 The Basics of Theoretical and Computational Chemistry
ISBN: 978-3-527-31773-8
Hardcover
195 pages
March 2007
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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.
5.6.1.1 Overlap Integrals.
5.6.1.2 Integrals of One-Electron Operators.
5.6.1.3 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.
8.1.2.1 Configuration Interaction Methods.
8.1.2.2 Multi-Configuration Methods.
8.1.2.3 Coupled Cluster Methods.
8.1.2.4 Pair Methods.
8.1.2.5 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.
9.4.2.1 Alternate Conditional Expectations (ACE).
9.4.2.2 Project Pursuit Regression (PPR).
9.4.2.3 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.
