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Cheminformatics & ValidationMolecular modelling Introduction 25-Feb (JS) Molecular mechanics/dynamics 26-Feb (NG)

– Conformational analysis 27, 4 & 6th Feb/March Electronic structure methods 13-Mar (JS)

– Transition states 18th & 20th Mar Density functional theory 26-Mar (PM)

– Crystalline state 27th Mar & 1 & 3 Apr

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Introduction to molecular modelling Predicting properties of molecules, such as

energy, structure, polarisability, dipole moment, etc. including reaction profiles and transition states

Focus on the application Spartan Practical sessions: Monday afternoons 2am

– Feb: 17 & 24 (NG)– Mar: 3 & 10 (JS) 17, 24 (PM)– Location: Corrib suite

Registration, usernames, passwords, etc.

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Informatics (normally Wed 9am)

World wide web (JS)– Tue March 25th

Chemical Abstracts via STN (LS)– 12th & 19th March

Beilstein CrossFire (NG)– 11th March

Cambridge crystallography database (PM)– 26th March & 2nd April

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Comparisons at a glance

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Molecular mechanics: Introduction

Molecular mechanics (each different force field)– eg AMBER, OPLS, BIO+, MM+

Potential energy of molecule location of atoms Atom types? Just elements?

– eg 5 different oxygens– carbonyl, hydroxyl, carboxylic, ester or water

Parameter sets; elements parametrised Interaction of nuclei not electrons

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Force fields

Bond str.: ES = (k/2) (r - r0)2

Angle bending: EB = k (- 0)2

Torsion: E = VN{1+cos (n -)}/2

van der Waals: ENB = AIJ r 12 - BIJ r 6

Electrostatic: EE = qI qJ/(r)

H-bonding: 10-12 potential

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Applications

Geometry optimisation

Molecules with 1,000s of atoms

Organics, oligonucleotides, peptides, etc.

Metallo-organics and inorganics

Vacuum and solvent

Ground states only

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Electronic structure methods

ab initio: purely theoretical– many different approximations– Hartree-Fock, e correlation: MPn, MCSCF– basis sets: STO-3G, 6-31G(d), 6-311+G(d,p), etc

Semi-empirical: some exptal. data– many different expressions: MNDO, AM1, PM3

Density functional theory (ab initio?)– many different– B3LYP, SVWN, etc

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Semi-empirical methods

Very large systems & 1st step for large systems Ground state organic molecules

– Calibration: parametrised– AM1: H, B/Al, C/Si/Ge, N/P, O/S, F/Cl/Br, Zn

Energies E = f(x) Geometry optimisation dE/dx Frequencies d2E/dx2

Molecular orbitals (!?)

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Example

Bredt’s rule: “Elimination to give a double bond in a bridged

bicyclic system always leads away from the bridgehead”

Build #2 and #3 optimise and record the energy; which is more stable?

Why? Measure C=C bond lengths (130-132 pm)Effect of increasing ring size?

OH 32 X

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Practical: acetone

Build, minimise & optimise via AM1 (H3C)2CO Experimental data:

– Heat of formation HF = -51.9 kcal/mol– Dipole moment = 2.88 Debyes

Energy levels and MOs– Identify HOMO– View HOMO & LUMO (Setup/Surfaces/Add/HOMO then up to

Setup/Submit) Vibrational analysis

– Identify vibrations and IR spectrum– C=O stretching vibration?

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Structure versus Energy Hexasilabenzene can exist in several

isomeric forms; Sax et al. [J. Comp. Chem. 1988, 9:564–77] found that the prismane, isomer 2, is the most stable, do you agree (AM1)?

Si

SiSi

SiSi

HH

H

HH Si

Si

SiSi

Si

SiSi

H

H

H

H

H

H

SiSi Si

Si SiSiH

HH

H

HH Si

SiSi

Si

SiSi

H

HH

H

H H

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Exercise: Walsh Diagrams

Walsh diagrams are useful in predicting molecular geometry. They correlate energy changes of molecular orbitals between a reference geometry, frequently of high symmetry, and a deformed structure of lower symmetry.

Sketch the water molecule, aligning it on screen; set a restraint or constraint (by clicking on ‘angle padlock’ icon) select the H–O–H angle so that the angle is forced to be say 90º. Do a geometry optimisation with AM1.

