystal Builder)

Screening of Zeolites for Gas Separation Properties:

Repeat for eachAdsorbate

An overview of the solution

Set up forcefield

Set up Sorptionsimulation and run

Analyze results



model from a file into the current model window. Create a zeolitemodel from a published paper describes how to create a crystal struc-ture of a zeolite from a published paper.

1. Start Cerius2

If necessary, refer to Cerius2 Tutorials—Basics for information onrunning Cerius2.

2. Load zeolite.

The crystal structure of Li-X is loaded into the first model space andsome basic information about the crystal structure (space group, lat-tice centering) appears in the text window. The zeolite frameworkappears as a stick representation with cations shown as pink points.

This display option will illustrate the channel nature of the zeolite tobest effect by drawing polyhedra between the bonded frameworkatoms. The framework comprises oxygen (red), aluminium (pink) andsilicon (yellow) atoms with lithium cations being shown as pinkspheres. The choice of display style is largely up to the user. You may

Start a new session of Cerius2 by typing cerius2 at the UNIXprompt and pressing <Enter>.

Open the Load Model control panel by choosing the LoadModel… item from the File pulldown.

Load the file Cerius2-Resources/EXAMPLES/data/ sep_LiX_CAT03.msi.


Change the display style popup on the tool bar from Stickto Polyhedra.



like to try some of the other display formats available— ball, cylinder,ball and stick.

3. Improve your view of the 110 plane.

The main pore system for this zeolite is normal to the 110 plane. Thefollowing steps will help to highlight this plane.

This card should already be at the front but if not you will find it onthe Builders 1 stack.

From this card you will be able to select a Miller plane and orientation.

To view the model from all angles, rotate the model by drag-ging the mouse over the model window with the right but-ton depressed.

To scale the model, hold the <Shift> key down and drag themouse over the model window with the center buttondepressed or hold down the left and center mouse buttonswhile dragging.

Click the Crystal Builder card to the front of the Builders 1deck of cards.

Click on the Visualization menu item on the CrystalBuilder card.

Set the Miller indices to h=1, k=1, l=0, and press the<Enter> button on the Crystal Visualization control panel.

Check the Show Miller Plane box on the Visualization con-trol panel.



The 1 1 0 plane is highlighted in red.

The zeolite is now oriented correctly and you should be viewing downthe main channel.

In most cases full structural information will not be available directlyfrom a database. In such an instance section C should be followed.Where the user wishes to input a structure from a published paper sec-tion B should first be followed. If you are happy with creating andediting crystal structures skip to section D.

Create a zeolite model from a published paper

This section shows how to proceed when a zeolite structure is notavailable in the database and needs to be input from a publishedpaper. The minimum information required from the paper are thesix unit cell parameters, the space group and the coordinates (x, y,z) of the various atoms. The coordinates may be either cartesian orfractional. Additional information regarding occupancy and iso-thermal parameters may also be used if available. In this sectionwe will rebuild the Li-X structure previously loaded from the data-base.

Select the More… button to open the Miller Plane Optionscontrol panel, then press the Run Orient button, makingsure that the adjacent popup is set to parallel.

Check off the Show Miller plane checkbox on the CrystalVisualization control panel and close this panel.



1. Open Crystal Builder.

A new model, Model2, is reported in the model manager.

This card should already be at the front, but if not you will find it onthe Builders 1 deck.

2. Enter the space group.

You may now enter the space group for the structure you wish tobuild. This may be input formally or as the table number from Inter-national Crystallography Tables if known.

The other fields on the card fill with information about this spacegroup: lattice type, crystal settings, and symmetry positions.

Choose a new model window by pressing the “+” iconabove the model manager.

Click the Crystal Builder card to the front of the Builders 1deck of cards.

Select Crystal Building on the Crystal Builder card to openthe Crystal Building control panel.

Select the Edit button to the right of the Space Group buttonon the Crystal Building control panel.

In the Visualizer tool bar, set the display style to STICK andreset the view.

Enter F d -3 m or the table number 227 into the box titledSpace Group and hit <Enter> on your keyboard.



3. Select the origin.

Many space groups have a number of options relating to the definitionof the origin of the system. In this case we use option 2 of space group227. When entering published crystallographic data you should findthat a full description of the space group is given.

You will see six boxes that must be filled with the cell parameter infor-mation as indicated. Since we have chosen a cubic space group for ourexample you only need enter a parameter into the first box, a, as theprogram will automatically set the other parameters to conform withthe crystal type chosen.

4. Provide cell dimensions.

Note that because the space group selected is cubic, the a, b, and c

In the Space Groups control panel, select Origin Choice 2from the Option popup.

Close the Space Groups control panel.

Select Edit Cell Parameters on the Crystal Building controlpanel.

Enter the value 24.6716 into one of the a, b or c Cell Dimen-sions box on the Cell Parameters control panel and hit<Enter> on your keyboard.



parameters are all set to 24.6716Å and the angles set to 90.0o.

If you rotate it around you will see that an empty unit cell has beencreated in the model window. All that now remains is to add someatoms.

5. Add silicon.

This changes the input coordinate system from cartesian (XYZ) tofractional (ABC).

The first atom to be input will be a silicon. In fact the paper being usedgives no information as to the presence of Al atoms. These will beadded later via the disorder function by substituting Al for Si atomsin the correct ratio to preserve charge neutrality once cations havebeen added to the structure. For now the framework will be treated asbeing purely silicious.

An alternative would be to define the framework Si and Al atoms asbeing of type T, which is an element mixture of Si and Al atomattributes. These attributes may be altered in the Element attributes

Close the Cell Parameters control panel.

Click the Build Crystal button on the Crystal Building con-trol panel.

Select the Add Atoms… card on the Crystal Building con-trol panel.

Change the coordinate system popup from XYZ to ABC onthe Add Atom control panel.

Change the Element type from C to Si on the Add Atomcontrol panel and hit <Enter> on your keyboard.



control panel.

These are the fractional coordinates for the silicon atoms. Rememberto include spaces between the coordinates.

A silicon atom and all its symmetry-related copies have appeared inthe model window. Normally you might also wish to set an occupancy(default 1), charge (default 0.0), name and temperature factor (isotro-pic or anisotropic). These are not important in this example.

Steps 13 to 15 now need to be repeated for the other atoms in the crys-tal.

6. Add oxygen.

Into the coordinates box on the Add Atom control paneltype 0.1242 0.9495 0.0378 and hit <Enter> on your key-board.

Click the Add Atom button on the Add Atom control panel.

Change the Element type from Si to O on the Add Atomcontrol panel and hit <Enter>.

Into the coordinates box on the Add Atom control paneltype 0.1014 0.8986 0.0000 and hit <Enter>.



These are the fractional coordinates for the oxygen atoms.

This completes the addition of framework atoms.

7. Build the crystal.

As the Automatically calculate bonds checkbox (in the CrystalBuilding/Preferences panel) is toggled on by default, the structureshould appear as a fully bonded framework. You have now success-fully built the zeolite framework.

The next step is to incorporate cations into the framework, which willbe accompanied by an alteration of the Si:Al ratio in a zeolite frame-work.


Into the coordinates box on the Add Atom control paneltype 0.2505 0.2505 0.1518 and <Enter>.






Close the Add Atom control panel.

Click the Build Crystal button on the Crystal Building con-trol panel.



Incorporate cations and alter the Si:Al ratio

In this section we add some cations (lithium) to the structure justcreated in the previous section and then alter the Si:Al ratio of theframework to compensate for charge in balance.

1. Add barium.

If continuing from section B this will already be open.

The cations will be added in exactly the same way as the frameworkwas built in the previous section. There are in fact 3 lithium positionsto be input, but because the occupancy of each is different we mustassign different atom types, as will be made clear shortly.

If it is not already open, open the Crystal Building controlpanel by choosing Crystal Builder/Crystal Building.

Press the ADD ATOM button on the Crystal Building con-trol panel.

Change the input coordinates from cartesian (XYZ) to frac-tional (ABC) on the coordinate system popup on the AddAtom control panel.



Again if continuing from the previous section this will already be set.

A barium atom (light blue) and all its symmetry related copies appearin the model window. Remember that in some circumstances you mayin addition wish to set an occupancy (default 1), charge (default 0.0),name and temperature factor (isotropic or anisotropic). We now repeatthis procedure for the remaining two cation positions.

2. Add calcium and potassium cations.

This completes the addition of cations. The next step is to take theoccupancy of these cations into account. There are two ways of defin-ing partial occupancy. The first uses the occupancy factor on the AddAtom panel and keeps the number of atoms constant, assigning a par-

Set the Element type to Ba on the Add Atom control paneland <Enter>.

Enter 0.0462 0.0462 0.0462 into the coordinates box on theAdd Atom control panel and <Enter>.

Click the ADD ATOM button on the Add Atom controlpanel.

Set the element type to Ca on the Add Atom control paneland <Enter>.



Set the Element type to K on the Add Atom control paneland <Enter>.





tial occupancy to each. This is useful for applications like calculatingpowder pattern, where it would ensure correct scaling of scatteringamplitudes. Here, for charge neutrality, we need to take the secondapproach — a partial filling of the sites available with whole atoms.

3. Build a crystalline superlattice.

This is a necessary step before proceeding to the Disorder functionwhere one atom type can be randomly changed for another. If any sym-metry existed the Disorder function would not be able to change oneatom for another without changing all the symmetry related copies aswell. This would defeat the object of random substitutions!

4. Set up the Ba–Li substitution and run it.

You will see the default option is to substitute Si by Al atoms. In thiscase we wish to substitute barium, calcium, and potassium atoms forlithium atoms.

Half of the barium atoms will change to lithium atoms. The numberof each atom type is given in the text window (16 lithiums and 16 bar-

Close the Add Atom control panel.

Click the Crystalline Superlattice button on the CrystalBuilding card.

Select Build/Disorder on the Visualizer manu bar.

Enter Ba to be substituted by Li in the element boxes on theDisorder control panel.

Enter a Target ratio of 1.00 on the Disorder control paneland <Enter>.

Click the SUBSTITUTE box on the Disorder control panel.



iums in this case).

Next we need to repeat this procedure for the calcium and potassiumcations.

5. Further substitute Li for Ca and K.

There are now a total of 36 lithium atoms in the crystal. Note thatwhen deciding the ratio for substitution you must take into accountany existing atoms of the type to be substituted which are alreadypresent.

You should now have a total of 80 lithium atoms randomly distributedthroughout the zeolite A framework. All that remains is to delete theunwanted barium, calcium and potassium atoms.

Enter Ca to be substituted by Li in the element box on theDisorder control panel.

Enter a Target ratio of 0.333 on the Disorder control paneland <Enter>.

Click the SUBSTITUTE button on the Disorder controlpanel.

Enter K to be substituted by Li in the element box on theDisorder control panel.

Enter a Target ratio of 0.65 on the Disorder control paneland <Enter>. Click the SUBSTITUTE button again.



6. Delete the remaining Ba, Ca, and K atoms.

Note that because the atom selection is on Element, all barium, cal-cium, and potassium atoms have been highlighted. Distinguishing thedifferent element types should present no problem since the lithiumatoms are pink while barium, calcium and potassium atoms are eithergreen or blue.

All barium, calcium, and potassium atoms are deleted, leaving justthe 80 lithium cations and framework atoms in the unit cell.

Finally the Si:Al ratio in the framework must be altered. In this exam-ple the crystal was initially built as a purely silicon structure. To com-pensate for the 80 lithium cations we need to incorporate 80 Al atomsinto the framework.

7. Adjust the Si:Al ratio.

Change the Selection criterion popup (the right-hand“Atom”) on the Visualizer tool bar from Atom to Element.

Using the left mouse button and holding down the <Shift>key, pick one each of a barium, a calcium, and a potassiumatom.

Hold down the <Control> key and hit <Delete> on yourkeyboard, or select Edit/Delete on the main tool bar.

Reset the Disorder control panel by entering Si to be substi-tuted by Al.

Input a Target ratio of 0.65 on the Disorder control paneland <Enter>.

Toggle the Apply Loewenstein’s Rule check box to on inthe Disorder control panel.



Applying Loewenstein’s rule to the calculation will exclude substitu-tion where Al-O-Al linkages would result.

The number of Si atoms substituted by Al atoms appears in the text-port window. Note that because random numbers are used to definethe first atom for substitution and because Loewenstein’s rule hasbeen included the actual ratio achieved might not be the same as thatdesired. In this example 60–80 of the Si atoms should be substitutedfor Al atoms.

The structure built is that of Li-X according to Forano et al. (1989).

Calculate Connolly surface

In this section, we will return to Li-X and calculate a Connolly sur-face in order to estimate the accessible free volume in the zeolite.This may be seen as a first check or prelude to performing theactual Monte Carlo simulation. This calculation will determinewhether the pore size of the zeolite is large enough to allow adsor-bates to enter and also whether blocking atoms are required.

Blocking atoms are necessary where there may be a cavity largeenough to accept adsorbates which would in practice remainunfilled because the window openings to that cavity are too smallfor molecules to pass into them. If these cavities are not blockedthe Monte Carlo simulation produces an elevated loading, sincethe algorithm would try to fill them.

A classic example of this is in the zeolite A structure just created.Here the large α-cages are accessible to all potential adsorbateswhich can enter the cage via the 8-membered rings, while the

Press the SUBSTITUTE button on the Disorder controlpanel.

Close the Disorder control panel.

Close the Crystal Building control panel.



smaller β-cages are usually not accessible from the smaller 6-mem-bered rings surrounding this cage (which may additionally con-tain cations, most notably calcium, potassium, and sodium). Insuch a case dummy atoms, which have volume but do not partici-pate in the forcefield interactions, should be placed in the β-cagesto effectively fill and so block them from the Monte Carlo algo-rithm.

Let us now investigate if there are any such sites in Li-X.

1. Load the Li-X structure.

This window contains the Li-X structure loaded at the start of thistutorial.

The panel has various features including buttons to calculate anddelete a surface for either all or selected atoms and a section for prefer-ences.

The panel includes options to alter the probe radius, set by default at1.4å, the dot density, VDW scale factor and dot color. The proberadius of 1.4Å is actually the van der Waals radius of a water moleculeand is sufficient for the type of molecules we will be investigating. Theother defaults are also fine; bear in mind that for some applicationsyou may need to change these default values.

Select Model Window 1 (sep_LiX_CAT03) in the modelmanager.

Select the Geometry/Connolly Surfaces menu item on theVisualizer menu bar.



2. Set up the Connolly surface calculation for oxygen only.

The Connolly surfaces calculation is expensive computationally andfor the purposes of this investigation we need only use the oxygenatoms in the framework.

All the framework oxygens will now be selected.

It may take several minutes for a Connolly dot surface to be producedand overlaid d on Li-X. Other information about the number of dotsproduced is displayed in the text window.

3. View the surfaces of the zeolite.

As you rotate you should observe that the main channel is certainly

Change both the Atoms to be surfaced and the Atoms incalculation options on the Connolly Surfaces card toSelected.

Make sure that the Selection criterion is still set to Elementon the Visualizer tool bar and use the left mouse button topick a framework oxygen.

Click the CALCULATE button on the Connolly Surfacescontrol panel.

Use the right mouse button to view the zeolite from differ-ent orientations.

Orient Li-X in different ways in order to view the accessiblevolume down the various channels.



accessible, but that there are also small cavities which, although theyappear accessible, are not. These are the 8 α sites and need to be filledwith blocking atoms.

The blocking atoms would be added in exactly the same way as the cat-ions were added in the previous section. The element type can be takento be Am — recognized in Cerius2 as being a blocking atom. They willhave a van der Waals radius but no charge. Forcefield parameters havebeen especially assigned for these atom types so as not to participatein any forcefield calculations.

In the example here a database structure already exists with the block-ing atoms incorporated.

4. Delete the Connolly surface.

The Connolly surface is deleted.

5. Load a model from the database.

We are now going to load in Li-X with blocking atoms from our data-

Click the DELETE button in the Connolly Surfaces panel.

Close the Connolly Surfaces control panel.

Select File/Load Model on the Visualizer menu bar.



base.

All the framework atoms should be highlighted.

6. View and study the cations and blocking atoms.

What you should now have is the zeolite framework as a stick repre-sentation with the cations and blocking atoms shown respectively aspink and brown spheres.

Again you may wish to rotate and look at the model from differentviews and examine the structure more carefully.

7. Adjust the charges.

Load the file Cerius2-Resources/Examples/data/ sep_LiX_blocked_CAT03.msi.

Change the Display Style popup on the tool bar to Ball andStick.

Change the Selection rules popups on the tool bar to Atomand Fragment (“Frag”).

Pick one of the framework atoms.

Change the Display Style popup on the tool bar to Stick.

Change the Selection criterion to El. Pick an Si atom in themodel.



All the Si atoms should be selected.

When performing calculations using charges and an Ewald summa-tion, such as will be performed later, it is essential to ensure that theframework has no net charge. Here, the charges on the Si and Al atomswere modified to remove the small charge which currently exists onthis framework model.

Load the adsorbate molecules

The next step is to load some adsorbates. In our example we willload oxygen and nitrogen molecules which are readily available inthe sorbates database. In practice you may wish use molecules notavailable in the databases, in which case you will probably need tosketch them using the Sketcher facility available under Build onthe Visualize menu bar. The use of the Cerius2•3D-Sketcher isexplained fully in Cerius2 Modeling Environment and Cerius2 Tutori-als—Basics.

On the menu bar, select the Build/Edit Atoms… item toopen the Edit Atom control panel. Set the Charge to1.5833333 and hit <Enter> on your keyboard.

Pick an Si atom in the model.

Repeat the charge adjustment for silicon: in the Edit Atomcontrol panel, set the Charge to 1.5833333 and hit <Enter>on your keyboard.

Close the Edit Atoms control panel.



1. Load and study the oxygen adsorbate.

An oxygen molecule will be loaded into a new model window. Youmay wish to examine the molecule more closely using the orientationand scaling functions. You should note that the molecule consists of 2oxygen atoms plus a point charge between the two. This 3 site repre-sentation is necessary to describe the small quadrupole moment thatexists in oxygen.

You can now see the charges that have been assigned to the 3 sitemodel of oxygen. It is in accordance with Stogryn and Stogryn [1966]and consists of -0.1120 on the oxygens and 0.2240 on the point charge.

2. Load and study the nitrogen adsorbate.

A nitrogen molecule loads into a new model window. You may wishto examine the molecule more closely using the orientation and scal-ing functions. Again you should be aware that the nitrogen molecule

Open the Load Model control panel by choosing File/LoadModel… item on the Visualizer menu bar.

Load the file Cerius2-Models/sorbates/O2.msi.

Change the Labels popup on the tool bar to Charges.

Change the Labels popup on the tool bar back to No Label.

Change the Display Style popup on the tool bar to Ball.

Load the file Cerius2-Models/sorbates/N2.msi from theLoad Model control panel already open.



is also represented as a 3-site model.

You can now see the charges that have been assigned to nitrogen. It isin accordance with Murthy et al [1980] and consists of -0.5090 on thenitrogens and 1.0180 on the point charge. Note that the quadrupolemoment for nitrogen is significantly larger than that for oxygen.

Load the forcefield

To enable simulations to be performed it is necessary to invoke aforcefield. There are a number of forcefields readily available inCerius2. The merits of each are described in the Cerius2 SimulationTools, to which you would refer when selecting the most suitableforcefield for a specific application. You might also wish to edit anexisting forcefield withy our own forcefield parameters. This pro-cess is described fully in Cerius2 Simulation Tools).

In this section we will simply load and set up an appropriate force-field for the simulation of nitrogen and oxygen in Li-X.

1. Load the Watanabe-Austin forcefield.

The forcefield loads and some reference information appears in the tex-tport. Note the diverse set of forcefields available on this control panel.

Change the Display Style popup on the tool bar to Stick.

Change the Labels popup on the tool bar to Charges.


Use the Load item on the Open Force Field card (OFFSETUP deck) to open the Load Force Field control panel.

Select the Watanabe-Austin forcefield and click Load.



2. Set up the forcefield type.

The forcefield type must be set up for each structure. This is done viaa set of selection rules in the forcefield. At the same time it assignsother forcefield attributes, for example, forcefield masses, hybridiza-tion, and charges.

For the Watanabe-Austin forcefield, only mass and hybridizationattributes are assigned. Hence the charges already present on the mod-els will not be overwritten. This is important to note since some force-fields have charges associated with them, for example, BKS andBurchart. These would overwrite any charges in the model. No furtheraction needs to be taken here.

3. Display the forcefield type.

The current model (nitrogen) will be labelled with “?” indicating thatno forcefield type has been assigned.

Close the Load Force Field control panel.

Select the OPEN FORCE FIELD/Typing-> Atom menuitem to open the Force Field Atom Typing control panel.

Press the Assign force field attributes Preferences buttonto open the Attribute Assignment control panel.

Close the Attribute Assignment panel.

Make sure the Display Style popup on the Visualizer toolbar is set to Stick.

Change the Labels popup on the tool bar to FFtype.



4. Calculate the forcefield and atom types.

This assigns the forcefield types according to the selection rules. Notethat the “?” on the model have now changed. The atom type is denotedby a name of up to 5 characters. This is fully described in Cerius2

Simulation Tools.

5. Atom type the other models.

The oxygen model should now be in view. This needs to be atom typed.

The Li-X model, complete with blocking atoms, should now be in view.

We have now atom-typed each of the structures we will use in the sim-ulation.

Click the Calculate using typing rules button on the ForceField Atom Typing control panel.

Change the Labels popup on the tool bar to No Label.

Change the Display Style popup on the tool bar to Ball.

Change the Model Window to the previous one (4).


Change the Model Window to the previous one (3).




6. Set up the energy expression.

This panel essentially consists of buttons to set up the energy expres-sion and to evaluate an energy (accompanied by a popup) and also aTerm Selection… box.

This panel is divided into 4 sections — Valence, Valence Cross-terms, Non-bond, and Restraint. Under each heading are the asso-ciated energy terms toggled on and off according to the default force-field options. You may wish to switch off some components that areturned on. For example, when running short test jobs it may be wiseto turn the coulomb component off, since this is expensive computa-tionally. In this instance the default settings are fine.

A summary of the energy expression set-up appears in the textport.This completes the setting up of the forcefield. At this stage you maylike to calculate the lattice energy of the zeolite. To do this, simply clickthe Evaluate button. The energy will appear in the textport.

You will see later that the steps in this section need not have been per-formed since in the Sorption module there is a button to allow auto-matic set-up of the forcefield. If this button is clicked on thenwhichever forcefield is loaded (Universal force field is default) is atom-

Close the Force Field Atom Typing control panel.

Use the OPEN FORCE FIELD/Energy Expressions menuitem to open the Energy Expression control panel.

Select the Term Selection… box.

Close the Energy Terms Selection panel.

Click the Run button for Set up expression button on theEnergy Expression control panel.

Close the Energy Expression control panel.



typed and set up. However, should you wish to change any of thedefaults or use atom constraints (not applicable here) then the force-field must be set up manually as described above.

Set up the Monte Carlo simulation

In this section you will be shown how to set up the Monte Carlosimulation for the adsorption of nitrogen and oxygen in Li-X. Thebasic requirements are to select the adsorbates, set a pressure andtemperature, length of run, step sizes, move probabilities, force-field and output options. The method used here will be the grandcanonical ensemble, otherwise called the fixed pressure simula-tion. The simulation will generate random configurations bytranslating, rotating, creating and destroying adsorbate moleculeswhich are accepted or rejected on the basis of energy. Configura-tions with lower energy are more likely to be accepted. As the sim-ulation proceeds convergence is reached when both the energyand loading converge. This may take several million steps. Formore information on the Monte Carlo methods refer to the Compu-tational Instruments: Property Prediction manual.

1. Set up the run parameters.

You will probably find this card on the Instruments 2 deck.

Bring the Sorption card to the front.

Select the Run card on the Sorption control panel.

Set the Type of simulation to Fixed Pressure on the RunSorption control panel.



This should already be set by default.

This value has been set deliberately low in order that the simulationwill finish in minutes rather than hours. Should you have time tospend (for example, overnight) then you might like to use a realisticvalue of 1500000, which will actually produce convergence for thesystem in question.

2. Identify the sorbates.

This adds the molecule in model window 4 (Oxygen) to the Sorbatelist above. A pressure for this molecule is required.

This relates to a pressure of approximately 4 atmospheres.

This adds the molecule in model window 5 (Nitrogen) to the Sorbate

Set the Temperature to be 300.0K and <Enter>.

Set the Length of run to be 50000 and <Enter>.

Enter 4 into the first Sorbate text entry box or use the pull-down to select Oxygen, which is in model window 4, andhit <Enter>.

Type 400.0 into the Pressure text entry box next to O2 Sor-bate and hit <Enter>.

Type 5 or select Nitrogen to fill the next Sorbate text entrybox and hit <Enter>.



list above. A pressure for this molecule is required.

This relates to a pressure of approximately 4 atmospheres.

3. Set up the output parameters.

Output of models to the screen is expensive both computationally andtime-wise so when performing long simulations it is wise to eitherturn the Update model during simulation box off altogether or onlyupdate at less frequent intervals, for example, 20000.

You will almost certainly want this box ticked on for every simulationsince it gives you a final structure which you may then store and ana-lyze later.

Type 400.0 into the Pressure box for N2 Sorbate and hit<Enter>.

Open the Output control panel using the Sorption/Simula-tion Controls menu item.

Make sure Update model during simulation has a check-mark.

Set the Model update frequency to 200 and hit <Enter>.

Make sure Update model at end of simulation has a check-mark.

Make sure Use graphical simulation monitor has a check-mark.

Set the Monitor update frequency to 1000 and hit <Enter>.



Again you will almost certainly want the graphical simulation mon-itor switched on during the simulation so you can ascertain whetherthe simulation is converging or not. The graphical monitor, unlike themodel window updates, is not expensive computationally or time-wise.

This will write information about the simulation to a trajectory filethat you may later analyze.

4. Set up the trajectory file.

As with the model update frequency, care must be taken to choose arealistic value, for this is by far the most computationally expensiveand time consuming part of the Monte Carlo algorithm. It is recom-mended that the update frequency is set to 1% of the total number ofconfigurations. For example, for a run of 1,500,000, an output fre-quency of 15,000 would be satisfactory.

The trajectory file that we will create during the sorption simulationwill be called Li-X_test.sor. You could of course select any suitable file-name.

Toggle Write trajectory file during simulation to on.

Set the Trajectory write frequency to 100 and hit <Enter>.

Type Li-X_test in the Filename seed and hit <Enter>.



5. Set up the text output.

This will ensure frequent updates to the textport window where a run-ning total of the number of steps performed is output. From this infor-mation it will be possible to estimate the length of time the simulationwill take.

6. Set up step sizes.

You will see that it is possible to change the prescribed maximumtranslation and rotation allowed in a single step move. This may beimportant in some systems. For example if the zeolite cage is particu-larly small then a high maximum translation would lead to a highnumber of rejections due to bad contacts and convergence would beslow. The reverse also applies — if the cavity is large and the step sizesmall then it will take far longer to generate configurations coveringall accessible phase space and again convergence would be slow. Thereis also a box labeled Rescale Controls.

This panel sets the rescale frequency and the target ratio which isdetermined by the success rate. If this target ratio is not achieved thenrescaling occurs according to the rescale factor. In this instance nei-ther the Sorption Step Scaling or Sorption Step Sizes card need be

Make sure that Output text during the simulation has acheckmark.

Type 100 into the Text write frequency box and hit <Enter>.

Close the Sorption Output control panel.

Select the Sorption/Simulation Controls->Step Sizesmenu item to open the Sorption Step Sizes control panel.

Click the Rescale Controls button.



changed, though you should be aware of their existence.

This card allows the user to alter the relative probability that duringa step an adsorbate molecule will be translated, rotated, created ordestroyed. Again this need not be altered here though the user shouldbe aware of this facility. For example, if argon were an adsorbate undertest, the rotation probability could be reduced to zero since the adsor-bate (an argon atom) is spherically symmetrical.

7. Set automatic forcefield toggle.

In most circumstance you would probably want this box ticked on toallow Cerius2 to automatically load, atom-type, and set up the force-field expression for all simulation models. However, in this case wehave already done this in the previous section (F). There is also a BadContact Rejection Factor box which sets how close (measured in frac-tions of the VDW radii) atoms can approach each other before they arerejected. The default value of 0.5 is fine for this simulation.

8. Define the interaction cut-off.

Close the Sorption Step Scaling and Sorption Step Sizes con-trol panels.

Open the Move Probabilities control panel using the Sorp-tion/Simulation Controls.

Close the Move Probabilities control panel.

Select the Sorption/Energy Calculation menu item to openthe Sorption Energy control panel.

Uncheck Use Automatic Force-Field options.

Enter 12.3 into the Interaction Cut-off box.



This sets the value beyond which interactions between atoms areignored. Because a minimum image convention is used this should beless than half the smallest parameter for the simulation cell to avoidwrap-around. Since the unit cell parameters for Li-X are 24.67Å wecan input a value of 12.3Å for the Interaction Cut-off.

9. Set up and run Ewald calculation.

Electrostatic charge interactions will now be included using theEwald method. You should note that if the framework and sorbates arenot highly charged then it may be possible to increase the speed of cal-culation by not including the Coulombic calculation. The next step,having chosen to include Coulombic interactions, is to set up theEwald parameters.

You will immediately note that the Real space cut-off has been set tothe same as the Interaction Cut-off on the Sorption Energy controlpanel (12.3Å). There is also a Required accuracy value set to 0.100kcal/mol by default.

This automatically uses the value of the Real space cut-off and theRequired accuracy to generate the Reciprocal-space cut-off and Ewaldsum constant. It is always advisable to use this automatic set-up facil-

Add a checkmark to Include Coulomb energy.

Click the Ewald Parameters… button.

Click the Run button for Estimate Ewald parameters.



ity since choosing values by hand can be difficult.

10.Run the simulation.

We are now ready to run the simulation.

