Reviews in Computational Chemistry Volume...

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Reviews in Computational Chemistry Volume 20 Edited by Kenny B. Lipkowitz, Raima Larter, and Thomas R. Cundari Editor Emeritus Donald B. Boyd

Transcript of Reviews in Computational Chemistry Volume...

  • Reviews inComputationalChemistryVolume 20

    Edited by

    Kenny B. Lipkowitz, Raima Larter,and Thomas R. Cundari

    Editor Emeritus

    Donald B. Boyd

    Innodata0471678848.jpg

  • Reviews inComputationalChemistryVolume 20

  • Reviews inComputationalChemistryVolume 20

    Edited by

    Kenny B. Lipkowitz, Raima Larter,and Thomas R. Cundari

    Editor Emeritus

    Donald B. Boyd

  • Copyright # 2004 by John Wiley & Sons, Inc. All rights reserved.

    Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.

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    10 9 8 7 6 5 4 3 2 1

    Kenny B. LipkowitzDepartment of Chemistry

    Ladd Hall 104

    North Dakota State UniversityFargo, North Dakota 58105-5516, USA

    [email protected]

    Raima LarterDepartment of Chemistry

    Indiana University-Purdue University

    at Indianapolis,

    402 North Blackford StreetIndianapolis, Indiana 46202-3274, USA

    [email protected]

    Thomas R. CundariDepartment of Chemistry

    University of North Texas

    Box 305070Denton, Texas 76203-5070, USA

    [email protected]

    Donald B. BoydDepartment of Chemistry

    Indiana University-Purdue University

    at Indianapolis

    402 North Blackford StreetIndianapolis, Indiana 46202-3274, USA

    [email protected]

    http://www.copyright.com

  • Preface

    Our goal over the years has been to provide tutorial-like reviews cover-ing all aspects of computational chemistry. In this, our twentieth volume, wepresent six chapters covering a diverse range of topics that are of interest tocomputational chemists. When one thinks of modern quantum chemical meth-ods there is a proclivity to think about molecular orbital theory (MOT). Thistheory has proved itself to be a useful theoretical tool that allows the compu-tation of energies, properties and, nowadays, dynamical aspects of molecularand supramolecular systems. Molecular orbital theory is, thus, valuable to theaverage bench chemist, but that bench chemist invariably wants to describechemical transformations to other chemists in a parlance based on the use ofresonance structures. So, an orbital localization scheme must be used to con-vert the fully delocalized MO results to a valence bond type representationthat is consonant with the chemists working language. One of the great meritsof valence bond theory (VBT) is its intuitive wave function. So, why not useVBT? If VBT is the lingua franca of most synthetic chemists, shouldnt thosechemists be relying on the VBT method more than they now do, and, if they donot, how can those scientists learn about this quantum method? In Chapter 1,Professors Sason Shaik and Philippe Hiberty provide a detailed view of VBTvis-a-vis MOT, its demise, and then its renaissance; in short they give us a his-tory lesson about the topic. Following this, they outline the basic concepts ofVBT, describe the relationship between MOT and VBT, and provide insightsabout qualitative VBT. Comparisons with other quantum theories and withexperiment are made throughout. The VB state correlation method for electro-nic delocalization is defined and the controversial issue of what makes benzenehave its D6h structure is discussed. Aspects of photochemistry are then cov-ered. The spin Hamiltonian VBT and ab initio VB methods are also describedand reviewed, which provides a compelling historical account of VBT alongwith a tutorial and a review. It uses a parlance that is consistent with theway synthetic chemists naturally speak, and it contains insights concerningthe many uses of this vibrant field of quantum theory from two veteran VBtheorists.

    Most chemists solving problemswith quantum chemical tools typicallyworkon a single potential energy surface. There are many chemical transformations,

    v

  • however, where two or more potential energy surfaces need to be included todescribe properly the event that is taking place as is the case, for example, inphotoisomerizations. In many examples of photoexcitation, nonradiativeinternal conversion processes are followed that involve the decay of an excitedstate having the same multiplicity as the lower electronic state. In other pro-cesses, however, a nonradiative decay path can be followed where, say, a sing-let state can access a triplet state. How one goes about treating such changes inspin multiplicity is a daunting task, to both novice and seasoned computa-tional chemists alike. Professors Nikita Matsunaga and Shiro Koseki providea tutorial on the topic of modeling spin-forbidden reactions in Chapter 2. Theauthors describe for the novice the importance of the minimum energy cross-ing point (MEXP) and rationalize how spinorbit coupling provides a mechan-ism for spin-forbidden reactions. An explanation of crossing probabilities, theFermi golden rule, and the LandauZener semiclassical approximation aregiven. Methodologies for obtaining spinorbit matrix elements are presentedincluding, among others, the KleinGordon equation, the Dirac equation, theFoldyWouthuysen transformation, and the BreitPauli Hamiltonian. Withthis background the authors take the novice through a tutorial that explainshow to locate the MEXP. They describe programs available for modelingspin-forbidden reactions, and they then provide examples of such calculationson diatomic and polyatomic molecules.

