Q-Chem 5.2 User's Manual · Q-CHEM User’s Manual Version 5.2 edited by: Dr. Andrew Gilbert Versions 5.0 and 5.1 editors: Dr. Andrew Gilbert Prof. John Herbert Version 4 editors:

Q-Chem 5.2 User’s Manual

Version 5.2May, 2019

Q-CHEM User’s Manual

Version 5.2 edited by:Dr. Andrew Gilbert

Versions 5.0 and 5.1 editors:Dr. Andrew Gilbert Prof. John Herbert

Version 4 editors:Prof. John HerbertProf. Anna KrylovDr. Narbe MardirossianProf. Martin Head-GordonDr. Emil ProynovDr. Andrew GilbertDr. Jing Kong

The contributions of individual developers to each version are highlighted in “New Features”,Section 1.3

Published by: Customer Support:Q-Chem, Inc. Telephone: (412) 687-06956601 Owens Dr. Facsimile: (412) 687-0698Suite 105 email: [email protected], CA 94588 website: www.q-chem.com

Q-CHEM is a trademark of Q-Chem, Inc. All rights reserved.The information in this document applies to version 5.2 of Q-CHEM.This document version generated on November 23, 2019.

© Copyright 2000–2019 Q-Chem, Inc. This document is protected under the U.S. Copyright Act of 1976 and statetrade secret laws. Unauthorized disclosure, reproduction, distribution, or use is prohibited and may violate federal andstate laws.

mailto:[email protected]://www.q-chem.com

CONTENTS 3

Contents

1 Introduction 151.1 About This Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.2 Q-CHEM, Inc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.2.1 Contact Information and Customer Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.2.2 About the Company . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.2.3 Company Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.3 Q-CHEM Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.3.1 New Features in Q-CHEM 5.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.3.2 New Features in Q-CHEM 5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.3.3 New Features in Q-CHEM 5.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.3.4 New Features in Q-CHEM 4.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.3.5 New Features in Q-CHEM 4.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221.3.6 New Features in Q-CHEM 4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231.3.7 New Features in Q-CHEM 4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241.3.8 New Features in Q-CHEM 4.0.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251.3.9 New Features in Q-CHEM 4.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251.3.10 Summary of Features in Q-CHEM versions 3. x . . . . . . . . . . . . . . . . . . . . . . . . . . 281.3.11 Summary of Features Prior to Q-CHEM 3.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

1.4 Citing Q-CHEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2 Installation, Customization, and Execution 342.1 Installation Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.1.1 Execution Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.1.2 Hardware Platforms and Operating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.1.3 Memory and Disk Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.2 Installing Q-CHEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.3 Q-CHEM Auxiliary files ($QCAUX) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.4 Q-CHEM Run-time Environment Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.5 User Account Adjustments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.6 Further Customization: .qchemrc and preferences Files . . . . . . . . . . . . . . . . . . . . . . . . 372.7 Running Q-CHEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.8 Parallel Q-CHEM Jobs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.9 IQMOL Installation Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.10 Testing and Exploring Q-CHEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3 Q-CHEM Inputs 423.1 IQMOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.2 General Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.3 Molecular Coordinate Input ($molecule) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

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3.3.1 Specifying the Molecular Coordinates Manually . . . . . . . . . . . . . . . . . . . . . . . . . 453.3.2 Reading Molecular Coordinates from a Previous Job or File . . . . . . . . . . . . . . . . . . . 49

3.4 Job Specification: The $rem Input Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.5 Additional Input Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.6 Multiple Jobs in a Single File: Q-CHEM Batch Jobs . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.7 Q-CHEM Output File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4 Self-Consistent Field Ground-State Methods 584.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.2.1 SCF and LCAO Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.2.2 Hartree-Fock Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.3 Basic SCF Job Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.3.2 Additional Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.3.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.3.4 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.4 SCF Initial Guess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.4.2 Simple Initial Guesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.4.3 Reading MOs from Disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754.4.4 Modifying the Occupied Molecular Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.4.5 Basis Set Projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.5 Converging SCF Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.5.2 Basic Convergence Control Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824.5.3 Direct Inversion in the Iterative Subspace (DIIS) . . . . . . . . . . . . . . . . . . . . . . . . . 844.5.4 Geometric Direct Minimization (GDM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864.5.5 Direct Minimization (DM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.5.6 Maximum Overlap Method (MOM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.5.7 Relaxed Constraint Algorithm (RCA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.5.8 User-Customized Hybrid SCF Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954.5.9 Internal Stability Analysis and Automated Correction for Energy Minima . . . . . . . . . . . . 974.5.10 Small-Gap Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.6 Large Molecules and Linear Scaling Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1034.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1034.6.2 Continuous Fast Multipole Method (CFMM) . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044.6.3 Linear Scaling Exchange (LinK) Matrix Evaluation . . . . . . . . . . . . . . . . . . . . . . . 1064.6.4 Incremental and Variable Thresh Fock Matrix Building . . . . . . . . . . . . . . . . . . . . . 1074.6.5 Fourier Transform Coulomb Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1084.6.6 Resolution of the Identity Fock Matrix Methods . . . . . . . . . . . . . . . . . . . . . . . . . 1104.6.7 PARI-K Fast Exchange Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1124.6.8 CASE Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1134.6.9 occ-RI-K Exchange Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

4.7 Dual-Basis Self-Consistent Field Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1164.7.1 Dual-Basis MP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1174.7.2 Dual-Basis Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1174.7.3 Basis-Set Pairings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1174.7.4 Job Control and Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

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4.8 Hartree-Fock and Density-Functional Perturbative Corrections . . . . . . . . . . . . . . . . . . . . . 1234.9 Unconventional SCF Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

4.9.1 Polarized Atomic Orbital (PAO) Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 1254.9.2 SCF Metadynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1264.9.3 Multiple SCF Solutions for Non-Orthogonal CI . . . . . . . . . . . . . . . . . . . . . . . . . 1314.9.4 Holomorphic Hartree–Fock Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

4.10 Ground State Method Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

5 Density Functional Theory 1395.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1395.2 Kohn-Sham Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1395.3 Overview of Available Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

5.3.1 Suggested Density Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1435.3.2 Exchange Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1455.3.3 Correlation Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1465.3.4 Exchange-Correlation Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1475.3.5 Specialized Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1535.3.6 User-Defined Density Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

5.4 Basic DFT Job Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1565.5 DFT Numerical Quadrature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

5.5.1 Angular Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1605.5.2 Standard Quadrature Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1615.5.3 Consistency Check and Cutoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1625.5.4 Multi-resolution Exchange-Correlation (MRXC) Method . . . . . . . . . . . . . . . . . . . . 1625.5.5 Incremental DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

5.6 Range-Separated Hybrid Density Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1665.6.1 Semi-Empirical RSH Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1665.6.2 User-Defined RSH Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1665.6.3 Tuned RSH Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1715.6.4 Tuned RSH Functionals Based on the Global Density-Dependent Condition . . . . . . . . . . 172

5.7 DFT Methods for van der Waals Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1745.7.1 Non-Local Correlation (NLC) Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1745.7.2 Empirical Dispersion Corrections: DFT-D . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1775.7.3 Exchange-Dipole Model (XDM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1845.7.4 Tkatchenko-Scheffler van der Waals Model (TS-vdW) . . . . . . . . . . . . . . . . . . . . . . 1885.7.5 Many-Body Dispersion (MBD) Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

5.8 Empirical Corrections for Basis Set Superposition Error . . . . . . . . . . . . . . . . . . . . . . . . . 1935.9 Double-Hybrid Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1955.10 Asymptotically Corrected Exchange-Correlation Potentials . . . . . . . . . . . . . . . . . . . . . . . 199

5.10.1 LB94 Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2005.10.2 Localized Fermi-Amaldi (LFA) Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