You will see that information regarding the number of steps completedis given in the textport, while the model window is periodicallyupdated with snapshots of the framework and adsorbates. The graphwindow will also appear containing two graphs showing how theenergy and loading vary with time. If the simulation were run for longenough, both graphs would show convergence, that is, the energywould converge to a minimum while the loading would converge to amaximum. In this instance, unless you have set the length of run tobe around 1.5 million steps, neither graph will converge. However, itshould be clear that the adsorption of nitrogen far exceeds that of oxy-gen.

Analyze the adsorption results

In this section you may choose to analyze the results which havejust been calculated using a limited number of configurations orwork performed previously using 1.5 million steps. The only dif-ference being which trajectory file to choose to load. The text willrefer to the latter case and will therefore use files from previous

Close the Sorption Ewald and Sorption Energy control pan-els.

Click Run Simulation on the Run Sorption control panel.

Close the Run Sorption control panel once the simulation iscomplete.



runs. It is suggested you follow this section through using the filesindicated and then repeat it using the trajectory file you have justcreated. The results should be similar.

There are five types of analysis which will be encountered — tra-jectory file, mass distribution, energy distribution, loading curve,and mass cloud.

1. Load a trajectory file.

The first operation is to load a trajectory file for analysis from thebrowser box.

This trajectory file contains information about a sorption simulationfor a nitrogen and oxygen binary mixture on Li-X performed for 1.5million configuration steps. It is part of a series of related simulationsperformed at different pressures but constant temperature (300K).

2. Plot trajectory.

Two graphs will appear; one a plot of energy versus step number andthe other a plot of cell loading versus step number. These plots are sim-ilar to the graphical output seen during the simulation, the only dif-ference being that these plots represent the raw data of the trajectoryfile which are instantaneous data rather than cumulative averagedvalues.

Select the Analysis menu item from the Sorption menucard.

Select the file Cerius2-Resources/EXAMPLES/data/ non-ascii/mixture_300_1.sor from the browser box and clickLoad.

Click the Plot Trajectory file button.



From these graphs it should clear that the system had reached equilib-rium since the plots converge to a minimum energy and maximumloading.

Note that it is possible to set an analysis range from the SorptionAnalysis control panel. For instance you might only wish to examinethe last 50,000 steps of a run to ascertain whether convergence hadtaken place. Also note that the shift key and middle mouse buttonwhen depressed together over one of the graphs will allow magnifica-tion of that graph, that is, vertical movements will scale the y axiswhile horizontal movements will scale the x axis.

3. Plot loading curve.

This displays a plot of combined average cell-loading values from a setof fixed sorption simulations. In this case it will plot the results fromthe series of trajectory files with the seed Cerius2-Resources/EXAM-PLES/data/ nonascii/mixture_300_*.sor (where * has values 1, 2,3…). This set of data actually corresponds to simulations run underthe same conditions except for varying pressure — so the plot is actu-ally an adsorption isotherm for nitrogen and oxygen adsorption in Li-X.

Again plots may be made over a given range of steps, as for trajectoryfile analysis. In the textport window values for the adsorption of eachcomponent for each pressure are given.

It should be clear that nitrogen is preferentially adsorbed to oxygenover the entire pressure range. For example at 1 atmosphere the ratioof adsorbed nitrogen to oxygen is predicted to be 6.3. This is due to thegreater interaction of the large quadrupole moment on the nitrogenwith the lithium cations as will be shown shortly.

4. Plot energy distribution.

Click the Plot Loading curve button.

Click the Plot Energy distribution radio button.



A histogram of energy distribution for each sorbate is plotted. If youpress the Preferences box accompanying the Plot Energy distribu-tion radio button, you will see that you can additionally set the max-imum energy, minimum energy and resolution (bin size) of the plots.The default distribution is between -50 to 50 kcal/mol, divided into100 bins.

In the example used here there are two well-defined peaks with max-ima at -7 and -2 kcal/mol for nitrogen and oxygen respectively. Thenitrogen molecules are, on average, more favorably adsorbed than theoxygen molecules, due to their lower energies. The peak height is aconsequence of the greater loading exhibited for nitrogen. Both adsor-bates produce just one energy peak indicating that each of the sitesadsorbed at in the framework has equal preference. In some examplesyou might see two discrete peaks for an adsorbate indicating that thereare two separate adsorption sites, one of which (the lowest energy one)is the preferred site.

5. Plot mass distribution.

Mass distribution plots for nitrogen (on the right) and oxygen (on theleft) will be plotted in the graphs window for the analysis range spec-ified. The distribution is projected down a particular zone axis whichmay be set, along with the bin resolution, in the Preferences box. Theplot is calculated by dividing the cell into bins, with each bin beingcolored according to the number of molecules having centers that fallwithin each bin. In this case the lighter the area the more moleculesadsorbed.

6. Change the projection zone and number of bins.

Click the Plot Mass distribution radio button.

Click the Preferences button next to the Plot Mass distribu-tion radio button.

Set the Projection zone to be 1 1 0 and hit <Enter>.



This projection zone allows a view down the main channel of the zeo-lite. You will notice that the 1st and 2nd axes in plane have beenupdated to read 0 0 1 and 1 -1 0 respectively.

This will increase the resolution of the plot.

The mass distribution is now replotted at higher resolution along the1 1 0 projection zone. It may help here to refer back to the model win-dow but it should be immediately clear that nitrogen and oxygen mol-ecules may occupy all sites within the main cavities. Further, thenitrogen molecules exhibit considerable localization which is not evi-dent for the adsorbed oxygen, the distribution of which remains dif-fuse throughout. There are various ways in which the plot may bemade clearer using the functionality in the Graphs module. Here wewill content ourselves with displaying the plot in color.

7. Adjust the graph.

Set the Number of bins for each axis in plane to 50 and hit<Enter>.

Click the Plot Mass distribution radio button.

Close the Sorption Mass Plot control panel.

Open the Graphs menu card (Tables and Graphs deck).

Select the Gallery->Manager menu item on the Graph card.

Checkmark both boxes in the Edit column relating to theMass Distribution plots.



This ensures that both plots will be updated together.

The mass distribution plots will now be colored. Blue areas are for lowadsorption and red areas for high adsorption. The user might also liketo experiment with other functions on this control panel, e.g., thestyle, polarity, exposure, brightness, contrast, conversion, interpola-tion and data range may all be changed.

This redisplays Li-X without adsorbed nitrogen and oxygen mole-cules.

8. Plot the mass cloud.

A mass cloud will appear superimposed onto the zeolite framework inthe model window. The center of mass of each adsorbate molecule ineach configuration is displayed as a dot in the model space. The dis-play is analogous to the mass density plot except that it is a 3D picturethat may be manipulated along with the zeolite model: it will trans-late, rotate and magnify as the model is translated, rotated or magni-fied. This is a very powerful analysis tool which shows the preferredpositions of the adsorbates in the zeolite.

By default the dots are displayed according to energy ranging from red(low energy) to violet (high energy). Here it should be noted that only

Close the Gallery Manager control panel.

Open the Plotting Attributes control panel from theGraphs/Data->Plotting Attributes.

Alter the Color popup from Grey-Scale to Color.

Close the Plotting Attributes control panel.

Change the current model to model number 1.

Click the Plot Mass Cloud radio button.



green and blue colored dots are present, representing two closelyrelated energies. The blue dots are diffuse throughout the zeolite and,as will be seen presently, represent the oxygen molecules. Recall thatthese have slightly higher energy than the nitrogen molecules, repre-sented by the green dots. The nitrogen molecules exhibit considerablelocalization.

In this case the distinction is clear since the energy distribution plotsshowed two distinct peaks with little overlapping. In other examplesthis may not be so and the mass cloud should be colored according toadsorbate.

9. Color the mass cloud by sorbate.

This control panel allows the user to select the cloud color by energyof adsorbate, delete a mass cloud or temporarily hide a mass cloud.There are also boxes where the property (which is either the energyrange or adsorbate depending on the type of plot) and color mapping(which ranges from 1 for red to 360 for violet) can be user defined.

This will cause the range for adsorbate 1 (nitrogen) to have a maxi-mum value of 0, that is, all nitrogen molecules will be displayed aswhite dots while the oxygen molecules will have a range from 1 to 360:the entire spectrum excluding white.

Press the Preferences button next to the Plot Mass Cloudradio button.

Change the Color cloud by popup to Sorbate.

Enter 0 in the Color Map box for adsorbate 1 and hit<Enter>.

Press the Plot Mass Cloud radio button.



The mass cloud plot will be redisplayed according to adsorbate. It willnow be clear that the nitrogen molecules (white dots) are localizedwhile the oxygens (red dots) are diffuse. On closer inspection it willbeen seen that the localization of the nitrogens is associated with thelithium cations in the zeolite framework. This is clear evidence thatthere is a strong quadrupole-cation interaction present in the nitro-gen–Li-X adsorbed system which is absent in the diffuse oxygen–Li-X system.

Note that the Property box changed from energy to adsorbates, thatis, the range is now from 1 to 2, representing nitrogen and oxygenrespectively.

This concludes our investigation into the effects of nitrogen andoxygen separation in Li-X. The Sorption module has been used topredict adsorption isotherms for nitrogen and oxygen gases, andshowed that, due to the strong nitrogen quadrupole moment caus-ing localization of nitrogen to lithium, this zeolite would make anexcellent candidate for such gas separations.

10.Finishing up

Review

In this tutorial exercise you have seen how Cerius2 could be usedto rationalize and predict the gas separations properties of a zeo-lite. There are a number of assumptions and approximations

Close all open windows by selecting the close visible controlpanels icon on the main menu deck.

To end the Cerius2 session, select File/Exit from the Visual-izer menu bar.




which need to be taken into account – indeed you have alreadyseen how to allow for one weakness of the Monte Carlo simulationby blocking inaccessible pore using “dummy” atoms. Here aresome further issues you may wish to consider:

♦ The simulation predicts the most favorable binding sites for gasmolecules, it does not account for their abilities to pass throughthe framework (although blocking inaccessible pores is oneway in which you can use your chemical intuition to accountfor this). Diffusion properties can be studied using moleculardynamics simulations.

♦ The simulation assumes that the framework is rigid - this, ofcourse, is not the case. Again, molecular dynamics may be usedto study the framework behavior and qualitative conclusionscan be drawn as to its likely effect on the adsorption.

♦ The results will be very dependent on the model you have usedfor cation positions. In the exercise you have manually gener-ated one possible model – you should at least run over a num-ber of such models and average the results. Even where amodel is not accurate in every respect it may give you valuableinformation – such as the conclusion in the exercise that thenitrogen tends to localize to lithium cation sites.

♦ Inaccuracies in forcefield or charge models may lead to incor-rect results. These factors need to be borne in mind whenextrapolating the techniques outlined above to other systems –particularly where sorbate molecules contain hetero-atoms orhave complicated charge structures.

References

Forano, C.; Slade, R.C.T.; Krough Andersen, E.; Krough Andersen,I.R.; Prince, E., J. Solid State Chemistry, 82, 95ê102 (1989)

Pluth, J.J.; Smith, J.V., J. Amer. Chem. Soc., 102, 4704ê8, 1980

Stogryn, D.E.; Stogryn, A.P., Mol Phys, 11, 371, 1966

Murthy, C.S.; Singer, K.; Klein, M.L.; McDonald, I.R., Mol Phys, 41,1387, 1980

Part 3Chemical Reactions


7 Vibrational Frequency andElectronic Property Calculation ofAspirin

This tutorial describes how to model the electronic properties of anorganic compound using the MOPAC semi-empirical quantummechanics program.

Before you begin

You need these modules To complete this tutorial, you need a licensed copy of Cerius2 thatincludes these modules:


♦ Minimizer

♦ MOPAC

Overview of the tutorial This tutorial provides an overview of the application of MOPAC topredict structural, electronic and spectral properties.

A. Building an atomistic model of aspirin

B. Initial optimization of the structure using molecular mechanics

C. Modeling aspirin using quantum mechanics

D. Analyzing the quantum mechanics model to obtain predictionsof structural and electronic properties:

- Heat of formation

- Dipole moment

- Electron distribution

- Electrostatic potential


7. Vibrational Frequency and Electronic Property Calculation of Aspirin

- Molecular orbitals

E. Predicting vibrational spectra and normal modes


1. Start Cerius2


2. Sketch the molecule

The mouse cursor should change to a “T”.


Go to the top menu bar and select the Build/3-D Sketcheritem.

Select the phenyl template (click the T icon)

Click near the center of the model window to place a phenylring and start the aspirin sketch.



3. Correct bond lengths and angles

Click the Edit Element icon and pick one hydrogen with themouse, changing it to carbon. Change the Edit Element textbox to O (for oxygen) and select one of the adjacent hydro-gens.

Click the Sketch With icon and continue to build the model,changing the Sketch With text box to O to include the oxy-gen atoms as needed and using the Edit Bond icon to definethe double bonds.

Press the H ADJUST button to add hydrogens.

Click and hold down the Clean button to correct bondlengths and angles.

COOH O-COCH3



B. Initial optimization of the structure usingmolecular mechanics

1. Choose a forcefield

The PCFF forcefield gives good predictions of small molecule organicstructures.

Molecular mechanics methods have no knowledge of electron distribu-tion or molecular orbital environment, so atom types and partialcharges must be assigned using an empirical rule based system.

Return to the select mode by picking the arrow icon.

Locate the OFF Setup card deck and bring the OPENFORCEFIELD card to the front.

Load the PCFF forcefield by double clicking onpcff_300_1.01

Select the Typing/Atoms item and click Calculate usingtyping rules.



2. Minimize the energy

The structure is updated on the screen as it is relaxed. The Graph win-dow displays a plot of energy vs. minimization step.

3. Change the molecule display style


1. Set up the MOPAC optimization

Semi-empirical quantum mechanics methods rarely provide signifi-cantly better predictions of small molecule organic structures (bondangles, bond lengths etc.) than well-parameterized forcefields. Themain reason for carrying out structural optimization using MOPACis as a first step in calculating electronic level properties

Locate the OFF METHODS card deck and bring the MINI-MIZER card to the front and select the Run item. Leave allthe options at their default settings and click Minimize theEnergy.

Close the Cerius2 Graphs window.

Select View/Display Attributes from the top menu bar andchange the Style from Stick to Ball to obtain a better visu-alization of the structure.

Return the display style to the default, STICK.

Locate the MOPAC card and select the Run item.



MOPAC is usually in the Quantum 1 card deck

2. Run the MOPAC optimization

The text window indicates that the MOPAC job has started. The jobappears in the Job Status window on the MOPAC Job Control panel.You can click UPDATE to see the status of the job as it progresses.

3. Monitor the MOPAC job

This is updated periodically.

You will know that the job is completed if the Status on MOPAC JobStatus panel says completed when you click UPDATE.

Change the File Prefix to aspirin and the Task to GeometryOptimization.

Select the Job Control item and change the Run Mode fromINTERACTIVE to BACKGROUND.

Move the MOPAC Job Control panel out of the way (butdon’t close it yet), return to the MOPAC Run panel and clickRUN to start the MOPAC optimization of aspirin.

Click Monitor Logfile to see the output from MOPAC.

Once the job has completed, close the MOPAC Job Control,output, and MOPAC Run panels.

D. Analyzing the quantum mechanics model to obtain predictions of structural and


D. Analyzing the quantum mechanics model toobtain predictions of structural and electronicproperties

1. Dipole Moment & Heat of Formation

This loads the information from the completed MOPAC job intoCerius2. The model on the screen is updated to show the minimumenergy structure found during the geometry optimization. The modelshows a green arrow over it, indicating the direction of the dipolemoment.

The Heat of Formation and Dipole Moment for the optimized mole-cule are displayed in the Summary of Calculation box on theMOPAC File Analysis panel.

The heat of formation ∆Ηf gives a prediction of the chemical stabilityof the molecule. One simple application of quantum mechanics is topredict the relative stabilities for different reaction products. In a reac-tion under thermodynamic control this predicts the relative amountsof each that will be formed.

2. Enthalpy of reaction

The difference in ∆Ηf for reactants and products gives the enthalpy ofa reaction. Such analysis can be used to explain and optimize chemical

Go to the MOPAC card again and select the Analyze/Filesitem.

Double-click on the file aspirin.out.

Rotate the molecule using the mouse to view the dipolearrow more clearly.



reactions.

3. Electron density

A light blue surface appears around the molecule. This is a physicalrepresentation of the electron density around the molecule

You might want to change the molecule display mode to Ball andStick or Cylinder so that you can see the molecular structure moreclearly below the charge density surface.

You can also change the Isosurface Value. As the value becomessmaller the volume increases. In principle if you took it to zero the sur-face would have to encompass the whole universe.

4. Electrostatic potential

When you are finished, close the MOPAC File Analysispanel.

Select the Analyze/Density item from the MOPAC cardand click Calculate Total Charge Density.

Select the Analyze/Surfaces item. Change Transparency to50% and click Create New Surface.

Select the Analyze/Potential item and click CalculateElectrostatic Potential.

D. Analyzing the quantum mechanics model to obtain predictions of structural and


The light blue surface is now multi-colored.

The more negatively charged parts of the molecule are purple or bluewhile the positively charged sections are red or orange.

The electrostatic potential surface can be used to predict which siteson a molecule will be most open to electrophilic or neutrophilic attach.A comparison between different molecules would suggest whichwould be most stable to attack.

You can move the slice through the molecule using the Position arrowkeys. To change the direction of the slice plane rotate the moleculeusing the mouse keys, click the More Editing Options button, andclick Set Slice Direction Parallel to Screen.

A graph window appears containing a colored representation of theslice.

Select the Analyze/Property Maps item. Locate the fileaspirin_Potential.mbk and double-click to load it. Add theProperty asprin_Potential to the model

Go back to the MOPAC Surfaces panel and turn off theShow Surface toggle. Close the panel.

Select the Analyze/Slices item from the MOPAC card. Setthe Edit Slice to asprin_Potential and click Create NewSlice.

Click Create Slice Plot in Graph Window (one of theoptions on the MOPAC Slices menu).



Note

5. Molecular orbitals

Here you see a list of the molecular orbitals calculated for this modeland their corresponding energies in electron volts.

This is a representation of the wavefunction for the highest occupiedmolecular orbital for aspirin. The positive lobes of the orbital are lightblue and the negative lobes are yellow. Note the pi-bonding of the phe-nyl group. You can change the colors and transparency of the orbitals.

Note that there are more antibonding interactions in the phenyl groupin the LUMO than in the HOMO.

The graph window is not automatically updated.

Close the graph window. Delete the Slice and close theMOPAC Slices panel.

Select the Analyze/Orbitals item.

Be sure the popups are set to Alpha and HOMO, then clickCalculate.

Now set the popups to Alpha and LUMO and clickCalculate.

When you are finished, got to the MOPAC Analyze/Sur-faces panel and click Delete Surfaces.

E. Predicting vibrational spectra and normal modes


E. Predicting vibrational spectra and normalmodes

1. Run a MOPAC frequency analysis

As before you can monitor the progress of the background job usingthe MOPAC Job Control menu.

2. Read in the MOPAC data

3. Analyze the vibrations

Here you see a list of modes and their corresponding frequencies. Thepredicted IR spectrum is plotted in the graph window.

4. Display the molecular motion

Select the Run item from the MOPAC card and select Fre-quency as the Task. You can either select a new File Prefixor overwrite the earlier results.

Select the Analyze/Files item to read in the output file fromthe latest calculation

Select the Analyze/Vibrations item.



You can display the mode of motion associated with each frequency.

The structure in the model window moves.

5. Finishing up

Choose one of the CO stretching frequencies (around 1700 –1800 cm-1) either by selecting from the list or picking fromthe IR spectrum.

Set the popup to ANIMATE mode.

To end the Cerius2 session, close all open panels and selectFile/Exit from the top menu bar.



8 Studying a Ziegler-NattaPolymerization Catalyst

This chapter shows how modeling is employed to rationalize, witha view to improving the design, the action of a homogeneous met-allocene catalyst used in the polymerization of the commerciallyimportant polymer polypropylene.

This chapter is divided into five parts:


♦ Solving the problem step-by-step — gives you specificinstructions to follow in order to solve the problem.

♦ Reviewing the solution — discusses the scientific significanceof the solution and gives a checklist of the Cerius2 skills you’velearned.

♦ What to do next — tells how you can learn more about themodules used in this tutorial.

♦ References and related material — points you to relevant MSIdocumentation and published work.

Before you begin

You’ll need these modules To complete this tutorial, you will need a licensed copy of Cerius2



♦ Minimizer

♦ Dynamics


8. Studying a Ziegler-Natta Polymerization Catalyst

Overview of the problem The first phase in the manufacture of commercially important bulkpolymers such as polypropylene is polymerization from the gasphase. Applications of these polymers include packaging, pipe-lines, and barrier and insulating materials. Engineering the tactic-ity of the polymer at the polymerization stage can have a criticaleffect on important properties such as opacity and mechanicalbehavior.

Control over tacticity during polymerization is achieved by theuse of stereospecific Ziegler-Natta catalysts. Polymerizationoccurs through the complexation of an olefin fragment at a metalcenter. The complex binds to the polymer chain, which grows outof the metal center, and leaves a vacant site for further olefin com-plexation. The tacticity of the growing polymer is controlled by theparticular arrangement of ligands surrounding the metal center —these define the orientation of the olefin fragment. Accurateknowledge of the geometry, stability, and catalytic mechanism ofthese molecules leads to design of better catalysts and more effi-cient catalytic processes.

Overview of the solution Molecular modeling can contribute substantially to the investiga-tion and rationalization of the catalysis process.

Researchers at Colorado State University have studied the behav-ior of an ansa-zirconium metallocene catalyst known from experi-ment to give isotactic polypropylene (Castonguay and Rappé1992). They used empirical force field techniques based on theirUniversal Force Field (Rappé et al 1992; developed in collaborationwith Molecular Simulations) to rationalize the action of the cata-lyst and suggest an alternative syndiotactic polymerization cata-lyst.

In this tutorial example, you explore some of the tools used for car-rying out such work within the Cerius2 modeling environment:molecular sketching and rapid force field calculations using theUniversal Force Field. You take the molecular structure of the zir-conium complex and justify theoretically the experimental obser-vation that it catalyzes polymerization of isotactic polypropylenepreferentially to syndiotactic.


logfile CAT_ziegler_natta.log, which illustrates the procedure. Torun this logfile:



The logfile demonstrates the methodology you will follow in thistutorial lesson. You investigate the likely path of the reaction byperforming energy minimization calculations on two possibletransition states.

Summary of procedure This method is summarized as follows:

A. Sketching in the ansa-zirconium catalyst

B. Creating the syndiotactic transition state

C. Optimizing the transition state

D. Creating and optimizing the isotactic transition state

E. Comparing energies and rationalizing tacticity


This section takes you through the procedure outlined above. Youwill see how Cerius2 has been used to explain why the polymer-ization reaction favors isotacticity.

Type cerius2 to run the program.

Open the Examples control panel from the Help pulldown.

Double click CAT_ziegler_natta.log to run the logfile.



Edit to syndiotactictransition state

Minimize usingUniversal FF

ChargeEquilibration

Reminimize

Sketch in theZiegler-Nattacatalyst

Investigating a Ziegler-Natta polymerization catalyst:

Repeat until energyconsistent

An overview of the solution

MD to disturb fromlocal minimum

Repeat for isotactictransition

state

Compare energies

Rationalize tacticity

Investigate effectof structural



A. Sketching in the ansa-zirconium catalyst

1. Start Cerius2


2. Open the Sketcher

You begin by sketching the ansa-zirconium Ziegler-Natta catalystusing the tools in the 3D molecular Sketcher.

3. Draw a zirconium atom

The Sketcher is now ready to place a zirconium atom. The mouse cur-sor appears as an inverted V in the model window; this indicates thatit is currently acting as a sketcher tool.

Troubleshooting


Open the 3D-Sketcher control panel by selecting the Build/3D-Sketcher… command.

Click in the Sketch With text box and type Zr; then press<Enter>.

If the mouse cursor isn’t an inverted V in the model window?

Be certain that you pressed the <Enter> key located above the<Shift> key, and not the <Enter> key located in the number pad.Also check that the Sketch With icon is highlighted.



A light blue cross representing the zirconium atom appears.

4. Open a template

This browser box allows you to choose a template.

In the model window, the mouse cursor appears as a T; this indicatesthat the template tool is active. Notice that the template tool (the “T”icon) is automatically activated and the word “pentadienyl” appearsnext to the icon.

5. Apply the template to the model

Two pentadienyl ligands are added.

Click near the center of the model window.

In the Sketcher control panel, click the Templates... buttonto open the Sketcher Templates control panel.

Use the browser box to find the template file called ligands/pentadienyl. Load the template by double-clicking on thefilename.

Click twice on the zirconium atom.



6. Label the atoms in the model

All the atoms in the model window should now be labeled accordingto their element type.

There are two pairs of hydrogen atoms in the adjacent pentadienylrings that are close together. In the catalyst molecule, one of thesepairs is the site of a carbon atom bridge.

7. Add a carbon bridge to the model

This allows you to click on any atom and change it to a carbon. (Besure that C is in the Edit Element text box.)

The hydrogen changes to a carbon.

Label the atoms in the model with their element type:change the Atom Labeling popup on the tool bar from NOLABEL to ELEMENTS.

Rotate the model to view it by clicking the right mouse but-ton and dragging the cursor over the model window.

Click the Edit Element icon in the Sketcher control panel.

Click on one of the pentadienyl hydrogens that is close to ahydrogen in the other pentadienyl ring.

Click on the nearest hydrogen in the other ring.



It too becomes a carbon. In the next step, you bond these two new car-bons.

Be sure that the Edit Bond popup is set to Single. When the EditBond icon is selected, the mouse cursor in the model window appearsas a special arrow.

A single bond between the two carbons is created.

8. Clean the model

Clean uses a fast molecular mechanics algorithm to produce a sensi-ble molecular geometry.

The molecule should look something like this:

Click the Edit Bond icon in the Sketcher.

Click once on each of the new carbons.

Hold down the Clean button until the molecule stops mov-ing. Rotate to view.



9. Create a carbon ring

This changes the hydrogen atom into a carbon.

It too becomes a carbon atom.

In the ansa-zirconium molecule, these two new carbons are part of asix-membered ring structure. In the next steps, you sketch the remain-ing two atoms in the ring.

Now click the Edit Element icon. Pick a hydrogen atom thatis attached to one of the pentadienyl carbons adjacent towhere the bridge joins the ring.

Pick the next hydrogen around the ring.



To do this you may type directly into the text box or use the popupmenu to set the element type.

You should now have formed a six-membered carbon ring having onecommon side with the pentadienyl ring.

10.Clean the model again

The molecule should look like the figure below. (Here, the zirconiumatom is drawn in Ball style.)

Change the Sketch With element to C.

Pick one of the new carbons, draw in two new atoms, andfinish by clicking on the other new carbon.

Hold down the Clean button until the molecule stops mov-ing.



11. Make another carbon ring

The ring that you build this time should share carbons with the otherpentadienyl ring. You should end up with a centro-symmetric systemthat looks something like the figure below.

Set the Atom Labeling popup back to No Label.

Now repeat Steps 9 through 10 above, but make the linkageon the other pentadienyl ring and make sure to start it on theopposite of the bridge from the linkage you have just built.



12.Add hydrogens to the model

This adds hydrogens to the molecule.

13.Replace the hydrogens with chlorine atoms

To do this, you can either type Cl into the Sketch With text box oruse the popup menu to set the element type to chlorine.

Click the H Adjust button on the Sketcher control panel.

Change the element in the Sketch With text box to Cl forchlorine.



14.Clean the molecule again

15.Optimize the model geometry

You have now sketched the ground state of the ansa-zirconium cata-lyst molecule. So far, you’ve used the crude minimization techniquesof the Sketcher Clean tool to optimize geometry. Next you use thefull power of the Minimizer module to improve the model geometry.

This returns the mouse to normal mode: the cursor should now appearas a simple arrow both inside and outside the model window.

Click on the Zr atom and then click again close to the atomto create a single Zr-Cl bond.

Repeat this step so that two Cl atoms are attached to the Zratom.

Hold down the Clean button until the molecule stops mov-ing.

Click the Selection Mode icon. (The arrow in the top left ofthe Sketcher control panel.)

Tidy up by closing all open control panels.

Find the Minimizer card on the OFF Methods deck.



The minimization loads and uses the default Universal Force Field(Castonguay and Rappé 1992). This is the most suitable forcefield forthe study of metal-containing complexes such as the one that you arestudying here.

The minimization plots a graph of energy against iterations as it pro-ceeds. Move this graph to the bottom right of the screen so that youcan see the model window.

16.View the model in Ball mode

Notice how the organic ligands restrict access to the central zirconiumatom, which is the site of the homogeneous catalytic reaction duringpolymerization.

17.Save the model

If you need help with general Visualizer functions, see Cerius2 Tuto-rials— Basics, or Cerius2 Modeling Environment.

Click Run to open the Energy Minimization control paneland then click the Run button for Minimize the Energy tominimize the energy.

Change the Display Style from Stick to Ball. Rotate andview the model.

Use the Visualizer’s File/Save Model… menu item to savethe model into an msi format file called ansa_Zr.msi.



Time for a Break?

B. Creating the syndiotactic transition state

Follow the steps in this section to create a model of the transitionstate for the syndiotactic polymerization reaction. During the reac-tion, the growing polypropylene chain is bound to the zirconiumatom in place of one of the chlorine atoms. The polymerizationreaction takes place with a propylene fragment that is π-bound atthe site of the other chlorine.

If you want to take a break now, exit from Cerius2 by choosingthe File/Exit command.When you want to continue with the tutorial, select the File/Load command and load in the ansa_Zr.msi structure filebefore going on to the next section.



1. Change the display style and orient the model

The model is easier to rotate in stick display.

Match the orientation to the screenshot page 139.

2. Begin adding a polypropylene chain to the model

This is the starting point for the growing polypropylene chain.

You may have to zoom out (use the Shift key and middle mouse but-

Change the Display Style from Ball back to Stick.

Orient the molecule so that the two chlorines are at the topof the screen.

Open the Sketcher control panel by selecting the Build/3D-Sketcher… item.

Use the Edit Element tool to change one of the chlorines toa carbon.