    Chapter 3 continues the theme of quantum chemistry and the excitedstate. In this chapter, Professor Stefan Grimme provides a tutorial explaininghow best to calculate electronic spectra of large molecules. Great care must betaken in the interpretation of electronic spectra because significant reorganiza-tion of the electronic and nuclear coordinates occurs upon excitation. Even formedium-sized molecules, the density of states in small energy regions canbe large, which leads to overlapping spectral features that are difficult toresolve (experimentally and theoretically). Other complications arise as well andthe novice computational chemist can become overwhelmed with the manydecisions that are needed to carry out the calculations in a meaningful manner.Professor Grimme addresses these challenges in this chapter by first introdu-cing and categorizing the types of electronic spectra and types of excited states,and then explaining the various theoretical aspects associated with simulatingelectronic spectra. In particular, excitation energies, transition moments, andvibrational structure are covered. Quantum chemical methods used for com-puting excited states of large molecules are highlighted with emphases on CI,perturbation methods, and time-dependent HartreeFock and density func-tional theory (DFT) methods. A set of recommendations that summarize themethods that can (and should) be used for calculating electronic spectra areprovided. Case studies on vertical absorption spectra, circular dichroism,and vibrational structure are then given. The author provides for the reader a basicunderstanding of which computational methodologies work while alerting thereader to those that do not. This tutorial imparts to the novice many years ofexperience by Professor Grimme about pitfalls to avoid.

    vi Preface

  • In Chapter 4, Professor Raymond Kapral reviews the computationaltechniques used in simulating chemical waves and patterns produced by cer-tain chemical reactions such as the BelousovZhabotinsky reaction. He beginswith a brief discussion of the different length and time scales involved and anexplanation for the usual choice of a macroscopic modeling approach. Thefinite difference approach to modeling reaction-diffusion systems is nextreviewed and illustrated for a couple of simple model systems. One of these,the FitzHughNagumo model, exhibits waves and patterns typical of excitablemedia. Kapral goes on to review other modeling approaches for excitablemedia, including the use of cellular automata and coupled map lattices.Finally, mesoscopic modeling techniques including Markov chain models forthe chemical dynamics of excitable systems are reviewed.

    Chapter 5 by Professors Costel Sarbu and Horia Pop on Fuzzy Logiccomplements previous contributions to this series on Neural Networks(Volume 16) and Genetic Algorithms (Volume 10). Like the other artificialintelligence techniques, fuzzy logic has seen increasing usage in chemistry inthe past decade. Here, for the first time, the many different techniques thatfall within the arena of fuzzy logic are organized and presented. As delineatedby the authors, fuzzy logic is ideally suited for those areas in which impreciseor incomplete measurements are an issue. Its primary application has beenthe mining of large data sets. The fuzzy techniques discussed in this chapter areequally suited for achieving an effective reduction of the data in terms of eitherthe number of objects (by clustering of data) or a reduction in dimensionality.Additionally, cross-classification techniques make it possible to simultaneouslycluster data based on the objects and the characteristics that describe them. Inthis way, the characteristics that are responsible for two objects belonging tothe same (or different) chemical families can be probed directly. In either case,fuzzy methods afford the ability to probe relationships among the data that arenot apparent from traditional methods. An eclectic assortment of examplesfrom the literature of fuzzy logic in chemistry is provided, with special empha-sis on a subject near and dear to the heart of all chemiststhe periodic table.Through the application of fuzzy logic, the chemical groups evident since thetime of Mendeleev emerge as the techniques evolve from being crisp to increas-ingly fuzzy. Professors Sarbu and Pop show how the different fuzzy classifica-tion schemes can be used to unearth relationships among the elements that arenot evident from a quick perusal of standard periodic tables. Other areas ofapplication include analysis of structural databases, toxicity profiling, struc-tureactivity relationships (SAR) and quantitative structureactivity relation-ships (QSAR). The chapter concludes with a discussion about interfacing offuzzy set theory with other soft computing techniques.

    The final chapter in this volume (Chapter 6) covers a topic that has beenof major concern to computational chemists working in the pharmaceuticalindustry: Absorption, Metabolism, Distribution, Excretion, and Toxicology(ADME/Tox) of drugs. The authors of this chapter, Dr. Sean Ekins and Pro-fessor Peter Swaan, an industrial scientist and an academician, respectively,

    Preface vii

  • provide a selective review of the current status of ADME/Tox covering severalintensely studied proteins. The common thread interconnecting these differentclasses of proteins is that the same computational techniques can be applied tounravel the intricacies of several individual systems. The authors begin bydescribing the concerted actions of transport and metabolism in mammalianphysiology. They then delineate the various approaches used to modelenzymes, transporters, channels, and receptors by describing, first, classicalQSAR methods and, then, pharmacophore models. Specific programs thatare used for the latter include Catalyst, DISCO, CoMFA, CoMSIA, GOLPE,and ALMOND, all of which are described in this chapter. The use of homol-ogy models are also explained. Following this introductory section on tech-niques, the authors review examples of ADME/Tox studies beginning withTransporter Systems, proceeding to Enzyme Systems, and then to Channelsand Receptors. Seventeen different case studies are presented to illustratehow the various modeling techniques have been used to evaluate ADME/Tox. A set of Ten Commandments that are applicable to many ADME/Tox properties as well as bioactivity models is given for the novice computa-tional chemist. A prognostication of future developments completes the chapter.