5.11 Derivative Discontinuity Restoration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2025.12 Thermally-Assisted-Occupation Density Functional Theory (TAO-DFT) . . . . . . . . . . . . . . . . 2035.13 Methods Based on “Constrained” DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

5.13.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2065.13.2 CDFT Job Control and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2085.13.3 Configuration Interaction with Constrained DFT (CDFT-CI) . . . . . . . . . . . . . . . . . . . 2125.13.4 CDFT-CI Job Control and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

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References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

6 Wave Function-Based Correlation Methods 2306.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2306.2 Treatment and the Definition of Core Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2326.3 Møller-Plesset Perturbation Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2346.4 Exact MP2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236

6.4.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2366.4.2 Algorithm Control and Customization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

6.5 Local MP2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2386.5.1 Local Triatomics in Molecules (TRIM) Model . . . . . . . . . . . . . . . . . . . . . . . . . . 2386.5.2 EPAO Evaluation Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

6.6 Auxiliary Basis (Resolution of the Identity) MP2 Methods . . . . . . . . . . . . . . . . . . . . . . . 2436.6.1 RI-MP2 Energies and Gradients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2446.6.2 OpenMP Implementation of RI-MP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2466.6.3 GPU Implementation of RI-MP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2466.6.4 Spin-Biased MP2 Methods (SCS-MP2, SOS-MP2, and MOS-MP2) . . . . . . . . . . . . . . . 2496.6.5 Orbital-Optimized MP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2516.6.6 RI-TRIM MP2 Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2566.6.7 Dual-Basis MP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

6.7 Attenuated MP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2576.8 Coupled-Cluster Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

6.8.1 Coupled Cluster Singles and Doubles (CCSD) . . . . . . . . . . . . . . . . . . . . . . . . . . 2596.8.2 Quadratic Configuration Interaction (QCISD) . . . . . . . . . . . . . . . . . . . . . . . . . . 2616.8.3 Optimized Orbital Coupled Cluster Doubles (OD) . . . . . . . . . . . . . . . . . . . . . . . . 2616.8.4 Quadratic Coupled Cluster Doubles (QCCD) . . . . . . . . . . . . . . . . . . . . . . . . . . . 2626.8.5 Resolution of the Identity with CC (RI-CC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2626.8.6 Cholesky decomposition with CC (CD-CC) . . . . . . . . . . . . . . . . . . . . . . . . . . . 2636.8.7 Job Control Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2636.8.8 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

6.9 Non-Iterative Corrections to Coupled Cluster Energies . . . . . . . . . . . . . . . . . . . . . . . . . 2676.9.1 (T) Triples Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2676.9.2 (2) Triples and Quadruples Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2686.9.3 (dT) and (fT) corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2686.9.4 Job Control Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2696.9.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

6.10 Coupled Cluster Active Space Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2716.10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2716.10.2 VOD and VOD(2) Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2736.10.3 VQCCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2746.10.4 CCVB-SD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2756.10.5 Local Pair Models for Valence Correlations Beyond Doubles . . . . . . . . . . . . . . . . . . 2766.10.6 Convergence Strategies and More Advanced Options . . . . . . . . . . . . . . . . . . . . . . . 278

6.11 Frozen Natural Orbitals in CCD, CCSD, OD, QCCD, and QCISD Calculations . . . . . . . . . . . . 2816.12 Non-Hartree-Fock Orbitals in Correlated Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 2826.13 Analytic Gradients and Properties for Coupled-Cluster Methods . . . . . . . . . . . . . . . . . . . . 2836.14 Memory Options and Parallelization of Coupled-Cluster Calculations . . . . . . . . . . . . . . . . . 2856.15 Using single-precision arithmetics in coupled-cluster calculations . . . . . . . . . . . . . . . . . . . . 2876.16 Simplified Coupled-Cluster Methods Based on a Perfect-Pairing Active Space . . . . . . . . . . . . . 290

CONTENTS 7

6.16.1 Perfect pairing (PP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2926.16.2 Coupled Cluster Valence Bond (CCVB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2936.16.3 Second-order Correction to Perfect Pairing: PP(2) . . . . . . . . . . . . . . . . . . . . . . . . 2976.16.4 Other GVBMAN Methods and Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

6.17 Geminal Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3066.18 Variational Two-Electron Reduced-Density-Matrix Methods . . . . . . . . . . . . . . . . . . . . . . 308

6.18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3086.18.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3096.18.3 v2RDM Job Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3116.18.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316


7 Open-Shell and Excited-State Methods 3237.1 General Excited-State Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3237.2 Uncorrelated Wave Function Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326

7.2.1 Single Excitation Configuration Interaction (CIS) . . . . . . . . . . . . . . . . . . . . . . . . 3277.2.2 Random Phase Approximation (RPA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3287.2.3 Extended CIS (XCIS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3297.2.4 Spin-Flip Extended CIS (SF-XCIS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3307.2.5 Spin-Adapted Spin-Flip CIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3317.2.6 CIS Analytical Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3327.2.7 Basic CIS Job Control Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3347.2.8 CIS Job Customization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338

7.3 Time-Dependent Density Functional Theory (TDDFT) . . . . . . . . . . . . . . . . . . . . . . . . . 3417.3.1 Brief Introduction to TDDFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3417.3.2 TDDFT within a Reduced Single-Excitation Space . . . . . . . . . . . . . . . . . . . . . . . . 3427.3.3 Job Control for TDDFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3437.3.4 TDDFT Coupled with C-PCM for Excitation Energies and Properties Calculations . . . . . . . 3477.3.5 Analytical Excited-State Hessian in TDDFT . . . . . . . . . . . . . . . . . . . . . . . . . . . 3477.3.6 Calculations of Spin-Orbit Couplings Between TDDFT States . . . . . . . . . . . . . . . . . . 3527.3.7 Various TDDFT-Based Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

7.4 Non-Orthogonal Configuration Interaction (NOCI) . . . . . . . . . . . . . . . . . . . . . . . . . . . 3597.5 Maximum Overlap Method (MOM) for SCF Excited States . . . . . . . . . . . . . . . . . . . . . . . 3627.6 Restricted Open-Shell Kohn-Sham Method for ∆-SCF Calculations of Excited States . . . . . . . . . 3687.7 Correlated Excited State Methods: The CIS(D) Family . . . . . . . . . . . . . . . . . . . . . . . . . 369

7.7.1 CIS(D) Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3697.7.2 Resolution of the Identity CIS(D) Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3707.7.3 SOS-CIS(D) Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3717.7.4 SOS-CIS(D0) Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3717.7.5 CIS(D) Job Control and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3717.7.6 RI-CIS(D), SOS-CIS(D), and SOS-CIS(D0): Job Control . . . . . . . . . . . . . . . . . . . . 3757.7.7 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

7.8 Coupled-Cluster Excited-State and Open-Shell Methods . . . . . . . . . . . . . . . . . . . . . . . . . 3807.8.1 Excited States via EOM-EE-CCSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3807.8.2 EOM-XX-CCSD and CI Suite of Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3837.8.3 Spin-Flip Methods for Di- and Triradicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3847.8.4 EOM-DIP-CCSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3847.8.5 EOM-DEA-CCSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3857.8.6 EOM-CC Calculations of Core-Level States: Core-Valence Separation within EOM-CCSD . . 385

CONTENTS 8

7.8.7 EOM-CC Calculations of Metastable States: Super-Excited Electronic States, TemporaryAnions, and More . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