Use the Sketch tool to add three more carbons to this newcarbon, forming a chain pointing away from the molecule.



ton) to make room for the chain.

In effect you should now have added a 2-methyl butyl group to the zir-conium atom. The 2-methyl group added in this step is a methyl groupin the polypropylene chain. (The hydrogen atoms are added in a stepbelow.)

3. Clean the model

4. Add a propylene monomer

You now have the end of a polypropylene chain growing from the cat-alyst. Next you need to add a propylene monomer to the system.

This ethenyl fragment will form the basis of the propylene monomer.When the ethenyl template is loaded, the word “ethenyl” appears next

Sketch another carbon atom and attach it to the second atomin the new chain.

Click the H Adjust button and hold down the Clean buttonuntil the molecule stops moving.

Click the Delete Atom icon and click on the remaining chlo-rine atom.

Click the Templates... button to open the Sketcher Tem-plates control panel; use the template file browser box toopen the ligands/ethenyl template file.



to the template icon on the Sketcher panel.

The next sketching step is to turn the ligand into a propylene mono-mer by the addition of a methyl group, but first you should minimize.It is the relative positions of the methyl groups on the propylene frag-ment that will determine the tacticity of the polymer.

This generate s a better geometry for the ethylene molecule; you needto consider the model geometry before deciding where to add themethyl group.

Click on the zirconium atom with the template tool to addthe ethenyl ligand to the catalytic site.

Find the Minimizer card on the OFF Methods deck, clickRun to open the Energy Minimization control panel, andclick the Run button to Minimize the energy.



The molecule should look something like the above picture, although itmay not look identical (see Step 5, below). It may be necessary to movethe graph window aside so that you can see the model window.

During the polymerization reaction, the carbon at D bonds to the car-bon at A. The bond between D and the zirconium is broken leaving avacancy for the addition of a new propylene in the continuing poly-merization reaction. The tacticity of the growing polymer depends onwhether the methyl group resides at position B or C. B gives syndio-tactic polypropylene, C gives isotactic.

5. Adjust the model orientation

Rotate the model so that its orientation is as close as possibleto that in the screenshot above (i.e., ethenyl group to thefront, polymer chain at the back). Identify the hydrogenatoms B and C.



Depending on how you drew in the growing polymer chain, themethyl group may be on the other side of the chain from the moleculepictured. In this case, B and C would be reversed (i.e., B is always thehydrogen in the syndiotactic position relative to the methyl group if abond is drawn between A and D).

Note

6. Add a methyl group

You will have to go up the directory tree using the popup menu abovethe file browser to find the organic directory.

Remember, as explained in Step 5 above, B and C may be switched ifthe polypropylene methyl is on the other side of the chain.

You should now have the syndiotactic transition state.

7. Save the model

Doing this overwrites the ansa_Zr.msi file that you created at the endof Section A.

You may find it helpful to name the atoms as shown in thefigure above. To do this, select the Build/Edit Atoms... item toopen the Edit Selected Atoms control panel and give names tothe atoms using the Name text boxBe sure to set the AtomLabeling tool on the Visualizer toolbar to NAME for each ofthose atoms.

Use the browser box in the Sketcher Templates control panelto load the fragment file organic/methyl.

Click on atom B to add the methyl group.

Save the model into an msi format file called ansa_Zr.msi.



Note

Time for a break?

C. Optimizing the transition state

In this section, you optimize the syndiotactic polymerization tran-sition state that you have just constructed and compute an energyfor the minimized structure. You will carry out minimizations andmolecular dynamics using the Universal Force Field and accountfor charges using the Charge Equilibration method (Rappé andGoddard 1991).

Tidy up by closing all open control panels except for theEnergy Minimization control panel.

You may want to confirm that this is indeed the syndiotactictransition state. To do this, follow the instructions below. Becertain that you’ve saved the current model to file ( above) sothat you can resume the exercise afterwards.1. Use the Sketcher to break the bond between carbon D (inscreenshot) and the zirconium.2. Delete the π-bond between the propylene monomer and thezirconium atom.3. Make a bond between atoms A and D.4. Clean and manipulate this new little polypropylene chain tosee that the methyl groups are in syndiotactic positions.5. Finally, reload the original model and continue with thetutorial exercise.

If you want to take a break now, exit Cerius2 by selecting theFile/Exit item.When you want to continue with the tutorial, load theansa_Zr.msi file before going on to the next section.



1. Minimize the model

This carries out an initial minimization of the structure — again, notethe graph of energy versus iteration.

2. Calculate and apply partial charges

All the atoms in the model window are labeled zero. Because the mol-ecule is uncharged, the Coulombic component of the minimizationenergy calculation is zero. In order to account for the Coulombicenergy during the minimization, you must first calculate or assignpartial charges to the model.

This card allows you calculate and apply partial charges. Here, youare going to use the Charge Equilibration method to calculate chargesfor the model.

This opens the Charge Equilibration Preferences control panel.

Note that the Charge Equilibration method is the recommended tech-

Click the Run button for Minimize the Energy in theEnergy Minimization control panel.

Change the Labeling tool on the Visualizer toolbar toCHARGES.

Click the Charges card to the front of the deck — you willprobably find this on the OFF Setup deck.

Click Charges to open the control panel, then click theCharge-Equilibration Preferences... button.



nique for assigning charges for use with the Universal Forcefield.

This sets up the charge calculation with parameters for a neutral sys-tem.

You now see the charge labels on all the atoms change to display thenewly calculated partial charges.

3. Minimize the model again

Note the discontinuity in the energy graph. This reflects the Coulom-bic energy that was not included in the minimization of the unchargedmodel.

4. Calculate the charges again

Because the Charge Equilibration calculation is geometry dependent,it is important to recompute charges after minimization.

Load the file QEq_neutral1.0.

Close the Charge Equilibration Preferences control panel,and click the CALCULATE button on the Charges controlpanel.

Click the Run button for Minimize the Energy again.

Return to the Charges control panel and click the CALCU-LATE button again.



5. Minimize the model once more

6. Review the data

7. Disturb the structure

In the next step, you will disturb the structure (in case it has got stuckin a local minimum), and then minimize once more.

Now you use molecular dynamics to disturb the structure.

This relatively high temperature puts more energy into the system,and therefore causes a greater displacement of the molecule from equi-

Select the Reset menu item on the MINIMIZER card. Clickthe Run button for Minimize the Energy again.

Study the output in the text window: the minimizationshould have converged. Note down the Total Energy at con-vergence.

Change the Atom Labeling popup from Charges back toNo Label.

Click the Dynamics Simulation card on the OFF Methodsstack to the front of the deck.

Click Run to open the Dynamics Simulation control panel;set the Required Temperature to 800K.



librium.

This performs 500 cycles of constant NVE dynamics. If the graphwindow obscures the model window, move it aside.

Click the RUN DYNAMICS button.



8. Minimize, adjust charges, and minimize again

Note the final minimized energy — is it different from the energy thatyou noted under Step 6? If it is close (for these purposes, within 1 kcalwill suffice), then move on to the next step. Otherwise iterate throughSteps 7–8 again.

Time for a break?

D. Creating and optimizing the isotactic transition state

In this section, you optimize the structure of the alternative transi-tion state. This requires you to edit the syndiotactic state to formthe isotactic state and to repeat the steps of Section C for this iso-tactic structure.

1. Modify the syndiotactic model

Click the Run button for Minimize the Energy to minimizethe structure.

Recalculate the charges as in Step 4. Click the Run buttonfor Minimize the Energy again.

Once the minimization is converged, write down theenergy.

If you want to take a break now, save the model and then exitfrom Cerius2 by selecting the File/Exit item.When you are ready to continue with the tutorial, load in thesaved file before going on to the next section.

Highlight the entry Model1 in the Model Manager list andtype Syndiotactic. Press the <Enter> key.



The first model space is now named “Syndiotactic”.

There are three ways to select all atoms: using the Edit/Select Allitem, dragging the mouse across the model window, and clicking theSelect All button on the tool bar.

The new workspace, called Model2, is created.

The syndiotactic transition state appears in the model window.

2. Create the isotactic model

To create the isotactic state you need to swap the position of this

Select all the atoms and select the Edit/Copy command.

Create a new model space by clicking the “+” icon above theModel Manager list.

Select the Edit/Paste item.

Name the new model Isotactic.

Reset the view and rotate the model. Find the propylenefragment and identify the point at which you added themethyl fragment in Step 6 on page 144.



methyl group.

This is the isotactic transition state.

3. Optimize the isotactic model

You should finish with an energy for the optimized isotactic state.

E. Comparing energies and rationalizing tacticity

You have now optimized both transition states. In this section, youcompare the results of those optimizations and draw conclusions.

Open the 3-D Sketcher and delete the three hydrogen atomsfrom the methyl group.

Use the Edit Element tool and text box to change the methylcarbon atom to a hydrogen.

Change the adjacent hydrogen to a carbon.

Click the H Adjust button. Clean the molecule by holdingdown the Clean button until the model stops moving.

Repeat the steps in Section C (pages 146-150).



1. Compare the two optimized states

You should find that the isotactic state has a lower energy than thesyndiotactic. The exact figures will depend on a number of factors (see“Reviewing the solution” on page 154). Notably, this exercise has notbeen as rigorous as possible in optimizing structures, making theresults more dependent on how you sketched in the original startingstructure. The difference should, however, be significant enough foryou to draw conclusions.

2. Create a grid display

You can see the two structures side-by-side.

The lower energy of the isotactic state indicates that this state will befavored: that is, the ligands surrounding the metal center constrainthe isotactic state less than the syndiotactic one. This observationexplains why the ansa-zirconium catalyst promotes the production ofisotactic rather than syndiotactic polypropylene.

Compare the two energies that you have calculated.

Click the grid display mode icon above the ModelManager.

Click the check box to the right of Syndiotactic in the ModelManager list. Reset the view and rotate.



3. Finishing up


In this tutorial exercise, you have seen how Cerius2 can be used toexplain why a particular polymerization catalyst favors isotacticpolymerization.

Having completed this tutorial, you should be able to see how acombination of modeling, visualization, and energy calculationsare used to design catalysts with a greater energy gap (i.e., thosewhich favor isotactic polypropylene even more) or in which syn-diotactic polypropylene is favored.

Of course, this tutorial exercise presents a very “rough and ready”approach. There are many issues that a more rigorous treatmentwould need to take into account. These include:

♦ Molecular mechanics is necessarily dependent on the startingconfiguration of the molecule. The original sketching of a fairlyflexible molecule is likely to vary radically each time you con-duct the exercise. This is the main reason why this tutorial textcannot give exact energies with which you can compare yourend results. Alternative approaches include starting with someknown coordinate data (for example crystallographic coordi-nates) or repeating the procedure with a large number of start-ing configurations and averaging over these.

♦ It may be that simply running molecular dynamics in the man-ner described is insufficient to disturb the structure from a localminimum. It may be wise to use alternative molecular dynam-ics such as a conformational search or a Monte Carlo method toensure that the perturbation is sufficient. Most likely you found



What to do next


that the methods used above simply returned the structure toits previous minimum, or very close to this minimum.

♦ Both the Universal Force Field and the Charge Equilibrationmethod are approximations. They are extremely useful approx-imations because they enable you to study geometry and ener-getics interactively instead of relying on time-consuming QMmethods. However, you must remember what they are usefulfor — comparing and ranking similar structures — and thatthey do not necessarily give you accurate absolute energies.

♦ As with most modeling, here you have reduced the overallproblem to one particular issue that is tractable with the simu-lation techniques available. This provides important insight,but it is always important to bear in mind the other factors —alternative reactions and transitions states, the likely effects ofthe chemical environment, and the implications of competitiveprocesses — which might affect the polymerization.

In this tutorial you learned or reviewed…

♦ Sketching complex molecules (page 129)

♦ Optimizing molecular structure using the Universal force Field(page 139)

♦ Calculating partial charges (page 139)

♦ Copying, pasting, and editing structures (page 150)

♦ Running dynamics to shake a structure out of a local minimum(page 149)

What to do next

You may wish to follow up on this lesson by reading the refer-ences.

To learn more about applying molecular mechanics and dynamicstechniques, read the Minimizer and Dynamics chapters of Cerius2

Simulation Tools.



You may wish to experiment further with the transition states thatyou have sketched. A major structural parameter that moleculardynamics alone is unlikely to fully sample is the rotation of thepropylene fragment about the π-bond. To find a more accurate glo-bal minimum, you could study how rotation around this torsionaffects the energy of the system. You could use the Conformersmodule to do this. Try defining a grid scan about the torsion andminimizing the conformation at each point to determine the low-est energy value.

References and related material

Castonguay, L.A., and Rappé, A.K., J. Amer. Chem. Soc., 114 5832(1992).

Rappé, A.K., Casewit, C.J., Colwell, K.S., Goddard, W.A., andSkiff, W.M., J. Am. Chem. Soc., 114 10024 (1992).

Rappé, A.K., and Goddard, W. A., J. Phys. Chem., 95 3358 (1991).

Part 4Crystallization and Crystal Growth


9 Predicting an Ab-initio CrystalStructure for Urea

This chapter shows how modeling can be used to predict the crys-tal structure of a molecular crystal — a problem which is particu-larly important in the development and application of productsthat do not crystallize as particles large or pure enough for singlecrystal X-ray diffraction techniques. This tutorial guides youthrough a series of steps to a solution. Along the way, you learnabout constructing and visualizing crystal structures and aboutthe innovative Polymorph Predictor method (Gdanitz 1992, Kar-funkel and Gdanitz 1992, Karfunkel et al. 1993a, Karfunkel andLeusen 1992, Gdanitz et al. 1993, Karfunkel et al. 1993b).


♦ Before you begin — provides some background informationabout the problem and an overview of the solution.

♦ Solving the problem step-by-step — gives you specific instruc-tions to follow in order to solve the problem.

♦ Finishing up — discusses the scientific significance of the solu-tion and provides a checklist of the Cerius2 skills you’velearned.



Before you begin

You’ll need these modules To complete this tutorial, you need a licensed copy of Cerius2 thatincludes these modules:


9. Predicting an Ab-initio Crystal Structure for Urea

♦ Crystal Builder

♦ Polymorph


♦ Minimizer


Overview of the problem Pharmaceuticals, agrochemicals, pigments, dyes, specialty chemi-cals, and explosives are all, at some stage during the manufactur-ing process, organic crystalline materials. Polymorphism affectsthese products during down-stream development and formula-tion.

It is important to know which crystal forms are present in a givenproduct because the crystal form determines the properties of thematerial:

Shelf-life Vapor pressure

Solubility Bioavailability

Morphology Density

Shock sensitivity

It is vital that researchers involved in crystalline product formula-tion select the polymorph with the correct properties, and be ableto anticipate such problems as competing crystallization of unde-sirable polymorphs. In order to do this, it is first necessary to estab-lish the most likely polymorphic forms. Knowledge ofpolymorphic forms is also important for patenting and registra-tion purposes.

It is often impossible or impractical to use single crystal X-ray dif-fraction, the standard experimental procedure, for elucidating thestructure of a molecular crystal. Thus, computational techniquesthat predict crystal structures without experimental data are ofgreat value.

Overview of the solution Over the past six years, researchers at Ciba-Geigy (Switzerland)and Molecular Simulations (United Kingdom) have developed anovel computational methodology (Gdanitz 1992, Karfunkel andGdanitz 1992, Karfunkel et al. 1993a, Karfunkel and Leusen 1992,Gdanitz et al. 1993, Karfunkel et al. 1993b) to predict the polymor-phic structures of organic compounds from scratch, that is, usingonly the molecular structure as a starting point.

Before you begin


Structure prediction with the Polymorph Predictor may involvelong computation times, particularly for large or flexible mole-cules. In this tutorial, you predict the crystal structure of urea. Ureahas been chosen because it is a small, rigid molecule — predictionof its structure can be accomplished quite quickly. But, predictingthe crystal structure of urea is not trivial; the crystal packing ofurea is complex because of the extensive inter-molecular 3Dhydrogen bonding present in the crystal.


logfile CGR_pmorph_urea.log, which illustrates the procedure.To run this logfile:

The logfile shows the methodology that you follow in this exam-ple. You sketch in a model of a urea molecule, calculate its chargedistribution, perform a Polymorph Predictor run on this molecule,and then analyze the results by comparing them with the experi-mentally determined structure.


A. Creating a urea molecule

B. Prediction sequence setup

C. Running prediction sequence

D. Evaluating the results

Type cerius2 in a UNIX shell to run the program.

Select the Help/Examples item from the menu bar.

Double click on CGR_pmorph_urea.log to run the logfile.



Optimize geometryCompute charges

Set up a polymorphpredictionsequence

Run the predictionsequence

Extract predictedcrystal structure

Construct a modelof the ureamolecule

Predicting the crystal structure of Urea,

Compare withexperimental

pattern to validateprediction

Simulate powderpattern from

predicted structure

an overview of the solution




This section takes you through the procedure outlined above. Youlearn how Cerius2 can be used to predict crystal structures.

Begin with a new session of Cerius2.

A. Creating a urea molecule

In this section, you sketch the molecular structure of urea andcompute a sensible geometry and charge distribution for the mol-ecule.

1. Start Cerius2


2. Sketch the molecule

The 3D-Sketcher control panel appears.


Open the Sketcher panel by selecting theBuild/3D- Sketcher item menu bar.

Use the Sketcher to construct a model of urea.



Your completed structure should look like this:

3. Clean the molecule

4. Compute the charges

In the next steps, you compute charges on the molecule and run amore accurate minimization algorithm.

The Charges panel provides the controls for the Charge Equilibrationmethod (Rappe’ and Goddard 1991)— a fast, empirical, charge calcu-lation method, which provides adequate charges for this exercise.

Click and hold the CLEAN button until the molecule stopsmoving.

Choose the Selection Mode icon (the arrow at the top left) inthe Sketcher panel. Then close the Sketcher panel.

Find the OFF Setup stack on the deck of cards. Click theCharges card to the front of the stack, and select theCharges item.

Confirm that the Charge-Equilibration radio button isselected.

C

O

N N



This carries out the charge equilibration calculation.

This lets you see the results of the partial charge calculation.

Now that partial charges are assigned to the molecule, electrostaticsare included in the energy expression.

5. Calculating and minimizing with Dreiding-II force field

Next, you use the Dreiding-II force field to calculate and minimize

On the Charges control panel, click the CALCULATE but-ton.

Change the label popup on the tool bar from NO LABEL toCHARGES.

Rotate the molecule to view the charges, and then reset thepopup to NO LABEL.

-0.3926

0.58470.2765

-0.6149

0.24240.2424

-0.6149

0.2765



energy.

A confirmation message is sent to the text window when the force fieldis loaded. Dreiding2.21(Mayo et al. 1990) has been parameterized togive good results for predictions of organic crystal structures.

This iterative charge calculation – minimization process is necessarybecause the QEq charge calculation method depends upon model

Click the OPEN FORCE FIELD card to the front of thestack, and choose the Load item to open the Load ForceField control panel.

Select the Dreiding2.21 force field by double clicking on itsfile name in the file browser box.

Go to the OFF Methods stack and find the Minimizer card.Select the Run item to open the Energy Minimization con-trol panel.

Confirm that the top popup is set to SMART MINIMIZERand click Minimize the Energy.

Return to the Charges control panel and click theCALCULATE button.

Go back to the Energy Minimization panel and click Mini-mize the Energy again.



geometry.

6. Change the Display style

7. Name the molecule

B. Prediction sequence setup

Follow the steps in this section to set up a run of the Polymorph Pre-dictor method.

1. Set up the force field

Close all open control panels, and close the graph windowby double-clicking in the top left hand corner of its frame.

Change the display style popup on the tool bar from STICKto BALL.

Rotate to view.

Change back to STICK display style.

Edit the name of the model in the Model Manager. Changeit from Model1 to Urea.

Find the OPEN FORCE FIELD card (usually on the OFFSETUP stack), and select the Energy Terms/Coulomb itemfrom the card.



This opens the Coulomb Preferences control panel.

For periodic systems, the Ewald summation method (Ewald 1921,Karasawa and Goddard 1989) is a better way of estimating long rangeelectrostatics than the default spline method. For more informationabout the long range interaction treatment, see the Cerius2 Simula-tion Tools book.

2. Start the Polymorph Predictor setup

This card gives you access to the controls for the Polymorph Predictormethod.

This is the main panel for the Polymorph Predictor.

Click on the EWALD radio button. Then close the panel.

Find the POLYMORPH card (usually on the OFF INSTRU-MENTS 1 stack) and bring it to the front of the deck.

Select the Run item on the POLYMORPH card to open thePolymorph Run control panel.

Use the down arrow key to specify Urea as the only Modelin the asymmetric unit.



3. Set up the Monte Carlo simulation

The first stage in a prediction is a Monte Carlo simulation to generatemany potential crystal structures. The options to control this stage ofthe prediction are in the panel that you’ve just opened.

This popup offers a fast single-button way of choosing the full set ofsearch parameters that control the simulation speed and accuracy.There are three options: COARSE, MEDIUM, and FINE; three lev-els offering progressively more accuracy and longer computing time.You may also alter the individual parameters within the preferencesbox.

The prediction can search all space groups. By default, it searches thefive most common groups (these are the ones in the list by default). Tospeed up the demonstration of the technique, you are setting Poly-morph Predictor to search just one space group.

The experimental crystal structure of urea is in a higher symmetry

Click the Preferences… button beside the Run Monte Carlobutton to open the Polymorph MC Preferences controlpanel.

Set the Search Level popup to COARSE.

Enter 6 in the Number of trials to accept before coolingtext box.

Delete all space groups in the Space Groups To Use listexcept P21. Delete a space group by clicking in the text boxcontaining its name, typing a space, and pressing enter.



space group than P21, with only half a molecule in the asymmetricunit. But, in order to reproduce this structure with force field calcula-tions, which are limited to whole molecules, you have to reduce thesymmetry to P21.

4. Set up the cluster analysis

After the Monte Carlo simulation has generated possible crystalstructures, they are sorted into groups of similar structure. Similarityis defined by the geometric tolerances in this control panel. The clus-tering reduces the number of possible structures significantly beforethe next stage of the prediction.

Close the Polymorph MC Preferences control panel.

On the Polymorph Run control panel, click the Prefer-ences… button beside Run Cluster Analysis to open thePolymorph Cluster Prefs control panel.

Set the Search level popup to COARSE.

Set the Number of clusters to output to 6.

Close the Polymorph Cluster Prefs control panel.



5. Set up the energy minimization preferences

The final step in the prediction sequence is to minimize the energy ofthe lowest energy structure from each cluster, providing a set of opti-mized polymorphs. Subsequent to this step, further clustering can becarried out to check whether any of the structures converge to similarenergy minima. The controls in this panel are for the Polymorph min-imizer.

6. Create a new model space

All of the models constructed during the course of the simulation willbe displayed in this space.

C. Running prediction sequence

In this section, you run a Polymorph Prediction sequence. You coulddo this by running each step in the sequence separately, but becauseyou have already set up all the steps in the three preferences controlpanels, you can now use a single button-press method to carry out theprediction.

On the Polymorph Run control panel, click the Prefer-ences… button beside the Energy Minimize button to openthe Polymorph Minimize Prefs control panel.

Set Minimization steps to 500, and close the control panel.

Click the “+” icon on the Model Manager to create a newmodel space.



1. Carry out the polymorph prediction

The entire sequence takes some minutes. During this time, it does thefollowing:

♦ Runs a Monte Carlo simulation to generate hundreds of potentialcrystal structures for urea in the P21 space group.

♦ Runs a clustering analysis to group the crystals into clusters ofsimilar structure.

♦ Minimizes each cluster to get a set of optimized polymorphs.

♦ Clusters again to remove duplicates after minimization.

D. Evaluating the results

In this section, you analyze the output from the Polymorph Predictorrun and establish the match between the lowest energy predictedstructure and the experimental crystal structure of urea.

1. Close the graph

In the Polymorph Run control panel, click the Predict Poly-morphs button.

If necessary during the run, you can move and resize thegraphs and model window so that you can see the contents.

Close the graph window by double-clicking in the top leftcorner of the frame.



2. Extract the model

The clustered and energy minimized crystal structures are stored in atrajectory file as frames in ascending order of energy. The minimumenergy structure is in Frame Number 1.

The lowest energy polymorph appears.

3. Visualize the model as a crystal

You can use the Crystal Visualization control panel to modify the waythe crystal is displayed and to reveal the key structural features of theurea crystal.

Open the Model Extraction control panel by selecting theAnalysis/Model Extraction item from the POLYMORPHcard.

Click the Extract frame into current model button.

Close all open control panels.

Go to the BUILDERS 1 stack and find the Crystal Buildercard.

Select the Visualization item to open the Crystal Visualiza-tion control panel.

Enter the Crystal Cell Display Range as a:2 b:2 c:2, andclick the ENTER button.



The model is now displayed as a block of eight unit cells.

4. Calculate the hydrogen bonds

The hydrogen bonds in the urea crystal are drawn as dotted lines inthe model window.

Select Build/Edit H-Bonds from the top menu bar to openthe Edit Hydrogen Bonding control panel. Click the CAL-CULATE H-Bonds button.



5. Rotate and view the model

This is the predicted structure.

6. Load the experimentally-determined structure

You next load the experimentally-determined structure for compari-

Reset the view, and then rotate the model to view it.



son.

Hydrogen bonding for the model is displayed.

7. Compare the structures

Select the File/Load Model item from the top menu bar toopen the Load Model control panel.

Select the file Cerius2-Models/molecular-crystals/misc/Urea.msi and click the LOAD button.

Use the Crystal Visualization control panel to extend theCrystal Cell Display Range to an eight cell block by enter-ing 2, 2, 2 as before.

Click CALCULATE H-Bonds in the Edit Hydrogen Bond-ing control panel.


Use the Model Manager to make PPframe1 (the predictedurea structure) visible (check the box to the right of itsname).

Click the grid mode icon to display the two structures side-by-side.



Now you can easily compare the predicted structure to the experimen-tal one.

You see that the structures are essentially the same, although the axesmay be rotated relative to one another.

8. Calculate powder patterns

You conclude this tutorial by using Diffraction-Crystal to calculateand compare the powder patterns of the two structures.


This automatically compares two successively calculated patterns.

Rotate the structures for comparison.

Go to the ANALYTICAL 1 stack and find the DIFFRAC-TION-CRYSTAL card.

Select the Calculate Diffraction item to open the CalculateCrystal Diffraction control panel. Click the Preferences…button beside the checked POWDER box.

Check Include previous simulation? and close the panel.

In the Calculate Crystal Diffraction control panel, click theCALCULATE button.



A simulated powder pattern for the experimental structure is sent tothe graph window.

9. Compare the powder patterns

(Check the box to the left of the model name in the Model Manager.)

The X-ray diffraction pattern from the predicted urea appears super-imposed on the experimental pattern.

10.Graph the data

This card provides tools for manipulating the data in the graph win-dow.

This opens the Graph Manager control panel.

Be sure that you open the Graph Manager control panel and not theGallery Manager control panel (which does look similar). The GraphManager specifies which data-sets are displayed in a specific graph,while the Gallery Manager specifies which graphs are displayed in the

Use the Model Manager to make Model 2, the predictedurea structure PPFrame1, the current model.

In the Calculate Crystal Diffraction control panel, click theCALCULATE button again.

Find the GRAPHS card (on the TABLES & GRAPHSstack).

Select the Graph/Manager item on the card.



window.

This removes the difference, delta, and tick plots from the graph mak-ing it easier to see the two diffraction patterns.

11. Manipulate the graph window

Uncheck the display boxes for the Powder/sim - prev v1,Powder/delta v1, and Powder/ticks v1 data-sets.

Expand the graph window by clicking on and dragging thebottom left corner of the frame using the left mouse button.

Zoom in on the graph by holding down the <Shift> key anddragging the mouse from left to right over the graph win-dow with the middle mouse button depressed. Release the<Shift> key and use the middle mouse button to scroll thegraph on the axis.



You see that the two patterns are very similar, but that some of thepeaks in one are slightly displaced relative to the other. This is becausethe unit cell of the experimental urea is slightly larger in two crystal-lographic directions than for the predicted structure, and slightlyshorter in the other. The reason for this is the approximate nature ofthe simple charge calculation used, which underestimates the partialcharges on the atoms.

12.Finishing up






In this tutorial exercise, you have seen how Cerius2 can be used topredict the crystal structure of an organic compound from themolecular structure alone. The general solution of this problemcan be extremely complex — especially because the degrees offreedom increase radically with molecular flexibility. You have justattempted a very simple example. A typical commercial applica-tion of the Polymorph Predictor method requires many morehours of preparation and analysis, but the results can proveinvaluable. These are some of the issues you might have to con-sider in a fuller solution of a crystal polymorphism problem:

♦ Flexibility — The urea molecule is small and rigid. As mole-cules increase in size and number of flexible torsions, thedegrees of freedom in solving the polymorph problem rise rap-idly. The Polymorph Predictor method has been successfullyapplied to relatively rigid pigment molecules such as quinacri-done and small pharmaceutical molecules. Alternative strate-gies include making predictions with distinct conformers.

♦ Charges — Electrostatics can be crucial to determining the crys-tal structure. It is thus usual that highly accurate quantummechanical methods (such as Gaussian’s 6-31G*) are used tocompute partial charges. You can calculate partial charges inCerius2 using the Gaussian and MOPAC interfaces.

♦ Force field accuracy — Accurate parameterization is mostimportant. The parameterization used needs to be suited forcomputations on the type molecule studied. See the MSI bookForcefield-Based Simulations: General Theory & Methodology forfurther information on this topic.

♦ Symmetry — In general, you would need to search in morethan one space group. Some 75% of all known structures are inthe five most common space groups — a fact that usuallyenables you to narrow down the search. In some cases, you willhave data (for example, from indexing powder patterns) thatindicates the space group.

♦ Co-crystallization and solvents — Crystals may, in fact, con-tain more than one molecule in the asymmetric unit. The Poly-



morph Predictor can take account of more than one molecule,but it will increase the degree of difficulty of the calculation.