    We invite our readers to visit the Reviews in Computational Chemistrywebsite at http://www.chem.ndsu.nodak.edu/RCC. It includes the author andsubject indexes, color graphics, errata, and other materials supplementing thechapters. We are delighted to report that the Google search engine (http://www.google.com/) ranks our website among the top hits in a search on theterm computational chemistry. This search engine has become popularbecause it ranks hits in terms of their relevance and frequency of visits. Weare also pleased to report that the Institute for Scientific information, Inc.(ISI) rates the Reviews in Computational Chemistry book series in the top10 in the category of general journals and periodicals. The reason for theseaccomplishments rests firmly on the shoulders of the authors whom we havecontacted to provide the pedagogically driven reviews that have made thisongoing book series so popular. To those authors we are especially grateful.

    We are also glad to note that our publisher has plans to make our mostrecent volumes available in an online form through Wiley InterScience. Pleasecheck the Web (http://www.interscience.wiley.com/onlinebooks) or [email protected] for the latest information. For readers who appreciatethe permanence and convenience of bound books, thesewill, of course, continue.

    We thank the authors of this and previous volumes for their excellentchapters.

    Kenny B. LipkowitzFargo, North Dakota

    Raima LarterIndianapolis, IndianaThomas R. Cundari

    Denton, TexasDecember 2003

    viii Preface

  • Contents

    1. Valence Bond Theory, Its History, Fundamentals,and Applications: A Primer 1Sason Shaik and Philippe C. Hiberty

    Introduction 1A Story of Valence Bond Theory, Its Rivalry with Molecular

    Orbital Theory, Its Demise, and Eventual Resurgence 2Roots of VB Theory 2Origins of MO Theory and the Roots of VBMO Rivalry 5The Dance of Two Theories: One Is Up, the

    Other Is Down 7Are the Failures of VB Theory Real Ones? 11Modern VB Theory: VB Theory Is Coming of Age 14

    Basic VB Theory 16Writing and Representing VB Wave Functions 16The Relationship between MO and VB Wave Functions 22Formalism Using the Exact Hamiltonian 24Qualitative VB Theory 26Some Simple Formulas for Elementary Interactions 29

    Insights of Qualitative VB Theory 34Are the Failures of VB Theory Real? 35Can VB Theory Bring New Insight into

    Chemical Bonding? 42VB Diagrams for Chemical Reactivity 44

    VBSCD: A General Model for Electronic Delocalization andIts Comparison with the Pseudo-JahnTeller Model 56

    What Is the Driving Force, s or p, Responsible forthe D6h Geometry of Benzene? 57

    VBSCD: The Twin-State Concept and Its Link toPhotochemical Reactivity 60

    The Spin Hamiltonian VB Theory 65Theory 65Applications 67

    Ab Initio VB Methods 69Orbital-Optimized Single-Configuration Methods 70Orbital-Optimized Multiconfiguration VB Methods 75

    Prospective 84

    ix

  • Appendix 84A.1 Expansion of MO Determinants in Terms of AO

    Determinants 84A.2 Guidelines for VB Mixing 86A.3 Computing Mono-Determinantal VB Wave

    Functions with Standard Ab Initio Programs 87Acknowledgments 87References 87

    2. Modeling of Spin-Forbidden Reactions 101Nikita Matsunaga and Shiro Koseki

    Overview of Reactions Requiring Two States 101Spin-Forbidden Reaction, Intersystem Crossing 103

    SpinOrbit Coupling as a Mechanism for Spin-ForbiddenReaction 105

    General Considerations 105Atomic SpinOrbit Coupling 106Molecular SpinOrbit Coupling 107

    Crossing Probability 110Fermi Golden Rule 110LandauZener Semiclassical Approximation 111

    Methodologies for Obtaining SpinOrbit Matrix Elements 111Electron Spin in Nonrelativistic Quantum Mechanics 112KleinGordon Equation 114Dirac Equation 115FoldyWouthuysen Transformation 117BreitPauli Hamiltonian 121Zeff Method 121Effective Core Potential-Based Method 123Model Core Potential-Based Method 124DouglasKroll Transformation 124

    Potential Energy Surfaces 127Minimum Energy Crossing-Point Location 128

    Available Programs for Modeling Spin-Forbidden Reactions 131Applications to Spin-Forbidden Reactions 132

    Diatomic Molecules 132Polyatomic Molecules 134Phenyl Cation 137Norborene 138Conjugated Polymers 138CH2 N2 ! HCNN4S 139Molecular Properties 140Dynamical Aspects 141

    Other Reactions 142

    x Contents

  • Biological Chemistry 143Concluding Remarks 144Acknowledgments 145References 145

    3. Calculation of the Electronic Spectra of Large Molecules 153Stefan Grimme

    Introduction 153Types of Electronic Spectra 155Types of Excited States 158

    Theory 162Excitation Energies 162Transition Moments 165Vibrational Structure 171Quantum Chemical Methods 175

