Introduction To Computational Chemistry
Second EditionIntroduction toComputational Chemistry
Department of Chemistry, University of Southern Denmark, Odense, DenmarkFrank JensenSecond EditionIntroduction toComputational Chemistry
John Wiley & Sons LtdThe Atrium, Southern Gate, Chichester,West Sussex PO19 8SQ, EnglandTelephone ( 44) 1243 779777This book is printed on acid-free paper responsibly manufactured from sustainable forestryin which at least two trees are planted for each one used for paper production.Typeset in 10/12 Times by SNP Best-set Typesetter Ltd., Hong KongPrinted and bound in Great Britain by Antony RoweISBN-13 978-0-470-01186-7 (HB) ISBN-13 978-0-470-01187-4 (PB)ISBN-10 0-470-01186-6 (PB)ISBN-10 0-470-01187-4 (PB)A catalogue record for this book is available from the British LibraryJensen, Frank.Introduction to computational chemistry / Frank Jensen. – 2nd ed.p. cm.Includes bibliographical references and index.ISBN-13: 978-0-470-01186-7 (cloth : alk. paper)ISBN-10: 0-470-01186-6 (cloth : alk. paper)ISBN-13: 978-0-470-01187-4 (pbk. : alk. paper)ISBN-10: 0-470-01187-4 (pbk. : alk. paper)1. Chemistry, Physical and theoretical – Data processing. 2. Chemistry, Physical andtheoretical – Mathematics. I. Title.QD455.3.E4J46 2006541.0285 – dc222006023998Library of Congress Cataloging-in-Publication DataWiley also publishes its books in a variety of electronic formats. Some content that appears in print maynot be available in electronic books.John Wily & Sons Canada Ltd, 6045 Freemont Blvd, Mississauga, ONT, Canada, L5R 4J3John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, AustraliaWiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, GermanyJossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USAJohn Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USAOther Wiley Editorial OfficesThis publication is designed to provide accurate and authoritative information in regard to the subjectmatter covered. It is sold on the understanding that the Publisher is not engaged in rendering professionalservices. If professional advice or other expert assistance is required, the services of a competentprofessional should be sought.Designations used by companies to distinguish their products are often claimed as trademarks. All brandnames and product names used in this book are trade names, service marks, trademarks or registeredtrademarks of their respective owners. The Publisher is not associated with any product or vendormentioned in this book.All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system ortransmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning orotherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of alicence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK,without the permission in writing of the Publisher. Requests to the Publisher should be addressed to thePermissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West SussexPO19 8SQ, England, or emailed to permreq@wiley.co.uk, or faxed to ( 44) 1243 770620.Email (for orders and customer service enquiries): cs-books@wiley.co.ukVisit our Home Page on www.wiley.comCopyright 2007Fundamental IssuesDescribing the SystemFundamental ForcesThe Dynamical EquationSolving the Dynamical EquationSeparation of Variables1.6.1 Separating space and time variables1.6.2 Separating nuclear and electronic variables1.6.3 Separating variables in generalClassical Mechanics1.7.1 The Sun–Earth system1.7.2 The solar systemQuantum Mechanics1.8.1 A hydrogen-like atom1.8.2 The helium atomChemistryReferences2.12.2IntroductionThe Force Field Energy2.2.1 The stretch energy2.2.2 The bending energy2.2.3 The out-of-plane bending energy2.2.4 The torsional energy2.2.5 The van der Waals energy2.2.6 The electrostatic energy: charges and dipoles2.2.7 The electrostatic energy: multipoles and polarizabilities2 Force Field Methods1.91.81.71.11.21.31.41.51.61 IntroductionPreface to the First EditionPreface to the Second 21314141719211xvxix
