Preface.

Chapter 1: Introduction.

• 1.1 Background.

Chapter 2: Force Field Methods.

• 2.1 Introduction.
• 2.2 The Force Field Energy.
  • 2.2.1 The Stretch Energy.
  • 2.2.2 The Bending Energy.
  • 2.2.3 The out-of-plane Bending Energy.
  • 2.2.4 The Torsional Energy.
  • 2.2.5 The van der Waals Energy.
  • 2.2.6 The Electrostatic Energy.
  • 2.2.7 Cross Terms.
  • 2.2.8 Conjugated Systems.
  • 2.2.9 Comparing Energies of Structurally Different Molecules.
• 2.3 Force Field Parameterization.
  • 2.3.1 Parameter Reductions in Force Fields.
  • 2.3.2 Force Fields for Compounds Containing Metals.
  • 2.3.3 Universal Force Fields.
• 2.4 Differences between Force Fields.
• 2.5 Computational Considerations.
• 2.6 Validation of Force Fields.
• 2.7 Practical Considerations.
• 2.8 Advantages and Limitations of Force Field Methods.
• 2.9 Transition Structure Modelling.
  • 2.9.1 Modelling the TS as a Minimum Energy Structure.
  • 2.9.2 Modelling the TS as a Minimum Energy Structure on the Reactant/Product Energy Seam.
• 2.10 Hybrid Force Field-Electronic Structure Methods.

Chapter 3: Electronic Structure Theory.

• 3.1 The Adiabatic and Born-Oppenheimer Approximations.
• 3.2 Self Consistent Field Theory.
• 3.3 The Energy of a Slater Determinant.
• 3.4 Koopmans' Theorem.
• 3.5 The Basis Set Approximation.
• 3.6 Alternative Formulation of the Variational Problem.
• 3.7 Restricted and Unrestricted Hartree-Fock.
• 3.8 SCF Techniques.
  • 3.8.1 SCF Convergence.
  • 3.8.2 Use of Symmetry.
  • 3.8.3 Ensuring that the HF Energy is a Minimum.
  • 3.8.4 Initial Guess Orbitals.
  • 3.8.5 Direct SCF.
  • 3.8.6 Linear Scaling Techniques.
• 3.9 Semi-Empirical Methods.
  • 3.9.1 Neglect of Diatomic Differential Overlap Approximation (NDDO).
  • 3.9.2 Intermediate Neglect of Differential Overlap Approximation (INDO).
  • 3.9.3 Complete Neglect of Differential Overlap Approximation (CNDO).
• 3.10 Parameterization.
  • 3.10.1 Modified Intermediate Neglect of Differential Overlap (MINDO).
  • 3.10.2 Modified NDDO Models.
  • 3.10.3 Modified Neglect of Diatomic Overlap (MNDO).
  • 3.10.4 Austin Model 1 (AM1).
  • 3.10.5 Modified Neglect of Diatomic Overlap, Parametric Method Number 3 (MNDO-PM3).
  • 3.10.6 The MNDO/d Method.
  • 3.10.7 Semi-Ab Initio Method 1.
• 3.11 Performance of Semi-empirical Methods.
• 3.12 Extended Hückel Theory.
  • 3.12.1 Simple Hückel Theory.
• 3.13 Limitations and Advantages of Semi-empirical Methods.

Chapter 4: Electron Correlation.