    Case Studies 188Vertical Absorption Spectra 188Circular Dichroism 200Vibrational Structure 204

    Summary and Outlook 210Acknowledgments 211References 211

    4. Simulating Chemical Waves and Patterns 219Raymond Kapral

    Introduction 219ReactionDiffusion Systems 221Cellular Automata 227Coupled Map Lattices 232Mesoscopic Models 237Summary 243References 244

    5. Fuzzy Soft-Computing Methods and Their Applicationsin Chemistry 249Costel Sarbu and Horia F. Pop

    Introduction 249Methods for Exploratory Data Analysis 250

    Visualization of High-Dimensional Data 250Clustering Methods 251Projection Methods 252Linear Projection Methods 252Nonlinear Projection Methods 253

    Artificial Neural Networks 254

    Contents xi

  • Perceptron 254Multilayer Nets: Backpropagation 256Associative Memories: Hopfield Net 259Self-Organizing Map 260Properties 261Mathematical Characterization 262Relation between SOM and MDS 263Multiple Views of the SOM 263Other Architectures 263

    Evolutionary Algorithms 264Genetic Algorithms 265

    Canonical GA 265Evolution Strategies 266Evolutionary Programming 267

    Fuzzy Sets and Fuzzy Logic 268Fuzzy Sets 269Fuzzy Logic 271Fuzzy Clustering 273Fuzzy Regression 274

    Fuzzy Principal Component Analysis (FPCA) 278Fuzzy PCA (Optimizing the First Component) 278Fuzzy PCA (Nonorthogonal Procedure) 279Fuzzy PCA (Orthogonal) 280

    Fuzzy Expert Systems (Fuzzy Controllers) 282Hybrid Systems 284

    Combinations of Fuzzy Systems and Neutral Networks 284Fuzzy Genetic Algorithms 285Neuro-Genetic Systems 286

    Fuzzy Characterization and Classification of the ChemicalElements and Their Properties 286

    Hierarchical Fuzzy Classification of Chemical ElementsBased on Ten Physical Properties 288

    Hierarchical Fuzzy Classification of Chemical ElementsBased on Ten Physical, Chemical, and Structural Properties 293

    Fuzzy Hierarchical Cross-Classification of Chemical ElementsBased on Ten Physical Properties 297

    Fuzzy Hierarchical Characteristics Clustering 304Fuzzy Horizontal Characteristics Clustering 305Characterization and Classification of Lanthanides and

    Their Properties by PCA and FPCA 307Properties of Lanthanides Considered in This Study 308Classical PCA 310Fuzzy PCA 313Miscellaneous Applications of FPCA 317

    xii Contents

  • Fuzzy Modeling of Environmental, SAR and QSAR Data 318Spectral Library Search and Spectra Interpretation 319Fuzzy Calibration of Analytical Methods and Fuzzy

    Robust Estimation of Location and Spread 320Application of Fuzzy Neural Networks Systems in Chemistry 322Applications of Fuzzy Sets Theory and Fuzzy Logic in

    Theoretical Chemistry 324Conclusions and Remarks 325References 325

    6. Development of Computational Models for Enzymes,Transporters, Channels, and Receptors Relevant to ADME/Tox 333Sean Ekins and Peter W. Swaan

    Introduction 333ADME/Tox Modeling: An Expansive Vision 333The Concerted Actions of Transport and Metabolism 335Metabolism 335Transporters 336

    Approaches to Modeling Enzymes, Transporters, Channels,and Receptors 338

    Classical QSAR 340Pharmacophore Models 341Homology Modeling 348

    Transporter Modeling 348Applications of Transporters 349The Human Small Peptide Transporter, hPEPT1 350The Apical Sodium-Dependent Bile Acid Transporter 351P-Glycoprotein 353Vitamin Transporters 361Organic Cation Transporter 362Organic AnionTransporters 363Nucleoside Transporter 363Breast Cancer Resistance Protein 364Sodium Taurocholate Transporting Polypeptide 365

    Enzymes 365Cytochrome P450 365Epoxide Hydrolase 370Monoamine Oxidase 370Flavin-Containing Monooxygenase 372Sulfotransferases 372Glucuronosyltransferases 373Glutathione S-transferases 375

    Channels 376

    Contents xiii

  • Human Ether-a-gogo Related Gene 376Receptors 382

    Pregnane X-Receptor 382Constitutive Androstane Receptor 385

    Future Developments 388Acknowledgments 392Abbreviations 393References 393

    Author Index 417

    Subject Index 443

    xiv Contents

  • Contributors

    Sean Ekins, GeneCo, 500 Renaissance Drive, Suite 106, St. Joseph, MI 49085,USA.(Electronic mail: [email protected])

    Stefan Grimme, Theoretische Organische Chemie, Organisch-ChemischesInstitut der Universitat Munster, Correnstrasse 40, D-48149 Munster,Germany. (Electronic mail: [email protected])

    Philippe C. Hiberty, Laboratoire de Chimie Physique, Groupe de ChimieTherique, Universite de Paris-Sud, 91405 Orsay, Cedex France.(Electronic mail: [email protected])

