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 methods Throughout 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. 1 Introduction. 1.1 Theory and Models - Interpretation of Experimental Data. 1.2 The Notation. 1.3 Vector Space Vn and Function Space Fn. The Scalar Product. 1.4 Linear Transformation - Change of Basis. 1.5 Normalisation and Orthogonalisation of Vectors. 1.6 Matrix Representation of the Scalar Product. 1.7 Dual Vector Space and Hilbert Space. 1.8 Probability Concept and the C Function. 1.9 Operators. 1.10 Representation of Operators in a Basis. 1.11 Change of Basis in Representations of Operators. Test Questions Related to this Chapter. 2 Basic Concepts of Vector Space Theory of Matter. 2.1 The Wave Equation as Probability Function. 2.2 The Postulates of Quantum Mechanics. 2.3 The Schro..dinger Equation. 2.4 Hermicity. 2.5 Exact Measurability and Eigenvalue Problems. 2.6 Eigenvalue Problem of Hermitian Operators. 2.7 The Eigenvalue Equation of the Hamiltonian. 2.8 Eigenvalue Spectrum. Test Questions Related to this Chapter. 3 Consequences of Quantum Mechanics. 3.1 Geometrical Interpretation of Eigenvalue Equations in Vector Space. 3.2 Commutators and Uncertainty Relationships. 3.3 Virtual Particles and the Forces in Nature. Test Questions Related to this Chapter. 4 Chemistry and Quantum Mechanics. 4.1 Eigenvalue Problem of Angular Momentum and 'Orbital' Concept. 4.2 Molecular Orbital and Valence Bond Models. 4.3 Spin and the Antisymmetry Principle. 4.4 The Virial Theorem. 4.5 The Chemical Bond. 4.5.1 General Considerations and One-Electron Contributions. 4.5.2 Chemical Bonds in n-Electron Systems. 4.5.3 Qualitative MO Models for Molecules. Test Questions Related to this Chapter. 5 Approximations for Many-Electron Systems. 5.1 Non-Relativistic Stationary Systems. 5.2 Adiabatic Approximation - The Born-Oppenheimer Approximation. 5.3 The Independent Particle Approximation. 5.4 Spin Orbitals and Slater Determinants. 5.5 Atomic and Molecular Orbitals: The LCAO-MO Approach. 5.6 Quantitative Molecular Orbital Calculations. 5.6.1 Calculations with Slater Determinants. 22.214.171.124 Overlap Integrals. 126.96.36.199 Integrals of One-Electron Operators. 188.8.131.52 Integrals of Two-Electron Operators. 5.6.2 The Hartree-Fock Method. 5.6.3 Hartree-Fock Calculations in the LCAO-MO Approach: The Roothaan-Hall Equation. 5.7 Canonical and Localised Molecular Orbitals and Chemical Model Concepts. Test Questions Related to this Chapter. 6 Perturbation Theory in Quantum Chemistry. 6.1 Projections and Projectors. 6.2 Principles of Perturbation Theory. 6.3 The Rayleigh-Schro..dinger Perturbation Method. 6.4 Applications of Perturbation Theory in Quantum Chemistry. Test Questions Related to this Chapter. 7 Group Theory in Theoretical Chemistry. 7.1 Definition of a Group. 7.2 Symmetry Groups. 7.2.1 Symmetry Operators. 7.2.2 Symmetry Groups and their Representations. 7.2.3 Reducible and Irreducible Representations and Character Tables. 7.3 Applications of Group Theory in Quantum Chemistry. 7.4 Applications of Group Theory in Spectroscopy. 7.4.1 Example 1: Electron Spectroscopy. 7.4.2 Example 2: Infrared/Raman Spectroscopy. Test Questions Related to this Chapter. 8 Computational Quantum Chemistry Methods. 8.1 Ab Initio Methods. 8.1.1 Ab Initio Hartree-Fock (HF) Methods. 8.1.2 Ab Initio Correlated Methods. 184.108.40.206 Configuration Interaction Methods. 220.127.116.11 Multi-Configuration Methods. 18.104.22.168 Coupled Cluster Methods. 22.214.171.124 Pair Methods. 126.96.36.199 Perturbational Methods. 8.2 Semiempirical MO Methods. 8.3 Density Functional Methods. 8.3.1 Local Density Approximation (LDA). 8.3.2 Generalised Gradient Approximation (GGA). 8.3.3 Hybrid Functionals. Test Questions Related to this Chapter. 9 Force Field Methods and Molecular Modelling. 9.1 Empirical Force Fields. 9.2 Molecular Modelling Programs. 9.3 Docking. 9.4 Quantitative Structure-Activity Relationships (QSARs). 9.4.1 Multivariate Linear Regression (MLR). 9.4.2 Nonlinear Regression. 188.8.131.52 Alternate Conditional Expectations (ACE). 184.108.40.206 Project Pursuit Regression (PPR). 220.127.116.11 Multivariate Adaptive Regression Splines (MARS). 9.4.3 Example Calculation. Test Questions Related to this Chapter. 10 Statistical Simulations: Monte Carlo and Molecular Dynamics Methods. 10.1 Common Features. 10.2 Monte Carlo Simulations. 10.3 Molecular Dynamics Simulations. 10.4 Evaluation and Visualisation of Simulation Results. 10.4.1 Structure. 10.4.2 Dynamics. 10.4.3 Specific Evaluations in Macromolecule Simulations. 10.5 Quantum Mechanical Simulations. 10.5.1 Ab initio QM/MM Simulations. 10.5.2 Car-Parrinello DFT Simulations. Test Questions Related to this Chapter. 11 Synopsis. Appendix 1 Ab Initio Hartree-Fock Calculations for Hyposulfuric Acid (H2SO3), including Optimisation of the Geometry. Appendix 2 Books Recommended for Further Reading. Index.