Review

❏ Sketching molecules (page 163)

❏ Calculating partial charges using the Charge Equilibrationmethod (page 163)

❏ Setting up a Polymorph Predictor sequence (page 167)

❏ Running a Polymorph Predictor sequence (page 171)

❏ Retrieving predicted structures from a Polymorph Predictorrun (page 172)

❏ Calculating hydrogen bonding patterns (page 172)

❏ Comparing powder diffraction patterns (page 172)

What to do next

To learn more about polymorph prediction read the Polymorphchapter of the Cerius2 Computational Instruments User’s Refer-ence.

The theory underlying the Polymorph Predictor is described in theseries of papers below in References and related material.


Ewald, P.P., Ann. d. Physik, 64 253 (1921).

Gdanitz, R.J., Chem. Phys. Lett., 190 391–395 (1992).

Gdanitz, R. J., Karfunkel, H.R., and Leusen, F.J.J., J. Mol. Graphics,11 275–276 (1993).

Karasawa, N. and Goddard, W., J. Phys. Chem., 93 7320 (1989).



Karfunkel, H.R., and Gdanitz, R.J., J. Comp. Chem., 13 1171–1183(1992a).

Karfunkel, H.R., and Leusen, F.J.J., Speedup, 6 43–50 (1992b).

Karfunkel, H.R., Rohde, B., Leusen, F.J.J., Gdanitz R.J., and Rihs G.,J. Comp. Chem., 14 1125–1135 (1993a).

Karfunkel, H.R., Leusen, F.J.J., and Gdanitz, R.J., J. Comp. AidedMat. Des., 1 177–185 (1993b).

Karfunkel, H.R., Wu, Z.J., Burkhard, A., Rihs, G., Sinnreich, D.,Buerger, H.M., and Stanek, J., Acta Cryst, B52 555-561 (1996)

Leusen, F.J.J., Z. Kristallogr., Suppl. 8 161 (1994)

Leusen, F.J.J., J. Cryst. Growth, 166 900-903 (1996)

Leusen, F.J.J., Proceedings of the 5th World Congress on Chemical Engi-neering, San Diego USA, Vol. IV, 134-138 (1996)

Mayo, S.L., Olafson, B.D., and Goddard, W.A., J. Phys. Chem., 948897 (1990).

Rappé, A.K., and Goddard, W.A., J. Phys. Chem., 95 3358 (1991).




10 Investigating the Inhibition ofInorganic Scales

This chapter shows how modeling has been used to study a partic-ular crystal growth problem — the design of growth-mediatingmolecules that inhibit the development of inorganic scales inwater-containing systems. This tutorial guides you through aseries of steps to a solution. Along the way, you learn about pre-dicting crystal morphology, creating surface models, minimizingsimple molecules, and measuring structural parameters.




♦ Reviewing the solution — discusses the scientific significanceof the solution and gives a checklist of the Cerius2 skills you’velearned.



Before you begin


♦ Morphology

♦ Surface Builder


10. Investigating the Inhibition of Inorganic Scales


♦ Minimizer

Overview of the problem Insoluble inorganic “scales” frequently grow in water-containingsystems due to the precipitation of mineral salts — a familiar phe-nomenon through its unpleasant results in domestic coffee-mak-ers! Scale growth causes greater problems in ventilation and air-conditioning systems, and is a major cause of production loss in oilwells where salts from the rock precipitate and block pipelines.Wells are treated with growth-mediating chemicals (known asscale inhibitors) that prevent the development of scale. The well isusually “flushed” with the chemical prior to the injection of highpressure water during the pumping of the reservoir. More effectiveinhibitors mean lower costs — both because less inhibitor is usedand because the well has to be taken out of commission less fre-quently in order to be treated. This example illustrates moleculardesign work that was carried out to improve the effectiveness ofinhibitors.

Overview of the solution Inhibitors have typically been discovered empirically by investi-gating the effects of different chemicals on the growth of crystalsunder simulated well conditions in the laboratory. Recent workhas rationalized the action of these chemicals. A better under-standing of this action has led to the design of more efficient inhib-itors, and modeling has played its part in this process. Researchersat ICI and British Petroleum have published work investigatingthe action of inhibitors on the growth of barium sulphate (barytes)scale (Black et al. 1991, Benton et al. 1993). Certain classes ofdiphosphonate molecule are known to inhibit the growth ofbarytes. Molecular modeling of crystal shape, molecular geometry,and surface chemistry was used as a tool to explain the action ofthe inhibitors and to guide suggestions for improvements.

In this tutorial, you explore some of the tools used for carrying outsuch work within the Cerius2 modeling environment — sketchingand surface building tools, rapid force field calculations and crys-tal morphology prediction.

Before you begin



logfile CGR_scale_inhibit.log, which illustrates the proce-dure. To run this logfile:

The logfile shows the methodology that you follow in this tutorial.The idea is to investigate the interaction of the inhibitor moleculewith possible growth faces. You’ll see how the molecule can be“keyed in” to a particular face by replacing the sulphate ions onthe surface with the phosphonate groups on the molecule. Thiseffectively disrupts the growth of the scale.


A. Loading a model of barium sulphate

B. Predicting the crystal morphology of barium sulphate

C. Creating a surface model from the barium sulphate (2 0 0) crys-tal face

D. Viewing and saving the (2 0 0) surface

E. Measuring the sulphate ion spacings on the (2 0 0) crystal face

F. Creating and measuring surfaces for the other barytes faces

G. Sketching the potential inhibitor, a diphosphonate molecule

H. Optimizing the potential inhibitor

I. Comparing the inhibitor molecule spacings with surface ionspacings

J. Visualizing the surface/inhibitor interaction

Type cerius2 at the UNIX prompt to run the program.

Select the Help/Examples... item from the top menu bar.

Double-click CGR_scale_inhibit.log to run the logfile.



Predictmorphology of thecrystal

Identify the growthfaces

Build surfacemodel of crystalface

Measure surfaceion spacing

Load crystal modelfrom file

Inhibiting scale, an overview of the solution

Optimize thepotential inhibitormolecule

Compare inhibitorspacings with ionspacings

“Key in” theinhibitor onto thesurface

Sketch thepotential inhibitormolecule

Repeat foreach crystalface




This section takes you through the procedure outlined above. Youlearn how Cerius2 has been used to show how the diphosphonatemolecule might inhibit barytes scale formation.

Begin with a new session of Cerius2. See Cerius2 Tutorials—Basicsfor information on running Cerius2.

A. Loading a model of barium sulphate

1. Start Cerius2


2. Load the model

The barium sulphate model, Ba(SO4) is saved in the fileCerius2-Models/minerals/baryte.msi. In this section,you load and view this model in the current model window.

The crystal structure baryte is loaded into the first model space and


Open the Load Model control panel by selecting the File/Load Model… item from the top menu bar.

Load the file Cerius2-Models/minerals/7-Sulfates/baryte.msi.



some basic information about the crystal structure appears in the textwindow.

3. Adjust the model display

To scale the model, hold the Shift key down and drag the mouse overthe model window with the right button depressed.

The model you see is a representation of one triclinic unit cell contain-ing four BaSO4 groups. In the next section, you use the Morphologymodule to identify the key crystal faces in the growth of barytes scale.

B. Predicting the crystal morphology of barium sulphate

Follow the steps in this section to predict the crystal morphology of thebarium sulphate structure that you loaded in Section above.

1. Calculate the crystal morphology


Change the popup on the tool bar from STICK to BALL.

To view the model from all angles, rotate it by dragging themouse over the model window with the right button

Go to the OFF INSTRUMENTS 1 stack and click theMORPHOLOGY card to the front of the card deck.



Here you are using the Bravais Friedel Donnay Harker (BFDH)method (Donnay and Harker 1937), which provides an approximationto the crystal morphology based on a set of geometrical rules. Themain purpose of performing this calculation is to identify the keygrowth faces.

The only calculation parameter for this method is the Minimum SliceThickness. In this case, begin with the default value of 1Å; if the Mor-phology module finds that this is too small a number, it automaticallyincreases the minimum thickness to 2Å.

A picture of the predicted morphology appears on the screen; it shouldlook similar to the following figure.

Select the Calculate item on the MORPHOLOGY card toopen the Calculate control panel.

Click the Calculate BFDH Morphology button.



2. Label the Crystal faces

You use the Morphology Display control panel for labeling the crystalfaces with their Miller indices.

Select the Display item to open the Morphology Displaycontrol panel.

Change the Face Label popup to INDICES.



The Miller indices of each face are now displayed on the model.

Note the faces that are present. These are of the following types:(2 0 0), (2 1 0), (1 1 1), (1 0 1), and (0 1 1).

3. Examine the crystal face growth rates

You see a table of crystal faces. Each face has a distance associated withit. This distance is the output from the BFDH calculation and is ameasure of the growth rate of the face. Faces with slower growth ratesare usually morphologically more important. The faces are ranked inincreasing order of growth rate — thus, those at the top of the list aremore likely to be important growth faces. The faces with Yes specifiedunder Visible? in the table are seen in the morphology shown in themodel window.

Rotate the model to view it.

Select the Edit/Add Faces item to open the Edit/Add Facescontrol panel.



C. Creating a surface model from the barium sulphate (2 0 0)crystal face

In the following steps, you return to the model of the barytes crystaland cut from it an atomistic model of the (2 0 0) growth face. Of pri-mary interest are the sulphate ion layers that are laid down on thesefaces. In order to make the measurement of the ion spacing easy, youcut only a very thin surface that corresponds to the sulphate ion layer.

1. Adjust the morphology display

In the Morphology Display control panel, change the Visu-alization popup to MOLECULAR.



The semi-transparent morphology shape disappears from the modelwindow leaving only the barytes unit cell structure.

Remember that you can use the Clear Panels button on the tool bar todo this; alternatively, you can click the close control panel box on eachpanel.

2. Set up the crystal slice parameters

Here you only want to cut a thin layer.

The second Depth box (which gives the depth in unit cells) is auto-matically updated; 0.2 Å is equivalent to 0.0225 of the depth required


Go to the BUILDERS 1 stack and click the SURFACEBUILDER card to the front of the deck.

Select the Cleave Crystal Surface item to open the CleaveCrystal Surface control panel.

Specify the surface by typing 2 0 0 in the Direction (h,k,l)text box. Leave spaces between each digit.

Type 0.2 in the first Depth box, and press <Enter>.



to enclose a complete unit cell of the 3D periodic structure.

The yellow dots show where the surface box will be, you will laterreposition this with the arrow keys to include the sulfate ions.

3. Adjust the model display

This makes the center positions of the atoms easier to see.

4. Cleave the slice and move to a new model space

This creates a new empty model space. You are going to cut out the

Click the check box Display Surface Box.

Change display style from BALL to STICK. on the tool bar.

Rotate the model using the mouse until you are looking atthe surface sideways.

Use the arrow keys to move the box perpendicular to thesurface until the box contains one of the yellow sulfuratoms.

Click the “+” icon above the Model Manager list.



surface and place it into this new model space.

With the MOLECULAR cleave rule, the surface model will containwhole SO4 units. If you were to choose the ATOMIC rule, then onlythe sulphur atoms contained within the mesh box would be copied intothe surface model.

A surface model containing one SO4 molecule should appear in themodel window.

Note

D. Viewing and saving the (2 0 0) surface

In this section, you use the visualization options to extend the (2 0 0)surface cell and save the surface model to file.

1. Extend the surface cell

Change the Cleave Rule popup from DEFAULT toMOLECULAR.

Click the CLEAVE button.

Rotate the molecule to view it.

If your surface model doesn’t appear?

Be sure that you had an empty model window as the currentmodel space before you clicked the CLEAVE button.

Select the Visualization item on the SURFACE BUILDERcard to open the Surface Visualization control panel.



The (2 0 0) baryte surface is now displayed as a spread of nine cells.This gives a better picture of how surface looks.

2. Save the surface to a file

E. Measuring the sulphate ion spacings on the (2 0 0) crystalface

In this section, you measure the ion spacings for the (2 0 0) surface.You use the mouse to measure the sulphate spacings of the (2 0 0) sur-face. Make a note of the spacing when you measure it. This and theother spacings that you measure later will be compared to the spacingof the potential inhibitor.

1. Make the measurements

This highlights the distance icon, and in the model window, the cursor

Type 3 in the first (u) text box and 3 in the second (v) textbox and press the <Enter> key.

Rotate to view the surface from above.

Save the model into an msi format file called Baryte200.msi.

Open the Measurements control panel by selecting theGeometry/Measurements… item from the top menu bar.

Click the Distance icon.



appears as a question mark instead of an arrow.

Cerius2 draws a line between the two atoms and writes the distancebetween them in angstroms. Note down this distance.

If you have trouble reading the distance clearly, you may need to rotateor zoom in on the model or choose the List Measurements button onthe Measurements control panel to write the distances in the text win-dow.

There are two possible “nearest neighbor” pairs: one pair parallel tothe u axis and one parallel to the v.

2. Note down the measurements

Your model window should look like the one below, with two inter-sul-phur distances marked.

To measure the sulphate ion spacings click on two adjacentsulphur atoms.

Click on the other “nearest neighbor” pair and note downthis second measurement.

After making these measurements, click the arrow buttonon the Measurements control panel to return the mouse tonormal Selection Mode.



3. Create a table of measurements

In this section, you’ve found the sulphur ion spacings for the (2 0 0)surface of the baryte crystal; they are listed in the table below. You nowwant to make models of the other surfaces of baryte and measure theirion spacings to complete the table below.

SurfaceDistance between the “nearestneighbor” sulphur atoms [Å]

(2 0 0) 5.458 7.153

(2 1 0)

(1 1 1)

(1 0 1)

(0 1 1)



F. Creating and measuring surfaces for the other barytes faces

In this section, you measure the ion spacings on each of the othergrowth faces. For each of the Miller indices: (2 1 0), (1 1 1), (1 0 1),and (0 1 1), you need to build a surface model and measure its ionspacings.

1. Build the first surface model

Remember to leave spaces between each digit.

This shows a yellow dotted box corresponding to what will be the 2Dperiodic unit in the surface. You will later position this to include the

Use the Model Manager to make the crystal named barytethe current model.

If the Cleave Crystal Surface control panel is not alreadyopen, open it by selecting the Cleave Crystal Surface itemon the SURFACE BUILDER card.

Specify the surface by typing its Miller indices into theDirection (hkl) text box: 2 1 0, 1 1 1, 1 0 1, or 0 1 1.

Be certain that the 1st Depth text box is still set to 0.2 Å, thatDisplay Surface Box is checked, and that the Cleave Ruleis set to MOLECULAR.



sulphate ions.

A new empty model space appears as the current model.

A surface model should appear in the model window.

2. Adjust the surface display

Rotate the model using the mouse until you are looking atthe surface from the side.

As before, use the arrow buttons to move the box perpen-dicular to the surface until at least one sulfur atom is withinthe box

Click the “+” icon above the Model Manager list.

Click the CLEAVE button.

Select the Visualization item from the SURFACEBUILDER card.

Type 3 in the first (u) text box and 3 in the second (v) textbox, then press the <Enter> key.



The barytes surface is now displayed as a block of nine cells.

3. Save the surface model

It’s a good idea to include the Miller indices in the file name to makethe file easy to recognize. For example, call the (1 0 1) surface fileBaryte101.msi.

4. Measure the surface

Remember to note down the distances.

5. Repeat steps 1-4 for the remaining surfaces

Return to page 201 and repeat these steps for the next surface untilyou’ve built and measured surfaces for all five surfaces of baryte. Your

Rotate the molecule to view the surface from above.

Save the model into an msi format file.

If the Measurements control panel is not already open, openit by selecting the Geometry/Measurements… item fromthe top menu bar.

Click the Distance icon, then find the inter-sulphate dis-tances of the “nearest neighbor” atom pairs as before.



list of measurements should look similar to the table below.

Note

G. Sketching the potential inhibitor, a diphosphonatemolecule

You now sketch the ionic form of the diphosphonate inhibitor mole-cule:

[PO3 – CH2 – NH2 – CH2 – PO3] –3

1. Make a new model space

SurfaceDistance between the “nearestneighbor” sulphur atoms [Å]

(2 0 0) 5.458 7.153

(2 1 0) 7.087 7.153

(1 1 1) 8.998 10.427

(1 0 1) 5.458 11.406

(0 1 1) 5.593 7.153

If you want to take a break now, exit Cerius2 by selecting theFile/Exit item from the top menu bar.

When you want to continue with the tutorial, load in the barytefile and those surface models you’ve created; then build theremaining surfaces before going on to section G.

Create a new model space by clicking the “+” icon on theModel Manager.



2. Name the new model

3. Build the model

Please see the tutorials guide Part One, “Building and VisualizingMolecular Models” for directions on building molecules using theSketcher.

H. Optimizing the potential inhibitor

In this section, you use the Minimizer to further optimize the geom-etry of the diphosphonate. Cerius2 calculates the minimization ener-gies using the Universal Force Field. After the first minimization, youcalculate partial charges for the molecule by the charge equilibrationmethod, and then reminimize the molecule taking into account elec-trostatic forces.

In the Model Manager list, name this modeldiphosphonate.

Open the Sketcher control panel by selecting the Build/3D-Sketcher… item from the top menu bar and sketch thediphosphonate inhibitor molecule shown above.

Hold down the CLEAN button until the molecule stopsmoving.

Click the Selection Mode icon in the Sketcher panel andclose the Sketcher panel.



1. Minimize the diphosphonate

Cerius2 automatically loads the Universal Force Field (Rappé’ et al.1992, 1993, Casewit et al. 1992a, 1992b) and sets up the energyexpression; by default Cerius2 includes the bond, angle, torsion,VDW, and Coulomb energy terms in the Universal Force Fieldexpression.

You can follow the loading of the force field and the minimization inthe text window. Cerius2 also plots the progress of the minimizationin the graph window. If the graph window overlaps the model window,move or shrink it so that you can see the model window clearly.

2. Calculate partial charges

The partial charge of each atom in the model window is now labeledzero. You have carried out this minimization on a completelyuncharged molecule. Now, you are going to calculate the partialcharges on the charged ion using the charge equilibration method(Rappé’ and Goddard 1991). This is the recommended method when

Go to the OFF METHODS card deck and click theMINIMIZER card to the front of the card deck and selectthe Run item to open the Energy Minimization controlpanel.

Click the Minimize the Energy button.

Change the Label Style popup on the tool bar from NOLABEL to CHARGES.



using the OFF.

The charges determined by this method are highly dependent on themolecule geometry — hence, it was important to minimize the struc-ture before calculating them.

This sets the overall charge of the diphosphonate molecule to -3. Youcan see from the charge labels in the model window that the charge isevenly spread across the molecule. The charge equilibration methodthat you carry out next distributes this charge more sensibly.

3. Minimize again

Go to the OFF SETUP deck and click the CHARGES card tothe front.

Select the Charges item from the card to open the controlpanel.

In the Average to text box type -3.

Click the radio button beside this box.

Click the CALCULATE atomic charges button.

Change the Label Style popup on the tool bar fromCHARGES to NO LABEL.

Find the Energy Minimization control panel and again clickMinimize the Energy.



This time the minimization takes into account the electrostatic energy.

4. Save the file

Now you have a minimized structure for the scale inhibitor diphos-phonate.

I. Comparing the inhibitor molecule spacings with surface ionspacings

In the following section, you measure the phosphorus spacing in thediphosphonate molecule and compare it to the sulphur ion spacings ofbarytes crystal faces. You choose the face where the spacings matchbest and create a larger surface model of that face. Later, in Section J,you see how the diphosphonate molecule fits onto this crystal surface.

1. Measure the phosphorus spacing

Close the graph window by double-clicking in the top leftcorner of the frame.

Save the model into an msi format file, entering a file namethat makes the contents easy to recognize: for example,diphosphonate_min.msi.


Select the Geometry/Measurements item from the topmenu bar to open the Measurements control panel.

Measure the distance between the two purple phosphorusatoms in the diphosphonate model as you did earlier.



Remember to return the mouse to Selection Mode (it is highlightedblue when in this mode) after making the measurement.

2. Adjust the display

3. Compare the spacing with previous results

The closest match is the (0 1 1) surface; its sulphate spacing of 5.593Å compares best with the phosphonate spacing of 5.582 Å. This sug-gests that diphosphonate may work by inhibiting growth of thebarytes (0 1 1) crystal face.

Next, you study the how the molecule might be placed on that surface.

4. Cleave a new representative surface

Change the display style from STICK to BALL on the toolbar.

Compare this inter-phosphate distance with the list of sul-phate ion spacings you compiled earlier (page 204).

Go to the Model Manager list and check the (0 1 1) surfaceto make it the current model.

Go to the BUILDERS 1 card deck and click the SURFACEBUILDER card to the front of the card deck.

Select the Cleave Crystal Surface item to open the controlpanel.



This time you want to cut a proper representation of surface, severalatomic layers thick.

The old (0 1 1) surface is lost and replaced by the new 5.0 Å deep sur-face model.

5. Generate a non-periodic surface

Check that the control panel says the crystal will CLEAVEfrom ‘baryte’. If necessary, use the down arrow to open thepulldown menu and select baryte.

Check that the Miller Indices specified in the Direction(hkl) text box are 0 1 1. Enter these numbers in the text boxif necessary.

Enter 5.0 in the first Depth text box and click the CLEAVEbutton.

Go to the Surface Builder card and select the Visualizationitem to open the Surface Visualization control panel.

Type 4 in the first (u) text box and 4 in the second (v) textbox, then click ENTER.



You have generated a non-periodic “piece” of the barytes surface. Younow use this model to visualize the interaction between the surfaceand the inhibitor.

J. Visualizing the surface/inhibitor interaction

1. Make both surface and inhibitor visible

This allows you to view both the surface and the inhibitor in their sep-arate model spaces.

2. Copy the molecule into the surface model space

The molecule is now copied into the surface model space.

3. Make diphosphonate invisible

Now go to the Cleave Crystal Surface control panel andclick the CLEAVE button to create a non-periodic super-structure.

Check the box to the right of the name “diphosphonate” inthe Model Manager.

Click over the molecule display away from the model withthe left mouse button and drag the dotted box that appearsinto the surface space.

Use the Model Manager to remove the diphosphonatemodel from the display.



4. Prepare the molecule for positioning on the surface

You are now set up to manipulate the molecule and place it on the sur-face.

You have to rotate the model around to decide whether the atom isindeed on top of the surface. You use this as a destination point to posi-tion one end of the molecule.

5. Select a destination point

Rotate the model view until you are looking down onto thesurface (the diphosphonate molecule should be in the bot-tom left of the screen).

Zoom in on the surface (shift key + middle mouse button orboth middle and right mouse buttons simultaneously) untilit fills the model window.

Select a sulphur atom in one of the sulphate groups that istowards the middle of the structure and on the surface ofthe barytes.

Go to the top menu bar and select the Move/Atoms Posi-tion... item to open the control panel.



The selected sulfur is the destination point for the inhibitor molecule.

The xyz coordinates are automatically entered in the Goes to DES-TINATION point text box.

6. Select a reference point

This is the reference point in the molecule that will be moved.

You have now set this point up as a reference point for the move tool.This moves selected atoms such that the reference point is superim-posed on the destination point. Now define which atoms will bemoved.

7. Position the molecule

Click the DEFINE from selected atoms button to define thispoint.

Select one of the phosphorus atoms in the molecule.

Click the Define from selected atoms button again.

Go to the main tool bar and change the second popuplabeled Atom to Frag, then click on an atom in the molecule.



All the atoms in the molecule should now appear selected.

The phosphonate molecule has been moved to a selected position on thesurface. Now, you want to rotate it so that it lies on the surface.

8. Adjust the molecule position


Zoom in on the molecule by holding down the shift key and draggingthe middle mouse button over the model window.

Click the Position Selected atoms button in the PositionAtoms control panel, and then deselect all the atoms.

Change the selection rule popup from Frag to Atom.

Select the phosphorus that is currently superimposed on asulphur.

Go to the top menu bar and select the Move/Atoms Rotate...item to open the Rotate Atoms control panel. Click theDEFINE from selected atoms button to define the destina-tion point.

Go to the tool bar and change the selection rule back to Frag,and click on any atom in the diphosphonate molecule.

Rescale so that the molecule fills the screen, then go to thetool bar and change the display style to STICK.



10.Reposition the molecule

Select the two nearest neighbor sulfur atoms on the surface.

Go to the Position Atoms control panel and click DEFINE toset these atoms as the destination point.

Select the two phosphorus atoms of the baryte molecule.

Go to the Position Atoms control panel and DEFINE theseas the REFERENCE point.

Go to the tool bar and change the second Atom popup toFrag, then select any atom of the baryte molecule.

Go to the Position Atoms control panel and click thePOSITION button to position these selected atoms.

Pick any atom in the overlapped sulfate group and deletethe group by simultaneously pressing the <Ctrl> and<Delete> keys.

Repeat for the other overlapped sulfate group.




This shows how the inhibitor molecule might key in to the surface. Thepresence of this molecule acts as a steric hindrance to the deposition offurther barium and sulphate ions, and thus inhibits the growth of thecrystal.

Use the dial in the Rotate Atoms control panel to rotate themolecule about its own axis so that the two CH2 groups areuppermost.

Deselect all atoms, zoom out, and rotate the model to viewit.



12.Finishing up


In this tutorial exercise, you’ve seen how you can use Cerius2 torationalize the inhibiting action of a diphosphonate ion on barytesscale formation. The methodologies described apply equally toinvestigating the interaction of any molecule with an inorganicsurface or crystal.

ICI researchers used findings from such work to design a moreeffective inhibitor than the diphosphonate used above. This was apolymeric molecule with diphosphonate units linked by hydro-carbon chains bonded to the central nitrogen. Modeling was usedto select the optimal length for the hydrocarbon chain.

This real research work had to consider many more parametersand simulation options than have been described here. Theseincluded:

♦ Is the “keying in” mechanism the correct description of theinhibition process? Other possibilities include prevention ofprecipitation by complexation with the inhibitor in solution.

♦ Are there any competitive binding processes that effect inhibi-tor performance? Energy calculations could be used to estab-lish the relative binding energies of such processes.

♦ How accurate is the force field minimization? The ICI research-ers quoted in the example actually used MOPAC semi-empiri-cal quantum mechanics calculations to compute the chargesand geometry of the inhibitor molecule. Users of MOPAC couldrepeat this work within Cerius2. Force fields are sufficient for

To end the Cerius2 session, close all open panels and selectFile/Exit from Visualizer menu bar.




the many cases where a semi-quantitative “feel” for the geom-etry of a system is required.

♦ In this exercise, you have only considered the geometric matchbetween the phosphonate and sulphate groups — a goodcharge match would be required for the inhibitor to replace sul-phate groups. The ICI group’s use of MOPAC confirmed thatthis was the case.

♦ The BFDH method gives an approximation of the morphologyand identifies important faces. It does not take account of theenergetics involved in growing a crystal face, or of the possibleeffects of solvents and excipients. It may be worth studying awider range of crystal faces than simply those which are visiblein the predicted morphology (you could use the list in the Edit/Add Faces control panel). Molecular crystals can be modeledmore accurately using the attachment energy method.

Review

In this lesson you learned or reviewed:

❏ Loading molecules from file into Cerius2 (page 189)

❏ Model viewing and display (page 189)

❏ Predicting crystal morphology (page 190)

❏ Creating a surface model from a crystal (page 194)

❏ Measuring inter-atomic distances (page 198)

❏ Sketching a simple molecule (page 198)

❏ Optimizing molecular geometry with the Minimizer module(page 205)

❏ Manipulating a small molecule relative to a surface superstruc-ture (page 211)

What to do next


What to do next

This application and the work on which it is based are describedin Black et al. (1991) — you may want to refer to these.

To learn more about Morphology prediction, including the theoryof the Bravais Friedel Donnay Harker calculation, read the Mor-phology chapter of the Cerius2 Computational Instruments: PropertyPrediction book.

If you want to take this example further, you could try sketchingand optimizing a dimer of the disphosphonate ion linked togetherby a simple carbon chain between the nitrogens. What length ofchain produces an optimal spacing between the diphosphonatessuch that they bridge pairs of sulphate ions on the (0 1 1) surface?




Benton W. J., Collins I. R., Grimsey I. M., Parkinson G. M., andRodger S. A., Faraday Discussions, 95 281 (1993).

Black S. N., Bromley L. A., Cottier D., Davey R. J., Dobbs B., andRout J. E., J. Chem. Soc. Faraday Trans., 87(20) 3409 (1991).

Casewit, C. J., Colwell, K. S., and Rappé, A. K., J. Am. Chem. Soc.,114 10046 (1992a).

Casewit, C. J., Colwell, K. S., and Rappé, A. K., J. Am. Chem. Soc.,114 10035 (1992b).

Donnay J. D. H. and Harker D., Amer. Mineralogist, 22 463 (1937).

Rappé, A. K. and Goddard, W. A., J. Phys. Chem., 95 3358 (1991).

Rappé, A. K., Casewit, C. J., Colwell, K. S., Goddard, W. A., andSkiff, W. M., J. Am. Chem. Soc., 114 10024 (1992).

Rappé, A. K., Colwell, K. S., and Casewit, C. J., Inorg. Chem., 323438 (1993).

Part 5Electronic, Optical, and Magnetic

Properties


11 Density and Bandstructure ofAluminum Arsenide

In this lesson, you will load a crystal of aluminum arsenide usingthe model-loading facility of the C2•Visualizer. A self-consistentCASTEP job will be performed, and the charge density will be cal-culated and visualized. A second non-self-consistent job will belaunched using the density output from the first run as a startingpoint. The results will be analyzed by means of the quantum anal-ysis facility.

Topics covered in this lesson include:

♦ Loading structures with the Load Model control panel.

♦ Visualizing densities.

♦ Restarting band-structure runs from the output of a self-consis-tent run.

♦ Displaying band structures with CASTEP’s Analyze controlpanels.

Note This lesson involves running several CASTEP jobs which may,depending on your hardware, require several minutes of CPUtime to complete. The jobs must each be complete before thelesson is continued, because subsequent analytical steps requirethe correct CASTEP output files. This lesson is thereforedesigned so that the CASTEP jobs are run in interactive mode.Cerius2 waits until the jobs are complete and is thereforeunavailable while the job is running.