• 4.1 Excited Slater Determinants.
• 4.2 Configuration Interaction.
  • 4.2.1 CI Matrix Elements.
  • 4.2.2 Size of the CI Matrix.
  • 4.2.3 Truncated CI Methods.
  • 4.2.4 Direct CI Methods.
• 4.3 Illustrating how CI Accounts for Electron Correlation, and the RHF Dissociation Problem.
• 4.4 The UHF Dissociation and the Spin Contamination Problem.
• 4.5 Size Consistency and Size Extensivity.
• 4.6 Multi-configurational Self Consistent Field.
• 4.7 Multi-reference Configuration Interaction.
• 4.8 Many-body Perturbation Theory.
  • 4.8.1 Møller-Plesset Perturbation Theory.
  • 4.8.2 Unrestricted and Projected Møller-Plesset Methods.
• 4.9 Coupled Cluster Methods.
  • 4.9.1 Truncated Coupled Cluster Methods.
• 4.10 Connections between Coupled Cluster, Configuration Interaction and Perturbation Theory.
• 4.11 Methods Involving Interelectronic Distances.
• 4.12 Direct Methods.
• 4.13 Localized Orbital Methods.
• 4.14 Summary of Electron Correlation Methods.
• 4.15 Excited States.

Chapter 5: Basis Sets.

• 5.1 Slater and Gaussian Type Orbitals.
• 5.2 Classification of Basis Sets.
• 5.3 Even- and Well-tempered Basis Sets.
• 5.4 Contracted Basis Sets.
  • 5.4.1 Pople Style Basis Sets.
  • 5.4.2 Dunning-Huzinaga Basis Sets.
  • 5.4.3 MINI, MIDI, MAXI Basis Sets.
  • 5.4.4 Atomic Natural Orbitals Basis Sets.
  • 5.4.5 Correlation Consistent Basis Sets.
• 5.5 Extrapolation Procedures.
• 5.6 Isodesmic and Isogyric Reactions.
• 5.7 Effective Core Potentials.
• 5.8 Basis Set Superposition Errors.
• 5.9 Pseudospectral Methods.

Chapter 6: Density Functional Theory.

• 6.1 Local Density Methods.
• 6.2 Gradient Corrected Methods.
• 6.3 Hybrid Methods.
• 6.4 Performance.
• 6.5 Computational Considerations.

Chapter 7: Valence Bond Methods.

• 7.1 Classical Valence Bond.
• 7.2 Spin Coupled Valence Bond.
• 7.3 Generalized Valence Bond.

Chapter 8: Relativistic Methods.

• 8.1 Connection Between the Dirac and Schrödinger Equations.
• 8.2 Many-particle Systems.
• 8.3 Four-component Calculations.

Chapter 9: Wave Function Analysis.

• 9.1 Population Analysis Based on Basis Functions.
• 9.2 Population Analysis Based on the Electrostatic Potential.
• 9.3 Population Analysis Based on the Wave Function.
• 9.4 Localized Orbitals.
• 9.5 Natural Orbitals.
• 9.6 Natural Atomic Orbital and Natural Bond Orbital Analysis.
• 9.7 Computational Considerations.
• 9.8 Examples.

Chapter 10: Molecular Properties.

• 10.1 Examples.
  • 10.1.1 External Electric Field.
  • 10.1.2 External Magnetic Field.
  • 10.1.3 Internal Magnetic Field.
  • 10.1.4 Geometry Change.
  • 10.1.5 Mixed Derivatives.
• 10.2 Perturbation Methods.
• 10.3 Derivative Techniques.
• 10.4 Lagrangian Techniques.
• 10.5 Coupled Perturbed Hartree-Fock.
• 10.6 Electric Field Perturbation.
• 10.7 Magnetic Field Perturbation.
  • 10.7.1 External Magnetic Field.
  • 10.7.2 Nuclear Spin.
  • 10.7.3 Gauge Dependence of Magnetic Properties.
• 10.8 Geometry Perturbations.
• 10.9 Propagator Methods.
• 10.10 Property Basis Sets.

Chapter 11: Illustrating the Concepts.