    Raymond Kapral, Chemical Physics Theory Group, Department of Chemistry,University of Toronto, Toronto, Ontario M5S 3H6, Canada.(Electronic mail: [email protected])

    Shiro Koseki, Department of Material Sciences, College of Integrated Arts andSciences, Osaka Prefecture University, 1-1, Gakuen-cho, Sakai 599-8531,Japan. (Electronic Mail: [email protected])

    Nikita Matsunaga, Department of Chemistry and Biochemistry, Long IslandUniversity, 1 University Plaza, Brooklyn, NY 11201 USA.(Electronic mail: [email protected])

    Horia F. Pop, Babes-Bolyai University, Faculty of Mathematics and ComputerScience, Department of Computer Science, 1, M. Kogalniceanu Street,RO-3400 Cluj-Napoca, Romania. (Electronic mail: [email protected])

    Costel Sarbu, Babes-Bolyai University, Faculty of Chemistry and ChemicalEngineering, Department of Analytical Chemistry, 11 Arany Janos Street,RO-3400 Cluj-Napoca, Romania. (Electronic mail: [email protected])

    xv

  • Sason Shaik, Department of Organic Chemistry and Lise Meitner-MinervaCenter for Computational Chemistry, Hebrew University, 91904 Jerusalem,Israel. (Electronic mail: [email protected])

    Peter Swaan, Department of Pharmaceutical Sciences, University of Maryland,HSF2, 20 Penn Street, Baltimore, MD 21201 USA.(Electronic mail: [email protected])

    xvi Contributors

  • Contributors toPrevious Volumes

    Volume 1 (1990)

    David Feller and Ernest R. Davidson, Basis Sets for Ab Initio MolecularOrbital Calculations and Intermolecular Interactions.

    James J. P. Stewart, Semiempirical Molecular Orbital Methods.

    Clifford E. Dykstra, Joseph D. Augspurger, Bernard Kirtman, and David J.Malik, Properties of Molecules by Direct Calculation.

    Ernest L. Plummer, The Application of Quantitative Design Strategies inPesticide Design.

    Peter C. Jurs, Chemometrics andMultivariate Analysis inAnalytical Chemistry.

    Yvonne C. Martin, Mark G. Bures, and Peter Willett, Searching Databases ofThree-Dimensional Structures.

    Paul G. Mezey, Molecular Surfaces.

    Terry P. Lybrand, Computer Simulation of Biomolecular Systems UsingMolecular Dynamics and Free Energy Perturbation Methods.

    Donald B. Boyd, Aspects of Molecular Modeling.

    Donald B. Boyd, Successes of Computer-Assisted Molecular Design.

    Ernest R. Davidson, Perspectives on Ab Initio Calculations.

    xvii

  • Volume 2 (1991)

    Andrew R. Leach, A Survey of Methods for Searching the ConformationalSpace of Small and Medium-Sized Molecules.

    John M. Troyer and Fred E. Cohen, Simplified Models for Understanding andPredicting Protein Structure.

    J. Phillip Bowen and Norman L. Allinger, Molecular Mechanics: The Art andScience of Parameterization.

    Uri Dinur and Arnold T. Hagler, New Approaches to Empirical Force Fields.

    Steve Scheiner, Calculating the Properties of Hydrogen Bonds by Ab InitioMethods.

    Donald E. Williams, Net Atomic Charge and Multipole Models for theAb Initio Molecular Electric Potential.

    Peter Politzer and Jane S. Murray, Molecular Electrostatic Potentials andChemical Reactivity.

    Michael C. Zerner, Semiempirical Molecular Orbital Methods.

    Lowell H. Hall and Lemont B. Kier, The Molecular Connectivity Chi Indexesand Kappa Shape Indexes in StructureProperty Modeling.

    I. B. Bersuker and A. S. Dimoglo, The Electron-Topological Approach to theQSAR Problem.

    Donald B. Boyd, The Computational Chemistry Literature.

    Volume 3 (1992)

    Tamar Schlick, Optimization Methods in Computational Chemistry.

    Harold A. Scheraga, Predicting Three-Dimensional Structures of Oligo-peptides.

    Andrew E. Torda and Wilfred F. van Gunsteren, Molecular Modeling UsingNMR Data.

    David F. V. Lewis, Computer-Assisted Methods in the Evaluation of ChemicalToxicity.

    xviii Contributors to Previous Volumes

  • Volume 4 (1993)

    Jerzy Cioslowski, Ab Initio Calculations on Large Molecules: Methodologyand Applications.

    Michael L. McKee and Michael Page, Computing Reaction Pathways onMolecular Potential Energy Surfaces.

    Robert M. Whitnell and Kent R. Wilson, Computational MolecularDynamics of Chemical Reactions in Solution.

    Roger L. DeKock, Jeffry D. Madura, Frank Rioux, and Joseph Casanova,Computational Chemistry in the Undergraduate Curriculum.

    Volume 5 (1994)

    John D. Bolcer and Robert B. Hermann, The Development of ComputationalChemistry in the United States.