7.8.8 Charge Stabilization for EOM-DIP and Other Methods . . . . . . . . . . . . . . . . . . . . . 3977.8.9 Frozen Natural Orbitals in CC and IP-CC Calculations . . . . . . . . . . . . . . . . . . . . . . 3977.8.10 Single-precision arithmetics in EOM-CC calculations . . . . . . . . . . . . . . . . . . . . . . 3977.8.11 Approximate EOM-CC Methods: EOM-MP2 and EOM-MP2T . . . . . . . . . . . . . . . . . 4017.8.12 Approximate EOM-CC Methods: EOM-CCSD-S(D) and EOM-MP2-S(D) . . . . . . . . . . . 4017.8.13 Implicit solvent models in EOM-CC/MP2 calculations. . . . . . . . . . . . . . . . . . . . . . 4017.8.14 EOM-CC Jobs: Controlling Guess Formation and Iterative Diagonalizers . . . . . . . . . . . . 4017.8.15 Equation-of-Motion Coupled-Cluster Job Control . . . . . . . . . . . . . . . . . . . . . . . . 4027.8.16 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4157.8.17 Non-Hartree-Fock Orbitals in EOM Calculations . . . . . . . . . . . . . . . . . . . . . . . . . 4287.8.18 Analytic Gradients and Properties for the CCSD and EOM-XX-CCSD Methods . . . . . . . . 4287.8.19 EOM-CC Optimization and Properties Job Control . . . . . . . . . . . . . . . . . . . . . . . . 4337.8.20 EOM(2,3) Methods for Higher-Accuracy and Problematic Situations (CCMAN only) . . . . . 4497.8.21 Active-Space EOM-CC(2,3): Tricks of the Trade (CCMAN only) . . . . . . . . . . . . . . . . 4507.8.22 Job Control for EOM-CC(2,3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4517.8.23 Non-Iterative Triples Corrections to EOM-CCSD and CCSD . . . . . . . . . . . . . . . . . . 4547.8.24 Potential Energy Surface Crossing Minimization . . . . . . . . . . . . . . . . . . . . . . . . . 4577.8.25 Dyson Orbitals for Ionized or Attached States within the EOM-CCSD Formalism . . . . . . . 4607.8.26 Interpretation of EOM/CI Wave Functions and Orbital Numbering . . . . . . . . . . . . . . . 469

7.9 Correlated Excited State Methods: The ADC(n) Family . . . . . . . . . . . . . . . . . . . . . . . . . 4727.9.1 The Algebraic Diagrammatic Construction (ADC) Scheme . . . . . . . . . . . . . . . . . . . 4727.9.2 Resolution of the Identity ADC Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4737.9.3 Spin Opposite Scaling ADC(2) Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4737.9.4 Core-Excitation ADC Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4747.9.5 Spin-Flip ADC Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4747.9.6 Properties and Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4757.9.7 Excited States in Solution with ADC/SS-PCM . . . . . . . . . . . . . . . . . . . . . . . . . . 4757.9.8 Frozen-Density Embedding: FDE-ADC methods . . . . . . . . . . . . . . . . . . . . . . . . . 4817.9.9 ADC Job Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4817.9.10 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492

7.10 Restricted Active Space Spin-Flip (RAS-SF) and Configuration Interaction (RAS-CI) . . . . . . . . . 5007.10.1 The Restricted Active Space (RAS) Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 5007.10.2 Second-Order Perturbative Corrections to RAS-CI . . . . . . . . . . . . . . . . . . . . . . . . 5017.10.3 Short-Range Density Functional Correlation within RAS-CI . . . . . . . . . . . . . . . . . . . 5017.10.4 Excitonic Analysis of the RAS-CI Wave Function . . . . . . . . . . . . . . . . . . . . . . . . 5027.10.5 Job Control for the RASCI1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 5027.10.6 Job Control Options for RASCI2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5097.10.7 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511

7.11 Core Ionization Energies and Core-Excited States . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5147.11.1 Calculations of Core-Level States with (TD)DFT . . . . . . . . . . . . . . . . . . . . . . . . . 5177.11.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518

7.12 Real-Time SCF Methods (RT-TDDFT, RT-HF, OSCF2) . . . . . . . . . . . . . . . . . . . . . . . . . 5227.13 Visualization of Excited States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524

7.13.1 Attachment/Detachment Density Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5257.13.2 Natural Transition Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526


CONTENTS 9

8 Basis Sets 5348.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5348.2 Built-In Basis Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5358.3 Basis Set Symbolic Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535

8.3.1 Customization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5398.4 User-Defined Basis Sets ($basis) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540

8.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5408.4.2 Job Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5408.4.3 Format for User-Defined Basis Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540

8.5 Mixed Basis Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5428.6 Dual Basis Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5448.7 Auxiliary Basis Sets for RI (Density Fitting) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5458.8 Ghost Atoms and Basis Set Superposition Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550

9 Effective Core Potentials 5529.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5529.2 ECP Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5539.3 Built-In ECPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5539.4 User-Defined ECPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5569.5 ECPs and Electron Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5599.6 Forces and Vibrational Frequencies with ECPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5599.7 A Brief Guide to Q-CHEM’s Built-In ECPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560

9.7.1 The fit-HWMB ECP at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5619.7.2 The fit-LANL2DZ ECP at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5629.7.3 The fit-SBKJC ECP at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5639.7.4 The fit-CRENBS ECP at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5649.7.5 The fit-CRENBL ECP at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5659.7.6 The SRLC ECP at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5669.7.7 The SRSC ECP at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5679.7.8 The Karlsruhe “def2” ECP at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568


10 Exploring Potential Energy Surfaces: Critical Points and Molecular Dynamics 57110.1 Equilibrium Geometries and Transition-State Structures . . . . . . . . . . . . . . . . . . . . . . . . . 571

10.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57110.1.2 Job Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57210.1.3 Hessian-Free Characterization of Stationary Points . . . . . . . . . . . . . . . . . . . . . . . . 579

10.2 Improved Algorithms for Transition-Structure Optimization . . . . . . . . . . . . . . . . . . . . . . . 58210.2.1 Freezing String Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58210.2.2 Hessian-Free Transition-State Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58410.2.3 Improved Dimer Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585

10.3 Constrained Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58610.3.1 Geometry Optimization with General Constraints . . . . . . . . . . . . . . . . . . . . . . . . 58710.3.2 Frozen Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58710.3.3 Dummy Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58810.3.4 Dummy Atom Placement in Dihedral Constraints . . . . . . . . . . . . . . . . . . . . . . . . 58810.3.5 Additional Atom Connectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58910.3.6 Application of External Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590

CONTENTS 10

10.4 Potential Energy Scans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59110.5 Intrinsic Reaction Coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59510.6 Nonadiabatic Couplings and Optimization of Minimum-Energy Crossing Points . . . . . . . . . . . . 598

10.6.1 Nonadiabatic Couplings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59810.6.2 Job Control and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59910.6.3 Minimum-Energy Crossing Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60210.6.4 Job Control and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60310.6.5 State-Tracking Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608

10.7 Ab Initio Molecular Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60910.7.1 Overview and Basic Job Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60910.7.2 Additional Job Control and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61510.7.3 Thermostats: Sampling the NVT Ensemble . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61910.7.4 Vibrational Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62310.7.5 Quasi-Classical Molecular Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62410.7.6 Fewest-Switches Surface Hopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629

10.8 Ab Initio Path Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63410.8.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63410.8.2 Job Control and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636


11 Molecular Properties and Analysis 64311.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64311.2 Wave Function Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644

11.2.1 Population Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64411.2.2 Multipole Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65111.2.3 Symmetry Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65211.2.4 Localized Orbital Bonding Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65311.2.5 Basic Excited-State Analysis of CIS and TDDFT Wave Functions . . . . . . . . . . . . . . . . 65411.2.6 General Excited-State Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656

11.3 Interface to the NBO Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66211.4 Orbital Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66211.5 Visualizing and Plotting Orbitals, Densities, and Other Volumetric Data . . . . . . . . . . . . . . . . 664

