Introduction 1

Some Terminology 4

Gaussian Compared to Exponential Functions 4

Contracted Gaussians 4

Polarization Functions 7

Complete Sets 8

The Basis Set Superposition Error 9

Choosing a Basis Set 10

Molecular Geometries 11

Energy Differences 15

One-Electron Properties 20

In-Depth Discussion 20

Sources of Gaussian Primitives and Contraction Coefficients 20

Even-Tempered Gaussians 21

Well-Tempered Gaussians 22

MINI-/, MIDI-/ and MAXI-/ etc. 26

Still Others 27

Atomic Natural Orbitals 27

Functions for Augmenting Basis Sets 29

Weak Interactions 34

Conclusion 36

References 37

2. Semiempirical Molecular Orbital Methods 45
James J. P. Stewart

Introduction 45

History of Semiempirical Methods 46

Complete Neglect of Differential Overlap 47

Complete Neglect of Differential Overlap Version 2 50

Intermediate Neglect of Differential Overlap 51

Neglect of Diatomic Differential Overlap (NDDO) 52

Modified Neglect of Diatomic Overlap 55

Austin Model 1 57

Parametric Method Number 3 58

Self-Consistent Field Convergers 58

Strong and Weak Points of NDDO Semiempirical Methods 61

MINDO/3 62

MNDO, AMI, and PM3 62

Theoretical Experiments 73

Stationary Points 74

General Procedure for Characterizing a Reaction 74

Reaction Path 75

Time-Dependent Phenomena 76

Future of Semiempirical Methods 77

Summary 78

References 78

3. Properties of Molecules by Direct Calculation 83
Clifford E. Dykstra, Joseph D. Augspurger, Bernard Kirtman, and David J. Malik

Introduction 83

Overview of Quantum Mechanical Properties 84

Correspondence between Energy Derivatives and Properties 84

Differentiation of the Schrodinger Equation 85

The Development of Methods for Property Determinations 87

Semiempirical Approaches 87

Ab Initio Methods 89

Detailed View of Ab Initio Methods 92

Hamiltonians and Operators 92

Computational Organization of the Differentiation Process 95

Derivatives of Electronic Wavefunctions 97

Local Space Concepts for Extended Systems 99

Vibrations and Rotations 100

Direct Property Calculations 103

Electrical Properties 103

Magnetic Properties 107

Force Constants 109

Transition Probabilities and Optical Properties 110

Summary 111

References 112

4. The Application of Quantitative Design Strategies in Pesticide Discovery 119
Ernest L. Plummer

Introduction 119

The Selection of a Strategy 122

The Well-Designed Substituent Set 126

The Ideal Substituent Set Should Cover All Factors That Control Activity 127

The Ideal Substituent Set Should Cover the Selected Factor Space as Completely as Possible 128

The Ideal Substituent Set Should Span Orthogonal Dimensions of Parameter Space 129

The Ideal Set Should Contain the Minimum Number of Substituents Necessary to Avoid Chance Correlations and Still Meet the Desired Goal 130

Target Compounds Should Be Chosen to Preserve Synthetic Resources But Should Not Be Chosen Just Because They Are Easy to Synthesize 131

The Derivatives Must Be Stable under the Conditions of Bioevaluation 131

Analysis Strategies 132

The Topliss Tree 132

Free-Wilson Analysis 135

A Strategy for Lead Optimization Using Multiple Linear Regression Analysis 138

Choose the Optimal Pattern for Substitution 139

Choose the Factors (Parameters) That Are Likely to Be Important 142

Select a Substituent Set 143

Synthesize and Submit for Biological Evaluation 152

Plot Each Parameter versus Activity 154

Generate Squared Terms if Justified by the Single Parameter Plots 157

Run All Combinations of the Chosen Parameters through Linear Regression Analysis to the Limits of Statistical Significance 158

Repeat the Process Until the QSAR Is Stable 160

Sequential Simplex Optimization (SSO) 161

Conclusion 164

References 165

5. Chemometrics and Multivariate Analysis in Analytical Chemistry 169
Peter C. Jurs

Introduction 169

Response Surfaces, Sampling, and Optimization 170

Signal Processing 173

Principal Components Analysis and Factor Analysis 175

Calibration and Mixture Analysis 178

Classification and Clustering 182

Classification 183

Clustering 184

Library Searching 186

Molecular Structure-Property Relationships 188

Gas Chromatographic Retention Indices for Diverse Drug Compounds 192

Simulation of Carbon-13 Nuclear Magnetic Resonance Spectra of Methyl-Substituted Norbornan-2-ols 198