2.2.8 Cross terms2.2.9 Small rings and conjugated systems2.2.10 Comparing energies of structurally different moleculesForce Field Parameterization2.3.1 Parameter reductions in force fields2.3.2 Force fields for metal coordination compounds2.3.3 Universal force fieldsDifferences in Force FieldsComputational ConsiderationsValidation of Force FieldsPractical ConsiderationsAdvantages and Limitations of Force Field MethodsTransition Structure Modelling2.9.1 Modelling the TS as a minimum energy structure2.9.2 Modelling the TS as a minimum energy structure on the reactant/product energy seam2.9.3 Modelling the reactive energy surface by interacting forcefield functions or by geometry-dependent parametersHybrid Force Field Electronic Structure 53.63.73.8The Adiabatic and Born–Oppenheimer ApproximationsSelf-Consistent Field TheoryThe Energy of a Slater DeterminantKoopmans’ TheoremThe Basis Set ApproximationAn Alternative Formulation of the Variational ProblemRestricted and Unrestricted Hartree–FockSCF Techniques3.8.1 SCF convergence3.8.2 Use of symmetry3.8.3 Ensuring that the HF energy is a minimum, and thecorrect minimum3.8.4 Initial guess orbitals3.8.5 Direct SCF3.8.6 Reduced scaling techniquesPeriodic SystemsSemi-Empirical Methods3.10.1 Neglect of Diatomic Differential Overlap Approximation (NDDO)3.10.2 Intermediate Neglect of Differential Overlap Approximation (INDO)3.10.3 Complete Neglect of Differential Overlap Approximation (CNDO)Parameterization3.11.1 Modified Intermediate Neglect of Differential Overlap (MINDO)3.11.2 Modified NDDO models3.11.3 Modified Neglect of Diatomic Overlap (MNDO)3.11.4 Austin Model 1 (AM1)3.11.5 Modified Neglect of Diatomic Overlap, Parametric Method Number 3 (PM3)3.11.6 Parametric Method number 5 (PM5) and PDDG/PM3 methods3 Electronic Structure Methods: Independent-Particle 110480737477714748505157586262656769697070Excited Slater DeterminantsConfiguration Interaction4.2.1 CI Matrix elements4.2.2 Size of the CI matrix4.2.3 Truncated CI methods4.2.4 Direct CI methodsIllustrating how CI Accounts for Electron Correlation, and theRHF Dissociation ProblemThe UHF Dissociation, and the Spin Contamination ProblemSize Consistency and Size ExtensivityMulti-Configuration Self-Consistent FieldMulti-Reference Configuration InteractionMany-Body Perturbation Theory4.8.1 Møller–Plesset perturbation theory4.8.2 Unrestricted and projected Møller–Plesset methodsCoupled Cluster4.9.1 Truncated coupled cluster methodsConnections between Coupled Cluster, Configuration Interactionand Perturbation Theory4.10.1 Illustrating correlation methods for the beryllium atomMethods Involving the Interelectronic DistanceDirect MethodsLocalized Orbital MethodsSummary of Electron Correlation MethodsExcited StatesQuantum Monte Carlo MethodsReferences5.15.25.35.4Slater and Gaussian Type OrbitalsClassification of Basis SetsEven- and Well-Tempered Basis SetsContracted Basis Sets5.4.1 Pople style basis sets5.4.2 Dunning–Huzinaga basis sets5.4.3 MINI, MIDI and MAXI basis sets5.4.4 Ahlrichs type basis sets5.4.5 Atomic natural orbital basis sets5.4.6 Correlation consistent basis sets5 Basis 4.34.14.24 Electron Correlation Methods3.143.123.133.11.7 The MNDO/d and AM1/d methods3.11.8 Semi Ab initio Method 1Performance of Semi-Empirical MethodsHückel Theory3.13.1 Extended Hückel theory3.13.2 Simple Hückel theoryLimitations and Advantages of Semi-Empirical 7128129131vii
Orbital-Free Density Functional TheoryKohn–Sham TheoryReduced Density Matrix MethodsExchange and Correlation HolesExchange–Correlation Functionals6.5.1 Local Density Approximation6.5.2 Gradient-corrected methods6.5.3 Higher order gradient or meta-GGA methods6.5.4 Hybrid or hyper-GGA methods6.5.5 Generalized random phase methods6.5.6 Functionals overviewPerformance and Properties of Density Functional MethodsDFT ProblemsComputational ConsiderationsFinal ConsiderationsReferencesClassical Valence Bond TheorySpin-Coupled Valence Bond TheoryGeneralized Valence Bond TheoryReferencesThe Dirac EquationConnections Between the Dirac and Schrödinger Equations8.2.1 Including electric potentials8.2.2 Including both electric and