The Basics of Theoretical and Computational

This textbook does away with the classic, unimaginative approach and comes straight to the point with a bare minimum of mathematics-emphasizing the understanding of concepts rather than presenting endless strings of formulae. It nonetheless covers all important aspects of computational chemistry, such as vector space theory quantum mechanics approximation methods theoretical models and computational methodsThroughout the chapters, mathematics are differentiated by necessity for understanding - fundamental formulae, and all the others. All formulae are explained step by step without omission, but the non-vital ones are marked and can be skipped by those who do not relish complex mathematics.The reader will find the text a lucid and innovative introduction to theoretical and computational chemistry, with food for thought given at the end of each chapter in the shape of several questions that help develop understanding of the concepts.What the reader will not find in this book are condescending sentences such as, 'From (formula A) and (formula M) it is obvious that (formula Z).'

Bernd Michael Rode is professor of theoretical and inorganic chemistry at the University of Innsbruck, Austria. He has taught theoretical chemistry at numerous universities in Asia, where he has also built up new computational chemistry institutions. He has authored nearly 400 scientific publications and obtained numerous honours and awards, among them three honorary doctoral degrees. His present research is focused on theory of liquids and solutions, but he also maintains an experimental group studying chemical evolution towards the origin of life.

Thomas S. Hofer has graduated from a college of technology and obtained his M.Sc. degree in chemistry at the University of Innsbruck. Since 2005, he has been working as assistant professor in theoretical chemistry at the University of Innsbruck and will obtain his Ph.D. degree in this field in 2006. He has published 16 scientific articles, including two review articles. He has been awarded the Austrian nation-wide prize for outstanding studies.

Michael Kugler obtained his secondary education in Tyrol and Upper Austria and is at present a graduate student of physics and chemistry at the University of Innsbruck.

Preface	p. IX
Introduction	p. 1
Theory and Models - Interpretation of Experimental Data	p. 1
The Notation	p. 3
Vector Space V[superscript n] and Function Space F[superscript n]	p. 5
The Scalar Product	p. 5
Linear Transformation - Change of Basis	p. 6
Normalisation and Orthogonalisation of Vectors	p. 6
Matrix Representation of the Scalar Product	p. 7
Dual Vector Space and Hilbert Space	p. 8
Probability Concept and the [Psi] Function	p. 9
Operators	p. 9
Representation of Operators in a Basis	p. 10
Change of Basis in Representations of Operators	p. 11
Test Questions Related to this Chapter	p. 12
Basic Concepts of Vector Space Theory of Matter	p. 13
The Wave Equation as Probability Function	p. 13
The Postulates of Quantum Mechanics	p. 14
The Schrodinger Equation	p. 15
Hermicity	p. 18
Exact Measurability and Eigenvalue Problems	p. 19
Eigenvalue Problem of Hermitian Operators	p. 21
The Eigenvalue Equation of the Hamiltonian	p. 22
Eigenvalue Spectrum	p. 23
Test Questions Related to this Chapter	p. 24
Consequences of Quantum Mechanics	p. 25
Geometrical Interpretation of Eigenvalue Equations in Vector Space	p. 25
Commutators and Uncertainty Relationships	p. 26
Virtual Particles and the Forces in Nature	p. 28
Test Questions Related to this Chapter	p. 29
Chemistry and Quantum Mechanics	p. 31
Eigenvalue Problem of Angular Momentum and 'Orbital' Concept	p. 31
Molecular Orbital and Valence Bond Models	p. 32
Spin and the Antisymmetry Principle	p. 35
The Virial Theorem	p. 36
The Chemical Bond	p. 38
General Considerations and One-Electron Contributions	p. 38
Chemical Bonds in n-Electron Systems	p. 42
Qualitative MO Models for Molecules	p. 44
Test Questions Related to this Chapter	p. 45
Approximations for Many-Electron Systems	p. 47
Non-Relativistic Stationary Systems	p. 47
Adiabatic Approximation - The Born-Oppenheimer Approximation	p. 48
The Independent Particle Approximation	p. 49
Spin Orbitals and Slater Determinants	p. 50
Atomic and Molecular Orbitals: The LCAO-MO Approach	p. 52
Quantitative Molecular Orbital Calculations	p. 53
Calculations with Slater Determinants	p. 53
Overlap Integrals	p. 54
Integrals of One-Electron Operators	p. 54
Integrals of Two-Electron Operators	p. 55
The Hartree-Fock Method	p. 56
Hartree-Fock Calculations in the LCAO-MO Approach: The Roothaan-Hall Equation	p. 58
Canonical and Localised Molecular Orbitals and Chemical Model Concepts	p. 64
Test Questions Related to this Chapter	p. 71
Perturbation Theory in Quantum Chemistry	p. 73
Projections and Projectors	p. 73
Principles of Perturbation Theory	p. 75
The Rayleigh-Schrodinger Perturbation Method	p. 77
Applications of Perturbation Theory in Quantum Chemistry	p. 79
Test Questions Related to this Chapter	p. 80
Group Theory in Theoretical Chemistry	p. 81
Definition of a Group	p. 81
Symmetry Groups	p. 84
Symmetry Operators	p. 84
Symmetry Groups and their Representations	p. 84
Reducible and Irreducible Representations and Character Tables	p. 86
Applications of Group Theory in Quantum Chemistry	p. 93
Applications of Group Theory in Spectroscopy	p. 94
Fxample 1: Electron Spectroscopy	p. 95
Example 2: Infrared/Raman Spectroscopy	p. 96
Test Questions Related to this Chapter	p. 100
Computational Quantum Chemistry Methods	p. 101
Ab Initio Methods	p. 101
Ab Initio Hartree-Fock (HF) Methods	p. 101
Ab Initio Correlated Methods	p. 107
Configuration Interaction Methods	p. 108
Multi-Configuration Methods	p. 109
Coupled Cluster Methods	p. 109
Pair Methods	p. 111
Perturbational Methods	p. 111
Semiempirical MO Methods	p. 112
Density Functional Methods	p. 117
Local Density Approximation (LDA)	p. 121
Generalised Gradient Approximation (GGA)	p. 122
Hybrid Functionals	p. 122
Test Questions Related to this Chapter	p. 124
Force Field Methods and Molecular Modelling	p. 125
Empirical Force Fields	p. 125
Molecular Modelling Programs	p. 126
Docking	p. 127
Quantitative Structure-Activity Relationships (QSARs)	p. 129
Multivariate Linear Regression (MLR)	p. 131
Nonlinear Regression	p. 132
Alternate Conditional Expectations (ACE)	p. 132
Project Pursuit Regression (PPR)	p. 132
Multivariate Adaptive Regression Splines (MARS)	p. 133
Example Calculation	p. 134
Test Questions Related to this Chapter	p. 135
Statistical Simulations: Monte Carlo and Molecular Dynamics Methods	p. 137
Common Features	p. 137
Monte Carlo Simulations	p. 142
Molecular Dynamics Simulations	p. 144
Evaluation and Visualisation of Simulation Results	p. 151
Structure	p. 151
Dynamics	p. 155
Specific Evaluations in Macromolecule Simulations	p. 159
Quantum Mechanical Simulations	p. 162
Ab initio QM/MM Simulations	p. 163
Car-Parrinello DFT Simulations	p. 165
Test Questions Related to this Chapter	p. 166
Synopsis	p. 167
Ab Initio Hartree-Fock Calculations for Hyposulfuric Acid (H[subscript 2]SO[subscript 3]), including Optimisation of the Geometry	p. 169
Books Recommended for Further Reading	p. 173
Index	p. 175
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The Basics of Theoretical and Computational Chemistry

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