Summary and Conclusions 207

References 208

6. Searching Databases of Three-Dimensional Structures 213
Yvonne C. Martin, Mark G. Bures, and Peter Willet

Why Are Such Methods Needed? 213

Tools for Searching Two-Dimensional Chemical Structures of Small Molecules 217

Computer Representation of Two-Dimensional Chemical Structures 218

Searching Files of Two-Dimensional Chemical Structures 220 Languages for Chemical Programming 222

System Design for Chemical Information Systems 224

Similarity of Small Molecules Based on Two-Dimensional Structure 225

Substituent Effects on Molecular Properties 225

Two-Dimensional Topological Descriptors of Molecular Shape 226

Similarity of Small Molecules Based on Three-Dimensional Structure 226

Three-Dimensional Similarity Based on Geometric Properties 227

Three-Dimensional Similarity Based on Steric Properties 231

Databases of Three-Dimensional Structures of Molecules 234

Searching Files of Three-Dimensional Structures of Small Molecules 236

Programs from the Cambridge Crystallographic Data Centre 236

Searching Based Principally on Shape Properties 237

Strategies Based on Screen Searching 238

Strategies Based on a Substructure Specification Language 243

Databases and Searching of Multiple Three-Dimensional Pharmacophoric Patterns 248

Searching Files of Three-Dimensional Protein Structures 249

The Protein Data Bank 249

Identification of Patterns of Atoms 249

Identification of Secondary Structure Motifs 252

Conclusions 253

Appendix: Sources of Databases and Programs 255

References 256

7. Molecular Surfaces 265
Paul G. Mezey

Introduction 265

Molecular Body and Molecular Surface 266

Classical Models for Molecular Surfaces: Hard Spheres and van der Waals Surfaces (VDWSs) 267

Electron Density Contour Surfaces 269

The Density Domain Approach to Chemical Bonding (DDA) 271

Molecular Electrostatic Potential 274

Molecular Orbitals 276

Solvent Accessible Surfaces 278

Union Surfaces 279

Interpenetration of Molecular Contour Surfaces 281

Shape Analysis of Molecular Surfaces 282

Conclusions 288

References 289

8. Computer Simulation of Biomolecular Systems Using Molecular Dynamics and Free Energy Peturbation Methods 295
Terry P. Lybrand

Introduction 295

Models 296

Methods 297

Energy Minimization 298

Normal Mode Analysis 298

Monte Carlo 299

Molecular Dynamics 300

Free Energy Pertubation Methods 308

Summary 314

References 315

9. Aspects of Molecular Modeling 321
Donald B. Boyd

Introduction 321

Quantum Mechanics 323

Why Use Quantum Mechanics? 323

Theory 325

Approximations 326

Comparison of Ab Initio and Semiempirical MO Methods 328

Input 329

Output 331

Basis Sets for Ab Initio Calculations 332

Caveats on Basis Sets 334

Post-Hartree-Fock Treatments 334

Selection of an MO Method 336

Numerical Sensitivity of Geometry Optimization Procedures 337

Quality of Results from Quantum Mechanical Methods 339

Information from X-Ray Databases for Molecular Modeling 341

Standard Geometries 345

Distance Geometry 345

Summary 348

References 351

10. Successes of Computer-Assisted Molecular Design 355
Donald B. Boyd

Levels of Success 355

Norfloxacin 359

Metamitron 360

Bromobutide 361

Myclobutanil 362

Conclusion 364

References 365

11. Perspectives on Ab Initio Calculations 373
Ernest R. Davidson

Atomic Orbitals Do Not Work 375

The Error in 'P Is Largest Where 'P Is Largest 376

The Number of Electron Pairs Is N(N - l)/2 377

The Computer Cost, at Fixed Accuracy, Grows Like N! 378

Computers Do Not Solve Problems, People Do 379

Appendix: Compendium of Software for Molecular Modeling 383
Donald B. Boyd

Personal Computers 384

Minicomputers-Superminicomputers-Workstations 387

Supercomputers 392

Subject Index 393