• 11.1 Geometry Convergence.
  • 11.1.1 Ab Initio Methods.
  • 11.1.2 DFT Methods.
• 11.2 Total Energy Convergence.
• 11.3 Dipole Moment Convergence.
  • 11.3.1 Ab Initio Methods.
  • 11.3.2 DFT Methods.
• 11.4 Vibrational Frequencies' Convergence.
  • 11.4.1 Ab Initio Methods.
  • 11.4.2 DFT Methods.
• 11.5 Bond Dissociation Curve.
  • 11.5.1 Basis Set Effect at the HF Level.
  • 11.5.2 Performance of Different Types of Wave Functions.
  • 11.5.3 DFT Methods.
• 11.6 Angle Bending Curve.
• 11.7 Problematic Systems.
  • 11.7.1 The Geometry of FOOF.
  • 11.7.2 The Dipole Moment of CO.
  • 11.7.3 The Vibrational Frequencies of O₃.
• 11.8 Relative Energies of C₄H₆ Isomers.

Chapter 12: Transition State Theory and Statistical Mechanics.

• 12.1 Transition State Theory.
• 12.2 Statistical Mechanics.
  • 12.2.1 q_trans
  • 12.2.2 q_rot
  • 12.2.3 q_vib
  • 12.2.4 q_elec
• 12.3 Enthalpy and Entropy Contributions.

Chapter 13: Change of Coordinate System.

• 13.1 Vibrational Normal Coordinates.
• 13.2 Energy of a Slater Determinant.
• 13.3 Energy of a CI Wave Function.

Chapter 14: Optimization Techniques.

• 14.1 Steepest Descent.
• 14.2 Conjugate Gradient Methods.
• 14.3 Newton-Raphson Methods.
  • 14.3.1 Step Control.
  • 14.3.2 Obtaining the Hessian.
  • 14.3.3 Storing and Diagonalizing the Hessian.
• 14.4 Choice of Coordinates.
• 14.5 Transition Structure Optimization.
  • 14.5.1 Methods Based on Interpolation Between Reactant and Product.
  • 14.5.2 Linear and Quadratic Synchronous Transit.
  • 14.5.3 "Saddle" Optimization Method.
  • 14.5.4 The Chain Method.
  • 14.5.5 The Self Penalty Walk Method.
  • 14.5.6 The Sphere Optimization Technique.
  • 14.5.7 Methods Based on Local Information.
  • 14.5.8 Gradient Norm Minimizations.
  • 14.5.9 Newton-Raphson Methods.
  • 14.5.10 Gradient Extremal Methods.
• 14.6 Constrained Optimization Problems.
• 14.7 Locating the Global Minimum and Conformational Sampling.
  • 14.7.1 Stochastical and Monte Carlo Methods.
  • 14.7.2 Molecular Dynamics.
  • 14.7.3 Simulated Annealing.
  • 14.7.4 Genetic Algorithms.
  • 14.7.5 Diffusion Methods.
  • 14.7.6 Distance Geometry Methods.
• 14.8 Intrinsic Reaction Coordinate Methods.

Chapter 15: Qualitative Theories.

• 15.1 Frontier Molecular Orbital Theory.
• 15.2 Concepts from Density Functional Theory.
• 15.3 Qualitative Molecular Orbital Theory.
• 15.4 Woodward-Hoffmann Rules.
• 15.5 The Bell-Evans-Polanyi Principle / Hammond Postulate / Marcus Theory.
• 15.6 More O'Ferrall-Jenks Diagrams.

Chapter 16: Simulations, Time Dependent Methods and Solvation Models.

• 16.1 Simulation Methods.
  • 16.1.1 Free Energy Methods.
  • 16.1.2 Thermodynamic Perturbation Methods.
  • 16.1.3 Thermodynamic Integration Methods.
• 16.2 Time Dependent Methods.
  • 16.2.1 Classical Methods.
  • 16.2.2 Langevin Methods.
  • 16.2.3 Quantum Methods.
  • 16.2.4 Reaction Path Methods.
• 16.3 Continuum Solvation Models.

Chapter 17: Concluding Remarks.

Appendix A.

• Notation.

Appendix B.

• The Variational Principle.
• The Hohenberg-Kohn Theorems.
• The Adiabatic Connection Formula.

Appendix C.

• First and Second Quantization.

Appendix D.

• Atomic Units.

Appendix E.

• Z-matrix Construction.

Index.