Modelling Molecular Structures / Edition 2

Modelling Molecular Structures / Edition 2

by Alan Hinchliffe
     
 

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ISBN-10: 047148993X

ISBN-13: 9780471489931

Pub. Date: 10/11/2000

Publisher: Wiley

The application of mathematical models to molecules has now reached maturity. Scientists as diverse as astrophysicists, biologists, chemists, materials scientists and zoologists can reach for their PC, Mac or laptop to model molecular phenomena of unbelievable complexity.
Following the highly successful first edition of Modelling Molecular Structures, this

Overview

The application of mathematical models to molecules has now reached maturity. Scientists as diverse as astrophysicists, biologists, chemists, materials scientists and zoologists can reach for their PC, Mac or laptop to model molecular phenomena of unbelievable complexity.
Following the highly successful first edition of Modelling Molecular Structures, this newly updated edition is your guide through the myriad of applications for molecular modelling. This easy-to-read, highly illustrated text covers all areas of molecular modelling, including molecular dynamics, quantum mechanics, and the Hartree-Fock self-consistent field model, providing background information and critically discussing the latest techniques in the field.
Covering developments in the field since the first publication, this title also includes updated text and new material on:

• Molecular Dynamics

• Dealing with the Solvent
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.

Product Details

ISBN-13:
9780471489931
Publisher:
Wiley
Publication date:
10/11/2000
Series:
Wiley Series in Theoretical Chemistry Series, #3
Pages:
354
Product dimensions:
6.10(w) x 8.80(h) x 0.78(d)