11. Density and Bandstructure of Aluminum Arsenide

1. Setting up for the tutorial

It takes a while for Cerius2 to load.

2. Constructing a unit cell of crystalline aluminum arsenide

The browser that appears contains a list of files in your current direc-tory.

The conventional cell of aluminum arsenide appears in the Cerius2Models window.

Enter mkdir cst_tut1 at the UNIX prompt to make a direc-tory in which to run this tutorial. At the next prompt, entercd cst_tut1 to move to this directory. Now, to start upCerius2, enter cerius2 at the UNIX prompt.

Select the File/Load Model… menu item from the menu barin the main Visualizer control panel.

Double-click Cerius2-Models in the list box to access thelibrary of structures supplied with Cerius2. Scroll down thelist and double-click semiconductors to access the library ofcrystal structures of elementary and compound semicon-ductors. Finally, double-click AlAs.msi to load the AlAsmodel into the current session of Cerius2.


3. Accessing the CASTEP module

It may take a few seconds to appear, while Cerius2 reads in theCASTEP databases.

4. Setting up a self-consistent CASTEP run

Set up the CASTEP job to run in interactive mode (to freeze Cerius2

until the job completes):

Go to the C2•CASTEP module by clicking the menu deckspulldown in the main control panel (probably currentlylabeled BUILDERS 1) and selecting QUANTUM 2 fromthe list that appears.

This CASTEP card should already be in front of theQUANTUM 2 deck of cards. If not, click its name to bring itto the front.

Click the Run card menu item to open the Run CASTEPcontrol panel.

In the Run CASTEP control panel, change the default FilePrefix to AlAs. Transform the cell to the primitive by click-ing the Transform Cell to Primitive action button.

Select the Job Control menu item on the CASTEP card toopen the CASTEP Job Control control panel. Change theRun Mode popup to INTERACTIVE.



5. Running the CASTEP calculation

This sets up (and then starts) the CASTEP job. The .msi file contain-ing structural information for AlAs is written to disk; default k-pointfiles are generated; several CASTEP input files are written to disk(they will all have AlAs prefix and various extensions).

The CASTEP job is launched. A message to this effect appears in theCerius2 text window. It takes between a few seconds and a few min-utes for the CASTEP job to complete, depending on the type of hard-ware you are running it on. The job takes about 50 seconds of CPUtime on an IBM 370 RS6000 workstation or an Indigo II SiliconGraphics workstation with a 150 MHz R4400 processor.

To ensure that the output of the CASTEP run is available before youcontinue to the next stage of the lesson, Cerius2 is frozen while the jobis running. An interrupt window appears so that the job can be killed;or transferred to the background so that you regain access to Cerius2

(the job continues to run) or so you can completely exit Cerius2 andleave the CASTEP job running.

An xterm window is opened when the job starts so that you can mon-itor progress by looking at changes in the output file AlAs.cst. (Thiswindow opens automatically only if the run mode is interactive. Inany other mode you have to click the Monitor Logfile action buttonin the CASTEP Job Control control panel to open the xterm window.)

In addition, the Cerius2 CASTEP Job Status list box in the CASTEPJob Control control panel contains a new status line, which includesthe name of the host for running the job, the file prefix (AlAs), the jobstatus (started, running, complete, etc.) and information about thedirectories that contain input and output files for the job.

Click the RUN pushbutton in the Run CASTEP controlpanel.


6. Viewing the results of the CASTEP calculation

About halfway down the output file you find information about thetotal energy of the system:

>>>>>>>>>>>>>>>>>>>> ITERATION = 1 <<<<<<<<<<<<<<<<<<<<

------------------------------------------------------------ SCF loop Energy (eV) Energy gain Timer <-- SCF Initial Final per atom (sec) <-- SCF ------------------------------------------------------------ 1 -176.08499 -228.34957 26.132289 15.44 <-- SCF 2 -228.34957 -231.52944 1.589935 29.64 <-- SCF 3 -231.52944 -231.54857 0.009567 41.23 <-- SCF 4 -231.54857 -231.54907 0.000249 49.06 <-- SCF 5 -231.54907 -231.54909 0.000010 55.43 <-- SCF

TOTAL ENERGY IS -231.5490929 (eV)

The CASTEP calculation converged in 5 iterations to an energy of-231.5490929 eV. The .cst file is generally self-explanatory. The exactnumbers of energies at the beginning of your run will differ from thoseshown here because CASTEP uses a random number generator to pro-duce the initial guess for the wavefunctions.

7. Preparing to analyze the results

You need to load the results before you can analyze them:

The same AlAs model is loaded into a new model space. This model

Use a scroll bar to examine the AlAs.cst window (xterm dis-play of the output file).

Select the Analyze/Files menu item on the CASTEP card toopen the CASTEP File Analysis control panel. It contains abrowser that shows a list of files in the current directory.Double-click AlAs.cst to load the results of your most recentrun for analysis.



would of course be different from the original one if the GeometryOptimization or Dynamics task had been chosen from the RunCASTEP control panel.

8. Displaying the charge density of AlAs

The Cerius2 interface loads the charge density data generated by theCASTEP run and displays them as a 3D-isosurface.

This control panel shows the range of values of electron charge densityfor the system and the current settings for the graphical representa-tion of the isosurface.

The previously displayed isosurface disappears and a new one isshown instead.

Select the Analyze/Density menu item from the CASTEPcard to open the CASTEP Charge Density control panel.Assure that the Density Surface popup is set to Total andclick the Display action button.

Select the Analyze/Surfaces card menu item to open theCASTEP Surfaces control panel.

Change the Isosurface Value to 0.2 and click the CreateNew Surface action button.


Two isosurfaces are now displayed on the model.

The second created surface should appear as four lumps of charge clus-tered around the arsenic atom. The CASTEP Surfaces panel showsthat the density of the system varies between 0.0145 and 0.639 elec-trons Å-3 in the unit cell. A contour level of 0.55 electrons Å-3 corre-sponds to a region of high density. The high-density regions are thebond charges of AlAs. The bonds are closely clustered around the Asatoms because AlAs is a partially ionic system and the electrons preferto sit in the vicinity of the more electronegative arsenic atoms.

9. Computing the band structure of AlAs

The final part of the lesson shows you how to perform a bandstructurerun on AlAs. In the first part of the lesson you generated a self-con-sistent density for AlAs. The self-consistent density can be used toprovide a starting potential for the bandstructure run using theCASTEP interface.

In order to select the directions in reciprocal space in which to plot the

Rotate the model to get a better understanding of the natureof the surface. To create an additional isosurface in themodel window, deselect the currently highlighted item in theEdit Surface list box in the CASTEP Surfaces control panel.Change the Isosurface Value to 0.55 and the Color of theisosurface to LIGHT GREEN, then click the Create NewSurface action button again.

Select the Analyze/Band Structure card menu item to openthe CASTEP Band Structure control panel. Click the SetupK-points… pushbutton to open the CASTEP Band Struc-ture K-Points control panel, which shows the default set ofhigh-symmetry k-points for the given structure. This con-trol panel can be used to modify this set, the density ofk-points along high-symmetry directions, etc.



bandstructure, it is useful to display the Brillouin zone of AlAs:

The Brillouin zone of AlAs appears in the model window. Some of thehigh-symmetry points of the zone are labeled, and the default k-pointpath for bandstructure calculations is shown by a yellow dashed line.The display parameters (color, visibility) can be changed with controlsin the Brillouin Zone Display control panel.

Let’s change the first line of the path from W–L to X–L:

The symbols and coordinates for the initial and final points along thisline are now shown in the entry boxes and associated popups below thek-points list box.

The path in the Brillouin zone as displayed in the model windowchanges to reflect this change.

Click the Brillouin Zone Display… pushbutton on theCASTEP Band Structure K-Points control panel to open theBrillouin Zone Display control panel. Check the ShowReciprocal Space Constructs check box.

Select the first line in the list box in the CASTEP Band Struc-ture K-Points control panel.

Change the symbol for the initial point from W to X using thepopup.

To speed up the calculation, delete directions number 4 and5 by selecting each of these lines in turn and clicking theDelete Directions action button. Leave all other controls attheir default settings.


You have now specified the path for the band-structure calculationwhich is X–L–Gamma–X.

The bandstructure job is launched. As before, Cerius2 is unavailableuntil the background job has completed.

10.Displaying the bandstructure of aluminum arsenide

When the band structure calculation is completed, the entry box con-taining the file name in the Band Structure Display section of theCASTEP Band Structure control panel is automatically changed to./AlAs_band_str.bands.

The bandstructure plot appears.

Energy is plotted vertically against wavevector (which is on the hori-zontal axis). The lowest eight bands are plotted. Because the 3rd and4th, as well as 7th and 8th, bands are degenerate in the Gamma–X andL–Gamma directions, only 6 energy points appear at each k-point inthese directions. The 3 lowest points in each direction are the occupiedvalence bands, and the 3 highest points are the lowest unoccupied con-duction band states. The band gap between occupied and unoccupiedstates is clearly visible. The valence band maximum in AlAs occurs atthe Gamma point (the right hand edge of the bandstructure plot).AlAs is an indirect band gap material, and the conduction band min-imum occurs at X, at the left hand edge of the band structure plot.

You can display the band structure plot side by side with the density-

Change the Number of Bands in the CASTEP Band Struc-ture control panel to 8 so that both valence and conductionbands are calculated (the default value of 4 corresponds tothe occupied states only). Click the Calculate Band Struc-ture push button.

Click the Plot action button in the CASTEP Band Structurecontrol panel.



of-states (DOS) plot:

Two panels are now shown in the graph window. DOS in this exampleis estimated using the data from the original self-consistent run, soonly valence states are included. Also the sampling is poor, since youneed more k-points to reproduce the fine structure of the DOS thanyou do to achieve convergence in total-energy calculations.

Additional changes to the graph style can be made using the Graphsmodule of Cerius2 (changFurthering the vertical scale, labels, title,plotting attributes, etc.).

11. Finishing up

sc

Check the Display Density of States check box in theCASTEP Band Structure control panel and click the Plotaction button again.




12 Optimizing the Geometry ofStishovite

Before you begin


♦ Crystal Builder

♦ CASTEP


Note

Running the tutorial lesson


This lesson involves running several CASTEP jobs which may,depending on your hardware, require several minutes of CPU timeto complete. The jobs must each be complete before the lesson iscontinued, because subsequent analytical steps require the correctCASTEP output files. This lesson is therefore designed so that theCASTEP jobs are run in interactive mode. Cerius2 waits until the jobsare complete and is therefore unavailable while the job is running.

Enter mkdir cst_tut2 at the UNIX prompt to create a direc-tory in which to run this tutorial. At the next prompt, entercd cst_tut2 to move to this directory. Now, start up Cerius2

by entering cerius2 at the UNIX prompt.


12. Optimizing the Geometry of Stishovite


2. Retrieving TiO2 in the rutile structure from the database

The stishovite polymorph of SiO2 is already in the Cerius2 library ofcrystal structures. However, it is instructive to consider how theC2•Crystal Builder module can be used to transform a closely relatedstructure, TiO2 in the rutile structure, into stishovite. Rutile andstishovite have the same space group label and identical numbers ofatoms in the unit cell. So, in the next two steps of this lesson you learnhow to transform TiO2 into SiO2 using the C2•Crystal Builder.

The browser that appears contains a list of files in your current direc-tory.

The conventional cell of titanium dioxide in its rutile structureappears in the model window.

3. Transforming TiO2 to stishovite

The next step is to modify the structure by changing titanium atomsto silicon, modifying the cell dimensions to those of SiO2, and adjust-


Double-click Cerius2-Models in the list box to access thelibrary of structures supplied with Cerius2. Double-clickmetal-oxides to access the library of crystal structures ofoxides. Finally, scroll the list and double-click TiO2_rutile.msi to load the desired structure into the current ses-sion of Cerius2.


ing the position of the oxygen atom in the cell:

The Cell Contents control panel shows that the cell contains 4 oxygenatoms and 2 titanium atoms . It also gives information on cell volumeand density.

The selected atom becomes highlighted, and a message appears in thetext window with details of the selected item, for example:

Model(name=TiO2_rutile):Cell(0,0,1):Atom(name=TI)

The titanium atoms are all changed to silicon.

Go to the C2•Crystal Builder module by bringing theCRYSTAL BUILDER card to the front of the BUILDERS 1card deck by clicking on its name (if it is not already infront).

Select the Unit Cell/Cell Contents card menu item to openthe Cell Contents control panel, which allows you to exam-ine the cell contents.

Select any of the titanium atoms (magenta) in the model.

Select the Build/Edit Atoms… menu item from the menubar in the main Visualizer control panel to open the EditSelected Atoms control panel. Click the periodic table iconto open the Periodic Table window.

Select Si in the table.



Now set the cell parameters:

The value of the b cell parameter changes automatically, as requiredby the current space group symmetry.

The cell vectors are now set to their experimental values, and the dis-play of the conventional cell shrinks slightly.

You get information both in the text window and in a message win-dow about all atomic attributes, including the fractional coordinatesof this atom. They are:

Select the Unit Cell/Cell Paramters menu item from theCRYSTAL BUILDER card to open the Cell Parameters con-trol panel.

Change the a cell constant to 4.18 by selecting that entrybox, typing in a new value, and pressing <Enter> or clickingelsewhere in the control panel.

Change the c cell constant to 2.67.

Now adjust the positions of the oxygen atoms. Select theoxygen atom (red) that is bonded to the silicon atom at theorigin (labelled O in the model window—you can rotate themodel to see it better). Query the coordinates of this oxygenatom by de pressing the right mouse button while holdingdown the <Shift> key.


Fractional Coordinates: 0.32757 0.32757 0.00000

The fractional coordinates of the currently selected oxygen atom arenow displayed in the associated entry box as 0.33 0.33 0.00

The new coordinates are displayed rounded to 0.31 0.31 0.0, butCerius2 uses the exact values when modifying the structure.

All the oxygen atoms in the cell change their positions since they arerelated by symmetry to the atom whose coordinates you modified.

This final step adjusts the positions of the oxygens to their experimen-tal values. You have now finished defining the experimental structureof stishovite.

4. Writing stishovite to disk

At this stage you could begin the CASTEP session, but it is useful towrite the stishovite structure to a file, to save all the changes you havemade to the TiO2 structure. This step also gives you an opportunity

Change the fractional coordinates by selecting the Move/Atoms Position… item from the menu bar to open the Posi-tion Atoms control panel.

Change the coordinate system from Cartesian (XYZ) to frac-tional (ABC) for both the reference and destination points.Click the DEFINE pushbutton for the reference point.

Enter the experimental fractional coordinates for stishovitein the destination point entry box as 0.306 0.306 0.0 .

Click the POSITION pushbutton to actually change thecoordinates.



to rename the structure, now that TIO2 is no longer appropriate.

The label in the model window changes to stishovite.

The file is saved in the current directory, and a message appears in thetext window:

MSI model file './stishovite.msi' successfully written.

5. Performing BFGS relaxation of the structure of stishovite

This part of the lesson relaxes the structure of stishovite using theBFGS relaxation scheme.

Highlight the TiO2_rutile model name in the model man-ager (by clicking it) and change it to stishovite.

Select the File/Save Model… item from the menu bar toopen the Save Model control panel. It shows a browser withthe list of files in your current directory. Enter stisho-vite.msi as the new file name and click the SAVE. pushbut-ton

Go to the C2•CASTEP module by clicking the BUILDERS 1name and selecting QUANTUM 2 from the list thatappears.


Change the File Prefix from castep to stishovite_geom. Setthe Task popup to Geometry Optimization.

Select the Geometry/Cell Constraints card menu item toopen the CASTEP Cell Constraints control panel.


The cell degrees of freedom are shown as a, b, and c being variable andalpha, beta, and gamma being fixed. The angles are fixed by symmetry.

Cell optimization requires a rather accurate calculation in terms of thenumber of k-points and the number of plane waves. For the purpose ofthis lesson, let’s fix the cell variables and optimize only internalatomic coordinates.

The b check box becomes unchecked automatically due to crystal sym-metry. By fixing cell parameters you change certain CASTEP set-tings, as illustrated below.

The Finite Basis Set Correction check box is currently unchecked inthe CASTEP Basis Set control panel and so is the Calculate StressTensor check box in the CASTEP Output control panel.

The Finite Basis Set Correction and the Calculate Stress Tensorcheck boxes change their states accordingly. The basis set correction is

Uncheck the a and c check boxes in the CASTEP Cell Con-straints panel.

Open the CASTEP Basis Set control panel by clicking theMore… pushbutton next to the Basis Set popup on the RunCASTEP control panel.

Also open the CASTEP Output control panel by clicking theOutput Options… pustbutton on the Run CASTEP controlpanel.

Change one of the Cell Degrees of Freedom check boxes inthe CASTEP Cell Constraints control panel from uncheckedto checked and back to unchecked and observe the status ofthe check boxes in the CASTEP output and CASTEP BasisSet control panels.



mainly needed when cell optimization is performed; the same is truefor the stress tensor. Unchecking them for calculations with fixed cellparameters saves computing time.

You have now specified that the next run will be a BFGS relaxationcalculation with fixed cell parameters and the default SCF settings.

6. Setting up the CASTEP job in interactive mode

The following message appears in the text window:

Generated 8 points using Monkhorst-Pack generator

Symmetrized set contains 2 k-points

Fixed coordinates by symmetry for 2 atoms on special positions…CASTEP job stishovite_geom has been started.

It takes a few seconds to generate the set of k-points (in this exampleit contains 8 points) and find symmetry-unrelated k-points (here thereare 2 of them). CASTEP also checks symmetry constraints for atomiccoordinates—in this run only oxygen atoms are allowed to move, andsilicon atoms are fixed in special positions. Cerius2 is unavailableuntil the interactive CASTEP job completes. This job takes about150–800 seconds of CPU time on typical IBM or Silicon Graphicsmachines.

7. Computing the density of states of stishovite

After the job finishes, you can calculate the density of states (DOS) ofstishovite using the density file, which was created at the end of the




self-consistent run.

The filename at the top of the CASTEP File Analysis panel changes tostishovite_geom. A new model is added to the model manager list —this is the final relaxed structure of stishovite.

You will see that it took approximately 4–5 iterations to achieve con-vergence.

This launches another interactive CASTEP job. This calculation isnon-self-consistent, but it uses 24 k-points instead of just 2 k-points.As a result, it may take 2–3 times longer to complete than the geome-try optimization run.

Select the Analyze/Files menu item on the CASTEP card toopen the CASTEP File Analysis control panel. It contains abrowser that shows a list of files in the current directory.Double-click stishovite_geom to load the results of yourmost recent run for analysis.

To open the output file from the geometry optimization run,click the Examine CASTEP Output action button on theCASTEP File Analysis control panel.

Select the Analyze/Density of States card menu item toopen the CASTEP Density of States control panel. Changethe Number of Bands from 16 (valence band only) to 24 sothat the conduction band is also included.

Click the Calculate Band Energies action button.



8. Plotting the density-of-states results

A plot of the density of states of SiO2 appears. Energy is plotted hori-zontally in eV. The lowest peak on the plot is associated with theweakly hybridized oxygen 2s band. About 2/3 of the way up the plotthere is a distinct dip in the density of states, which corresponds to theposition of the band gap. The position of the top of the valence band ismarked by the white vertical tick. Due to the broadening used in thecalculation, the density of states does not fall to zero in the band gapof this graph. You can change the smearing width to even higher val-ues, for example, 0.5 eV, to obtain a smoother density of states curve.

9. Analyzing ion motion during geometry optimization

You can analyze the ionic trajectories during the course of a relaxationrun by creating a trajectory file and using the Cerius2 analysis facili-ties.

The following messages appear in the text window:

Start writing trajectoryFinished writing trajectory

This trajectory file can be now loaded and analyzed by wsing theANALYSIS card in the OFF METHODS card deck.Select the Inputmenu item from the ANALYSIS card to access the Analysis Inputcontrol panel, which you use to load the trajectory file.This card is

When the DOS job is complete, click the Files… pushbuttonon the CASTEP Density of States control panel to open theCASTEP DOS File control panel. Select the stishovite_geom_DOS.bands file from the browser.

Now click the Display action button in the CASTEP Densityof States control panel.

Go to the CASTEP File Analysis panel and click the CreateTrajectory File action button.


fully documented in the book, Cerius2 Simulation Tools, which is pub-lished separately by MSI.

If you only want to animate the trajectory, you can select the View/Animation… menu item from the main control panel’s menu bar toaccess the Animation control panel. Use controls in this panel to load,filter, and replay the animation.

10.Analyzing the forces in stishovite unit cells

This last section shows you how to analyze the forces calculated in aCASTEP run.

There are no visible changes in the model. The forces at the final con-figuration are so small that the default linear scaling does not showany vectors at all.

Arrows appear on the oxygen atoms in the unit cell. In stishovitethere are no forces on the silicon atoms, by symmetry. Symmetryalso dictates that the forces on the oxygens should be along the

Select the Geometry/Vector Properties… item from themenu bar in the main Visualizer control panel to open theVector Properties control panel. Click the SHOW pushbut-ton.

Click the Preferences… pushbutton in the Vector Propertiescontrol panel to open the Vector Preferences control panel.Change the Scale entry box to 2.0 (that is, introduce a 20-fold magnification compared to the default).



{110} sets of directions in the tetragonal unit cell.

Numerical labels appear next to all atoms. Stishovite is a particularlysimple structure to optimize since there is only one undeterminedcoordinate in the structure (essentially the distance between the oxy-gen and the silicon). A few cycles of BFGS minimization are thereforesufficient to bring the forces on the ions close to zero. In more complexstructures with many more internal degrees of freedom, more BFGSiterations will be necessary to achieve this level of convergence.

11. Finishing up

sc

Make sure no atoms are selected and change the Label Typein the Vector Preferences control panel to MAGNITUDE tosee the absolute values of the forces in kcal mol-1 Å-1.




13 Optical Properties of Diamond

Before you begin

You need these modules To complete this tutorial lesson, you need a licensed copy ofCerius2 that includes the CASTEP module.

Note

Running the tutorial lesson



This lesson involves running several CASTEP jobs which may,depending on your hardware, require several minutes of CPUtime to complete. The jobs must each be complete before thelesson is continued, because subsequent analytical steps requirethe correct CASTEP output files. This lesson is thereforedesigned so that the CASTEP jobs are run in interactive mode.Cerius2 waits until the jobs are complete and is thereforeunavailable while the job is running.

Enter mkdir cst_tut3 at the UNIX prompt to make a direc-tory in which to run this tutorial. At the next prompt, entercd cst_tut3 to move to this directory. Now, to start upCerius2, enter cerius2 at the UNIX prompt.


13. Optical Properties of Diamond

2. Retrieving a diamond model from the database

The browser appears that contains a list of files in your current direc-tory.

The conventional cell of diamond appears in the model window.

3. Calculating the electronic ground state of diamond

The next step is to calculate ground state charge density of diamond.

It may take a few seconds to appear, while Cerius2 reads in the


Double-click Cerius2-Models in the list box to access thelibrary of structures supplied with Cerius2. Double-clickceramics to access the library of crystal structures ofceramic materials. Finally, scroll down the list and double-click diamond.msi to load the diamond model into the cur-rent session of Cerius2.

Go to the C2•CASTEP module by clicking the menu deckspulldown in the main control panel (probably currentlylabeled BUILDERS 1) and selecting QUANTUM 2 fromthe list that appears.

This CASTEP card should already be in front of theQUANTUM 2 deck of cards. If not, click its name to bring itto the front.



CASTEP databases.

The cubic cell on the screen is modified so that it now has only 2 atomsper unit cell rather than 8 as was the case for the conventional cubiccell.

We do this because gradient corrections are not important for dia-mond and they create uncontrolled errors in calculated optical prop-erties.

You have now specified that the next run will be a single-point energycalculation with the LDA method and a medium-sized basis set.

Set up the CASTEP job to run in interactive mode (to freeze Cerius2

until the job completes):

The following messages appear in the textport:

In the Run CASTEP control panel, change the default FilePrefix to diamond. Transform the cell to primitive by click-ing the Transform Cell to Primitive action button.

Change the Method popup in the Run CASTEP controlpanel to LDA.

Change the Basis Set popup to MEDIUM.





Generated 63 points using Monkhorst-Pack generator

Symmetrized set contains 10 k-points…CASTEP job diamond has been started.

It takes a few seconds to generate the set of k-points (in this exampleit contains 63 points) and find symmetry-unrelated k-points (herethere are 10 of them).

Cerius2 is unavailable until the interactive CASTEP job completes.

This job takes about 20–100 seconds of cpu time.

4. Computing optical properties of diamond

You can now calculate the optical properties of diamond using thedensity file that was created at the end of the self-consistent run.

The filename at the top of the CASTEP File Analysis panel changes todiamond.

You can see that it took approximately 4–5 SCF iterations to achieve

Select the Analyze/Files menu item on the CASTEP card toopen the CASTEP File Analysis control panel. It contains abrowser that shows a list of files in the current directory.Double-click diamond.cst to load the results of your mostrecent run for analysis.

Open the output file of the self-consistent run by clickingthe Examine CASTEP Output action button on theCASTEP File Analysis panel.


convergence at fixed atomic coordinates.

This has an effect of reducing the mesh parameters for generatingk-points to 6x6x6.

This launches another interactive CASTEP job, so Cerius2 freezesuntil the job is complete. This calculation is non-self-consistent, but ituses 28 k-points instead of 10 k-points. It also uses 12 bands insteadof 4. As a result, this job may take 2–3 times longer to complete thanthe first self-consistent run.

5. Plotting optical properties

A textport message similar to this one appears:

Select the Analyze/Optical Spectra card menu item to openthe CASTEP Optical Spectra control panel. For the purposesof this tutorial, reduce the number of k-points to be used inthe calculation by clicking the Setup K-points… pushbut-ton to open the CASTEP K-Points for Optics control panel.Change the Requested K-point Spacing from 0.04 to 0.08.

Click the Calculate Matrix Elements action button on theCASTEP Optical Spectra control panel.

When the job is complete, click the Calculate DielectricFunction action button on the CASTEP Optical Spectra con-trol panel.



=================================================Start calculation of complex dielectric functionfor ‘diamond’ job.Simulation for unpolarized light, with theincident direction of ( 0.0000, 0.0000, 1.0000).Energy range is from 0.0100 to 57.5375 eV.Reading symmetry data.Finished reading matrix elements,start calculating Epsilon(w).Integrate matrix elements over the Brillouin zoneusing Gaussian smearing with the width of 0.5000 eVto obtain imaginary part of Epsilon(w).Use Kramers-Kronig relation to obtain real partof Epsilon(w) from its imaginary part.Write complex dielectric function Epsilon(w)to file: diamond.Epsil_1Finished calculating optical propertiesfor ‘diamond’ job.=================================================

A plot of the optical adsorption and reflectivity of diamond appears.Energy is plotted horizontally in eV.

You can now visualize other optical properties, for example, real andcomplex parts of the refractive index (n and k), real and imaginaryparts of the dielectric function, and loss function

The specified quantities appear in a graph window, plotted as a func-

Click the More… pushbutton near the bottom of theCASTEP Optical Spectra control panel to open the CASTEPOptical Spectra Display Preferences control panel. Check oruncheck the desired check boxes to plot the desired otheroptical properties. Click the Plot Optical Properties actionbutton in the CASTEP Optical Spectra control panel to seethe effect of checking the properties listed in the precedingparagraph (or other properties).


tion of the energy in eV.

This message appears:

Calculated static dielectric constant is: 5.9979

The properties calculated are usually in error because of the DFTbandgap problem. Since the gap is too small in DFT, all spectra areshifted in energy and cannot be directly compared with experimentalvalues. You can use the scissors operator tool to compensate for thiserror:

A new set of optical properties is displayed.

This message appears:

Calculated static dielectric constant is: 5.6946

The value of the scissors operator has to be chosen as a differencebetween the calculated energy gap and the experimental one. This isthe same as trying to position the calculated edge of the adsorptionspectrum so as to coincide with the experimental one. When experi-mental information on band gap or adsorption edge is scarce, experi-ence shows that it is a good idea to try to match the experimental value

Click the Show Static Dielectric Constant action button inthe CASTEP Optical Spectra control panel to display thevalue of Re Epsilon(0) in the text window.

Enter 0.7 in the Scissors Operator entry box in the CASTEPOptical Spectra control panel and click the CalculateDielectric Function action button again.

Again click the Show Static Dielectric Constant action but-ton to display this value in the text window.



of the static dielectric constant.

A new set of spectra is displayed with a different energy scale.

For an optically anisotropic material you can specify the light polar-ization direction or the incidence direction for an unpolarized calcula-tion (see the CASTEP Optical Spectra Preferences control panel andits on-screen help for details). However, light polarization is irrelevantfor a cubic cell of diamond.

6. Finishing up

sc

Change the energy units popup (near the bottom of theCASTEP Optical Spectra control panel) from eV to nm andagain click the Plot Optical Properties action button.




14 Calculating the Density of Statesof Ferromagnetic Gd

1. Start Cerius2


2. Construct a unit cell of gadolinium.

The conventional unit cell of Gd appears in the model window.

3. Calculating the density of states for ferromagneticgadolinium.


Select File/Load Model from the Visualizer menu bar. Thenselect Cerius2-Models in the file browser of the Load Modelcontrol panel. Load the metals/pure-metals files, makingsure the File Format is set to MSI, and select Gd in the filebrowser.

Open the Quantum 2/ESOCS card deck and select the Runmenu item. On the Run ESOCS control panel, change thedefault File Prefix name from esocs to gd_fm.


14. Calculating the Density of States of Ferromagnetic Gd

You now will find a “1” close to each Gd atom in the model area, whichshows that you set the spin of these atoms to UP. The spin on bothatoms changes because the two atoms in the Gd unit cell are related bysymmetry. If you choose DOWN spin, a “-1” would be displayed. A“0” indicates that no preferred spin direction is set. Since all theatoms have the same spin direction, a ferromagnetic calculation willbe performed. If you would reduce the symmetry of the model to P1you could choose one Gd atom to have spin up and the other spindown, which is an antiferromagnetic spin alignment.