11.5.1 Visualizing Orbitals Using MOLDEN and MACMOLPLT . . . . . . . . . . . . . . . . . . . . 66511.5.2 Visualization of Natural Transition Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66611.5.3 Generation of Volumetric Data Using $plots . . . . . . . . . . . . . . . . . . . . . . . . . . . 66711.5.4 Direct Generation of “Cube” Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67211.5.5 NCI Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67511.5.6 Electrostatic Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67511.5.7 ELF Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677

11.6 Spin and Charge Densities at the Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67811.7 Atoms in Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67911.8 Distributed Multipole Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67911.9 Intracules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 680

11.9.1 Position Intracules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68011.9.2 Momentum Intracules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68111.9.3 Wigner Intracules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68211.9.4 Intracule Job Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68311.9.5 Format for the $intracule Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685

11.10 Harmonic Vibrational Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686

CONTENTS 11

11.10.1 Job Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68711.10.2 Isotopic Substitutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68911.10.3 Partial Hessian Vibrational Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69111.10.4 Localized Mode Vibrational Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693

11.11 Anharmonic Vibrational Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69511.11.1 Vibration Configuration Interaction Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69611.11.2 Vibrational Perturbation Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69711.11.3 Transition-Optimized Shifted Hermite Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 69711.11.4 Job Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698

11.12 Linear-Scaling Computation of Electric Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70211.12.1 $fdpfreq Input Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70311.12.2 Job Control for the MOProp Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70411.12.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709

11.13 NMR and Other Magnetic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70911.13.1 NMR Chemical Shifts and J-Couplings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71011.13.2 Linear-Scaling NMR Chemical Shift Calculations . . . . . . . . . . . . . . . . . . . . . . . . 71611.13.3 Additional Magnetic Field-Related Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 718

11.14 Finite-Field Calculation of (Hyper)Polarizabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72011.14.1 Numerical Calculation of Static Polarizabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 72111.14.2 Romberg Finite-Field Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 722

11.15 General Response Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72511.15.1 Job Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72611.15.2 $response Section and Operator Specification . . . . . . . . . . . . . . . . . . . . . . . . . . 73111.15.3 Examples Including $response Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733

11.16 Electronic Couplings for Electron- and Energy Transfer . . . . . . . . . . . . . . . . . . . . . . . . . 73411.16.1 Eigenstate-Based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73411.16.2 Diabatic-State-Based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 741

11.17 Population of Effectively Unpaired Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74911.18 Molecular Junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 770

12 Molecules in Complex Environments: Solvent Models, QM/MM and QM/EFP Features, DensityEmbedding 77712.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77712.2 Chemical Solvent Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777

12.2.1 Kirkwood-Onsager Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78012.2.2 Polarizable Continuum Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78312.2.3 PCM Job Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78912.2.4 Linear-Scaling QM/MM/PCM Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 81012.2.5 Isodensity Implementation of SS(V)PE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81312.2.6 Composite Method for Implicit Representation of Solvent (CMIRS) . . . . . . . . . . . . . . . 82212.2.7 COSMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82512.2.8 SM8, SM12, and SMD Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82512.2.9 Langevin Dipoles Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83212.2.10 Poisson Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834

12.3 Stand-Alone QM/MM Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84912.3.1 Available QM/MM Methods and Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84912.3.2 Using the Stand-Alone QM/MM Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85012.3.3 Additional Job Control Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 858

CONTENTS 12

12.3.4 QM/MM Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86112.4 Q-CHEM/CHARMM Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86312.5 Effective Fragment Potential Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867

12.5.1 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86712.5.2 Excited-State Calculations with EFP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87012.5.3 Extension to Macromolecules: Fragmented EFP Scheme . . . . . . . . . . . . . . . . . . . . . 87112.5.4 Running EFP Jobs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87312.5.5 Library of Fragments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87312.5.6 Calculation of User-Defined EFP Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . 87412.5.7 fEFP Input Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87712.5.8 Input keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87812.5.9 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884

12.6 Projector-Based Density Embedding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88712.7 Frozen-Density Embedding Theory based methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 892

12.7.1 FDE-ADC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89212.8 Polarizable Embedding Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 898References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905

13 Fragment-Based Methods 91113.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91113.2 Specifying Fragments in the $molecule Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91213.3 FRAGMO Initial Guess for SCF Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91313.4 Locally-Projected SCF Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 917

13.4.1 Locally-Projected SCF Methods with Single Roothaan-Step Correction . . . . . . . . . . . . . 91813.4.2 Roothaan-Step Corrections to the FRAGMO Initial Guess . . . . . . . . . . . . . . . . . . . . 91913.4.3 Automated Evaluation of the Basis-Set Superposition Error . . . . . . . . . . . . . . . . . . . 919

13.5 The First-Generation ALMO-EDA and Charge-Transfer Analysis (CTA) . . . . . . . . . . . . . . . . 92013.5.1 Energy Decomposition Analysis Based on Absolutely Localized Molecular Orbitals . . . . . . 92013.5.2 Analysis of Charge-Transfer Based on Complementary Occupied/Virtual Pairs . . . . . . . . . 924

13.6 Job Control for Locally-Projected SCF Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92513.7 The Second-Generation ALMO-EDA Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 929

13.7.1 Generalized SCFMI Calculations and Additional Features . . . . . . . . . . . . . . . . . . . . 92913.7.2 Polarization Energy with a Well-defined Basis Set Limit . . . . . . . . . . . . . . . . . . . . . 93113.7.3 Further Decomposition of the Frozen Interaction Energy . . . . . . . . . . . . . . . . . . . . . 93313.7.4 Job Control for EDA2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93613.7.5 Visualization Tools in EDA2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 941

13.8 The MP2 ALMO-EDA Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94613.9 The Adiabatic ALMO-EDA Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94713.10 ALMO-EDA Involving Excited-State Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 952

13.10.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95213.10.2 Job Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953

13.11 The Explicit Polarization (XPol) Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95713.11.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95713.11.2 Supplementing XPol with Empirical Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . 95813.11.3 Job Control Variables for XPol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95813.11.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 960

13.12 Symmetry-Adapted Perturbation Theory (SAPT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96213.12.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96213.12.2 Job Control for SAPT Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 965

CONTENTS 13

13.13 The XPol+SAPT (XSAPT) Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96813.13.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96913.13.2 AO-XSAPT(KS)+aiD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 971

13.14 Energy Decomposition Analysis based on SAPT/cDFT . . . . . . . . . . . . . . . . . . . . . . . . . 97413.15 The Many-Body Expansion Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97813.16 Ab Initio Frenkel Davydov Exciton Model (AIFDEM) . . . . . . . . . . . . . . . . . . . . . . . . . . 982

13.16.1 Job Control and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98413.17 TDDFT for Molecular Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98713.18 The ALMO-CIS and ALMO-CIS+CT Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 989References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 992

A Geometry Optimization with Q-CHEM 996A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 996A.2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 997A.3 Eigenvector-Following (EF) Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 999A.4 Delocalized Internal Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1001A.5 Constrained Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1003A.6 Delocalized Internal Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1005A.7 GDIIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1007References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1008

B AOINTS 1010B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1010B.2 Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1010B.3 AOINTS: Calculating ERIs with Q-CHEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1011B.4 Shell-Pair Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1012B.5 Shell-Quartets and Integral Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1012B.6 Fundamental ERI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1013B.7 Angular Momentum Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1013B.8 Contraction Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1013B.9 Quadratic Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1014B.10 Algorithm Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1014B.11 More Efficient Hartree–Fock Gradient and Hessian Evaluations . . . . . . . . . . . . . . . . . . . . .1014B.12 User-Controllable Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1015References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1015

C Q-CHEM Quick Reference 1017C.1 Q-CHEM Text Input Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1017