    Rodney J. Bartlett and John F. Stanton, Applications of Post-HartreeFockMethods: A Tutorial.

    Steven M. Bachrach, Population Analysis and Electron Densities from Quan-tum Mechanics.

    Jeffry D. Madura, Malcolm E. Davis, Michael K. Gilson, Rebecca C. Wade,Brock A. Luty, and J. Andrew McCammon, Biological Applications ofElectrostatic Calculations and Brownian Dynamics Simulations.

    K. V. Damodaran and Kenneth M. Merz Jr., Computer Simulation of LipidSystems.

    Jeffrey M. Blaney and J. Scott Dixon, Distance Geometry in Molecular Mod-eling.

    Lisa M. Balbes, S. Wayne Mascarella, and Donald B. Boyd, A Perspective ofModern Methods in Computer-Aided Drug Design.

    Volume 6 (1995)

    Christopher J. Cramer and Donald G. Truhlar, Continuum Solvation Models:Classical and Quantum Mechanical Implementations.

    Contributors to Previous Volumes xix

  • Clark R. Landis, Daniel M. Root, and Thomas Cleveland, MolecularMechanics Force Fields for Modeling Inorganic and OrganometallicCompounds.

    Vassilios Galiatsatos, Computational Methods for Modeling Polymers: AnIntroduction.

    Rick A. Kendall, Robert J. Harrison, Rik J. Littlefield, and Martyn F. Guest,High Performance Computing in Computational Chemistry: Methods andMachines.

    Donald B. Boyd, Molecular Modeling Software in Use: Publication Trends.

    Eiji OOsawa and Kenny B. Lipkowitz, Appendix: Published Force FieldParameters.

    Volume 7 (1996)

    Geoffrey M. Downs and Peter Willett, Similarity Searching in Databases ofChemical Structures.

    Andrew C. Good and Jonathan S. Mason, Three-Dimensional Structure Data-base Searches.

    Jiali Gao, Methods and Applications of Combined Quantum Mechanical andMolecular Mechanical Potentials.

    Libero J. Bartolotti and Ken Flurchick, An Introduction to Density FunctionalTheory.

    Alain St-Amant, Density Functional Methods in Biomolecular Modeling.

    Danya Yang and Arvi Rauk, The A Priori Calculation of Vibrational CircularDichroism Intensities.

    Donald B. Boyd, Appendix: Compendium of Software for MolecularModeling.

    Volume 8 (1996)

    Zdenek Slanina, Shyi-Long Lee, and Chin-hui Yu, Computations in TreatingFullerenes and Carbon Aggregates.

    xx Contributors to Previous Volumes

  • Gernot Frenking, Iris Antes, Marlis Bohme, Stefan Dapprich, Andreas W.Ehlers, Volker Jonas, Arndt Neuhaus, Michael Otto, Ralf Stegmann, AchimVeldkamp, and Sergei F. Vyboishchikov, Pseudopotential Calculations ofTransition Metal Compounds: Scope and Limitations.

    Thomas R. Cundari, Michael T. Benson, M. Leigh Lutz, and Shaun O.Sommerer, Effective Core Potential Approaches to the Chemistry of theHeavier Elements.

    Jan Almlof and Odd Gropen, Relativistic Effects in Chemistry.

    Donald B. Chesnut, The Ab Initio Computation of Nuclear MagneticResonance Chemical Shielding.

    Volume 9 (1996)

    James R. Damewood, Jr., Peptide Mimetic Design with the Aid of Computa-tional Chemistry.

    T. P. Straatsma, Free Energy by Molecular Simulation.

    Robert J. Woods, The Application of Molecular Modeling Techniques to theDetermination of Oligosaccharide Solution Conformations.

    Ingrid Pettersson and Tommy Liljefors, Molecular Mechanics CalculatedConformational Energies of Organic Molecules: A Comparison of ForceFields.

    Gustavo A. Arteca, Molecular Shape Descriptors.

    Volume 10 (1997)

    Richard Judson, Genetic Algorithms and Their Use in Chemistry.

    Eric C. Martin, David C. Spellmeyer, Roger E. Critchlow Jr., and Jeffrey M.Blaney, Does Combinatorial Chemistry Obviate Computer-Aided DrugDesign?

    Robert Q. Topper, Visualizing Molecular Phase Space: Nonstatistical Effectsin Reaction Dynamics.

    Raima Larter and Kenneth Showalter, Computational Studies in NonlinearDynamics.

    Contributors to Previous Volumes xxi

  • Stephen J. Smith and Brian T. Sutcliffe, The Development of ComputationalChemistry in the United Kingdom.

    Volume 11 (1997)

    Mark A. Murcko, Recent Advances in Ligand Design Methods.

    David E. Clark, Christopher W. Murray, and Jin Li, Current Issues inDe Novo Molecular Design.

    Tudor I. Oprea and Chris L. Waller, Theoretical and Practical Aspects ofThree-Dimensional Quantitative StructureActivity Relationships.

    Giovanni Greco, Ettore Novellino, and Yvonne Connolly Martin, Approachesto Three-Dimensional Quantitative StructureActivity Relationships.