magnetic potentialsMany-Particle SystemsFour-Component CalculationsRelativistic EffectsReferences9.19.2Population Analysis Based on Basis FunctionsPopulation Analysis Based on the Electrostatic Potential9 Wave Function Analysis8.38.48.58.18.28 Relativistic Methods7.17.27.37 Valence Bond Methods6.66.76.86.96.16.26.36.46.5CONTENTS5.4.7 Polarization consistent basis sets5.4.8 Basis set extrapolationPlane Wave Basis FunctionsRecent Developments and Computational IssuesComposite Extrapolation ProceduresIsogyric and Isodesmic ReactionsEffective Core PotentialsBasis Set Superposition ErrorsPseudospectral MethodsReferences6 Density Functional try Convergence11.1.1 Ab Initio methods11.1.2 Density functional methodsTotal Energy ConvergenceDipole Moment Convergence11.3.1 Ab Initio methods11.3.2 Density functional methodsVibrational Frequency Convergence11.4.1 Ab Initio methods11.4.2 Density functional methodsIllustrating the ConceptsExamples of Molecular Properties10.1.1 External electric field10.1.2 External magnetic field10.1.3 Internal magnetic moments10.1.4 Geometry change10.1.5 Mixed derivativesPerturbation MethodsDerivative TechniquesLagrangian TechniquesCoupled Perturbed Hartree–FockElectric Field Perturbation10.6.1 External electric field10.6.2 Internal electric fieldMagnetic Field Perturbation10.7.1 External magnetic field10.7.2 Nuclear spin10.7.3 Electron spin10.7.4 Classical terms10.7.5 Relativistic terms10.7.6 Magnetic properties10.7.7 Gauge dependence of magnetic propertiesGeometry PerturbationsResponse and Propagator MethodsProperty Basis SetsReferencesMolecular PropertiesPopulation Analysis Based on the Electron Density9.3.1 Atoms In Molecules9.3.2 Voronoi, Hirshfeld and Stewart atomic charges9.3.3 Generalized atomic polar tensor chargesLocalized Orbitals9.4.1 Computational considerationsNatural OrbitalsNatural Atomic Orbital and Natural Bond Orbital AnalysisComputational 5299299303304304306308309311312313ix
xOptimizing Quadratic FunctionsOptimizing General Functions: Finding Minima12.2.1 Steepest descent12.2.2 Conjugate gradient methods12.2.3 Newton–Raphson methods12.2.4 Step control12.2.5 Obtaining the Hessian12.2.6 Storing and diagonalizing the Hessian12.2.7 Extrapolations: the GDIIS methodChoice of CoordinatesOptimizing General Functions: Finding Saddle Points (Transition Structures)12.4.1 One-structure interpolation methods: coordinate driving,linear and quadratic synchronous transit, and sphereoptimization12.4.2 Two-structure interpolation methods: saddle, line-thenplane, ridge and step-and-slide optimizations12.4.3 Multi-structure interpolation methods: chain, locallyupdated planes, self-penalty walk, conjugate peakrefinement and nudged elastic band12.4.4 Characteristics of interpolation methods12.4.5 Local methods: gradient norm minimization12.4.6 Local methods: Newton–Raphson12.4.7 Local methods: the dimer method12.4.8 Coordinates for TS searches12.4.9 Characteristics of local methods12.4.10 Dynamic methodsConstrained Optimization ProblemsConformational Sampling and the Global Minimum Problem12.6.1 Stochastic and Monte Carlo methods12.6.2 Molecular dynamics12.6.3 Simulated annealing12.6.4 Genetic algorithms12.6.5 Diffusion methods12.6.6 Distance geometry methodsMolecular DockingIntrinsic Reaction Coordinate MethodsReferencesOptimization TechniquesBond Dissociation Curves11.5.1 Basis set effect at the Hartree–Fock level11.5.2 Performance of different types of wave function11.5.3 Density functional methodsAngle Bending CurvesProblematic Systems11.7.1 The geometry of FOOF11.7.2 The dipole moment of CO11.7.3 The vibrational frequencies of O3Relative Energies of C4H6 4.514.214.11413.613.113.213.313.413.513Frontier Molecular Orbital TheoryConcepts from Density Functional TheoryQualitative Molecular Orbital TheoryWoodward–Hoffmann RulesThe Bell–Evans–Polanyi Principle/Hammond Postulate/Marcus TheoryMore O’Ferrall–Jencks DiagramsReferencesQualitative TheoriesMonte Carlo Methods14.1.1 Generating non-natural ensemblesTime-Dependent Methods14.2.1 Molecular dynamics methods14.2.2 