C.1.1 Keyword: $molecule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1017C.1.2 Keyword: $rem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1018C.1.3 Keyword: $basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1018C.1.4 Keyword: $comment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1019C.1.5 Keyword: $ecp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1019C.1.6 Keyword: $empirical_dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1019C.1.7 Keyword: $external_charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1019C.1.8 Keyword: $intracule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1020C.1.9 Keyword: $isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1020C.1.10 Keyword: $multipole_field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1020C.1.11 Keyword: $nbo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1020

Chapter 0: CONTENTS 14

C.1.12 Keyword: $occupied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1021C.1.13 Keyword: $opt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1021C.1.14 Keyword: $svp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1022C.1.15 Keyword: $svpirf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1022C.1.16 Keyword: $plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1022C.1.17 Keyword: $localized_diabatization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1022C.1.18 Keyword: $van_der_waals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1023C.1.19 Keyword: $xc_functional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1023

C.2 Geometry Optimization with General Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . .1023C.3 $rem Variable List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1024

C.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1025C.3.2 SCF Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1025C.3.3 DFT Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1025C.3.4 Large Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1026C.3.5 Correlated Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1026C.3.6 Correlated Methods Handled by CCMAN and CCMAN2 . . . . . . . . . . . . . . . . . . . .1026C.3.7 Perfect pairing, Coupled cluster valence bond, and related methods . . . . . . . . . . . . . . .1027C.3.8 Excited States: CIS, TDDFT, SF-XCIS and SOS-CIS(D) . . . . . . . . . . . . . . . . . . . .1027C.3.9 Excited States: EOM-CC and CI Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . .1027C.3.10 Geometry Optimizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1028C.3.11 Vibrational Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1028C.3.12 Reaction Coordinate Following . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1028C.3.13 NMR Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1028C.3.14 Wave function Analysis and Molecular Properties . . . . . . . . . . . . . . . . . . . . . . . .1029C.3.15 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1029C.3.16 Printing Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1029C.3.17 Resource Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1029

C.4 Alphabetical Listing of $rem Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1029References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1246

Chapter 1

Introduction

1.1 About This Manual

This manual is intended as a general-purpose user’s guide for Q-CHEM, a modern electronic structure program. Themanual contains background information that describes Q-CHEM methods and user-selected parameters. It is assumedthat the user has some familiarity with the Unix/Linux environment, an ASCII file editor, and a basic understanding ofquantum chemistry.

After installing Q-CHEM and making necessary adjustments to your user account, it is recommended that particularattention be given to Chapters 3 and 4. The latter, which describes Q-CHEM’s self-consistent field capabilities, hasbeen formatted so that advanced users can quickly find the information they require while supplying new users witha moderate level of important background information. This format has been maintained throughout the manual, andevery attempt has been made to guide the user forward and backward to other relevant information so that a logicalprogression through this manual is not necessary.

Documentation for IQMOL, a graphical user interface designed for use with Q-CHEM, can be found on the www.iqmol.org websitge. IQMOL functions as a molecular structure builder, as an interface for local or remote submis-sion of Q-CHEM jobs, and as a post-calculation visualization program for densities and molecular orbitals.

1.1.0.1 Chapter Summaries

Ch. 1: General overview of Q-CHEM’s features, contributors, and contact information.

Ch. 2: Procedures to install, test, and run Q-CHEM on your machine.

Ch. 3: Overview of the Q-CHEM command-line input.

Ch. 4: Running ground-state self-consistent field calculations.

Ch. 5: Details specific to running density functional theory (DFT) calculations.

Ch. 6: Running post-Hartree-Fock correlated wave function calculations for ground states.

Ch. 7: Running calculations for excited states and open-shell species.

Ch. 8: Using Q-CHEM’s built-in basis sets, or specifying a user-defined basis set.

Ch. 9: Using Q-CHEM’s effective core potential capabilities.

Ch. 10: Options available for exploring potential energy surfaces, such as determining critical points (transition statesand local minima on a single surface, or minimum-energy crossing points between surfaces) as well as ab initiomolecular dynamics.

www.iqmol.orgwww.iqmol.org

Chapter 1: Introduction 16

Ch. 11: Molecular properties and a posteriori wave function analysis.

Ch. 12: Methods for molecules in complex environments, including implicit solvation models, QM/MM models, theEffective Fragment Potential, and density embedding.

Ch. 13: Fragment-based approaches for efficient calculations on large systems, calculation of non-covalent interac-tions, and energy decomposition analysis.

App. A: Overview of the OPTIMIZE package used for determining molecular geometry critical points.

App. B: Overview of the AOINTS library, which contains some of the fastest two-electron integral code currentlyavailable.

App. C: Quick-reference section containing an alphabetized list of job control variables.

1.2 Q-CHEM, Inc.

1.2.1 Contact Information and Customer Support

For general information regarding Q-CHEM program, visit www.q-chem.com. Full customer support is promptlyprovided via telephone or email ([email protected]) for those customers who have purchased Q-CHEM’s“QMP” maintenance contract. In addition to free customer support, this contract provides discounts on future updatesand releases of Q-CHEM. For details of the maintenance contract please see www.q-chem.com.

1.2.2 About the Company

Q-CHEM, Inc. was founded in 1993 and was based in Pittsburgh, PA until 2013, when it relocated to Pleasanton,CA. Q-CHEM’s scientific contributors include leading quantum chemists around the world. The company is governedby the Board of Directors which currently consists of Peter Gill (Canberra), Anna Krylov (USC), John Herbert (OhioState), and Hilary Pople. Fritz Schaefer (Georgia) is a Board Member Emeritus. Martin Head-Gordon is a ScientificAdvisor to the Board. The close coupling between leading university research groups and Q-CHEM Inc. ensures thatthe methods and algorithms available in Q-CHEM are state-of-the-art.

In order to create this technology, the founders of Q-CHEM, Inc. built entirely new methodologies from the ground up,using the latest algorithms and modern programming techniques. Since 1993, well over 300 person-years have beendevoted to the development of the Q-CHEM program. The author list of the program shows the full list of contributorsto the current version, and the journal citations for Q-CHEM versions 2, 3, and 41,3,4 illustrate the breadth of the Q-CHEM developer community. The current group of developers consist of more than 100 people in 9 countries. A briefhistory of Q-CHEM is given in the recent article Q-Chem: An Engine for Innovation.2

1.2.3 Company Mission

The mission of Q-CHEM, Inc. is to develop, distribute, and support innovative and sustainable quantum chemistry soft-ware for industrial, government and academic researchers in the chemical, petrochemical, biochemical, pharmaceuticaland material sciences.

http://www.q-chem.commailto:[email protected]://www.q-chem.com


1.3 Q-CHEM Features

Quantum chemistry methods have proven invaluable for studying chemical and physical properties of molecules. TheQ-CHEM system brings together a variety of advanced computational methods and tools in an integrated ab initiosoftware package, greatly improving the speed and accuracy of calculations being performed. In addition, Q-CHEMwill accommodate larger molecular structures than previously possible, with no loss in accuracy, thereby bringing thepower of quantum chemistry to critical research projects for which this tool was previously unavailable. Below is areverse-chronological listing of new features added to Q-CHEM.

1.3.1 New Features in Q-CHEM 5.2

• Changes in default settings:

– Single-node shared-memory parallelism becomes default and recommended for most jobs. New commandline key -mpi is required to use distributed-memory MPI-parallel features (Section 2.8).

– Pure basis functions are used by default with BASIS=GEN.

– Default number of grid points in Lebedev grids in solvent models changed from 302 to 194 points (non-Hydrogen) and 110 points (Hydrogen) atoms.

– Use of SWIG charges for SMx models.

– Input format for XPol, SAPT and XSAPT, and MBE jobs has changed.

– Use EDA2 as the default driver for ALMO-EDA.

– Frozen core approximation no longer applied by default in RAS-CI calculations.