    Pierre-Alain Carrupt, Bernard Testa, and Patrick Gaillard, ComputationalApproaches to Lipophilicity: Methods and Applications.

    Ganesan Ravishanker, Pascal Auffinger, David R. Langley, BhyravabhotlaJayaram, Matthew A. Young, and David L. Beveridge, Treatment of Counter-ions in Computer Simulations of DNA.

    Donald B. Boyd, Appendix: Compendium of Software and Internet Tools forComputational Chemistry.

    Volume 12 (1998)

    Hagai Meirovitch, Calculation of the Free Energy and the Entropy ofMacromolecular Systems by Computer Simulation.

    Ramzi Kutteh and T. P. Straatsma, Molecular Dynamics with GeneralHolonomic Constraints and Application to Internal Coordinate Constraints.

    John C. Shelley and Daniel R. Berard, Computer Simulation of WaterPhysisorption at MetalWater Interfaces.

    Donald W. Brenner, Olga A. Shenderova, and Denis A. Areshkin, Quantum-Based Analytic Interatomic Forces and Materials Simulation.

    Henry A. Kurtz and Douglas S. Dudis, Quantum Mechanical Methods forPredicting Nonlinear Optical Properties.

    Chung F. Wong, Tom Thacher, and Herschel Rabitz, Sensitivity Analysis inBiomolecular Simulation.

    xxii Contributors to Previous Volumes

  • Paul Verwer and Frank J. J. Leusen, Computer Simulation to Predict PossibleCrystal Polymorphs.

    Jean-Louis Rivail and Bernard Maigret, Computational Chemistry in France:A Historical Survey.

    Volume 13 (1999)

    Thomas Bally and Weston Thatcher Borden, Calculations on Open-ShellMolecules: A Beginners Guide.

    Neil R. Kestner and Jaime E. Combariza, Basis Set Superposition Errors:Theory and Practice.

    James B. Anderson, Quantum Monte Carlo: Atoms, Molecules, Clusters,Liquids, and Solids.

    Anders Wallqvist and Raymond D. Mountain, Molecular Models of Water:Derivation and Description.

    James M. Briggs and Jan Antosiewicz, Simulation of pH-Dependent Proper-ties of Proteins Using Mesoscopic Models.

    Harold E. Helson, Structure Diagram Generation.

    Volume 14 (2000)

    Michelle Miller Francl and Lisa Emily Chirlian, The Pluses and Minuses ofMapping Atomic Charges to Electrostatic Potentials.

    T. Daniel Crawford and Henry F. Schaefer III, An Introduction to CoupledCluster Theory for Computational Chemists.

    Bastiaan van de Graaf, Swie Lan Njo, and Konstantin S. Smirnov, Introduc-tion to Zeolite Modeling.

    Sarah L. Price, Toward More Accurate Model Intermolecular Potentials forOrganic Molecules.

    Christopher J. Mundy, Sundaram Balasubramanian, Ken Bagchi, MarkE. Tuckerman, Glenn J. Martyna, and Michael L. Klein, NonequilibriumMolecular Dynamics.

    Donald B. Boyd and Kenny B. Lipkowitz, History of the Gordon ResearchConferences on Computational Chemistry.

    Contributors to Previous Volumes xxiii

  • Mehran Jalaie and Kenny B. Lipkowitz, Appendix: Published Force FieldParameters for Molecular Mechanics, Molecular Dynamics, and Monte CarloSimulations.

    Volume 15 (2000)

    F. Matthias Bickelhaupt and Evert Jan Baerends, KohnSham Density Func-tional Theory: Predicting and Understanding Chemistry.

    Michael A. Robb, Marco Garavelli, Massimo Olivucci, and FernandoBernardi, A Computational Strategy for Organic Photochemistry.

    Larry A. Curtiss, Paul C. Redfern, and David J. Frurip, Theoretical Methodsfor Computing Enthalpies of Formation of Gaseous Compounds.

    Russell J. Boyd, The Development of Computational Chemistry in Canada.

    Volume 16 (2000)

    Richard A. Lewis, Stephen D. Pickett, and David E. Clark, Computer-AidedMolecular Diversity Analysis and Combinatorial Library Design.

    Keith L. Peterson, Artificial Neural Networks and Their Use in Chemistry.

    Jorg-Rudiger Hill, Clive M. Freeman, and Lalitha Subramanian, Use of ForceFields in Materials Modeling.

    M. Rami Reddy, Mark D. Erion, and Atul Agarwal, Free Energy Calculations:Use and Limitations in Predicting Ligand Binding Affinities.

    Volume 17 (2001)

    Ingo Muegge and Matthias Rarey, Small Molecule Docking and Scoring.

    Lutz P. Ehrlich and Rebecca C. Wade, ProteinProtein Docking.

    Christel M. Marian, SpinOrbit Coupling in Molecules.

    Lemont B. Kier, Chao-Kun Cheng, and Paul G. Seybold, Cellular AutomataModels of Aqueous Solution Systems.

    Kenny B. Lipkowitz and Donald B. Boyd, Appendix: Books Published on theTopics of Computational Chemistry.

    xxiv Contributors to Previous Volumes

  • Volume 18 (2002)

    Geoff M. Downs and John M. Barnard, Clustering Methods and Their Uses inComputational Chemistry.

