Computational Quantum Chemistry - Molecular Structure and Properties in Silico

290 Pages·5.024 MB·English

Computational Quantum Chemistry
Molecular Structure and Properties in Silico
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RSC Theoretical and Computational Chemistry Series
Editor-in-Chief
Jonathan Hirst, University of Nottingham, Nottingham, UK
Series Editors:
1 Kenneth Jordan, University of Pittsburgh, Pittsburgh, USA
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9- Walter Thiel, Max Planck Institute for Coal Research, Mu¨lheim an der Ruhr,
28 Germany
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9 Titles in the Series:
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18 1:Knowledge-basedExpertSystemsinChemistry:NotCountingonComputers
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7 2: Non-Covalent Interactions: Theory and Experiment
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9/ 3: Single-Ion Solvation: Experimental and Theoretical Approaches to Elusive
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10 Thermodynamic Quantities
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doi: 5:ComputationalQuantumChemistry:MolecularStructureandPropertiesin
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Computational Quantum Chemistry
MolecularStructureandPropertiesinSilico
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P Joseph J W McDouall
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oi: RSC Theoretical and Computational Chemistry Series No. 5
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c.or ISBN: 978-1-84973-608-4
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3 o # Joseph J W McDouall, 2013
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d DesignsandPatentsAct1988andtheCopyrightandRelatedRightsRegulations
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s 2003,thispublicationmaynotbereproduced,storedortransmitted,inanyform
ubli orbyanymeans,withoutthepriorpermissioninwritingofTheRoyalSocietyof
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Chemistry or the copyright owner, or in the case of reproduction in accordance
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in accordance with the terms of the licences issued by the appropriate
Reproduction Rights Organization outside the UK. Enquiries concerning
reproduction outside the terms stated here should be sent to The Royal Society
of Chemistry at the address printed on this page.
The RSC is not responsible for individual opinions expressed in this work.
Published by The Royal Society of Chemistry,
Thomas Graham House, Science Park, Milton Road,
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For further information see our web site at www.rsc.org
PrintedintheUnitedKingdombyHenryLingLimited,Dorchester,DT11HD,UK
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9- Preface
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10 InwritingthisbookIhavehadinmindtheneedsofapostgraduatestudent,or
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d putational quantum chemistry. The standard methods of electronic structure
org | theory are presented, as are the principles necessary for the evaluation of
sc. molecular properties. The output of quantum chemical studies, in the form of
bs.r wavefunctions, densities and orbitals, allow connections to be made with
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htt methods of analysis are described. An increasingly important area of research
on is the quantum chemical treatment of molecules containing heavy elements.
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nloaded August 20 ienletcrotrdounciicnsgtrtuhcetubraeckmgerothuondds.theory to some of the commonly used relativistic
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ed graduate course in chemistry. Where necessary I have introduced numerical
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can be studied by theoretical and computational techniques. This chapter
might also find use at an undergraduate level in providing some connections
between quantum mechanics, computing and chemistry. The rest of the book
aims to fill in some of the details associated with the ideas introduced in
Chapter 1. At the risk of being old-fashioned, I have attempted to include
enough detail so that the reader can see how a computational method is
arrived at and how it might be implemented. The very nature of the subject is
technical and requires a, relatively straightforward, mathematical language. I
have made no attempt to use a sentence when an equation would do instead.
Computationalquantumchemistryisalargeandmaturesubject,withmany
specialist sub-fields. In a general introduction such as this there must, of
RSCTheoreticalandComputationalChemistrySeriesNo.5
ComputationalQuantumChemistry:MolecularStructureandPropertiesinSilico
ByJosephJWMcDouall
#JosephJWMcDouall2013
PublishedbytheRoyalSocietyofChemistry,www.rsc.org
v
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vi Preface
necessity, be omissions in the material covered. Some obvious omissions
relatedtoelectronicstructuretheoryincludesemi-empiricalmethods,effective
core potentials and explicitly correlated techniques. I have also omitted any
discussion of dynamics on potential energy surfaces.
Finally I must acknowledge that the preparation of this manuscript owes
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0. To all my family, past and present.
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39/ Chapter 1 Computational Quantum Chemistry
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Dowon 31 1.3.3 LanindkRinegacthtieviEtylectronic Energy with 17
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Correlation 28
1.4.2 Configuration Interaction Methods 35
1.4.3 Perturbation Theory Methods 37
1.4.4 Coupled-Cluster Methods 39
1.4.5 Multiconfigurational and Multireference
Methods 41
1.4.6 Density Functional Methods 46
1.5 How DoYou Select a Theoretical Model? 47
1.6 The Apparatus: Hardware and Software 48
Appendix1APhysicalConstants,AtomicUnitsandConversion
Factors 52
RSCTheoreticalandComputationalChemistrySeriesNo.5
ComputationalQuantumChemistry:MolecularStructureandPropertiesinSilico
ByJosephJWMcDouall
#JosephJWMcDouall2013
PublishedbytheRoyalSocietyofChemistry,www.rsc.org
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x Contents
Appendix1B Elementary Properties of Determinants 53
Appendix1C Diagonalisation of Matrices 56
Appendix1DMoments of Inertia and the Inertia Tensor 60
References 62
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49 2.1.1 Matrix Elements and Integrals 65
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doi: 2.2 Hartree–Fock Theory 74
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2.3.4 Spin Polarisation 92
2.4 Computational Realisation of the Hartree–Fock
Theory 94
2.4.1 The Roothaan–Hall Equations and Basis Set
Expansions 94
2.4.2 OrbitalOptimisation:TheSelf-ConsistentField
(SCF) Procedure for Closed Shells 99
2.4.3 Basis Set Expansions in the UHF Method 99
2.4.4 Convergence of the SCF Process 102
2.4.5 The Direct SCF Method 104
2.5 Molecular Basis Sets 106
2.5.1 Gaussian Type Functions 106
2.5.2 Types of Contracted Basis Sets 113
2.5.3 Basis Set Superposition Error: Non-Covalent
Interactions 116
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Contents xi
2.6 Electron Correlation: Background to Post Hartree–
Fock Methods 118
2.6.1 Brillouin’s Theorem 121
2.6.2 Spin Eigenfunctions/Configuration State
Functions 122
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2.12.3 The Local Density Approximation 175
2.12.4 Generalised Gradient Approximation 176
2.12.5 Meta-Generalised Gradient Approximation 178
2.12.6 Adiabatic Connection: Hybrid Functionals 178
2.12.7 Double Hybrid Functionals 179
2.12.8 Non-Covalent Interactions 180
2.12.9 Ionisation Energies in Density Functional
Theory 181
Appendix 2ATheMethodofLagrangeMultipliers 183
Appendix 2BOrthogonalisationMethods 184
Appendix 2CComputingEigenvaluesandEigenvectorsof
LargeMatrices 187
References 188