• General improvements:

– Increased availability of basis sets: High angular momentum basis functions (up to k-functions) supportedfor most SCF, RI-MP2, CC, EOM-CC, ADC calculations.

– Streamlined input format for RI-SCF calculations.

– Added the def2- family of density fitted (RI) basis sets for SCF and post-SCF calculations (Courtesy of Dr.Florian Weigend).

– On-the-fly generation for the superposition of atomic densities guess for SCF (K. Fenk, J. Herbert).

– Reintroduction of legacy ECPs without fitting.

– Easy specification of basis sets on fragments, reading of basis sets from an external file (Z. Pei and Y. Shao).

• Improvements to the DFT capabilities:

– Support for analytic frequency calculations using meta-GGA density functinoals (available only with shared-memory parallelism).

– Support for analytic frequency calculations using resolution-of-the-identity (density-fitted) Coulomb (avail-able only with shared-memory parallelism).

– Improved performance of analytic partial hessian calculations using DFT.

– New density functionals: revM06, revM11 (P. Morgante and R. Peverati).

• Improvements in implicit solvation models:

– Revised PCM tessellation grids for improved performance (J. Herbert).

– Improved performance of the general SCF program with SMx solvation models (Y. Mao).


• New MP2 features:

– Addition of regularized orbital-optimized second-order Møller-Plesset perturbation theory (κ-OOMP2) (J.Lee, M. Head-Gordon; Section 6.6.5).

• Enhancements to the coupled-cluster package:

– Mixed-precision CCSD and EOM-CCSD (P. Pokhilko, E. Epifanovsky, A.I. Krylov, with contributionsfrom I. Kaliman, K. Nanda, M. Vidal, S. Coriani; Sections 6.15 and 7.8.10).

– Damped response, dynamic polarizabilities for two-electron absorption using EOM-CC (K. Nanda and A.I.Krylov).

– Improved evaluation of spin-orbit coupling constants across EOM-CC states (P. Pokhilko and A.I. Krylov).

– Better handling of linear point groups in ADC and CC methods.

– Improved performance of disk-based ADC/CC algorithms.

– Projected and Voronoi CAP for CAP-EOM-CC/CC calculations (K. Bravaya, A. Kunitsa; Section 7.8.7).

– Dynamic polarizabilities for CCSD and EOM-CCSD (K. Nanda, A.I. Krylov; Section 7.8.18.4).

– New feaures for SOC calculation and analysis (P. Pokhilko, A.I. Krylov; Section 7.8.18.2).

– Dyson orbitals for CVS-EOM-CCSD (M. Vidal, S. Coriani, A.I. Krylov; Section 7.8.6).

• Improvements in energy decomposition analysis methods:

– Added electron density difference (EDD) plots and the ETS-NOCV analysis (Y. Mao).

– Added support for PCM and SMD solvation models in ALMO-EDA (Y. Mao).

– Resolved several issues that caused instabilities in MP2-EDA calculations (Y. Mao).

• New capabilities for explicit solvation modeling:

– Polarizable Embedding (PE) Model for ground-state and ADC calculations (M. Scheurer; Section 12.8).

• Other new methods and capabilities:

– Incremental FCI method (P. Zimmerman).

– Transition potential DFT for core-valence excitations.

– Analytic evaluation of Raman intensities (Z. Pei and Y. Shao).


• Improved OpenMP parallelization for:

– SCF vibrational frequency calculations (Z. Gan)

– RIMP2 gradient (F. Rob, Joonho Lee, X. Feng, & E. Epifanovsky)

• Complete active space self-consistent field (CASSCF) and adaptive sampling CI (D. Levine, M. Head-Gordon)

• Tkatchenko-Scheffler van der Waals method (Section 5.7.4) and many-body dispersion method (Section 5.7.5)(D. Barton, Ka Un Lao, & R. DiStasio)


– Core/valence separation for EOM-CCSD core-level excited and ionized states (M. Vidal, A.I. Krylov, X.Feng, E. Epifanovsky & S. Coriani), Section 7.8.6.


– NTO analysis of two-photon transitions (K. Nanda & A.I. Krylov), Section 7.8.18.1.

– NTO analysis of the complex-valued EOM wave functions (A.I. Krylov, W. Skomorowski), Section 7.8.18.

– Analytic gradients for Cholesky-decomposed and resolution-of-identity CCSD and EOM-CCSD (X. Feng,A.I. Krylov).

– Improved performance, reduced disk usage by coupled-cluster methods (E. Epifanovsky, I. Kaliman, & X.Feng).

• New features in NTO analysis: Energies of NTOs (A.I. Krylov), Section 11.2.6.

• Finite-difference evaluation of non-linear properties (M. de Wergifosse & A.I. Krylov), Section 11.14.2.

• Poisson boundary conditions for SCF calculations (M. Coons & J. Herbert), Section 12.2.10.

– Enables quantum chemistry calculations in an arbitrary (anisotropic and inhomogeneous) dielectric envi-ronment.

– Nonequilibrium solvent corrections for vertical ionization energies.

• Energy decomposition analysis (EDA):

– EDA based on symmetry-adapted perturbation theory and constrained DFT (SAPT/cDFT-EDA), Section 13.14(Ka Un Lao, K. Fenk, & J. Herbert)

– ALMO-EDA for CIS and TDDFT/TDA excited states, Section 13.10 (Qinghui Ge, Yuezhi Mao, & M.Head-Gordon)

– Perturbative ALMO-CTA and COVP analysis in EDA2 (Yuezhi Mao & M. Head-Gordon)

• Analytic derivative couplings for computing excitation/vibration energy couplings within the ab initio Frenkel-Davydov exciton model (A. Morrison & J. Herbert), Section 13.16.

• Hyperfine spin-spin couplings and nuclear electric quadrupole couplings, Section 11.13.3 (E. Berquist & D.Lambrecht)

• Variational two-electron reduced-density-matrix (v2RDM) and v2RDM-driven complete active space self-consistentfield (v2RDM-CASSCF) method (G. Gidofalvi, L. Koulias, J.W. Mullinax, & A.E. DePrince III)

• Frozen and restrained potential energy scans, Section 10.4 (Yihan Shao)

• Extended ESP charge fitting procedure to the computation of RESP charges (Yihan Shao)



– Analytic gradients for Cholesky-decomposed CCSD and EOM-CCSD; efficiency improvement for canon-ical CCSD and EOM-CCSD gradients (X. Feng, E. Epifanovsky).

– CAP-EOM-CCSD analytic gradients (Z. Benda and T.-C. Jagau) and Dyson orbitals for metastable states(T.-C. Jagau, A.I. Krylov), Section 7.8.7).

– CAP-EOM-MP2 method (A. Kunitsa, K. Bravaya).

– Evaluation of polarizabilities using CCSD and EOM-CCSD (EE and SF) wave functions using full deriva-tive formulation (K. Nanda and A. Krylov, Section 7.8.18.4).

– Evaluation of 〈S2〉 for EOM-CCSD wave functions (X. Feng).


– Evaluation of NACs for EOM-CCSD wave functions (S. Faraji, A. Krylov, E. Epifanovski, X. Feng, Section7.8.18.3).

– Efficiency improvement and new multicore-parallel code for (T) correction (I. Kaliman).

– New coupled-cluster based methods for core states (A. Krylov).

• New capabilities for implicit solvation modeling:

– PCM capabilities for computing vertical excitation, ionization, and electron attachment energies at EOM-CC and MP2 levels (Section 7.8.13).

– State-specific equilibrium and non-equilibrium solvation for all orders and variants of ADC (J. M. Mewesand A. Dreuw; Section 7.9.7).

– Poisson equation boundary conditions allowing use of an arbitrary, anisotropic dielectric function ε(r),with full treatment of volume polarization (M. P. Coons and J. M. Herbert; Section 12.2.10).