    Hans-Joachim Bohm and Martin Stahl, The Use of Scoring Functions in DrugDiscovery Applications.

    Steven W. Rick and Steven J. Stuart, Potentials and Algorithms for Incorpor-ating Polarizability in Computer Simulations.

    Dmitry V. Matyushov and Gregory A. Voth, New Developments in theTheoretical Description of Charge-Transfer Reactions in Condensed Phases.

    George R. Famini and Leland Y. Wilson, Linear Free Energy RelationshipsUsing Quantum Mechanical Descriptors.

    Sigrid D. Peyerimhoff, The Development of Computational Chemistry inGermany.

    Donald B. Boyd and Kenny B. Lipkowitz, Appendix: Examination of theEmployment Environment for Computational Chemistry.

    Volume 19 (2003)

    Robert Q. Topper, David L. Freeman, Denise Bergin and KeirnanR. LaMarche, Computational Techniques and Strategies for Monte CarloThermodynamic Calculations, with Applications to Nanoclusters.

    David E. Smith and Anthony D. J. Haymet, Computing Hydrophobicity.

    Lipeng Sun and William L. Hase, BornOppenheimer Direct DynamicsClassical Trajectory Simulations.

    Gene Lamm, The PoissonBoltzmann Equation.

    Contributors to Previous Volumes xxv

  • CHAPTER 1

    Valence Bond Theory, Its History,Fundamentals, and Applications:A Primera

    Sason Shaik* and Philippe C. Hiberty{

    *Department of Organic Chemistry and Lise Meitner-MinervaCenter for Computational Chemistry, Hebrew University 91904Jerusalem, Israel{Laboratoire de Chimie Physique, Groupe de Chimie Theorique,Universite de Paris-Sud, 91405 Orsay Cedex, France

    INTRODUCTION

    The new quantum mechanics of Heisenberg and Schrodinger have pro-vided chemistry with two general theories of bonding: valence bond (VB)theory and molecular orbital (MO) theory. The two were developed at aboutthe same time, but quickly diverged into rival schools that have competed,sometimes fervently, in charting the mental map and epistemology of chemis-try. Until the mid-1950s, VB theory dominated chemistry; then, MO theorytook over while VB theory fell into disrepute and was soon almost completelyabandoned. From the 1980s onward, VB theory made a strong comeback andhas ever since been enjoying a renaissance both in qualitative applications of

    Reviews in Computational Chemistry, Volume 20edited by Kenny B. Lipkowitz, Raima Larter, and Thomas R. Cundari

    ISBN 0-471-44525-8 Copyright 2004 Wiley-VCH, John Wiley & Sons, Inc.

    aThis review is dedicated to Roald HoffmannA great teacher and a friend.

    1

  • the theory and the development of new methods for computational implemen-tation.1

    One of the great merits of VB theory is its visually intuitive wave func-tion, expressed as a linear combination of chemically meaningful structures. Itis this feature that made VB theory so popular in the 1930s1950s, and, iro-nically, it is the same feature that accounts for its temporary demise (and ulti-mate resurgence). The comeback of this theory is, therefore, an importantdevelopment. A review of VB theory that highlights its insight into chemicalproblems and discusses some of its state-of-the-art methodologies is timely.

    This chapter is aimed at the nonexpert and designed as a tutorial forfaculty and students who would like to teach and use VB theory, but possessonly a basic knowledge of quantum chemistry. As such, an important focus ofthe chapter will be the qualitative wisdom of the theory and the way it appliesto problems of bonding and reactivity. This part will draw on material dis-cussed in previous works by the authors. Another focus of the chapter willbe on the main methods available today for ab initio VB calculations. How-ever, much important work of a technical nature will, by necessity, be left out.Some of this work (but certainly not all) is covered in a recent monograph onVB theory.1

    A STORY OF VALENCE BOND THEORY, ITSRIVALRY WITH MOLECULAR ORBITAL THEORY,ITS DEMISE, AND EVENTUAL RESURGENCE

    Since VB has achieved a reputation in some circles as an obsolete theory,it is important to give a short historical account of its development includingthe rivalry of VB and MO theory, the fall from favor of VB theory, and thereasons for the dominance of MO theory and the eventual resurgence of VBtheory. Part of the historical review is based on material from the fascinatinghistorical accounts of Servos2 and Brush.3,4 Other parts are not published his-torical accounts, but rational analyses of historical events, reflecting our ownopinions and comments made by colleagues.

    Roots of VB Theory

    The roots of VB theory in chemistry can be traced to the famous paper ofLewis The Atom and The Molecule,5 which introduces the notions of elec-tron-pair bonding and the octet rule.2 Lewis was seeking an understanding ofweak and strong electrolytes in solution, and this interest led him to formulatethe concept of the chemical bond as an intrinsic property of the molecule thatvaries between the covalent (shared-pair) and ionic situations. Lewis paperpredated the introduction of quantum mechanics by 11 years, and constitutes

    2 VB Theory, Its History, Fundamentals, and Applications