Introduction
to Computational Chemistry. 2 Ed.
Preface.
Chapter 1: Introduction.
1.1 Fundamental Issues.
1.5 Solving the Dynamical Equation.
1.6.1 Separating space and time
variables.
1.6.2 Separating nuclear and electronic
variables.
1.6.3 Separating variables in general.
1.7 Classical Mechanics.
1.8.2 The helium atom.
1.9 Chemistry.
References
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: charges and dipoles.
2.2.7 The electrostatic
energy: multipoles and polarizabilities.
2.2.8 Cross terms.
2.2.9 Small rings and
conjugated systems.
2.2.10 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 metal
coordination compounds.
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.
2.9.3 Modelling the
reactive energy surface by interacting force field functions or by geometry
dependent parameters.
2.10 Hybrid Force Field Electronic
Structure Methods.
References
Chapter 3: Electronic Structure Theory. Independent
Particle Models.
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, and the correct minimum..
3.8.4 Initial guess orbitals.
3.8.5 Direct SCF.
3.8.6 Reduced scaling
techniques.
3.9 Periodic Systems.
3.10 Semi-Empirical Methods.
3.10.1 Neglect of Diatomic
Differential Overlap Approximation (NDDO).
3.10.2 Intermediate Neglect
of Differential Overlap Approximation (INDO).
3.10.3 Complete Neglect
of Differential Overlap Approximation (CNDO).
3.11 Parameterization.
3.11.1 Modified Intermediate
Neglect of Differential Overlap (MINDO).
3.11.2 Modified NDDO models.
3.11.3 Modified Neglect
of Diatomic Overlap (MNDO).
3.11.4 Austin Model 1
(AM1).
3.11.5 Modified Neglect
of Diatomic Overlap, Parametric Method number 3 (MNDO-PM3).
3.11.6 Parametric Method
number 5 (PM5) and PDDG/PM3 methods.
3.11.7 The MNDO/d and
AM1/d methods.
3.11.8 Semi Ab Initio
Method 1.
3.12 Performance of Semi-Empirical
Methods.
3.13 Hückel Theory.
3.13.1 Extended Hückel
theory.
3.13.2 Simple Hückel Theory.
3.14 Limitations and Advantages of
Semi-Empirical Methods.
References
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.
4.10.1
Illustrating correlation methods for the berylium atom.
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.
4.16 Quantum
References
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 Ahlrichs type basis
sets.
5.4.5 Atomic Natural
Orbitals basis sets.
5.4.6 Correlation
Consistent basis sets.
5.4.7 Polarization
Consistent basis sets.
5.4.8 Basis set
extrapolation.
5.5 Plane Wave Basis Functions.
5.6 Recent Developments and
Computational Issues.
5.7 Composite Extrapolation
Procedures.
5.8 Isogyric and Isodesmic
Reactions.
5.9 Effective Core Potentials.
5.10 Basis Set Superposition Errors.
5.11 Pseudospectral Methods.
References
Chapter 6: Density Functional Theory.
6.1 Orbital Free Density Functional
Theory.
6.2 Kohn-Sham Theory.
6.3 Reduced Density Matrix Methods.
6.4 Exchange and Correlation Holes.
6.5 Exchange-Correlation
Functionals.
6.5.1 Local Density
Approximation.
6.5.2
Gradient corrected methods.
6.5.3 Higher order gradient
or meta-GGA methods.
6.5.4 Hybrid or
hyper-GGA methods.
6.5.5 Generalized random
phase methods.
6.5.6 Functional
overview.
6.6 Performance and Properties of
Density Functional Methods.
6.7 DFT Problems.
6.8 Computational Considerations.
6.9 Final Considerations.
References
Chapter 7:
7.1 Classical
7.2 Spin Coupled
7.3 Generalized
References
Chapter 8: Relativistic Methods.
8.1 The Dirac Equation.
8.2 Connections Between the Dirac
and Schrödinger Equations.
8.2.1 Including electric
potentials.
8.2.2 Including both
electric and magnetic potentials.
8.3 Many Particle Systems.
8.4 Four Component Calculations.
8.5 Relativistic Effects.
References
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
Electron Density.
9.3.1 Atoms In
Molecules.
9.3.2 Voronoi, Hirshfeld
and Stewart atomic charges.
9.3.3 Generalized Atomic
Polar Tensor charges.
9.4 Localized Orbitals.
9.4.1 Computational
considerations.
9.5 Natural Orbitals.
9.6 Natural Atomic Orbital and Natural
Bond Orbital Analysis.
9.7 Computational Considerations.
9.8 Examples.
References
Chapter 10: Molecular Properties.
10.1 Examples of Molecular
Properties.
10.1.1 External electric
field.
10.1.2 External magnetic
field.
10.1.3 Internal magnetic
moments.