– Composite Model for Implicit Representation of Solvent (CMIRS), an accurate model for free energies ofsolvation (Section 12.2.6)

• New density functionals (N. Mardirossian and M. Head-Gordon; Section 5.3):

– GGA functionals: BEEF-vdW, HLE16, KT1, KT2, KT3, rVV10

– Meta-GGA functionals: B97M-rV, BLOC, mBEEF, oTPSS, TM

– Hybrids: CAM-QTP(00), CAM-QTP(01), HSE-HJS, LC-ωPBE08, MN15, rCAM-B3LYP, WC04, WP04

– Double hybrids: B2GP-PLYP, DSD-PBEB95-D3, DSD-PBEP86-D3, DSD-PBEPBE-D3, LS1DH-PBE,PBE-QIDH, PTPSS-D3, PWPB95-D3

– Grimme’s PBEh-3c “low-cost” composite method

– rVV10 non-local correlation functional

• Additional DFT developments:

– New forms of DFT-D3 (J. Witte; Section 5.7.2).

– New standard integration grids, SG-2 and SG-3 (S. Dasgupta and J. M. Herbert; Section 5.5.2).

– More efficient propagator algorithms for real-time TDDFT (Y. Zhu and J. M. Herbert; Section 7.12).

• New integral package for for computing effective core potential (ECP) integrals (S. C. McKenzie, E. Epi-fanovsky; Chapter 9).

– More efficient analytic algorithms for energies and first derivatives.

– Support for arbitrary projector angular momentum.

– Support up to h angular momentum in the basis set.

• Analytic derivative couplings for the ab initio Frenkel-Davydov exciton model (A. F. Morrison and J. M. Herbert;Section 13.16).

• New ALMO-based energy decomposition analysis (EDA) methods:

– The second-generation ALMO-EDA methods for DFT (P. R. Horn, Y. Mao and M. Head-Gordon; Sec-tion 13.7)

– The extension of ALMO-EDA to RIMP2 theory (J. Thirman and M. Head-Gordon; Section 13.8)

– The “adiabatic" EDA method for decomposing changes in molecular properties (Y. Mao, P. R. Horn andM. Head-Gordon; Section 13.9)


• Wave function correlation capabilities:

– Coupled cluster valence bond (CCVB) method for describing open-shell molecules with strong spin corre-lations (D. W. Small and M. Head-Gordon; Section 6.16.2).

– Implementation of coupled-cluster valence bond with singles and doubles (CCVB-SD) for closed-shellspecies (J. Lee, D. W. Small and M. Head-Gordon; Section 6.10.4).

Note: Several important changes in Q-CHEM’s default settings have occurred since version 4.4.

• Core electrons are now frozen by default in most post-Hartree-Fock calculations; see Section 6.2.

• The keywords for calculation of SOCs and NACs were renamed for consistency between different meth-ods.

• Some newer density functionals now use either the SG-2 or SG-3 quadrature grid by default, whereasall functionals used SG-1 by default in v. 4.4. Table 5.3 lists the default grid for various classes offunctionals.


• occ-RI-K algorithm for the evaluation of exact exchange in energy and force calculations (S. Manzer, F. Rob andM. Head-Gordon; Section 4.6.9)

• Combinatorially-optimized exchange-correlation functionals (N. Mardirossian and M. Head-Gordon; Section 5.3):

– ωB97M-V (range-separated hybrid, meta-GGA functional with VV10 non-local correlation)

– B97M-V (meta-GGA functional with VV10 non-local correlation)

– ωB97X-V (range-separated hybrid functional with VV10 non-local correlation)

• Implementation of new exchange-correlation functionals from the literature (N. Mardirossian and M. Head-Gordon; Section 5.3). These include:

– MGGA_MS0, MGGA_MS1, MGGA_MS2, MGGA_MS2h, MGGA_MVS, MGGA_MVSh, PKZB, revTPSS,revTPSSh, SCAN, SCAN0, PBEsol, revPBE, revPBE0

– N12, N12-SX, GAM, MN12-L, MN12-SX, MN15-L, dlDF

– VV10, LC-VV10

– B97-K, B97-D3(0), B97-3, τ -HCTH, τ -HCTHh

– SRC1-R1, SRC1-R2, SRC2-R1, SRC2-R2

– B1LYP, B1PW91, MPW1K, LRC-BOP, BHH, BB1K, PW6B95, PWB6K, B2PLYP

• Hessian-free minimum point verification (S. M. Sharada and M. Head-Gordon; Section 10.2.2)

• Exciton-based excited-state models:

– Ab initio Frenkel-Davydov model for coupled excitations in multi-chromophore systems (A. F. Morrisonand J. M. Herbert; Section 13.16).

– TDDFT for molecular interactions [TDDFT(MI)], a set of local excitation approximations for efficientTDDFT calculations in multi-chromophore systems and for single chromophores in the presence of explicitsolvent molecules (J. Liu and J. M. Herbert; Section 13.17).

• Improvements to many-body and XSAPT methods (K. U. Lao and J. M. Herbert)


– MPI-parallelized many-body expansion with analytic gradient (Section 13.15).

– Efficient atomic orbital implementation of XSAPT for both closed- and open-shell systems (Section 13.13.2).

• Thermostats for ab initio molecular dynamics (R. P. Steele and J. M. Herbert).

• Analytic energy gradient for the Ewald summation in QM/MM calculations (Z. C. Holden and J. M. Herbert)

• Zeolite QM/MM methods (J. Gomes and M. Head-Gordon).

• EOM-MP2 methods for excitation, ionization and electron attachment energies (A. Kunitsa and K. Bravaya;Section 7.8.11).

• Evaluation of polarizabilities using CCSD and EOM-CCSD wave functions (Section 7.8.18.4, K. Nanda and A. I.Krylov)

• Distributed-memory parallel implementation of CC and EOM-CC methods and performance improvements indisk-based algorithms (E. Epifanovsky, I. Kaliman, and A. I. Krylov)

• Improvements to the maximum overlap method (MOM) for SCF calculations (A. T. B. Gilbert; Section 7.5).

• Non-equilibrium PCM method to describe solvent effects in ADC excited-state calculations (J.-M. Mewes andA. Dreuw; Section 7.9.7).

• Spin-flip ADC method (D. Lefrancois and A. Dreuw; Section 7.9.5).


• Analytic derivative couplings (i.e., non-adiabatic couplings) between electronic states computed at the CIS, spin-flip CIS, TDDFT, and spin-flip TDDFT levels (S. Fatehi, Q. Ou, J. E. Subotnik, X. Zhang, and J. M. Herbert;Section 10.6).

• A third-generation (“+D3”) dispersion potential for XSAPT (K. U. Lao and J. M. Herbert; Section 13.13).

• Non-equilibrium PCM for computing vertical excitation energies (at the TDDFT level) and ionization energiesin solution (Z.-Q. You and J. M. Herbert; Section 12.2.2.3).

• Spin-orbit couplings between electronic states for CC and EOM-CC wave functions (E. Epifanovsky, J. Gauss,and A. I. Krylov; Section 7.8.18.2).

• PARI-K method for evaluation of exact exchange, which affords dramatic speed-ups for triple-ζ and larger basissets in hybrid DFT calculations (S. Manzer and M. Head-Gordon).

• Transition moments and cross sections for two-photon absorption using EOM-CC wave functions (K. Nanda andA. I. Krylov; Section 7.8.18.1).

• New excited-state analysis for ADC and CC/EOM-CC methods (M. Wormit; Section 11.2.6).

• New Dyson orbital code for EOM-IP-CCSD and EOM-EA-CCSD (A. Gunina and A. I. Krylov; Section 7.8.25).