You have specified that a self-consistent ESOCS run will be performedand the Density of States (DOS) will be calculated.

First the k-points for the self-consistent run and the DOS run are setup. You will find in the Cerius2 textport that ESOCS will use 36 k-points for the self-consistent cycling and for the DOS calculation.Then the ESOCS background job starts. It will take several minutes

To specify a spin-polarized calculation, select the Magneti-zation button. In the Magnetization control panel changethe Spin popup menu from NO to UP. Now pick a Gd atomin the model window and then click the Set button in theMagnetization control panel.

Now click the Density of States checkbox in the Run con-trol panel.

Now select the Run button in the Run ESOCS control panel.


for the ESOCS job to complete.

You will find a job with the file prefix gd_fm, which mighthave the status started, running, or complete.

The output of the self-consistent run is written to gd_fm.outscf. Thisfile may now be inspected from a UNIX window. You might use aneditor or use the UNIX command more. This file contains additionalinformation like the magnetic moment or the charge distribution fordifferent angular momenta. Examples of the output from this job areincluded at the end of this lesson.

4. Plot the density of states results.

The Summary of Calculation browser will be updated. It contains ashort summary of the performed calculation. This File Analysis con-trol panel also allows you to recover the model used to set up the cal-culation. The prefix of the.sum file is further used as a seed name forthe plotting the bandstructure, the Density of States, the optical spec-

To monitor the progress of the calculation, bring up the Jobcontrol panel: select ESOCS/Job Control. Click theUPDATE button to update the information.

Do not continue with this lesson until the status of your jobis complete. You may need to click the UPDATE button sev-eral times until the job is finished.

Bring up the ESOCS Files Analysis control panel from theAnalyze-->Files menu item on the ESOCS card. Select gd_fm.sum in the File Analysis browser.



tra and the magnetic moments.

The total DOS of Gd appears in the Cerius2 Graph window. Energyis plotted on the y-axis in eV, the DOS on the x-axis. Negative valuesfor the DOS indicate the DOS for the spin-down electrons, positivevalues the DOS for the spin-up electrons. The Fermi energy markedwith a white line is located at 0 eV. The plot features two major peaksdue to the 4f electrons of Gd.

The projected DOS will appear in the graph window. Every partialDOS will have a different color. You will find out that the f-states ofGd are the dominant contribution to the DOS.

A histogram plot will appears in the graph window. The magneticmoment is plotted on the y-axis, the x-axis is used to show the differ-ent atoms in the model.

On the ESOCS card, select the Analyze-->Density of Statesmenu item. Click the Plot Total Density of States Run but-ton on the ESOCS Density of States panel.

If you are interested in the site and angular momentum pro-jected DOS, uncheck the Sum checkbox and add check-marks for s, p, d and f. Then click the Plot Partial Densityof States button.

To plot the calculated magnetic moments, select MagneticMoments from the Analyze--> pullright. Click the PlotMagnetic Moments button in the Magnetic Moments con-trol panel.


5. Finishing up

Analyzing the result of a self-consistent calculation

Below are sections of the output file gd_fm.outscf that was producedby the ESOCS job for this lesson. Note that all energies in the outputare given in Ryberg units (1 Ryberg = 13.605698 eV).

START OF ITERATION 1

INPUT DATA

LATTICE CONSTANTS a= 6.86254 b/a= 1.00000 c/a= 1.59080 BRAVAIS MATRIX 1.00000 .00000 .00000 -.50000 .86603 .00000 .00000 .00000 1.59081 EXTERNAL MAGNTIC FIELD .00000

LOAD ATOMIC DATA

ATOM 1 WITH Z=64. AND RMAX= 3.75977 at: .33333 .66667 .25000 ( relative coordinates) at: .00000 .00000 .00000( shifted cartesian coordinates)

ATOM 2 WITH Z=64. AND RMAX= 3.75977 at: .66667 .33333 .75000 ( relative coordinates) at: .00000 .57735 .79540( shifted cartesian coordinates)

This part of the output reports the input data that was used for thisESOCS run. Note that the lattice constant a and the sphere radius(RMAX) are given in Bohr (1 Bohr = 0.5391772 Å). The shifted car-





tesian coordinates are given in units of the lattice constant a. a, b/aand c/a are the values for the conventional unit cell, whereas the BRA-VAIS MATRIX and the coordinates of the atoms represent the compu-tational unit cell.

The next few lines show the cpu time used in different subroutines toperform a calculation on a single k-point.

CPU TIME PER K-POINTsubroutine SDL1 : CPU time .01000 secsubroutine SDL2 : CPU time .06000 secsubroutine SDLSU: CPU time .00000 secsubroutine CGSIM: CPU time .00000 secsubroutine SECMT: CPU time .01000 secsubroutine DIAG : CPU time .04000 secsubroutine WRHO : CPU time .01000 sec

The routines shown in the output file are responsible for the followingfunctions:

- SDL1 calculates the reciprocal-space contribution to the structurefactors

- SDL2 evaluates the real-space contribution to the structure con-stants

- SDLSUM & CGSIGM sum up the structure constants

- SECMT sets up the secular matrix

- DIAG diagonalizes the secular matrix

- WRHO calculates the contribution to the density of states

KSCAN; SWGT = 1.00000000000000D+00 NKTOT= 36

NKTOT tells you how many k-points are used in this calculation.

The following lines give information on the deviation from neutralityand the magnetic moment for each atom. The numbering of the atomsis according to the list given in the input section at the top of the out-put file. In addition, line 3 shows you the total density of states at theFermi energy.


ATOM 1 DEVIATES FROM NEUTRALITY BY-1.776357E-15ATOM 2 DEVIATES FROM NEUTRALITY BY-1.776357E-15DENSITY OF STATES AT FERMI ENERGY= 5.993026E+01

MAGN. MOMENT OF ATOM 1 EQUALS 7.518713E+00

MAGN. MOMENT OF ATOM 2 EQUALS 7.518713E+00

The following section shows in detail the angular momentum pro-jected charge and density of states at the Fermi energy for each atom.Q1 and Q2 are the number of electrons in the spin-up and spin-downchannel, respectively. Q summarizes the number of electrons for bothspin directions. NEF1, NEF2 and NEF are the density of states at theFermi energy for the spin-up states, the spin-down states and theirsum, respectively. IBAS represents the different atoms in the unit cell.The angular momentum is given in the first column. The last line inthis section shows the calculated Fermi energy and the total numberof valence electrons.

PARTIAL CHARGE AND PARTIAL DOS AT THE FERMI ENERGY

L IBAS Q1 NEF1 Q2 NEF2 Q NEF 0 1 .39197 .21670 .37131 .46388 .76328 .68059 1 1 .32540 2.42531 .17644 1.70786 .50184 4.13317 2 1 1.03297 8.05036 .55371 6.97157 1.58669 15.02193 3 1 7.00369 .29352 .13798 9.76966 7.14167 10.06318 4 1 .00533 .04508 .00119 .02118 .00652 .06625 0 2 .39197 .21670 .37131 .46388 .76328 .68059 1 2 .32540 2.42531 .17644 1.70786 .50184 4.13317 2 2 1.03297 8.05036 .55371 6.97157 1.58669 15.02193 3 2 7.00369 .29352 .13798 9.76966 7.14167 10.06318 4 2 .00533 .04508 .00119 .02118 .00652 .06625 FOR EFERMI= .45237 QVALENCE= 20.000000

SPINPOLARIZED CALCULATION. BOHR MAGNETON*EXT.FIELD= 0.00000000E+00

UPDATING POTENTIALS

The next section summarizes the energy contribution of each atom inthe asymmetric unit to the total energy of the unit cell.

ATOM 2 WITH Z=64.



The following lines contain information about the charge and spindensities at the nucleus. These quantities are given in units of Bohr-3.Contribution from the core and valence electrons to the charge andspin density are listed separately.

RADIUS OF NUCLEUS : 1.17973D-04

CHARGE AND SPIN DENSITIES AT NUCLEUS:

STATE SPIN 1 SPIN 2 CHARGE DENSITY SPIN DENSITY

1s 2.6025105248D+05 2.6025106361D+05 5.2050211609D+05 -1.1122532916D-02

2s 3.4168520358D+04 3.4169857714D+04 6.8338378072D+04 -1.3373555124D+00

3s 7.3196933889D+03 7.3339105273D+03 1.4653603916D+04 -1.4217138435D+01

4s 1.7578672007D+03 1.7561851592D+03 3.5140523600D+03 1.6820414736D+00

5s 3.0414050102D+02 2.9088406312D+02 5.9502456414D+02 1.3256437896D+01

SUM CORE 3.0380127393D+05 3.0380190107D+05 6.0760317500D+05 -6.2713711109D-01

6s 1.8536730354D+01 1.7913187522D+01 3.6449917875D+01 6.2354283170D-01

SUM ALL 3.0381981066D+05 3.0381981426D+05 6.0763962492D+05 -3.5942793917D-03

The total energy contribution of each atom is broken into four constit-uent parts: energies for the spin up and spin down states, and energiesfor the core and valence states.

ENERGY ANALYSIS FOR SPIN UP

VALENCE ELECTRONS: PRESSURE AND CHARGE DENSITY AT THE SPHERE RADIUS

L DPL RPL 0 .137069 .022219 1 .200614 .028664 2 -.424494 .041086 3 -.051728 .005513 4 -.007197 .000993

TOTAL PRESSURE AND CHARGE DENSITY AT THE SPHERE RADIUS 3PV= -.145736 RHO(RMAX)= .098475

The next few lines show the eigenvalues (ECORE) of the core states,which are helpful to understand core level shifts. NQ is the principal


quantum number of the state and LCORE is the angular momentum.

CORE ELECTRON ENERGIES

NQ LCORE ECORE 1 0 -3677.3980 2 0 -606.8568 3 0 -134.2578 4 0 -26.8653 5 0 -3.4289 2 1 -540.1579 3 1 -113.6030 4 1 -20.0546 5 1 -1.7718 3 2 -86.2785 4 2 -10.6364

In the next section the eigenvalues (EL1 and EL2) of the valence stateare given. Note that each angular momentum of the valence states isrepresented by two wavefunctions. Finally the total energy contribu-tion for the spin up channel is given.

VALENCE ELCETRON ENERGIES

L EL1 EL2 0 -.4024 -.2390 1 -.3456 -.1615 2 -.3049 -.1595 3 -.4489 -.2044 4 -.4364 -.1567

TOTAL ENERGY CONTRIBUTION = -11261.702458

Bandlimits describe the bottom and the top of unhybridized valencebands. The first column shows the angular momentum of the band,whereas columns two and three give the bottom and the top of theband, respectively.



L BANDLIMITS 0 .06267 1.39368 1 .49959 2.20006 2 .32285 .86299 3 .11274 .12348 4 2.08361 4.05357

ENERGY ANALYSIS FOR SPIN DOWN

VALENCE ELECTRONS: PRESSURE AND CHARGE DENSITY AT THE SPHERE RADIUS

L DPL RPL 0 .199449 .021533 1 .147648 .016096 2 -.223141 .026277 3 -.043345 .002894 4 -.000977 .000219

TOTAL PRESSURE AND CHARGE DENSITY AT THE SPHERE RADIUS 3PV= .079633 RHO(RMAX)= .067020

CORE ELECTRON ENERGIES

NQ LCORE ECORE 1 0 -3677.3978 2 0 -606.8484 3 0 -134.0637 4 0 -26.4353 5 0 -3.2050 2 1 -540.1518 3 1 -113.4104 4 1 -19.6290 5 1 -1.6013 3 2 -86.1277 4 2 -10.2190

VALENCE ELCETRON ENERGIES

L EL1 EL2 0 -.3492 -.1966 1 -.3012 -.1611 2 -.2350 -.1470 3 -.2024 -.1271 4 -.2563 -.1458

TOTAL ENERGY CONTRIBUTION = -11265.885929


L BANDLIMITS 0 .12449 1.48828 1 .57644 2.30408 2 .38897 .97130 3 .47150 .49437 4 2.12726 4.10924

ZEEMAN ENERGY OF ATOM 2 EQUALS .000000

TOTAL ENERGY AND PRESSURE

MADELUNG ENERGY = .000000 TOTAL ZEEMAN ENERGY= .000000 VIRIAL ENERGY = -45055.175565 TOTAL 3PV = -.132207 VARIATIONAL ENERGY = -45055.176775

The VARIATIONAL ENERGY is the total energy of the system. Thisquantity can be used for analyzing the stability of a system. 3PV is thecalculated pressure on your unit cell times 3 multiplied by the volumeof the cell. This combination of quantities is given in Ryberg units, likethe energies.

CALCULATION CONVERGED AFTER 1 ITERATIONSQDIFF = .000001 LT .000001 and EDIFF= .00E+00 LT .10E-05

The calculation is only converged if both these criteria are fulfilled.




15 Calculating the DielectricConstant of GaP

1. Start Cerius2


2. Construct GaP.

The conventional unit cell of GaP appears now in the model window.You will find in the Cerius2 textport window that the crystal symme-try is F-43m, which has 96 symmetry operations in the conventionalunit cell.


Select File/Load Model… on the main panel menu bar.Then select Cerius2-Models in the file browser of the LoadModel panel. Browse the semiconductor files and load GaPfrom the file browser.


15. Calculating the Dielectric Constant of GaP

3. Find empty sphere positions.

ESOCS takes the current model in the model window for the calcula-tion. Since the model of GaP is a conventional unit cell, a warningmessage will come up informing you that the unit cell can be trans-formed to a primitive cell, which would speed up the calculation dra-matically.

Now ESOCS starts to calculate its default k-points, which can beviewed in the Cerius2 textport. Another warning message pops up,informing you that the overlap is too large. In the textport you willfind that the actual overlap is 23.63%, much larger than the maxi-mum recommended value of 15%.

ESOCS now tries to find optimized positions for 4 empty spheres inthe conventional unit cell of GaP. Ten attempts, as specified in theNumber_of_Attempts parameter box, will be made to minimize theoverlap in the cell.

Open the Quantum 2/ESOCS card deck and select the Runmenu item. On the control panel, change the default FilePrefix name from ESOCS to gap_1. Press the Run button.

Select Continue, using existing model since we do notwant to change the model at this stage.

To decrease the overlap of the atomic spheres, additionalempty spheres have to be inserted. Select Cancel in thewarning window.

Open the ESOCS Empty Spheres panel by selecting Geom-etry-> Empty Spheres on the ESOCS card. Enter 4 in theNumber of Spheres parameter box and click the CalculateEmpty Sphere Locations button.


After some seconds, the browser in the ESOCS Empty Spheres controlpanel is filled with the result of the calculation of optimized emptysphere positions. For each attempt, the overlap and the symmetry areshown in the ESOCS Empty Spheres control panel. Since the overlapis still larger than 15%, the number of empty spheres must beincreased.

After some seconds the browser is again updated. This time the over-lap of spheres is below 15% for all 10 attempts. You may now checkthe symmetries of the new unit cells. You will find that the first 5 unitcells have the symmetry label P-4M2, which has only 8 symmetryoperations in the conventional cell. The last 5 unit cells have the sym-metry label R3M with 6 symmetry operations. In almost all cases youwill find that the unit cell with the smallest overlap has the highestnumber of symmetry operations. By inserting more empty spheres,the number of symmetry operations may be increased.

With 8 additional empty spheres in the conventional unit cell of GaP,the overlap could be reduced to 8.63%. You will find that the symme-try label for all calculated unit cells is F-43M. This is the same sym-metry as the GaP unit cell without empty spheres.

Change the value of the Number of Spheres parameter to 6and select the Calculate button in the ESOCS EmptySpheres control panel.

Set the Number of Spheres parameter to 8 and select theCalculate button.

Now load a new unit cell by pressing the Load the SelectedModel button. Since all calculated unit cells have the sameoverlap and the same symmetry, you can choose any ofthem.



The model in the model window is now updated. The white crosses inthe model are showing the empty spheres positions.

Since you found a unit cell that has an overlap less than 15% and alsohas the highest possible symmetry, you can now proceed to set up anESOCS calculation.

4. Setting up an ESOCS bandstructure calculation for GaP.

In the model window the cell size and shape have now been changed.Since the conventional unit cell is an fcc lattice (the first letter in thesymmetry label is F) the primitive unit cell has only 2 empty spheresinstead of 8 in the conventional unit cell.

This specifies that after a self-consistent run, a bandstructure alongsome high symmetry lines in the Brillouin zone will be calculated.

Close the Empty Sphere control panel.

On the ESOCS card, select the Run menu item to open theRun ESOCS control panel and change the File Prefix param-eter to gap_2. Now transform the unit cell to a primitiveunit cell by toggling on the Transform Cell to Primitivebutton.

Now toggle the Band Structure checkbox to on.

You need to change the number of k-points for the calcula-tion: press the K-Points… button on the Run ESOCS controlpanel. On the K-Points… control panel, hange the Cutofffor SCF k-points (A) parameter to 15.0 and the Number ofDivisions for the bandstructure run to 20.


This reduces the number of k-points for the SCF calculation andincreases the number of k-points for the bandstructure plot.

You now have specified the following parameters for a self consistentrun: ESOCS will stop the self consistency cycling if the number ofiterations exceed 99 or the total energy difference between successiveiterations is smaller than 0.0001 Ry. A Monkhorst-Pack k-point meshis used that has a minimum real-space cutoff of 15 Å. The mixing coef-ficient is 0.5. This determines the feedback of the output vector used indetermination of an input vector for the next iteration.To build up anew input vector for the next iteration, 5 previous iterations will betaken into account.

This parameter set is typical for calculations on semiconductors andmay decrease the required cpu time substantially compared to therequirements with the default parameter setting.

The Cerius2 textport reports that ESOCS will use 10 k-points for theself-consistent cycling and 41 k-points for the bandstructure calcula-tion. Then the ESOCS background job is started. This job takes less

Close the K-Points… control panel.

Press the SCF Options… button. On the ESOCS SCFOptions control panel, The Mixing memory parametershould be set to 5.

Now select the Run button in the Run ESOCS control panel.First the k-points for the self-consistent run and the band-structure run are set up.



than 60 sec on an IBM/6000 370 workstation.

A job with the file prefix gap_2 is reported with a status of started,running, or complete.

5. Plot the bandstructure of GaP.

The Summary of Calculation browser is updated. It contains ashort summary of the performed calculation. This ESOCS File Anal-ysis control panel also allows you to recover the model used to setupthe calculation. The prefix of the .sum file is further used as seed namefor plotting the bandstructure, the density of states, the optical spec-tra, and the magnetic moments.

You can monitor the progress of the calculation by bringingup the Job Control panel: Select Job Control on the ESOCScard. If you click on the UPDATE button the information inthe ESOCS Job Status browser is updated.


Bring up the Files control panel by selecting Files on theAnalyze--> pullright. Select gap_2.sum in the File Analysisbrowser and press the SELECT button.

Open the ESOCS Band Structure control panel by selectingAnalyze->ESOCS Band Structure on the ESOCS card.Press the Plot ESOCS Band Structure button.


The bandstructure of GaP appears in the Cerius2 Graph window. Theblue crosses are the calculated eigenvalues and the red line marks theFermi energy. The bandstructure was calculated along the followinglines in the Brillouin: W - L - G(amma) - X - W - K.

To study the gap of GaP the bandstructure plot should be rescaled witha smaller energy window around the Fermi energy, which is at 0 eV.

You will now see the bandstructure of GaP between -1 eV and 3 eV.GaP has a theoretical indirect bandgap of about 1.5 eV between the Land the G(amma) point.

6. Calculate the dielectric constant for GaP.

Since we already created self consistent potentials for GaP in step 4,we can re-use these by using the Restart option.

When you checkmark this option, a Files… button appears in the con-

Bring up the Tables & Graphs/ Graphs card and select Scal-ing from the Graph--> pullright. Change the Min y value to-1.0, the Max y value to 3.0, and hit <Enter>.

Bring up again the Quantum 2/ ESOCS card and select theRun menu item. Change the File Prefix name to gap_3.Check off the Band Structure check box and checkmark theOptical spectra checkbox.

Press the Options… button in the Run ESOCS control panelto open the ESOCS Run Options control panel. Checkmarkthe Start Calculation using Potentials from Previous Runcheckbox.



trol panel.

The Summary of Calculation browser shows you a short summaryof the calculation done in step 4. The prefix of the .sum file will be usedby ESOCS to read in the potential files from the previous run.

The number of k-points used for the calculation is printed again theCerius2 textport. The calculation will take less than 40 sec on an IBM/6000 370 workstation.

Then bring up the ESOCS Re-Use Potentials Files controlpanel by clicking on the Files… button in the ESOCS RunOptions panel. Select gap_2.sum in the file browser. Pressthe SELECT button.

Since we do not want to repeat the self-consistent calcula-tion, check the Run a Non Self-Consistent Calculation boxin the ESOCS Run Options.

You can now submit the background job by pressing theRun button in the Run ESOCS control panel.

Monitor the progress of the calculation with the Job Controlpanel by clicking on the UPDATE button. Proceed with thistutorial if the status of the job with the file prefix gap_3 iscomplete.

Bring up the ESOCS File Analysis control panel by selectingthe Analyze-->Files menu item on the ESOCS card. Selectgap_3.sum in the File Analysis browser.


The Summary of Calculation browser is updated.

The absorption and the reflectivity spectra are now shown in theCerius2 Graph window.

From the absorption data you may verify that the bandgap is about 1.5eV.

The ESOCS Optical Spectra Properties control panel appears.

The graph window shows the real and the imaginary part of the dielec-tric constant.

Now open the ESOCS Optical Spectra panel by selecting theAnalyze--> Optical Spectra menu item on the ESOCS card.Change the Lifetime parameter to 0.25 and press the Runbutton for Plot Optical spectra.

You can use the Graphs/ Graph--> Scaling on the Tables &Graphs card to rescale the spectra.

To plot the dielectric constants, press the More… button inthe ESOCS Optical Spectra control panel.

Now uncheck the Reflectivity and the Absorption check-boxes and select the Real Dielectric Constant and Imagi-nary Dielectric Constant checkboxes. Then press the Runbutton for Plot Optical Properties in the ESOCS OpticalSpectra panel.



7. Finishing up

sc




16 Structure of Quartz

In this lesson you will learn how to use FastStructure to performgeometry optimization on an infinitely large crystal. As usual, thecrystal is represented by a unit cell with periodic boundary condi-tions. As far as the usage of FastStructure is concerned, the proce-dure is closely analogous to working on a molecule, except that thesystem chosen is an assembly with periodic boundary conditions.In this lesson, we take quartz as an example. We will not optimizethe charge density for the purpose of saving computer time. At theend of this lesson, we will also tell you how to set up and run a jobthat optimizes the charge density.

1. Set up the tutorial and start the Cerius2 program.

Make a new directory for this lesson by typing the followingcommands at the UNIX prompt:

> mkdir fs_lesson5

> cd fs_lesson5

Start Cerius2 by typing the following at the UNIX prompt:

> cerius2


16. Structure of Quartz

2. Construct a unit cell of quartz with P1 symmetry using theCrystal Builder.

The command executes automatically. A diamond cell appears in thecenter of the model window.

The quartz model was transformed into P1 symmetry (as indicated inthe text window). It is essential to make the symmetry P1 because cur-rently FastStructure can only take periodic systems with P1 symme-try.

3. Set up the FastStructure calculation.

After the Cerius2 Visualizer appears, select File/LoadModel from the menu bar.

Double-click Cerius2-Models and then metal-oxides in theLoad Model panel. Scroll down to find SiO2_quartz.msiand double-click to select it.

Select the Crystal Builder card in the Builders 1 card deck.Select the Crystal Building menu item and press the Runbutton for Crystalline Superlattice in the Crystal Buildingcontrol panel.

Open the QUANTUM2/FASTSTRUCTURE card andselect the Run menu item.


The Run FastStructure control panel appears on the screen.

A More… button appears to the right of the Task pulldown.

This tells FastStructure to optimize the geometry of the system byminimizing the total energy. Forces (gradients) on the atoms will becalculated to aid the minimization.

This gives you more output data in the quartz.outfs file and makesatomic units the input parameter units.

You have chosen to use the frozen core approximation, which is a verygood approximation for covalent bond systems. The cutoff radius forthe basis is set to be 6.0 Bohr Radii. In a system with periodic bound-ary conditions, it is much more efficient to use a smaller cutoff radiusthan in a molecule or cluster and this does not compromise the accu-racy.

Change the default File Prefix name from FastStructure toquartz. Select Geometry Optimization from the Taskpopup.

Click the More button and make sure that the Gradient Tol-erance is set to 0.002 HARTREE/BOHR.

Close the Geometry Optimization panel. Click the Prefer-ences... button on the Run FastStructure panel and selectNORMAL Output Detail. Set the Unit of Length buttonpopup to BOHR. Close the FastStructure Preferences panel.

Now, move back to the Run FastStructure panel. Set theCore popup to Frozen. Set the Cutoff field to 6.0.



4. Run FastStructure.

The job takes about 4 minutes to finish on an SGI R10000-processormachine.

You will find a job with the file prefix quartz, which might have thestatus started, running, or complete.

5. Analyze the final structure.

After the job is finished, we can read the final structure into Cerius2

and analyze it.

The unit cell of the final optimized structure appears in the model win-

To submit the job, click the Run button.

To monitor the progress of the calculation, bring up the Jobcontrol panel: select FASTSTRUCTURE/Job Control. Clickthe UPDATE button to update the information.


Select File/Load Model. Set the directory to be fs_lesson5 byselecting the Run directory selector at the top right corner ofthe file browser. Set the File Format to CAR in the LoadModel panel and double-click quartz.car in the browser.


dow.

An information panel appears and at the bottom of the panel are thefractional coordinates. These look like:

fractional coordinates: 0.46800 0.00000 0.33333

These are the relative coordinates and can be compared directly withexperimental results. The Y and Z coordinates of this Si atom are fixedto be 0 and 1/3, respectively, by symmetry. Although in the FastStruc-ture job, this symmetry requirement is not enforced, it is still very wellobeyed, as you can see. The X coordinate cannot be determined bysymmetry, and is one of the parameters that should be compared withexperiment.

The bottom of the information panel should read:

fractional coordinates: 0.40733 0.25897 0.21364

All the three coordinates are not fixed by symmetry and will be com-pared with experiment.

6. Compare results with experiment.

The results from this calculation are compared with experiment in thefollowing table.

The agreement with experiment is found to be very good, in spite of

While holding down the <Shift> key, pick the lowest Siatom with the right mouse button. (This atom is sitting onthe OAC plane, colored brown if you are using the defaultcolor scheme).

Click the information panel to close it.

Pick the O atom (default red) on the left shoulder of the Siatom described above with the right mouse button whileholding down the <Shift> key.



the fact that the charge density is not optimized.

7. Finishing up

Further study

You can study the same structure more accurately by optimizingthe charge density. Since oxygen and silicon have quite differentelectronegativities, a large charge transfer occurs (about 1 electronper Si atom). In the above study, this charge transfer is ignored. Asa result, the energy and the phonon frequencies are not very accu-rate, although the structure is very good.

Repeat steps 2 through 5, with the following exception: in step 3,also click the Charge Density... button located at the lower rightcorner of the Run FastStructure panel, and checkmark the Opti-mize Charge Density checkbox.

Table 1. Structure of quartz compared to experiment

Present Experiment % Error

Si (X)0.4680 0.4701 -0.4O (X)0.4073 0.4136 -1.5 (Y)0.2590 0.2676 -3.2 (Z)0.2136 0.2141 -0.2



Further study


The job takes about 90 minutes to finish on an SGI Indigo2. In theprocess, you can type at the UNIX prompt:

> grep % <job_name>.outfs

to monitor the optimization on charge density, and

> grep # <job_name>.outfs

to monitor the optimization on geometry. Remember that thecharge optimization maximizes the total energy while the geome-try optimization minimizes the total energy.

Compared with the study without charge optimization, the energyis improved by 8.43 eV, but the geometry is very similar.



Part 6Polymer Modeling and

Property Prediction

Cerius2 Tutorials— Materials Science/April 1997 285

17 Estimating Polymer PropertiesUsing QSPR Methods

This tutorial describes how semi-empirical structure/propertycorrelation methods can be used to estimate a wide range of struc-tural, mechanical, thermophysical, and transport properties.


♦ Before you begin — provides some background informationabout the problem and an overview of the solution.


♦ Reviewing the solution — discusses the scientific significanceof the solution and provides a checklist of the Cerius2 skillsyou’ve learned.

♦ References — points you to relevant MSI documentation andpublished work.

Before you begin


♦ Synthia

♦ OFF

♦ Minimizer

Overview of the problem Polymer scientists are often interested in properties with time andlength scales which are inaccessible to atomistic scale simulation,and for which fundamental theories do not exist. Even for thoseproperties which can be predicted using simulation methods, a

286 Cerius2 Tutorials— Materials Science/April 1997

17. Estimating Polymer Properties Using QSPR Methods

faster “first estimate” may be useful to screen large numbers ofcandidate materials.

Two examples are illustrated in this chapter.

♦ Example 1: Designing a polyimide for use in the dielectric baseof high performance computer chips.

♦ Example 2: designing a mixed acrylate copolymer to be com-patible with PVC.

Overview of the solution Mathematical correlations can bridge the gap between what weknow about a material and the properties we wish to predict.