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Example: geometry optimisation

Malonaldehyde– Simple example of

intramolecular H-bonding

– Cf. experimental structure with a geometry optimi-sation run

– Try molecular mechanics &

– Semi-empirical, PM3

– Key distance: long O...H

O O

H

H

H

H

1.234

1.454

1.68

1.348

1.32

0.969

1.091

1.0941.089

123°

124.5°

119.4°

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The log file

Orientation of molecule Mulliken population

analysis partitions total charge among the atoms of the molecule (widely used & criticized)

Dipole moment of 1.709– y-component of 1.709– So points from negative O

atom along Y-axis

HO

HX

Y

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Portion of log fileEigenvalues(a.u.) and Eigenvectors

Mol. Orbital 1 2 3 4 5 6 7

Eigenvalue -20.25158 -1.25755 -0.59385 -0.45973 -0.39262 0.58179 0.69267

S O 1 0.99422 0.23377 0.00001 -0.10404 0.00000 0.12582 0.00003

S O 1 0.02585 -0.84445 -0.00004 0.53817 0.00000 -0.82013 -0.00019

Px O 1 0.00000 0.00000 -0.61270 -0.00008 0.00000 -0.00024 0.95980

Py O 1 0.00416 -0.12284 0.00008 -0.75587 0.00000 -0.76356 -0.00023

Pz O 1 0.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000

S H 2 -0.00558 -0.15559 -0.44922 -0.29512 0.00000 0.76930 -0.81449

S H 3 -0.00558 -0.15560 0.44923 -0.29509 0.00000 0.76902 0.81480

EIGENVALUES(eV)

-551.073608 -34.219627 -16.159496 -12.509945 -10.683656 15.831361 18.848427

NET CHARGES AND COORDINATES

Atom Z Charge Coordinates(Angstrom) Mass

(Mulliken) x y z

1 8 -0.330524 -0.00000774 -0.07115177 0.00000000 15.99900

2 1 0.165255 0.75813931 0.56460971 -0.00000005 1.00800

3 1 0.165271 -0.75801641 0.56471276 0.00000005 1.00800

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Open versus closed shell

How to handle electron spin

Open shell (unrestricted)

– odd no. of e’s

– excited states

– 2 or more unpaired e’s

– bond dissociation

Closed shell (restricted)

1

2

3

4

1

2

3

4

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Relative Computation TimesMethylcyclohexane (7 heavy atoms)Lysergic acid (20)

Energy(Single-point)

GeometryOptimisation

Frequency

AM1 0.01 0.08 0.66

HF 3-21G 1 14 190

HF 6-31G* 5.4 90 1100AM1 0.05 1.9 11

3-21G 17 600

6-31G* 120

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Transition states Finding TSs (more difficult than minima) Mathematical procedures less well developed PE surface near TS probably “flatter” Only good ab initio methods will work

– bonds partially or fully broken Very little quantitative data on TSs anyway Guessing TSs

– Closely-related system– Average reactant & product (linear synchronous transit)– Chemical intuition

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Verifying TS

Frequency normal-mode analysis One (and one only) imaginary frequency

– eg a negative frequency in the range 400-2,000 cm-1

Check that the coordinate (corresponding to imaginary frequency) smoothly connects reactants and products by:– coordinate animation– follow the coordinate by intrinsic reaction coordinate

methods

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Pyrolysis of ethyl formate

Build ethyl formate, choosing the correct geometry, minimise with AM1, save one copy as– Ethyl_formate_pBP_DNss for later & another as– Ethyl_formate_pyrolysis_AM1 for use now.

Select Reaction from Build menu (or curved arrow icon); click on bond ‘a’ then on ‘b’; then on ‘c’ & ‘d’ and finally on ‘e’ followed by Shift click on methyl H to be transferred and on the O-atom to receive it.

With all three arrows in place, click on equilibrium icon (twin arrows) at the bottom right of screen

O

OH

H

H

H H

H O

HO

H

+

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Transition state of ethyl formate Result; shown on the right Enter Calculations dialogue, specify

TS geometry, semi-empirical & AM1 Click on frequencies Submit job, when finished examine

geometry & animate imaginary (-ve) frequency

Is vibrational motion consistent with reaction?

Turn off animation by re-entering Vibrations & clicking on imaginary frequency.

O

OH

H

a

bc

d

e

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Density iso-surface Bring up Surfaces dialogue,

click on Add … select density (bond) & none from Property menu & click on OK. Repeat with potential from Property.

Submit. Enter Surfaces & click on

density completed 0.08 Is CO bond in ethyl formate

nearly fully cleaved? Is the migrating H midway

between C & O?

Click anywhere on graphic, select either Transparent or Mesh from the menu to the right of Style (bottom right) to replace opaque solid density surface by a mesh or transparent solid view

Click on density Completed 0.08 then click again

Check migrating H colour code Is it ?

– H+ (blue)– H (green) or– H– (red)

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Computation of activation energy Use “ethyl_formate_pBP_DNss” Enter Calculations dialogue, specify single-point using the

pBP/DN** DFT model, click OK & submit job. Bring on-screen “ethyl_formate_pBP_DNss”.

Enter Calculations, specify pBP/DN** but start from an AM1 structure. Submit job

When both calculations are complete, compute the activation energy from the difference between the total energies of TS and ethyl formate (use molecular properties from the Display menu)

1 atomic unit (au) = 627.51 kcal/mol How does your value cf. with exptal. of 40-44 kcal/mol?