• Transition moments, state dipole moments, and Dyson orbitals for CAP-EOM-CCSD (T.-C. Jagau and A. I. Krylov;Sections 7.8.7 and 7.8.25).

• TAO-DFT: Thermally-assisted-occupation density functional theory (J.-D. Chai; Section 5.12).

• MP2[V], a dual basis method that approximates the MP2 energy (J. Deng and A. Gilbert).


• Iterative Hirshfeld population analysis for charged systems, and CM5 semi-empirical charge scheme (K. U. Laoand J. M. Herbert; Section 11.2.1).

• New DFT functionals: (Section 5.3):

– Long-range corrected functionals with empirical dispersion-: ωM05-D, ωB97X-D3 and ωM06-D3 (Y.-S.Lin, K. Hui, and J.-D. Chai.

– PBE0_DH and PBE0_2 double-hybrid functionals (K. Hui and J.-D. Chai; Section 5.9).

– AK13 (K. Hui and J.-D. Chai).

– LFAs asymptotic correction scheme (P.-T. Fang and J.-D. Chai).

• LDA/GGA fundamental gap using a frozen-orbital approximation (K. Hui and J.-D. Chai; Section 5.11).


• Input file changes:

– New keyword METHOD simplifies input in most cases by replacing the pair of keywords EXCHANGE andCORRELATION (see Chapter 4).

– Keywords for requesting excited-state calculations have been modified and simplified (see Chapter 7 fordetails).

– Keywords for solvation models have been modified and simplified (see Section 12.2 for details).

• New features for NMR calculations including spin-spin couplings (J. Kussmann, A. Luenser, and C. Ochsenfeld;Section 11.13.1).

• New built-in basis sets (see Chapter 8).

• New features and performance improvements in EOM-CC:

– EOM-CC methods extended to treat meta-stable electronic states (resonances) via complex scaling andcomplex absorbing potentials (D. Zuev, T.-C. Jagau, Y. Shao, and A. I. Krylov; Section 7.8.7).

– New features added to EOM-CC iterative solvers, such as methods for interior eigenvalues and user-specified guesses (D. Zuev; Section 7.8.14).

– Multi-threaded parallel code for (EOM-)CC gradients and improved CCSD(T) performance.

• New features and performance improvements in ADC methods (M. Wormit, A. Dreuw):

– RI-ADC can tackle much larger systems at reduced cost (Section 7.9.2).

– SOS-ADC methods (Section 7.9.3).

– State-to-state properties for ADC (Section 7.9.6).

• SM12 implicit solvation model (A. V. Marenich, D. G. Truhlar, and Y. Shao; Section 12.2.8.1).

• Interface to NBO v. 6 (Section 11.3).

• Optimization of MECPs between electronic states at the SOS-CIS(D) and TDDFT levels (X. Zhang and J. M.Herbert; Section 10.6.3).

• ROKS method for ∆SCF calculations of excited states (T. Kowalczyk and T. Van Voorhis; Section 7.6).

• Fragment-based initial guess for SCF methods (Section 13.3).


• Pseudo-fractional occupation number method for improved SCF convergence in small-gap systems (D. S. Lam-brecht; Section 4.5.10).

• Density embedding scheme (B. J. Albrecht, E. Berquist, and D. S. Lambrecht; Section 12.6).

• New features and enhancements in fragment-based many-body expansion methods (K. U. Lao and J. M. Herbert):

– XSAPT(KS)+D: A dispersion corrected version of symmetry-adapted perturbation theory for fast and ac-curate calculation of interaction energies in non-covalent clusters (Section 13.13).

– Many-body expansion and fragment molecular orbital (FMO) methods for clusters (Section 13.15).

• Periodic boundary conditions with proper Ewald summation, for energies only (Z. C. Holden and J. M. Herbert;Section 12.3).


• Fundamental algorithms:

– Improved parallel performance at all levels including new OpenMP capabilities for Hartree-Fock, DFT,MP2, and coupled cluster theory (Z. Gan, E. Epifanovsky, M. Goldey, and Y. Shao; Section 2.8).

– Significantly enhanced ECP capabilities, including gradients and frequencies in all basis sets for which theenergy can be evaluated (Y. Shao and M. Head-Gordon; Chap. 9).

• SCF and DFT capabilities:

– TDDFT energy with the M06, M08, and M11 series of functionals.

– XYGJ-OS analytical energy gradient.

– TDDFT/C-PCM excitation energies, gradient, and Hessian (J. Liu and W. Liang; Section 7.3.4).

– Additional features in the maximum overlap method (MOM) approach for converging difficult SCF calcu-lations (N. A. Besley; Section 4.5.6).

• Wave function correlation capabilities:

– RI and Cholesky decomposition implementation of all CC and EOM-CC methods enabling applications tolarger systems with reduced disk and memory requirements and improved performance (E. Epifanovsky,X. Feng, D. Zuev, Y. Shao, and A. I. Krylov; Sections 6.8.5 and 6.8.6).

– Attenuated MP2 theory in the aug-cc-pVDZ and aug-cc-pVTZ basis sets, which truncates two-electronintegrals to cancel basis set superposition error, yielding results for intermolecular interactions that are muchmore accurate than standard MP2 in the same basis set (M. Goldey and M. Head-Gordon; Section 6.7).

– Extended RAS-nSF methodology for ground and excited states involving strong non-dynamical correlation(P. M. Zimmerman, D. Casanova, and M. Head-Gordon; Section 7.10).

– Coupled cluster valence bond (CCVB) method for describing molecules with strong spin correlations (D. W.Small and M. Head-Gordon; Section 6.16.2).

• Searching and scanning potential energy surfaces:

– Potential energy surface scans (Y. Shao; Section 10.4).

– Improvements in automatic transition structure searching via the “freezing string” method, including theability to perform such calculations without a Hessian calculation (S. M. Sharada and M. Head-Gordon;Section 10.2.2).


– Enhancements to partial Hessian vibrational analysis (N. A. Besley; Section 11.10.3).

• Calculating and characterizing inter- and intramolecular interactions

– Extension of EFP to macromolecules: fEFP approach (A. Laurent, D. Ghosh, A. I. Krylov, and L. V.Slipchenko; Section 12.5.3).

– Symmetry-adapted perturbation theory level at the “SAPT0” level, for intermolecular interaction energy de-composition analysis into physically-meaningful components such as electrostatics, induction, dispersion,and exchange. An RI version is also available (L. D. Jacobson, J. M. Herbert; Section 13.12).

– The “explicit polarization” (XPol) monomer-based SCF calculations to compute many-body polarizationeffects in linear-scaling time via charge embedding (Section 13.11), which can be combined either withempirical potentials (e.g., Lennard-Jones) for the non-polarization parts of the intermolecular interactions,or better yet, with SAPT for an ab initio approach called XSAPT that extends SAPT to systems containingmore that two monomers (L. D. Jacobson and J. M. Herbert; Section 13.13).

– Extension of the absolutely-localized molecular orbital (ALMO)-based energy decomposition analysis tounrestricted cases (P. R. Horn and M. Head-Gordon; Section 13.5).

– Calculation of the populations of “effectively unpaired electrons” in low-spin state using DFT, a newmethod of evaluating localized atomic magnetic moments within Kohn-Sham without symmetry break-ing, and Mayer-type bond order analysis with inclusion of static correlation effects (E. I. Proynov; Sec-tion 11.17).

• Quantum transport calculations including electron transmission functions and electron tunneling curr

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Q-Chem 5.2 User's Manual · Q-CHEM User’s Manual Version 5.2 edited by: Dr. Andrew Gilbert Versions 5.0 and 5.1 editors: Dr. Andrew Gilbert Prof. John Herbert Version 4 editors: