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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Kenny B. LipkowitzDepartment of Chemistry

Ladd Hall 104

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

kenny.lipkowitz@ndsu.nodak.edu

Raima LarterDepartment of Chemistry

Indiana University-Purdue University

at Indianapolis,

402 North Blackford StreetIndianapolis, Indiana 46202-3274, USA

rlarter@nsf.gov

Thomas R. CundariDepartment of Chemistry

University of North Texas

Box 305070Denton, Texas 76203-5070, USA

tomc@unt.edu

Donald B. BoydDepartment of Chemistry

Indiana University-Purdue University

at Indianapolis

402 North Blackford StreetIndianapolis, Indiana 46202-3274, USA

boyd@chem.iupui.edu

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 contactreference@wiley.com 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