Generating non-natural ensembles14.2.3 Langevin methods14.2.4 Direct methods14.2.5 Extended Lagrange techniques (Car–Parrinello methods)14.2.6 Quantum methods using potential energy surfaces14.2.7 Reaction path methods14.2.8 Non-Born–Oppenheimer methods14.2.9 Constrained sampling methodsPeriodic Boundary ConditionsExtracting Information from SimulationsFree Energy Methods14.5.1 Thermodynamic perturbation methods14.5.2 Thermodynamic integration methodsSolvation ModelsContinuum Solvation Models14.7.1 Poisson–Boltzmann methods14.7.2 Born/Onsager/Kirkwood models14.7.3 Self-consistent reaction field modelsReferencesSimulation TechniquesTransition State TheoryRice–Ramsperger–Kassel–Marcus TheoryDynamical EffectsStatistical MechanicsThe Ideal Gas, Rigid-Rotor Harmonic-Oscillator Approximation13.5.1 Translational degrees of freedom13.5.2 Rotational degrees of freedom13.5.3 Vibrational degrees of freedom13.5.4 Electronic degrees of freedom13.5.5 Enthalpy and entropy contributionsCondensed PhasesReferencesStatistical Mechanics and Transition State i
.116.216xii570Appendix B570571572573565NotationB.1 The Variational PrincipleB.2 The Hohenberg–Kohn TheoremsB.3 The Adiabatic Connection FormulaReference562565Concluding 529529514Appendix AIntroductionElementary Statistical MeasuresCorrelation Between Two Sets of DataCorrelation between Many Sets of Data17.4.1 Multiple-descriptor data sets and quality analysis17.4.2 Multiple linear regression17.4.3 Principal component and partial least squares analysis17.4.4 Illustrative exampleQuantitative Structure–Activity Relationships (QSAR)ReferencesStatistics and QSARNumbers, Vectors, Matrices and TensorsChange of Coordinate System16.2.1 Examples of changing the coordinate system16.2.2 Vibrational normal coordinates16.2.3 Energy of a Slater determinant16.2.4 Energy of a CI wave function16.2.5 Computational ConsiderationCoordinates, Functions, Functionals, Operators andSuperoperators16.3.1 Differential operatorsNormalization, Orthogonalization and ProjectionDifferential Equations16.5.1 Simple first-order differential equations16.5.2 Less simple first-order differential equations16.5.3 Simple second-order differential equations16.5.4 Less simple second-order differential equations16.5.5 Second-order differential equations depending on thefunction itselfApproximating Functions16.6.1 Taylor expansion16.6.2 Basis set expansionFourier and Laplace TransformationsSurfacesReferencesMathematical MethodsCONTENTSIndexZ-Matrix ConstructionAppendix DAtomic UnitsAppendix CCONTENTS583575575574574xiii
Point (1) is part of every new field: there is not much to do about it. If you want to livein another country, you have to learn the language. If you want to use computationalchemistry methods, you need to learn the acronyms. I have tried in the present bookto include a good fraction of the most commonly used abbreviations and standard procedures.Point (2) is both hardware and software specific. It is not well suited for a text book,as the information rapidly becomes out of date. The average lifetime of computer hardware is a few years, the time between new versions of software is even less. Problemsof type (2) need to be solved “on location”. I have made one exception, however, andhave including a short discussion of how to make Z-matrices. A Z-matrix is a convenient way of specifying a molecular geometry in terms of internal coordinates, and it isused by many electronic structure programs. Furthermore, geometry optimizations areoften performed in Z-matrix variables, and since optimizations in a good set of internal coordinates are significantly faster than in Cartesian coordinates, it is important tohave a reasonable understanding of Z-matrix construction.As computer programs evolve they become easier to use. Modern programs oftencommunicate with the user in terms of a graphical interface, and many methods havebecome essential “black box” procedures: if you can draw the molecule, you can alsodo the calculation. This effectively means that you no longer have to be a highly trainedtheoretician to run even quite sophisticated calculations.(1) Deciphering the code. The language of computational chemistry is littered withacronyms, what do these abbreviations stand for in terms of underlying assumptions and approximations?(2) Technical problems. How does one actually run the program and what to look forin the output?(3) Quality assessment. How good is the number that has been calculated?Computational chemistry is rapidly emerging as a subfield of theoretical chemistry,where the primary focus is on solving chemically related problems by calculations. Forthe newcomer to the field, there are three main problems:Preface to the First Edition
should be able to understand the premises and limitations of different methods, andfollow the main steps in running a calculation. This means that I in many cases haveomitted to tell the reader of some of the finer details, which may annoy the purists.However, I believe the large overview is necessary before embarking on a more stringent and detailed derivation of the mathematics. The goal of this book is to providean overview of commonly used methods, giving enough theoretical background tounderstand why for example the AMBER force field is used for modelling proteinsbut MM2 is used for small organic molecules. Or why coupled cluster inherently is aniterative method, while perturbation theory and configuration interaction inherentlyare non-iterative methods, although the CI problem in practice is solved by iterativetechniques.The prime focus of this book is on calculating molecular structures and (relative)energies, and less on molecular properties or dynamical aspects. In my experience, predicting structures and energetics are the main uses of computational chemistry today,although this may well change in the coming years. I have tried to include mostmethods that are already extensively used, together with some that I expect to becomegenerally available in the near future. How detailed the methods are described dependspartly on how practical and commonly used the methods are (both in terms of computational resources and software), and partly reflects my own limitations in te
Introduction to computational chemistry / Frank Jensen. – 2nd ed. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-470-01186-7 (cloth : alk. paper) ISBN-10: 0-470-01186-6 (cloth : alk. paper) ISBN-13: 978-0-470-01187-4 (pbk. : alk. paper) ISBN-10: 0-470-01187-4 (pbk.
Chemistry ORU CH 210 Organic Chemistry I CHE 211 1,3 Chemistry OSU-OKC CH 210 Organic Chemistry I CHEM 2055 1,3,5 Chemistry OU CH 210 Organic Chemistry I CHEM 3064 1 Chemistry RCC CH 210 Organic Chemistry I CHEM 2115 1,3,5 Chemistry RSC CH 210 Organic Chemistry I CHEM 2103 1,3 Chemistry RSC CH 210 Organic Chemistry I CHEM 2112 1,3
E. Kwan Lecture 9: Introduction to Computational Chemistry Chem 117 February 22, 2010. Introduction to Computational Chemistry Scope of Lecture Eugene E. Kwan Key Questions the PES introduction to computational chemistry Key References 1. Molecular Modeling Basics Jensen, J.H. CRC Press, 2009. 2. Computati
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Introduction What is Computational Chemistry? Computational Chemistry is a branch of chemistry that uses computer science to assist in solving chemical problems. Incorporates the results of theoretical chemistry
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Computational chemistry is a rapidly growing field in chemistry. – Computers are getting faster. – Algorithims and programs are maturing. Some of the almost limitless properties that can be calculated with computational chemistry are: – Equilibrium and transition-state structures – dipole and quadrapole moments and polarizabilities
theoretical framework for computational dynamics. It allows applications to meet the broad range of computational modeling needs coherently and with fast, structure-based computational algorithms. The paper describes the SOA computational ar-chitecture, the DARTS computational dynamics software, and appl
