Modelling Molecular Structures

This title is an indispensable introduction for all chemists, materials scientists, molecular biologists, and researchers working in, and interested in, the field of molecular modelling.

<b>Alan Hnchliffe</b><br> Department of Chemistry, UMIST, Manchester, UK

Series Preface

xi

Preface to the First Edition

xiii

Preface to the Second Edition

xvii

Prerequisites

1

(23)

What is a Chapter 0?

3

(1)

Branches of Mechanics

4

(1)

Vectors, Vector Fields and Vector Calculus

4

(3)

Vector Calculus

7

(4)

Newton's Laws of Motion

11

(2)

Basic Electrostatics

13

(3)

The Schrodinger Equation

16

(4)

Systems of Units

20

(4)

Molecular Mechanics

24

(34)

Vibrational Motion

24

(4)

Normal Modes of Vibration

28

(1)

The Quantum-Mechanical Treatment

29

(6)

The Taylor Expansion

35

(1)

The Morse Potential

36

(1)

More Advanced Empirical Potentials

37

(1)

Molecular Mechanics

38

(6)

Professional Molecular Mechanics Force Fields

44

(2)

A Sample MM Calculation: Aspirin

46

(2)

The Graphical User Interface

48

(3)

General Features of Potential Energy Surfaces

51

(5)

Other Properties

56

(1)

Protein Docking

56

(1)

Unanswered Questions

57

(1)

Dynamics

58

(14)

Equipartition of Energy

59

(1)

Ensembles

60

(1)

The Boltzmann Distribution

60

(2)

Molecular Dynamics

62

(2)

Collection of Statistics

64

(1)

Simulation of Systems

64

(5)

The Monte Carlo Method

69

(3)

The Hydrogen Molecule Ion

72

(13)

The Born-Oppenheimer Approximation

73

(3)

The LCAO Model

76

(1)

Integral Evaluation

77

(3)

Improving the Atomic Orbital

80

(1)

More Advanced Calculations

81

(1)

Visualization

82

(3)

The Hydrogen Molecule

85

(14)

The Non-Interacting Electron Model

87

(1)

The Valence Bond Model

88

(1)

Indistinguishability

89

(2)

Electron Spin

91

(1)

The Pauli Principle

91

(1)

The Dihydrogen Molecule

92

(2)

Configuration Interaction

94

(1)

The LCAO-Molecular Orbital Model

95

(2)

Comparison of Simple VB AND LCAO Treatments

97

Slater Determinants

77

(22)

The Electron Density

99

(10)

The General LCAO Case

102

(1)

Population Analysis

103

(3)

Density Functions

106

(3)

The Hartree-Fock Model

109

(13)

The LCAO Procedure

113

(4)

The Electronic Energy

117

(1)

The Koopmans Theorem

117

(1)

Open-Shell Systems

118

(2)

Unrestricted Hartree-Fock Theory

120

(1)

The J and K Operators

121

(1)

The Huckel Model

122

(13)

Examples

124

(2)

Bond Lengths and the Huckel model

126

(1)

Molecular Mechanics of π-Electron Systems

127

(1)

Alternant Hydrocarbons

127

(1)

Treatment of Heteroatoms

128

(1)

Extended Huckel Theory

129

(4)

The Nightmare of the Inner Shells

133

(1)

But What is the Huckel Hamiltonian?

134

(1)

Neglect of Differential Overlap Models

135

(19)

The π-electron Zero Differential Overlap Models

136

(7)

The Identity of the Basis Functions

143

(1)

The `All Valence Electron' NDO models

144

(10)

Basis Sets

154

(19)

Hydrogenic Orbitals

155

(2)

Slater's Rules

157

(1)

Clementi and Raimondi

158

(3)

Gaussian Orbitals

161

(3)

The STO/nG Philosophy

164

(3)

The STO/4-31G Story

167

(1)

Extended Basis Sets

168

(2)

Diffuse and Polarization Functions

170

(1)

Effective Core Potentials

171

(2)

Ab Initio Packages

173

(13)

Level of Theory

174

(1)

Geometry Input

174

(4)

An Ab Initio HF-LCAO Calculation

178

(6)

Visualization

184

(2)

Electron Correlation

186

(23)

Configuration Interaction

189

(8)

Perturbation Theory

197

(2)

Moller-Plesset Perturbation Theory

199

(2)

The Dineon Pair Potential

201

(2)

Multiconfiguration SCF

203

(3)

Quadratic Configuration Interaction

206

(2)

Resource Consumption

208

(1)

Slater's Xα Model

209

(9)

The Exchange Potential

211

(1)

The Drude Model

211

(1)

Pauli's Model

212

(1)

The Thomas--Fermi Model

213

(1)

The Atomic Xα Model

214

(1)

Slater's Multiple Scattering Xα Method far Molecules

215

(3)

Density Functional Theory

218

(12)

The Hohenberg--Kohn Theorem

221

(3)

The Kohn-Sham Equations

224

(1)

The Local Density Approximation

225

(1)

Beyond the Local Density Approximation

225

(1)

The Becke Exchange correction

225

(1)

The Lee-Yang-Parr Correlation Potential

226

(1)

Quadrature

226

(1)

A Typical Implementation

227

(3)

Potential Energy Surfaces

230

(22)

A Diatomic Molecule

231

(1)

Characterizing points on a Potential Energy Surface

232

(2)

Locating Stationary Points

234

(4)

General Comments

238

(1)

Steepest Descents

238

(1)

The Fletcher-Reeves Algorithm

238

(1)

The Hellman-Feynman Theorem

239

(1)

The Coupled Hartree-Fock (CPHF) Model

240

(1)

Choice of Variables

241

(4)

Normal Coordinates

245

(4)

Searching for Transition States

249

(1)

Surface-Fitting

249

(3)

Dealing with the Solvent

252

(13)

Langevin Dynamics

252

(1)

The Solvent Box

253

(1)

The Onsager Model

254

(6)

Hybrid Quantum-Mechanical and Molecular Mechanical Methods

260

(5)

Primary Properties and their Derivatives

265

(17)

Electric Multipole Moments

266

(3)

The Multipole Expansion

269

(2)

Charge Distribution in an External Field

271

(1)

Implications of Brillouin's Theorem

271

(1)

Electric Dipole Moments

272

(4)

Analytical Gradients

276

(1)

Electric Quadrupole Moments

276

(1)

Electric Field Gradients

277

(2)

The Electrostatic Potential

279

(3)

Induced Properties

282

(20)

Induced Dipoles

282

(1)

Energy of Charge Distribution in Field

283

(1)

Multipole Polarizabilities

284

(1)

Polarizability Derivatives

285

(1)

A Classical Model of Dipole Polarizability

285

(2)

Quantum-Mechanical Calculations of Static Polarizabilities

287

(3)

Derivatives

290

(2)

Interaction Polarizabilities

292

(2)

The Hamiltonian

294

(2)

Magnetizabilities

296

(1)

Gauge Invariance

296

(2)

Non-Linear Optical Properties

298

(1)

Time-Dependent Perturbation Theory

298

(2)

Time-Dependent Hartree-Fock Theory

300

(2)

Miscellany

302

(23)

The Floating Spherical Gaussian (FSGO) Model

302

(2)

Hyperfine Interactions

304

(12)

Atoms in Molecules

316

(3)

Thermodynamic Quantities

319

(6)

References

325

(6)

Index

331

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Modelling Molecular Structures

Summary

Author Biography

Table of Contents

Supplemental Materials