Structure/Property correlation methods can quickly provide esti-mated values for a wide range of properties. Traditionally thesequantitative structure property relationship (QSPR) methods useddatabases of group contributions (van Krevelen 1976, Fedors1974). Properties could only be calculated for polymers made upof functional groups that were in these databases. More recently,correlations based on connectivity indices have been developed(Bicerano 1993). These allow properties to be estimated for anyamorphous homopolymer or random copolymer containing car-bon, hydrogen, silicon, sulfur, nitrogen, oxygen, chlorine, bro-mine, or iodine. The only input required is the repeat unitstructure. These new techniques are available in the Synthia mod-ule. With Synthia you can estimate the following properties:

Thermophysical properties

♦ Glass transition temperature

♦ Temperature of half decomposition

♦ Coefficient of volumetric thermal expansion

♦ Molar volume

♦ Density

♦ Molar heat capacity at constant pressure

♦ Cohesive energy

♦ Solubility parameter

♦ Surface tension

♦ Thermal conductivity

Before you begin


Mechanical properties

♦ Bulk modulus

♦ Shear modulus

♦ Young’s modulus

♦ Poisson’s ratio

♦ Shear yield stress

♦ Brittle fracture stress

Electrical, optical, & magnetic properties

♦ Refractive index

♦ Molar refraction

♦ Dielectric constant

♦ Volume resistivity

♦ Diamagnetic susceptibility

♦ Chain stiffness & entanglement properties

♦ Steric hindrance parameter

♦ Characteristic ratio

♦ Molar stiffness function

♦ Entanglement molecular weight

♦ Critical molecular weight

♦ Entanglement length

Transport properties

♦ Activation energy for viscous flow

♦ Permeability of gases




Example 1: Designing a polyimide for use in thedielectric base of high performance computer chips

Overview of the problem In an industrial design problem there are often many properties tobe considered. In the case of materials for this electronics applica-tion it might be important to predict the strength of the material,its thermal stability (whether it would change shape during thedramatic temperature changes it experiences during manufactureof the computer chip), its dielectric properties (a low dielectricconstant may minimize cross-talk and increase signal strength),and solubility parameter (a low solubility parameter suggests thatthe material will not absorb water, a solubility parameter close tothat of the proposed matrix material suggests that the wetting andadhesion between polyimide and matrix may be good).

Overview of the solution Quantitative structure property relationship methods (QSPR) maybe used to bridge the gap between the available theories of poly-mer behavior and the desired property predictions. Even for prop-erties which can be predicted using simulation methods orpolymer theory, QSPR methods may be used for a fast initialscreening to identify candidate materials for further, more timeconsuming, modeling or experimental studies.

In the following tutorial a number of polyimide structures are pro-posed and their properties are predicted using the Synthia Mod-ule.


A. Building structures and optimizing the candidate polyimiderepeat units

B. Predicting properties of the candidate polymers

A. Building structures and optimizing the candidate polyimiderepeat units

Four different polyimide repeat units are screened in this tutorial. Thestructures are:



1. Start Cerius2

If necessary, refer to Cerius2 Tutorials—Basics for information on


CO

NHC

OO

NC

OC

O

C

OA

B

C

D

CO

NC

CO

NC

O

CH3C

O

NHC

O

C

CF3 CF3

O

NHO

C

C

C

O

CH

CH2 C

O

N

C

O

N

C

C

O

O

CH2

CH C H

O

O

C

H

H

H

H



running Cerius2.

2. Build structure A.

We will build candidate polyimide structure A first.

The cursor symbol will change to a “T”.

This will be the tail end of repeat unit A.

The atom changes from white to grey.

Open the 3D-Sketcher by selecting the Build/3D-Sketcher...item from the top menu bar.

Select the templates “T” icon.

Make sure that the phenyl template is loaded, then click inthe Cerius2 Models window to create a benzene ring.

Select the Edit Element icon, check that the edit element isset to C (carbon) and pick one of the hydrogens on the ben-zene ring with the mouse.

Click the T icon again and pick the new carbon atom.



A second benzene ring is added to the structure.

A detailed description of the 3D-Sketcher commands is given in theIntroduction to Modeling book, chapter 3.

3. Add hydrogens and clean the structure.

This automatically saturates the structure by adding hydrogens toany unfilled valences.

Click the Sketch with icon, check that the text box is set toO (oxygen), and then pick twice: once on the bridging car-bon, and once near by, to bond an oxygen atom to the car-bon.

Change the Edit Bond popup to DOUBLE. Click the EditBond icon and then click on the oxygen-carbon bond tochange the single bond into a double bond.

Continue using the 3D-Sketcher to build up the structure ofcandidate polyimide A.

Click the H ADJUST button.

Click and hold down the CLEAN button until the moleculestops moving.



The bond lengths and angles adjust to more reasonable values.

This returns the mouse to its default select mode.

4. Optimize the repeat unit.

Although it is not essential to optimize a repeat unit before running aSynthia QSPR calculation, one of the inputs to Synthia is the repeatunit length. Repeat unit optimization will ensure a good estimate ofthis input parameter.

As the structure is refined the change in energy is displayed in theGraphs window.

Click the Selection Mode button and then close the Sketchermenu.

Go to the OFF METHODS card stack and click theMINIMIZER card to the front.

Select the Run item to open the control panel and click theMinimize the Energy radio button.

Close the Graphs window.



5. Define the polymer repeat unit.

To define this small molecule as a polymer repeat unit you must definethe “head” and “tail” atoms. These are the atoms that would bereplaced as this repeat unit was added to others to form a polymerchain.

The hydrogen becomes pink.

The tail atom becomes blue.

6. Rename the model to structureA.

This changes the name of this repeat unit to structureA.

Go to the Polymer card stack and select the Edit/Monomersitem from the POLYMER BUILDER card.

Confirm that the Monomer Editor control panel is set toSelect mode.

Now use the mouse to pick the hydrogen which is attachedto nitrogen in the last ring.

Double-click the Define Head icon.

Return the menu to Select mode by clicking the arrow icon.

Use the mouse to pick one of the hydrogens on the first ben-zene ring and double-click the Define Tail icon.

In the Model Manager use the mouse to drag over theModel2 name and type structureA.



7. Build a second structure.

A blank window is ready for building the new structure.

8. Build structures C and D.

You should now have four different optimized candidate structures infour different model windows. They should look something like this:

Open a new model window by clicking the “+” icon in theModel Manager.

Go to the top menu bar and select the Build/3D-Sketcheritem to return to the Sketcher control panel.

Build structure B, optimize the structure and define headand tail atoms as shown.

Repeat the previous step for structures C and D in new win-dows.



B. Predicting properties of the candidate polymers

We are in particular concerned with strength, thermal stability, lowdielectric constant (to minimize cross talk and increase signalstrength) and low solubility parameters (less tendency to absorbwater).

1. Predict properties of StructureA.


Go to the POLYMER card stack and click the SYNTHIAcard to the front.

Head Atom

Head Atom

Head Atom

Head Atom

Tail Atom

Tail Atom

Tail Atom

Tail Atom

A

B

C D



You should see StructureA, StructureB, StructureC and Struc-tureD in the list box.

You can now calculate any number of the properties available in theThermophysical, Structural, Elec_Opt_Magnetic,Stiff_Entanglement, or Transport property sections. Change sec-tions by clicking the section ID box (initially set to Thermophysi-cal). To make multiple selections, hold down the <Ctrl> key whilemaking the selections.

For this electronics application, the most critical properties includethe glass transition temperature Tg, the Coeff. Vol. Therm Expan-sion, Solubility Parameter, Thermal Conductivity, Dielectricconstant, and Bulk Modulus.

After a short pause a study table appears with results of the SynthiaQSPR calculation. Use the scroll bar in the table, if necessary, to seeall the predicted values.

2. Predict properties for other structures.

Select the Predict Properties... item to open the controlpanel. Use the down arrow key to open the repeat unitlibrary list and select Models.

Select StructureA and highlight the properties you wish topredict.

Click the Predict Properties of button at the top of thePredict control panel to predict the properties.



You now predict properties for the other structures.

The range of properties will be predicted for all the structures in thestudy table.

Select the Polymer/Homopolymer item from the studytable to open the Homopolymer menu.

Use the down arrow key to open the Monomer library oncemore and to access the Models section (which includes thestructures built earlier). Locate StructureB and add it to thestudy table.

Repeat the previous step with the other structures. Also addthe PTFE and Kevlar monomers from the Monomer library.

Click the PREDICT button on the study table.

Polymer TgCoef. Vol.Therm Exp.

SolubilityParam.

ThermalConduct.

DielectricConstant

Bulk Modu-lus

(K) ppm K -1 (Jcm-3)1/2 J/Kms-1 MPaA 519 192 25.5 0.203 3.65 6855B 788 129 27.0 0.204 3.74 7699C 571 175 23.9 0.189 3.27 6132D 473 209 25.3 0.21 3.63 6273

TFE 253 732 12.6 0.146 2.09 5941Kevlar 610 165 27.8 0.205 3.88 7951



3. Finishing up

Example 2: designing a mixed acrylate copolymer to becompatible with PVC

Overview of the problem At present PVC-based materials are used in a wide range of appli-cations. The objective of this modeling exercise is to identify anacrylate copolymer which might have similar or better perfor-mance and which could be used in a new PVC/polyacrylate blendmaterial.


A. Predicting properties for pure PVC

B. Building a new repeat unit

C. Calculating properties for a mixed acrylate copolymer

A. Predicting properties for pure PVC

1. Predict PVC properties.

To end the Cerius2 session, close all open panels and selectFile/Exit from the top menu bar.

If you want to go on to the next tutorial, or use Cerius2 torun an experiment, first close all panels and select File/NewSession from the menu bar.

Go to the POLYMER card stack and locate the SYNTHIAcard.

Select the PREDICT PROPERTIES..... item to open the Pre-dict control panel.



You can use this control panel to quickly predict properties for highmolecular weight homopolymers at room temperature.

Now you select the properties to predict.

For this example we might be interested in:

♦ Tg

♦ Solubility Parameter (as an indicator of miscibility)

♦ Surface tension

♦ Bulk and Shear modulii

♦ Brittle Fracture Stress

♦ Entanglement length

♦ Permeability of gases

Feel free to select any additional properties that you feel might be use-ful.

After a short pause a study table appears. At present the table only hasone row containing predicted properties for PVC. Use the scroll bar at

Use the down arrow to open the database of polymer repeatunits. Go to polyvinyl section and select PVC.

Go through the Thermophysical properties in the list boxand highlight the properties of interest by holding down the<Ctrl> key while selecting each property to be included.

Change to the Mechanical, Stiff_Entanglement, and Trans-port menus in turn and similarly highlight the properties ofinterest in these sections.

Click the Predict Properties of button.



the bottom of the study table to view the predicted values.

Note that by default properties are predicted for a molecular weight of100000 and at room temperature.

The PVC repeat unit — which was the only input to the property pre-diction — is displayed in the Cerius2 Models window.

The atoms colored pink and blue are the head and tail atoms. Theseshow where this repeat unit would be joined to the rest of the polymerchain. The chlorine atom is green.

B. Building a new repeat unit

In this section we are hoping to identify a mixed acrylate copolymerwhich might be blended with PVC.

The repeat unit library already contains repeat units for poly(propyl-methacrylate), poly (methyl methacrylate), and poly (acrylic acid),but we would also like to include poly (butyl acrylate) and poly(ethylacrylate). The next step is to build models of the butyl acrylate andethyl acrylate repeat units.

Move the Study table to one side (but don’t close it yet).

1. butyl acrylate

2. ethyl acrylate

C4H9O

C

CCH2

O

C2H5O

C

CHCH2

O



1. Sketch butyl acrylate.

A blank window is now ready for building the new structure.

Detailed descriptions of the 3D-Sketcher commands are given in theIntroduction to Modeling book, chapter 3.

2. Add hydrogens and clean the structure.

This automatically saturates the structure by adding hydrogens toany unfilled valencies.

Open a new model window by clicking the “+” icon in theModel Manager window.

Go to the top menu bar and select the Build/3D-Sketchermenu item on the Visualizer menu bar.

Click the Sketch with icon, check that the text box next to itis set to C, and then click in the model window to startbuilding the structure of the butyl acrylate repeat unit.

Change the Sketch with text box to O and change the bondorder as necessary to complete the structure.

Click the H ADJUST button.

Hold down the CLEAN button until the molecule stopsmoving.



This adjusts the bond lengths and angles to more reasonable values.

This returns the mouse to its default select mode.

3. Minimize the structure.

Although it is not essential to optimize a repeat unit before running aSynthia QSPR calculation, one of the inputs to Synthia is the repeatunit length. Repeat unit optimization will ensure that this inputparameter is correct.

As the structure is refined the change in energy is displayed in theGraphs window.

Click the Selection Mode arrow (the arrow at the top left ofthe menu) and then close the Sketcher control panel.

Go to the OFF METHODS card stack and locate theMINIMIZER card.

Select the Run item to open the control panel and click theMinimize the Energy button.

Close the Graphs window.



4. Define the repeat unit’s head and tail.

To define this small molecule as a polymer repeat unit we must definethe “head” and “tail” atoms. These are the atoms that would bereplaced as this repeat unit was added to others to form a polymerchain.

The hydrogen becomes pink.

The tail atom becomes blue.

Go to the POLYMER card stack and locate the POLYMERBUILDER card.

Select the Edit/Monomers item.

Verify that the Monomer Editor is in Select mode.

Use the mouse to pick one of the hydrogens attached to thecarbon that will be sp1 in the polymer chain.

Double-click the Define Head button.

Return the control panel to Select mode by clicking thearrow icon.

Now use the mouse to pick one of the hydrogens on theadjacent methyl group and double-click the Define Tail but-ton.

Change the name of this repeat unit to PBA (go to the ModelManager, mouse drag over the Model2 name, and typePBA).



5. Now open a new model window and follow a similarprocedure to build, refine and define the ethylacrylate repeatunit (PEA).

C. Calculating properties for a mixed acrylate copolymer

1. Select the monomer units to be studied.

Return to the POLYMER card stack and open theSYNTHIA card.

acrylic acidbutylacrylate ethylacrylate

methylmethacrylate

propylmethacrylate



The fourth component will be the polybutylacrylate repeat unit youjust built.

When this is open, you will see that it contains the new PBA repeatunit.

Notice that by default the copolymer contains equal amounts of each

Select the Study/Copolymer item.

Use the down arrow key under Monomer Name to openthe monomer or repeat unit library, select PAA (polyacrylicacid repeat unit) from the polyacrylate section as the firstrepeat unit in the copolymer.

Select PMMA (polymethylmethacrylate) and PPMA(polypropylmethacrylate) as the second and third compo-nents.

Click the down arrow for the next to a blank text box underMonomer name and select the Models section in thelibrary.

Select the PBA repeat unit.

Select the PEA (polyethylacrylate) repeat as the fifth compo-nent.



component, a mole fraction of 0.2.

2. Add the copolymers to the Study table.

The copolymer structure appears in the Study table, but properties arenot yet calculated.

This displays the range of polymer compositions in the table. Eightnew lines are added to the study table. The concentration of PAA var-ies from 20 to 60%. The properties of these copolymers are automati-cally estimated.

3. Plot the properties.

The selected properties are plotted over the concentration range. Weconclude that as the fraction of PAA increases the mechanical proper-

Change the popup in the Copolymer control panel fromNEW to CURRENT and click the Add Copolymer to but-ton.

Go to the Study table and select the Ranges/ConcentrationRange... item and select to Let PAA Range.

On the Concentration Range control panel, set the PAAStart Concentration to 0.2, the Final Concentration to0.6, and the Concentration Step to 0.05.

Toggle on Display Range in Table.

Select properties of interest from the plot list and click thePlot button.



ties improve. However the solubility parameter also increases.

Note down the concentration of PAA for which the solubility param-eter of the copolymer is closest to that of PVC. This is the compositionmost likely to be compatible with PVC.

4. Finishing up

Fraction PAASolubility

Parameter d Tg Bulk Modulus Density

0.2 18.62 305.15 3054 1.1320.25 18.93 306.82 3150 1.1390.3 19.25 308.56 3253 1.1480.35 19.58 310.37 3362 1.1570.4 19.93 312.25 3478 1.1660.45 20.29 314.21 3602 1.1760.5 20.67 316.26 3734 1.1870.55 21.06 318.41 3870 1.1980.6 21.47 320.65 3995 1.210

Pure PVC Solubility Param. δ Tg (K) Bulk Modulus Density

19.64 293 3990 1.38






Solubility parameters predicted using Synthia can be used toestimate phase diagrams. This can provide a quick estimate ofcompatibility - but a number of serious assumptions are beingmade. The method utilizes traditional Flory–Huggins theory:♦ No concentration fluctuations

♦ No correlations between segments

♦ All segments assumed to be the same size and shape

♦ No volume change on mixing

Using solubility parameters of the individual components toestimate miscibility♦ Will predict only UCST phase behavior

♦ Assumes that noncombinatorial entropy can be ignored

♦ Assumes that specific interactions, such as hydrogen bonds, arenot generated or lost as the blend is formed

♦ Concentration and temperature dependence of c cannot be pre-dicted from solubility parameters (chi assumed to have 1/Tdependence on temperature in FH theory)



Poly A/poly B phase diagram from solubility parameters

Density Poly A andMw of averagerepeat unit Poly A

3-D SketcherPolymer Builder

Minimizer

Poly A and PolyB Repeat Units

Synthia

Validation

Assume χ independent

of concentration and

dependence on temp.

1T---

χδ1 δ2 ) 2Vseg–

RT-------------------------------------------=

Blends module

Assume 1 repeat unit = 1 seg

Compare Synthiapredictions with knownproperties of Poly A andPoly B

Vseg

VsegMw PolyA( )density DP×----------------------------------=

Estimation of miscibility and/ormode of phase separationfor any temperature,concentration, or Mw

Assuming that Poly A will bedefined as component 1 inthe Phase Diagram module



Summary

In this lesson you learned or reviewed:

❏ Building polymer repeat units with the 3D-Sketcher.

❏ Minimizing the energy of polymer repeat units using the OFFMinimizer.

❏ Predicting a large array of properties for homopolymers andcopolymers.

❏ Displaying the results of copolymer calculations over a concen-tration range in tabular and graphical format.

References

Bicerano, J. Prediction of Polymer Properties. Marcel Dekker Inc.:New York (1993).

Fedors, R.F. Polym. Eng. Sci. 14, 147, 472 (1974).

van Krevelen, D.W. Properties of Polymers, Their Estimation and Cor-relation With Chemical Structure. Elsevier: New York (1976).


18 Evaluating the Miscibility of aPolymer/Solvent System

This chapter shows how modeling can be used to investigate thelocal interactions between polymers or between polymer and sol-vent by calculating local interaction energies, predicting coordina-tion, and estimating the phase diagram. This chapter focuses onthe use of the Cerius2•Blends module and is includes severalparts:

♦ Before you begin—Provides some background informationabout the problems and an overview of the solution (below).

♦ Solving the problem step-by-step—Gives specific instruc-tions for solving the problem (page 314).

♦ Reviewing the solution—Discusses the scientific significanceof the solution and gives a checklist of the Cerius2 skills you’velearned (page 337).

♦ What to do next—Tells how you can learn more about themodules used in this tutorial (page 338).

♦ References and related material—Directs you to relevantpublications (page 338).

Before you begin

Be sure you havethese modules

To complete this tutorial, you need a licensed copy of Cerius2 thatincludes these modules:

♦ Blends

♦ Polymer Builder



18. Evaluating the Miscibility of a Polymer/Solvent System

♦ Minimizer

Overview of the problem Today’s most successful product formulations tend to be complexmixtures. Because of this, properties of miscibility, mixing, com-patibility, and adhesion play critical roles in the development ofnew, value-added products.

Unfortunately, the number of experiments needed to obtain andrefine product formulations in the laboratory can be very large.Formulation problems such as phase segregation or incompletemixing can lead to a marked degradation in a product’s physicalproperties. Whether you are trying to solve these problems or totake advantage of differing compatibilities to create a novel formu-lation, you will often want to identify the temperature and concen-tration conditions that lead to the desired mixing or blend-miscibility behavior. Equally, you will want to understand the keyinteractions in any mixing process.

Overview of the solution Molecular modeling can be used to generate valuable qualitativeand quantitative information on the mixing process.

Several different techniques can be applied (Case and Honeycutt1994):

♦ Using empirical structure/property correlation methods topredict solubility parameters.

Solubility parameters can be predicted using quantitativestructure property relationship (QSPR) methods and applied inthe Flory–Huggins theory (Flory 1953, 1970) and in the “repul-sion” theory of copolymer blends. This approach may be usedto estimate trends in miscibility behavior for simple systemsnot dominated by specific interactions (such as hydrogen bond-ing) or by non-combinatorial entropy effects.

This approach is illustrated in the previous tutorial, “EstimatingPolymer Properties Using QSPR Methods”.

♦ Studying local interactions using molecular mechanics.

Simple atomistic calculations on realistic samples of polymerfragment-pair configurations can be used to predict interactionenergies and to estimate enthalpies of mixing for polymerblends, including the effects of specific interactions.

The approach has been proposed by several groups (Hopfingerand Koehler 1993, Nelson et al. 1992, Jacobson et al 1992, Fan et

Before you begin


al 1992, Tiller and Gorella in press) and is demonstrated in thistutorial.

♦ Analysis of bulk atomistic simulations.

Bulk atomistic simulations of blends and single-componentsystems can be analyzed to calculate energies of mixingdirectly, without using an estimated coordination number.

♦ Putting it all together to predict the phase diagram.

A generalized Flory–Huggins theory can be applied to extrap-olate results from theoretical and/or experimental work onmodel systems to predict the effects of temperature, concentra-tion and molecular weight on blend miscibility and modes ofphase separation.

The Cerius2•Blends module allows you to estimate local interac-tion energies and coordination numbers for clusters of molecules,applying Monte Carlo simulation techniques.

If we assume that miscibility is determined by the energy of mix-ing ∆Emix, and that ∆Emix is dominated by the local interactionsbetween polymer segments and solvent molecules, then polymermiscibility and the Flory–Huggins χ parameter can be estimated:

∆Emix = EAB - 0.5 (EAA + EBB)

At ∆Emix > 0, materials do not form a thermodynamically stableblend. At ∆Emix < 0, materials may form a thermodynamically sta-ble blend.

χFH = Z’ Vseg(∆Emix /RT)

Interaction energies are calculated by evaluating the energies ofthousands of molecular pairs generated by a Monte Carlo simula-tion. Coordination numbers come from a similar simulation thatgenerates thousands of clusters.

This exercise shows you how to set up and run a Blends calcula-tion and how to interpret some of the results. The system you willstudy here is a polymer/solvent blend—polystyrene and cyclo-hexane.



Run the logfile For an overview of the application of the Blends module, you maywant to run the Cerius2 example file POL_blends.log, which dis-plays an example similar to the one in this tutorial lesson.

The logfile shows the methodology that you follow in this tutorial. Seealso the flow chart below.

Summary of procedure This method is summarized by these steps:

A. Building a model of the polymer fragment.

B. Sketching a model of the solvent molecule.

C. Setting up the blends calculation.

D. Running the blends calculation.

E. Computing interaction parameters.


This section takes you through the procedure outlined above andshown in Figure 1. You will see how Cerius2 can been used tostudy blending and miscibility.

Begin a new session of Cerius2. If necessary, see page 1 for infor-mation on running Cerius2.

Type cerius2 at the UNIX prompt and press <Enter> to startthe Cerius2 program.

Open the Example files control panel by selecting the Help/Examples menu item from right side of the main controlpanel’s menu bar.

Double click POL_blends.log to run this logfile.



A. Building a model of the polymer fragment

Figure 1. Evaluating the miscibility of polymer blends: overview of thesolution

Construct polymerfragment

Sketch or load insolvent molecule

Run MC to calculateinteraction energiesE11, E12, E21, E22

Run MC to calculatecoordination nos. Z11,Z12, Z21, Z22

Determine energy ofmixing, Emix, as afunction of T: related toEij (T),Zij

Fit Emix (T) toanalytical expression

Compute phasediagram from thisexpression usingadapted Flory-Huggins theory

Input degree ofpolymerization andrecompute phasediagram



1. Start Cerius2

2. Start the Homopolymer Builder

This opens the Homopolymer Builder control panel, which you willuse to make a polymer fragment.

For the purposes of this tutorial, you will use a 1-mer of polystyrene(that is, a single repeat unit).

3. Build the 1-mer

If Cerius2 is not already running, start it by typing cerius2at the UNIX prompt and pressing <Enter>.

If Cerius2 is already running, start a new session by select-ing the File/New Session menu item.

Click the POLYMER BUILDER card to bring it to the frontof the BUILDERS 1 deck of cards, then select theHomopolymer menu item from that card.

Change the Number of monomers entry box to 1.

Use the down arrow tool next to the Monomer entry box toopen the list of available monomers (repeat units).

Select PS from the polyolefin section.

Click the BUILD button to create a 1-mer of polystyrene.



4. Optimize the 1-mer geometry

A file browser offering a choice of forcefields appears.

The Dreiding-II forcefield is loaded—the loading of various forcefieldcomponents is reported in the text window.

You’ll use the minimizer with the Dreiding-II force field to optimizethe geometry of the one-unit styrene polymer.

Find the OPEN FORCE FIELD card (its default location isin the OFF SETUP card deck.

Choose the Load menu item on the OPEN FORCE FIELDcard to open the Load Force Field control panel.

Double-click the filename DREIDING2.21.

Close the Load Force Field control panel and access theMinimizer module by going to the OFF METHODS deck ofcards. The MINIMIZER card should be in front.

Choose the Run menu item on the MINIMIZER card toopen the Energy Minimization control panel.



A graph appears showing energy against iteration during the minimi-zation process. Move the graph window so that you can see the modelwindow. Later calculations will display results in both windows.

You have now built a single unit polymer of styrene, minimized itusing the Dreiding-II forcefield with the default settings of theCerius2•Minimizer module, and saved it in a file.

B. Sketching a model of the solvent molecule

In this section, you load or build a model of the solvent, cyclohex-ane. You then compute partial charges for this model and mini-mize its energy, again using the Dreiding-II forcefield.

1. Load a cyclohexane molecule

Click the Minimize the Energy action button to minimizethe energy.

Select the File/Save Model… menu item from the main con-trol panel’s menu bar to access the Save Model controlpanel. Use it to save the model in a file called polymer.msi.

If you created and saved a model of the chair conformationof cyclohexane in Chapter 3 of the Tutorials—Basics book,Using the 3D Sketcher, load it now using the File/LoadModel… menu item.

If you didn’t create cyclohexane in the tutorial exercises ofthe Tutorials—Basics book, then follow the steps on pages 25to 28 to create a model of cyclohexane now.



2. Calculate charges for cyclohexane

You’ll use the charge equilibration method (Rappé and Goddard 1991)to calculate the partial charges on the cyclohexane solvent model.

This selects the correct QEq parameter file for an overall neutral mol-

Find the CHARGES card (in the OFF SETUP card deck) andclick its name to bring it to the front of the card deck.

Select the Charges menu item from the card to open theCharges control panel.

Choose the Charge-Equilibration radio button if it is notalready selected.

Click the Preferences... button next to the Charge-Equili-bration button to open the Charge Equilibration prefer-ences control panel.

Use the browser box to load the QEq_neutral1.0 parameterfile from the Cerius2-Resources/CHARGE directory. Thenclose the Charge Equilibration preferences control panel ifdesired.



ecule. You are now ready to run a charge calculation.

Notice that partial charges have been assigned to the atoms.

The Minimizer uses the Dreiding-II forcefield to carry out an accurateminimization. Electrostatic energy is now included in the Dreiding-II forcefield energy expression.

Because the QEq calculation is geometry dependent, you need to iter-ate between charge calculation and minimizations.

On the Charges control panel, click the CALCULATEatomic charges button. Change the label popup on the toolbar from NO LABEL to CHARGES to label your model.

Return to the MINIMIZER card and click the Run menuitem to open the Energy Minimization control panel (if it isnot still open).

Click the Minimize the Energy button to minimize theenergy.

Return to the Charges control panel and recalculate thecharges by clicking the CALCULATE atomic charges but-ton again.

Return to the Energy Minimization control panel and clickthe Minimize the Energy button again.



You’ve now prepared a minimized model of cyclohexane—the solventfor the polymer/solvent miscibility study.

Time for a break?

C. Setting up the blends calculation

You should now have a minimized solvent model (cyclohexane)and a minimized polymer model (polystyrene). In this section, youset up the miscibility calculation for the polystyrene/cyclohexanesystem by defining the polymer fragment and the solvent as themodels to be used in the Blends simulation.

1. Open Run Blends control panel

Change the label popup back to NO LABEL.

Change the model name to cyclohexane and save the cyclo-hexane model in a file called cyclohexane.msi.

If you want to take a break now, exit Cerius2 by selecting theFile/Exit menu item from the menu bar.When you want to continue with the tutorial:♦ Load the polymer.msi structure file that you saved in section

A (page 318).

♦ Load the cyclohexane.msi file that you saved in section Babove (page 321).

♦ Load the Dreiding-II forcefield as you did in section A(page 317).

Click the BLENDS card (located in the OFF INSTRU-MENTS 2 card deck) to bring it to the front of the deck ofcards.



2. Select the models

The control panel should now look like this:

Select the Calculate card menu item to open the Run Blendscontrol panel.

Use the down arrow tools to select Poly PS and cyclohex-ane as the Molecules to use in the blends calculation.

Make PolyPS the current model space by clicking its dia-mond in the Model Manager.



3. Define the contacts

This opens the Molecule 1 Packing control panel.

To treat the polystyrene polymer as a polymer fragment, we want toprevent any close contacts at the head and tail positions where, in real-ity, the polymer chain would be attached. The head and tail atoms arecolored magenta and cyan. Select by clicking one of them and thenholding down the <Shift> key and clicking the other.

Notice that the value after Number of atoms in list in the controlpanel changes to 2.

4. Evaluate the contacts

Although the two atoms that you have just defined as a head and tailare excluded from close contacts, these contacts should be evaluated as

Click the Packing... button next to PolyPS in the Run Blendscontrol panel.

Check the Use Non-contact atom list check box.

Click the Add selected atoms to list action button.

Close the Molecule 1 Packing control panel.

Select the Build/3D-Sketcher… menu item in the menu barto open the Sketcher control panel.



if the atoms were carbon atoms because they would be carbons in apolymer chain.

The two selected hydrogens change to carbons, as can be seen if youlabel the model according to ELEMENTS.


You will leave the carbons with zero charge, so that they act as “block-ing” atoms in the Monte Carlo simulations with only their van derWaals interactions accounted for.

Ensure that the Edit Element tool is set to C.

Double-click the Edit Element icon.

Return the mouse icon to Selection Mode—either choosethe arrow button in the top left of the Sketcher control panelor simply close the Sketcher control panel.

Go to the MINIMIZER card again, select the Run cardmenu item to access the Energy Minimization control panel,and click the Minimize the Energy button.

Change the label popup to NO LABEL.



D. Running the blends calculation

You are now set up to run the different stages of the blends calcu-lation. Two simulation stages are followed by a data analysis stagein which results are generated. The two simulations are:

♦ Monte Carlo simulation of molecular pairs to compute theinteraction energies.

♦ Monte Carlo simulation of molecular clusters to determinecoordination numbers.

In this section, you run these two simulations.

1. Compute the interaction energies

The models created during the Monte Carlo simulations will appearin this space.

The Interaction Energies control panel that is opened contains all theparameters for the Monte Carlo simulation of molecular pairs. Bydefault, all four possible interactions are calculated: PS–PS, PS–cyclohexane, cyclohexane–PS, and cyclohexane–cyclohexane. Theinteraction energies of each of these pairs are termedE11, E12, E21,and E22, respectively. It is possible to calculate each pair separatelyusing the buttons at the top of the control panel.

Click the + tool above the Model Manager to open a newmodel space.

In the Run Blends control panel, click the Preferences... but-ton nearest the Calculate Interaction Energies action but-ton.

Ensure that the Number of molecular pairs is 10000.



The Monte Carlo simulation generates 10,000 pairs for each interac-tion.

Data are saved in files named tutorialij.enr, where ij is the number ofthe pairing: 11, 12, 21, or 22.

One in every 200 pairs is displayed on the screen—this enables youto follow the simulation, but does not slow it down excessively.

A graph of interaction energy versus frequency is plotted as the sim-ulation progresses, and is updated every 100 steps.

When Cerius2 calculates the interaction energies (in the next step), itcreates several files. In addition to four blends interaction energy files(.enr), it creates two .msi structure files. The names of the structurefiles are taken from the names in the Model Manager list. You alter thenames of the polymer and cyclohexane models here in order to preventyour original polymer.msi and cyclohexane.msi files from being over-

Change the File prefix from blend to tutorial.

Change Update Model Frequency from 1 to 200.

Change Update Graph Frequency from 1 to 100.

Close the Interaction Energies control panel.

Change the names of cyclohexane and polymer in theModel Manager to cyclohexane_B and PolyPS_B.



written.

Model pairs are displayed in the model window, and the energy distri-butions are plotted in the graph window. This calculation runs for allfour possible pairings. The graph produced should resemble the onebelow. Note the equivalence of the E12 and E21 graphs.

These data are saved to file and are re-used when you analyze the sim-ulations in the next section. The next step is to compute the coordina-tion numbers.

Click the Calculate Interaction Energies button.



2. Determine the coordination numbers

This control panel contains the parameters for the Monte Carlo simu-lation that computes coordination number from model clusters. Thecoordination number Zij is the number of models of type i that sur-round a model of type j. The number is computed by generating thou-sands of clusters of model j surrounded by i models and computing theaverage number of i models. Again, four Z numbers are calculatedZ11, Z12, Z21, and Z22.

This speeds up your simulation.

The Monte Carlo simulation generates 20 clusters for each possiblemolecular pair.

In the Run Blends control panel, click the Preferences... but-ton nearest to the Calculate Coordination Numbers buttonto open the Z Number Calculation control panel.

Change the Number of clusters from 100 to 20.

Change Update Graph and Update Model to 2.

Close the Z Number Calculation control panel.

Click the Calculate Coordination Numbers button.



Each set of clusters is used to compute one of the average coordinationnumbers: Z11, Z12, Z21, or Z22. The coordination number of the cur-rent cluster and the on-going average are reported in the text window.The average is also recorded in a graph.

E. Computing interaction parameters

In this section, you use the results of the simulations to calculateimportant information about the miscibility of the system. First,you compute the energy of mixing Emix(T). Emix(T) is closelyrelated to the interaction parameter χ, which is also a function oftemperature; χ(T) can be calculated using the interaction energyand coordination number information that you have just gener-ated.

Emix(T) can be fitted to an analytical expression. The enthalpy andentropy of mixing, and hence the free energy of mixing ∆Gmix, arerelated to derivatives of Emix(T). Thus, once you have described



this function analytically, the software can determine ∆Gmix(T) andplot a phase diagram.

1. Compute the mixing energy

This opens the Fit Mixing Energy control panel.

Note that the values of Z11, Z12, Z21, and Z22 have been extractedfrom the coordination number simulation and are displayed abouthalfway down the control panel, in the Coordination Numbers sec-tion.

The fit takes a few moments. You will see from the text window thatthe calculation reads each of the interaction energy files tutorialij.enrin turn. It takes the 10,000 stored pairs and applies a MetropolisMonte Carlo sampling algorithm to process the energy data at differ-ent temperatures. The result is four data-sets—one for each pair—ofinteraction energy against temperature:

E11(T), E12(T), E21(T), and E22(T).

Now, the energy of mixing at each temperature, Emix(T), is computedas:

[E12(T) Z12 + E21(T) Z21 - E11(T) Z11 - E22(T) Z22] / 2

This produces a set of data points that are fitted to an analyticalexpression, in this example the default:

Click the Preferences... button nearest the CalculateEmix(T) Model button.

Change the lower limit of the Fitted Temperature Pointsfrom 100.00 K to 200.00 K.

Click the FIT button at the top of the panel.



A + BT + C/T

At the end of the calculation, a plot of the data points and the fittedexpression is returned. The values of A, B, and C are also returned inthe Fit Mixing Energy control panel.

2. Plot and analyze a phase diagram

A phase diagram is plotted in the graph window.

The phase diagram consists of two phase-boundary curves: the binodaland the spinodal (see the figure below). In the region above the bin-odal, the PS/cyclohexane blend is single phase, miscible. In the regionbelow the spinodal boundary, the blend is immiscible, and phasesimmediately segregate (by spinodal decomposition). The regionbetween the binodal and spinodal curves is the metastable region: thatis, the system is stable to small fluctuations of concentration or tem-perature but not for larger ones.

Close the Fit Mixing Energy control panel.

Click the Preferences... button in the Run Blends controlpanel next to the Calculate Phase Diagram button, to openthe Phase Diagram control panel.

Click the CALCULATE Phase Diagram button.



Both the spinodal and binodal curves are derived from the plot of ∆Gversus composition for a given temperature. ∆G is related to the firstderivative of the interaction parameter χ with respect to temperatureby Flory-Huggins theory and can thus be calculated using the analyt-ical expression for Emix(T) which you derived in Step 1 above.

You can draw the plot of ∆G versus composition at a series of temper-atures.

3. Create an isotherm plot

Open the Blends Isotherms control panel by selecting theAnalyze/Isotherms menu item from the BLENDS card.

Spinodal boundary

Binodal boundary

Critical temperature



The critical temperature corresponds to the highest temperature atwhich phase separation begins. For example, if the critical tempera-ture is around 200 K, an appropriate temperature range would be175 K to 225 K.

This draws a series of isotherms. The binodal curve in the phase dia-gram is related to the minima in those isotherms that have two min-ima. Beyond the temperature at which the isotherm has only oneminimum, there are no points in the binodal curve—the mixture isthus always fully miscible past this critical temperature.

Similarly, the spinodal curve is related to the inflection points of theisotherm curves, where the second derivative of the free energy withrespect to composition is zero.

Change the Isotherm Temperatures range so that it coversa 50 K range containing the critical temperature (as seen inthe phase diagram).

Change the number of Isotherms from 3 to 8.

Click the PLOT button.



This should correspond to the critical temperature which you identi-fied in Step 2 on page 331.

Identify the first isotherm that has only one minimum.

Close the Blends Isotherms control panel if desired.



4. Plot a modified phase diagram

You can alter parameters in the phase diagram calculation. One ofthese is the degree of polymerization of each of the components—a fac-tor in the Flory–Huggins equation. You can alter this and see how itaffects the phase diagram.

In the Run Blends control panel, click the Preferences... but-ton nearest the Calculate Phase Diagram button to open thePhase Diagram control panel.

Change the Degree Of Polymerization, X1, from 1 to 100.

Click the CALCULATE button to compute a modifiedphase diagram.

Translate and scale the phase diagram plot in the graphwindow using the mouse:

Drag the cursor over the graph window while pressing themiddle mouse button to translate the graph. Hold down<Shift> and drag the mouse while using the middle mousebutton to scale either axis.



5. Finishing up






In this tutorial exercise you’ve learned to use the Cerius2•Blendsmodule to study the miscibility of a polymer/solvent mixture. Youcan use the same approach to study polymer/polymer or solvent/solvent blends.

Consider the layout of the Blends module. The underlying theoryis complex, and you experimented with some of the parameters bychanging values in the various Preferences control panels. If, how-ever, the defaults were appropriate (either the MSI values, orbecause a colleague had set them for you), you would simply needto click each of the four buttons in the top level control panel inorder to compute a phase diagram.

Other issues should be borne in mind in conducting an accuratesimulation, which have not been touched on here. These include:

♦ Different conformations—The models in the blends simula-tion that you just ran were assumed to remain rigid. You canallow for conformational flexibility by introducing alternativeconformations to the Monte Carlo simulations. You would dothis using the Flexibility control panels, which are accessiblefrom the Run Blends control panel. Read the help text (click theright mouse button over the desired control panel or tool) for anexplanation of their functionalities.

♦ Getting the best fit for Emix(T)—You used one thermody-namic model (A+BT+C/T) to match to the energy of mixing. Inreality, you should try all the available models, choosing theone with the lowest standard deviation in the fit.

♦ The results are approximate—You used minimized geome-tries obtained by molecular mechanics and charges determinedby the charge equilibrium method. The Monte Carlo simulationis based on an empirical forcefields. You fit the mixing energyto a model curve and used an adapted form of Flory–Hugginstheory. So at each step of the calculations, you introducedapproximations. As long as you bear this in mind, however,you can gain valuable insight from the results. Each stage of thecalculation—evaluating interaction energies, calculating coor-dination numbers—provides useful information in its ownright. The resulting phase diagram can be correlated with



experimental results. Although it will not be accurate in everydetail, it can be used for activities such as establishing trendsfor different solvents.

In this tutorial you learned or reviewed…

❏ Building polymer fragments (Section A, page 315).

❏ Sketching models (Section B, page 318).

❏ Calculating partial charges (Section B, page 318).

❏ Setting up a polymer fragment for a blends calculation (SectionC, page 321).

❏ Running blends simulations (Section D, page 325).

❏ Details of the blends theory (Section D, page 325 and Section E,page 329).

❏ Analyzing blends results (Section E, page 329).

What to do next

This application and the work on which it is based are describedin the Molecular Simulations Application Note POL 09. Fan et al.(1992) give a particularly good overview of the application of theblends method. You may want to refer to these publications.

To learn more about creating models of homopolymers and copol-ymers, read the chapter about the Polymer Builder in Cerius2

Builders.

To learn more about the Cerius2•Blends module, read the Blendschapter in Cerius2 Computational Instruments Property Prediction.


Case, F. H.; Honeycutt, J. D. “Will my polymers mix?: Methods forstudying polymer miscibility” Trends in Polymer Science, 2, 8(1994).



Fan C. F.; Olafson B. D.; Blanco M.; Hsu S. L. Macromolecules, 25,3667 (1992).

Flory, P. J. Principles of Polymer Chemistry, Cornell UniversityPress:Ithaca (1953).

Flory, P. J. Discussions of the Faraday Society, 49, 7 (1970).

Hopfinger, A. J.; Koehler, M. G. ACS PMSE Preprints, 69, 43 (1993).

Nelson, G. V.; Jacobson, S. H.; Gordon, D. J., Chem. Design Autom.News, 39 (1992).

Tiller A. R.; Gorella B. “Prediction of polymer miscibility frommolecular mechanics calculations’, Polymer (in press).




19 Predicting Permeability ofAmorphous Polymers

This chapter describes how the permeability of small moleculegases through amorphous polymers systems can be calculated.



♦ Solving the problem step-by-step — gives you specificinstructions to follow in order to solve the problem.

♦ Reviewing the Solution — discusses the scientific significanceof the solution and gives a checklist of the Cerius2 skills you’velearned.


♦ References — points you to relevant MSI documentation andpublished work.

Before you begin


♦ Polymer Builder

♦ Amorphous Builder


♦ Minimizer

♦ Dynamics


19. Predicting Permeability of Amorphous Polymers

♦ Analysis

Overview of the problem Prediction of permeability is important in the design of productssuch as contact lenses, packaging materials, gas separation mem-branes and drug delivery devices. The permeability of a solutethrough a matrix is a function of both its solubility and diffusionrate

A number of different modeling techniques can be applied to pre-dict permeability and to gain insight into the diffusion process.

1. Atomistic simulation can be applied to study and directly pre-dict diffusion rates for fast moving gases in materials such aspolymer melts, solutions and gels, and to evaluate the effect ofchanges in molecular structure.

2. Trends in diffusion rates for slightly slower moving speciesmay be estimated by "pulling" the solute through the matrix

3. The solubility of a species in a particular matrix can be esti-mated from cohesive energy calculations or local interactionstudies. This is the thermodynamic driving force for permeabil-ity.

4. The rate of O2, N2, or CO2 diffusion in most amorphous, atactichomopolymers or random copolymers can be estimated usingquantitative structure property relationship methods (QSPR) inthe Synthia module.

5. Diffusion rates and permeability for other species may be esti-mated by correlation to predicted free volume or packing data.

The purpose of this tutorial is to demonstrate the first technique:direct prediction of gas diffusion using molecular dynamics. Theexample is nitrogen diffusion through PDMS

Overview of the solution The diffusion coefficient of molecules can be determined byrecording the motions of molecules during a molecular dynamicscalculation. Using the Analysis module, it is possible to determinethe mean squared displacement of diffusing molecules as a func-tion of time. The mean squared displacement (MSD) (Allen andTildesley 1987) is calculated by

Before you begin


Where rn (t) is the position of atom n at time t.

Note that this will give the mean square displacement of all "n"atoms averaged over all time periods of length t.

Once the MSD is calculated, the self-diffusion coefficient (which isequivalent to the experimentally measured solute diffusivity atlow solute concentrations) can be determined from the Einsteinrelationship:

Therefore, the diffusion coefficient, D, can be determined from theslope of a plot of the MSD versus time.

This exercise will show you how to build a periodic amorphouspolymer cell containing gas molecules and a PDMS chain, andhow to calculate the diffusion coefficient of nitrogen through thepolymer from analysis of the MSD calculated from a moleculardynamics simulation.

Run the logfile To get an overview of the method employed to calculate the diffu-sion coefficient for a gas in an amorphous polymer system, run theCerius2 example file POL_dyn_diffusion.log, which displays asimilar example.

Type cerius2 to start the program.

Go to the top menu bar and select the Examples/Help item.

MSD t( ) 1n---

i 1=

n

∑ rn t( ) rn 0( )–2⟨ ⟩=

D16---

t∂∂

MSD( )=



The logfile illustrates the methodology that you follow in this tuto-rial.


A. Building a model of bulk amorphous PDMS

B. Equilibrate using energy minimization and molecular dynamics

C. Calculate the mean squared displacement (MSD) of the oxygenmolecules and determine their diffusion coefficient


A. Building a model of bulk amorphous PDMS

To generate a realistic model of a bulk amorphous material we use arepeating periodic boundary condition (PBC) cell containing a realis-tic density of polymer and gas molecules. The cell must be of sufficientsize that atoms cannot "see" their images in adjacent cells.

1. Start Cerius2

Double-click on POL_dyn_diffusion.log in the list box torun the logfile.

If Cerius2 is not already running, start it by typing cerius2at the UNIX prompt.

If you already have Cerius2 running, go to the Visualizermenu bar and select the File/New Session item, then clickConfirm in the dialog box.



2. Build the polymer

You can also simply type in PDMS to set the Monomer type.

3. Create a new model space

This step is performed to create the model space for the nitrogen mol-ecules.

Click the POLYMER BUILDER card (located in the BUILD-ERS 1 deck) to bring it to the front of the deck of cards.

Select the Homopolymer item on the card to open the con-trol panel.

Click the down arrow next to Monomer access the repeatunit library, and select PDMS as the repeating unit (mono-mer).

Type in 80 as the Number of monomers and click theBUILD button to create the PDMS model

Click the + icon in the Model Manager to generate a newmodel space.



4. Sketch the nitrogen molecule

This produces a single blue cross representing a nitrogen atom.

This generates a second nitrogen atom bonded to the first.

This activates the edit bond tool.

Go to the top menu bar and select the Build/3D-Sketcheritem to open the Sketcher panel.

Click the yellow button next to the blue element name win-dow for Sketch with and change the setting to N (nitrogen).

Click the left mouse button with the cursor in the Cerius2

Models window.

Drag the mouse a small distance and click the left mousebutton again.

Change the setting of the yellow button next to the EditBond icon from SINGLE to TRIPLE.

Click the left mouse button on the first nitrogen atom, andthen on the second.



The atoms are now connected by a triple bond.

This puts the mouse back into Selection Mode and ensures that it isnot in the Edit Bond or Sketching mode.

The clean function corrects the nitrogen-nitrogen bond length.

The repeating cell that will model the bulk material will contain the80mer of PDMS and 4 nitrogen molecules.

5. Clone the nitrogen molecule

Select the name Model2 in the Model Manager list andchange it to N2.

Click the select arrow in the upper left corner of the Sketchercontrol panel.

Hold down the CLEAN button on the Sketcher panel for afew seconds.

Close the open panels.

Click the AMORPHOUS BUILDER card to bring it to thefront of the card deck.

Select the Clone item on the Amorphous Builder card.



This displays the model names of all the current models.

A new model space is generated which contains 4 copies of the nitro-gen molecule.

6. Combine the PDMS chain and nitrogen molecules

You can now combine the PDMS chain and the nitrogen moleculesinto one model space and build an amorphous cell.

Click the Show Model Information button on the Amor-phous Builder Clone panel.

For the model named N2 in the Model Name list, enter thenumber of Copies as 4.

Click the CLONE button.

Change the model name to nitrogens by dragging themouse cursor over the name and then typing in the newname.

Make Poly PDMS the active model by clicking the leftmouse button on the diamond-shaped icon next to its name.



The PDMS chain should now be visible.

The Cerius2 Models window is now in border mode, so that currentmodel PDMS is visible in a large window and the nitrogen moleculesare present in an adjacent smaller window.

This step copies the contents of one model space into another. In thiscase, the nitrogens have been copied over to the model space contain-ing the polymer chain.

This makes this model invisible. You are now back to displaying onemodel space which contains both the polymer and the gas molecules.

7. Build an amorphous cell

Click the square icon under the visible heading for modelnitrogens.

Click the left mouse button over the small model windowcontaining the nitrogens and drag the mouse while holdingthe mouse button over to the large model space containingthe PDMS chain.

Once again click the icon under the visible heading formodel nitrogen.

Go to the AMORHPOUS BUILDER card and select theBuild item to open the Amorphous Builder control panel.

Toggle on the 3D Periodic setting.



This displays the Amorphous Builder Output control panel.

This updates the display as the amorphous cell is constructed.

This constructs the amorphous PBC cell containing the PDMS andnitrogen molecules.

B. Equilibrate using energy minimization and moleculardynamics

The initial model built by the Amorphous Builder has the correct

Enter 0.8 as the Periodic Density. This is the total densitythat the amorphous cell will contain once it is built (ing/cm3).

Click the Output... button on the Amorphous Builder con-trol panel.

Toggle on the Update Model selection and then close thepanel.

Click the RUN BUILD button on the Amorphous Buildercontrol panel.

Close all the open control panels by clicking the Clear Pan-els button on the tool bar.



overall density, but the molecules are not yet well-distributed. If yourotate the model and change the visualization so that multiple PBCcells are displayed (you can do this using the Visualization controlpanel in the Crystal Builder) you will see that there are regions ofunrealistically high and low density.

In this section you load the PCFF forcefield (Maple et al. 1994, Hwanget al. 1994, sun et al. 1994, Sun 1994, 1995, Hill and Sauer 1994),assign atom types to all atoms, and then perform energy minimizationand molecular dynamics to start to equilibrate the bulk structure.

1. Load a forcefield

A file browser offering a choice of forcefields appears.

The PCFF forcefield gives good models for a wide range of small mol-ecule organic and polymeric materials, It is the recommended force-field for polymer applications.

The forcefield describes the freedom of bond lengths, bond angles andtorsions to change. It also contains a description of the non-bondedvan der Waals and electrostatic interactions between atoms. Beforeyou perform a simulation using the forcefield you must assign atomtypes and charges to the atoms in our model.

Go to the OFF SETUP card deck and find the OPEN FORCEFIELD card.

Select the Load item to open the Load Force Field controlpanel.

Double-click on the filename pcff_300_1.01 in the list box.



2. Assign atom types and charges

It is important to prevent atoms from "seeing" their images in adja-cent periodic cells. By specifying a non-bond cutoff of less than half thecell length we are ensuring this. The smaller cutoff value will alsospeed up the simulation.

Now that the forcefield is defined correctly you can optimize the modelusing molecular mechanics minimization and dynamics.


Go to the OPEN FORCEFIELD card and select theTyping/Atoms item.

Click the Calculate using typing rules button.

Now select the Energy Terms/Van der Waals item.

Change the Long-Range Interaction Treatment to Direct.

Click the Preferences... button next to the DIRECT buttonand be sure the Real space cut-off distance (A) is set to 8.5

Go to the OFF METHODS deck and locate theMINIMIZER Card

Select the Constraints/Cell item and turn off the option toVary All Cell Parameters by Default.



You do not want the density to change during the simulation

The objective is to generate an equilibrated system at the temperatureof interest, not a minimum energy conformation. Only a short mini-mization is required to remove close contacts and highly strained con-formations that might make the molecular dynamics simulationunstable. For less flexible materials 1000 steps might be required.

Minimization proceeds and a graph showing the energy versus thenumber of minimization steps appears. After every five steps of mini-mization, the model is updated with the most recent set of coordinates.

4. Optimize the molecule with molecular dynamics

Go to the MINIMIZER card and select the Run item.

Enter 200 as the Maximum Number of Iterations.

Click the Minimize the Energy button.

Close the open panels with the Clear Panels button on thetool bar.

Click the DYNAMICS SIMULATION card to bring it to thefront of the deck. Select the Run item to open the controlpanel.

Choose CONSTANT NVT as the dynamics method andenter 200 as the Number of Steps.



The default time step employed in molecular dynamics is 1fs. There-fore 200 steps will simulate the motions over 200 fs or 0.2 ps of time.This short time is specified for the purposes of this tutorial. A muchlonger simulation would be required to allow full equilibration andsimulation of sufficient time to predict gas diffusion.

The molecular dynamics simulation now begins and 200 steps ofdynamics at 450K are run. Four graphs will appear which display thetotal, potential, and kinetic energy, the components of the potentialenergy, the temperature, and the cell pressure. By turning off the plot-ting and model updating from the output panel, you can reduce thecalculation time.

C. Calculate the mean squared displacement (MSD) of theoxygen molecules and determine their diffusion coefficient

1. Load the molecular dynamics data

First you must load in the data from the long (576ps) moleculardynamics simulation.

Change the Required Temperature (K) to 450.

Click the RUN DYNAMICS button.

Close the open control panel.

Click the + icon above the Model Manager to generate anew model space.

Click the ANALYSIS card to the top of the card deck andselect the Input item



The range values are updated to show the data runs from 1 to 576 psand that frames were saved every 2ps during this simulation (288frames).

2. Replay the frames

The first frame of the simulation is displayed in the model window.You can now replay the other frames in sequence to see how the struc-ture changed during the simulation time.

It appears that the nitrogen molecules are moving through a vacuum,but in fact, because of the periodic boundary conditions, they are mov-ing though a bulk polymer matrix made up of images of the parentchains that are not displayed in this mode.

The animation is interesting, but in order to predict the diffusion rateit is necessary to analyze and quantify the motion of the nitrogen.

Go to the list box on the control panel and select the trajec-tory file n2_pdms.trj from the Cerius2-Resources/EXAM-PLES/data/nonascii directory.

Close the control panel.

Select the Show Frames item from the ANALYSIS card andclick on the forward arrow to Step Through Frames. Bydefault the animation stops at the end of the data.




3. Analyze the motion of nitrogen

An energy profile graph of energy against time appears in the graphwindow.

The graph shows the change in energy with time during the simula-tion. Note that during this simulation the energy fluctuates aroundan average value suggesting that the system was fairly well equili-brated before the dynamics run was started. If this were not the casethe trajectory file could be reloaded omitting the first few frames.

4. Calculate the Mean Squared Displacement

The Mean Squared Displacement control panel appears.

This is done since you are interested in calculating the diffusion of thenitrogen atoms only.

Select the Analyze/Statistics item and click the Profile but-ton on the control panel.


Select the Analyze/MSD item from the ANALYSIS card.

Change the yellow atom selection button from ALL toSELECTED.

Change the right-hand yellow Atom selection button on thevisualizer panel (at the top of your screen) from Atom to El.



This changes the selection mode to selection by element.

Now all nitrogen atoms are selected and will be highlighted in the dis-play since you are selecting by element.

The nitrogen atoms, since they are selected, are displayed in ball mode.The circles on these atoms show that they are selected.

The graph automatically updates as the trajectory file is analyzed

At this stage you could output the data from the graph using the File/Save Graphs command on the Graphs card and use a external mathpackage to check that the gradient of log(MSD) against log(time) isclose to 1.0 (see Discussion section).

5. Perform a fit to the MSD curve

A green line is fit through the section of the curve above 50 ps. The dif-fusion coefficient for the nitrogen molecules is printed in the text win-dow.

Click on one of the nitrogen atoms in the Model window.

Change the yellow display setting on the visualizer panelfrom STICK to BALL.

Go to the Mean Squared Displacement panel and click thebutton labeled Calculate the MSD for SELECTED Atoms.

Go to the blue MSD fit range text boxes and enter 50.0 inthe first box, and 212.0 in the second box.

Click the Calculate Line Fit to MSD Curve button.



6. Finishing up

Reviewing the Solution

This direct simulation technique is only suitable for studying thefast diffusion of small gas molecules through polymer gels, solu-tions, and some elastomers or bulk amorphous materials aboveTg. It is not recommended to study diffusion rates of less than10-6 cm2/sec.

To determine if sufficient time has been simulated to predict theexperimentally observed diffusion rate you can export the data toan external math package and plot log(MSD) against log(time). Ifthe slope of this graph is not close to 1.0 for the time segment ana-lyzed a longer simulation is required.



What to do next


The log MSD/log time plot for the data studied in this tutorial isthe following:

Review Checklist In this lesson you learned or reviewed:

❏ Loading molecules from files into Cerius2.

❏ Building polymer chains and generating amorphous cells con-taining multiple molecules.

❏ Performing energy minimization and molecular dynamicsusing the Open Force Field.

❏ Calculating the mean squared displacement of selected atomsfrom the analysis of a molecular dynamics trajectory file, anddetermination of the diffusion coefficient of gas molecules in apolymer matrix.

What to do next

The simulation described above could be repeated with differentpolymers or with different gas molecules to examine the effects ofpolymer structure on gas diffusion rates and selectivity (Taylorand Galiatsatos 1993). Inclusion of solvent molecules in the simu-lation would allow the study of diffusion in polymer solutions andgels (for example in contact lenses, see Eichinger et al. 1995, andCase 1996).



The same technique could be applied to study fast gas diffusionthrough inorganic matrices such as zeolites (see for example: Cat-low et al. 1991, Kawano et al. 1992, Demontis et al. 1990, and Yas-honath et al. 1988).

References

Allen, M.P., Tildesley, D.J., Computer Simulation of Liquids, Claren-don Press, Oxford Science Publications: Oxford (1987).

Case, F.H., “Applications of Modeling in Polymer Property Predic-tion.” Journal of Computer-Aided Materials Design, 3, 369-378(1996).

Catlow, C.R.A.; Freeman, C.M.; Vessal, B.; Tomlinson, S.M.; Leslie,M. “Molecular dynamics studies of hydrocarbon diffusion inzeolites”, J. Chem. Soc. Faraday Trans., 87, (1991).

Demontis, P.; Fois, E.S.; Suffritti, G.B.; Quartieri, S. “MolecularDynamics Studies on Zeolites. 4. Diffusion of Methane inSilicalite”, J. Phys. Chem., 94, 4329-4334, (1990).

Eichinger, B.E.; Rigby, D.R.; Muir. M.H., “Computational Chemis-try Applied to Materials Design—Contact Lenses.” Computa-tional Polymer Science, 5, 147-163, (1995).

Hill, J-R; Sauer, J., J. Phys. Chem. 98, 1238 (1994).

Hwang, M.-J.; Stockfisch, T. P.; Hagler, A. T., J. Amer. Chem. Soc.,116, 2515 (1994).

Kawano, M.; Vessal, B.; Catlow, C.R. A. “A Molecular DynamicsSimulation of the Temperature Dependence of the Diffusion ofMethane in Silicalite”, J. Chem. Soc. Chem. Commun., 1992, 879(1992).

Maple, J. A.; Hwang, M.-J.; Stockfisch, T. P.; Dinur, U.; Waldman,M.; Ewig, C. S.; Hagler, A. T., J. Comp. Chem. 15, 162 (1994).

Sun, H., Mumby, S. J., Maple, J. R., Hagler, A. T., J. Amer. Chem. Soc.,116, 2978 (1994).

Sun, H., J. Comp. Chem., 15, 752 (1994).

Sun, H., Macromolecules, 28, 701 (1995).

References


Taylor, G.; Galiatsatos, V., “Computer Simulation of the Diffusionof Gas Penetrants in Modified PDMS Networks.” ACS PMSEPreprints, 69, 16-17 (1993).

Yashonath, S.; Demontis, P.; Klein, M. L. “A Molecular DynamicsStudy of Methane in Zeolite NaY”, Chem. Phys. Lett., 153, 551-556, (1988).



Documents

Tutorials—Materials Science · Cerius2 Tutorials—Materials Science Release 3.0 April 1997 9685 Scranton Road San Diego, CA 92121-3752 619/458-9990 Fax: 619/458-0136