Table of Contents

Series Prefacexi
Preface to the First Editionxiii
Preface to the Second Editionxvii
0Prerequisites1
0.1What is a Chapter 0?3
0.2Branches of Mechanics4
0.3Vectors, Vector Fields and Vector Calculus4
0.4Vector Calculus7
0.5Newton's Laws of Motion11
0.6Basic Electrostatics13
0.7The Schrodinger Equation16
0.8Systems of Units20
1Molecular Mechanics24
1.1Vibrational Motion24
1.2Normal Modes of Vibration28
1.3The Quantum-Mechanical Treatment29
1.4The Taylor Expansion35
1.5The Morse Potential36
1.6More Advanced Empirical Potentials37
1.7Molecular Mechanics38
1.8Professional Molecular Mechanics Force Fields44
1.9A Sample MM Calculation: Aspirin46
1.10The Graphical User Interface48
1.11General Features of Potential Energy Surfaces51
1.12Other Properties56
1.13Protein Docking56
1.14Unanswered Questions57
2Dynamics58
2.1Equipartition of Energy59
2.2Ensembles60
2.3The Boltzmann Distribution60
2.4Molecular Dynamics62
2.5Collection of Statistics64
2.6Simulation of Systems64
2.7The Monte Carlo Method69
3The Hydrogen Molecule Ion72
3.1The Born--Oppenheimer Approximation73
3.2The LCAO Model76
3.3Integral Evaluation77
3.4Improving the Atomic Orbital80
3.5More Advanced Calculations81
3.6Visualization82
4The Hydrogen Molecule85
4.1The Non-Interacting Electron Model87
4.2The Valence Bond Model88
4.3Indistinguishability89
4.4Electron Spin91
4.5The Pauli Principle91
4.6The Dihydrogen Molecule92
4.7Configuration Interaction94
4.8The LCAO--Molecular Orbital Model95
4.9Comparison of Simple VB and LCAO Treatments97
4.10Slater Determinants97
5The Electron Density99
5.1The General LCAO Case102
5.2Population Analysis103
5.3Density Functions106
6The Hartree-Fock Model109
6.1The LCAO Procedure113
6.2The Electronic Energy117
6.3The Koopmans Theorem117
6.4Open-Shell Systems118
6.5Unrestricted Hartree--Fock Theory120
6.6The J and K Operators121
7The Huckel Model122
7.1Examples124
7.2Bond Lengths and the Huckel model126
7.3Molecular Mechanics of [pi]-Electron Systems127
7.4Alternant Hydrocarbons127
7.5Treatment of Heteroatoms128
7.6Extended Huckel Theory129
7.7The Nightmare of the Inner Shells133
7.8But What is the Huckel Hamiltonian?134
8Neglect of Differential Overlap Models135
8.1The [pi]-electron Zero Differential Overlap Models136
8.2The Identity of the Basis Functions143
8.3The 'All Valence Electron' NDO models144
9Basis Sets154
9.1Hydrogenic Orbitals155
9.2Slater's Rules157
9.3Clementi and Raimondi158
9.4Gaussian Orbitals161
9.5The STO/nG Philosophy164
9.6The STO/4--31G Story167
9.7Extended Basis Sets168
9.8Diffuse and Polarization Functions170
9.9Effective Core Potentials171
10Ab Initio Packages173
10.1Level of Theory174
10.2Geometry Input174
10.3An Ab Initio HF--LCAO Calculation178
10.4Visualization184
11Electron Correlation186
11.1Configuration Interaction189
11.2Perturbation Theory197
11.3Moller-Plesset Perturbation Theory199
11.4The Dineon Pair Potential201
11.5Multiconfiguration SCF203
11.6Quadratic Configuration Interaction206
11.7Resource Consumption208
12Slater's X[alpha] Model209
12.1The Exchange Potential211
12.2The Drude Model211
12.3Pauli's Model212
12.4The Thomas--Fermi Model213
12.5The Atomic X[alpha] Model214
12.6Slater's Multiple Scattering X[alpha] Method for Molecules215
13Density Functional Theory218
13.1The Hohenberg--Kohn Theorem221
13.2The Kohn--Sham Equations224
13.3The Local Density Approximation225
13.4Beyond the Local Density Approximation225
13.5The Becke Exchange correction225
13.6The Lee--Yang--Parr Correlation Potential226
13.7Quadrature226
13.8A Typical Implementation227
14Potential Energy Surfaces230
14.1A Diatomic Molecule231
14.2Characterizing points on a Potential Energy Surface232
14.3Locating Stationary Points234
14.4General Comments238
14.5Steepest Descents238
14.6The Fletcher--Reeves Algorithm238
14.7The Hellman--Feynman Theorem239
14.8The Coupled Hartree--Fock (CPHF) Model240
14.9Choice of Variables241
14.10Normal Coordinates245
14.11Searching for Transition States249
14.12Surface-Fitting249
15Dealing with the Solvent252
15.1Langevin Dynamics252
15.2The Solvent Box253
15.3The Onsager Model254
15.4Hybrid Quantum-Mechanical and Molecular Mechanical Methods260
16Primary Properties and their Derivatives265
16.1Electric Multipole Moments266
16.2The Multipole Expansion269
16.3Charge Distribution in an External Field271
16.4Implications of Brillouin's Theorem271
16.5Electric Dipole Moments272
16.6Analytical Gradients276
16.7Electric Quadrupole Moments276
16.8Electric Field Gradients277
16.9The Electrostatic Potential279
17Induced Properties282
17.1Induced Dipoles282
17.2Energy of Charge Distribution in Field283
17.3Multipole Polarizabilities284
17.4Polarizability Derivatives285
17.5A Classical Model of Dipole Polarizability285
17.6Quantum-Mechanical Calculations of Static Polarizabilities287
17.7Derivatives290
17.8Interaction Polarizabilities292
17.9The Hamiltonian294
17.10Magnetizabilities296
17.11Gauge Invariance296
17.12Non-Linear Optical Properties298
17.13Time-Dependent Perturbation Theory298
17.14Time-Dependent Hartree--Fock Theory300
18Miscellany302
18.1The Floating Spherical Gaussian (FSGO) Model302
18.2Hyperfine Interactions304
18.3Atoms in Molecules316
18.4Thermodynamic Quantities319
References325
Index331

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