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.
10.6.1 External electric
field.
10.6.2 Internal electric
field.
10.7 Magnetic Field Perturbation.
10.7.1 External magnetic
field.
10.7.2 Nuclear spin.
10.7.3 Electron spin.
10.7.4 Classical terms.
10.7.5 Relativistic
terms.
10.7.6 Magnetic
properties.
10.7.7 Gauge dependence
of magnetic properties.
10.8 Geometry Perturbations.
10.9 Response and Propagator
Methods.
10.10 Property Basis Sets.
References
Chapter 11: Illustrating the Concepts.
11.1 Geometry Convergence.
11.1.1 Ab Initio
methods.
11.1.2 Density
functional methods.
11.2 Total Energy Convergence.
11.3 Dipole Moment Convergence.
11.3.1 Ab Initio
methods.
11.3.2 Density
functional methods.
11.4 Vibrational Frequencies
Convergence.
11.4.1 Ab Initio methods.
11.4.2 Density
functional methods.
11.5 Bond Dissociation Curve.
11.5.1 Basis set effect
at the Hartree-Fock level.
11.5.2 Performance of
different types of wave functions.
11.5.3 Density
functional 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.
References
Chapter 12: Optimization Techniques.
12.1 Optimizing Quadratic Functions.
12.2 Optimizing General Functions:
Finding Minima.
12.2.1 Steepest Descent.
12.2.2 Conjugate
Gradient methods.
12.2.3 Newton-Raphson
methods.
12.2.4 Step control.
12.2.5 Obtaining the
Hessian.
12.2.6 Storing and
diagonalizing the Hessian.
12.2.7 Extrapolations:
the GDIIS method.
12.3 Choice of Coordinates.
12.4 Optimizing General Functions:
Finding Saddle Points (Transition Structures).
12.4.1 One-structure
interpolation methods: coordinate driving, linear and quadratic synchronous
transit, and sphere optimization.
12.4.2 Two-structure
interpolation methods: saddle, line-then-plane, ridge and step-and-slide
optimizations.
12.4.3 Multi-structure
interpolation methods: chain, locally updated planes, self penalty walk, conjugate
peak refinement and nudged elastic band.
12.4.4 Charateristics of
interpolation methods.
12.4.5 Local methods:
gradient norm minimization.
12.4.6 Local methods:
Newton-Raphson.
12.4.7 Local methods:
the dimer method.
12.4.8 Coordinates for
TS searches.
12.4.9 Charateristics of
local methods.
12.4.10 Dynamic methods.
12.5 Constrained Optimization
Problems.
12.6 Conformational Sampling and the
Global Minimum Problem.
12.6.1 Stochastical and
12.6.2 Molecular
Dynamics.
12.6.3 Simulated
Annealing.
12.6.4 Genetic
Algorithms.
12.6.5 Diffusion
methods.
12.6.6 Distance Geometry
methods.
12.7 Molecular Docking.
12.8 Intrinsic Reaction Coordinate
Methods.
References
Chapter 13: Statistical Mechanics and
13.1
13.2 Rice-Ramsperger-Kasel-Marcus (RRKM) Theory.
13.3 Dynamical Effects.
13.4 Statistical Mechanics.
13.5 The Ideal Gas, Rigid-Rotor
Harmonic-Oscillator Approximation.
13.5.1 Translational
degrees of freedom.
13.5.2
Rotational degrees of freedom.
13.5.3 Vibrational
degrees of freedom.
13.5.4 Electronic
degrees of freedom.
13.5.5 Enthalpy and
entropy contributions.
13.6 Condensed Phases.
References
Chapter 14: Simulation Techniques.
14.1
14.1.1 Generating
non-natural ensembles.
14.2 Time Dependent Methods.
14.2.1 Classical
methods, Molecular Dynamics.
14.2.2 Generating
non-natural ensembles.
14.2.3 Langevin methods.
14.2.4 Direct methods.
14.2.5 Extended Lagrange
techniques (Car-Parrinello methods).
14.2.6 Quantum methods
using potential energy surfaces.
14.2.7 Reaction path
methods.
14.2.8
Non-Born-Oppenheimer methods.
14.2.9 Constrained
sampling methods.
14.3 Periodic Boundary Conditions.
14.4 Extracting Information from
Simulations.
14.5 Free-Energy Methods.
14.5.1 Thermodynamic
perturbation methods.
14.5.2 Thermodynamic
integration methods.
14.6 Solvation Models.
14.7 Continuum Solvation Models.
14.7.1 Poisson-Boltzmann
methods.
14.7.2
Born/Onsager/Kirkwood models.
14.7.3 Self consistent
reaction field models.
References
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 /
15.6 More O’Ferrall-Jencks Diagrams.
Chapter 16: Mathematical Methods.
16.1 Numbers, Vectors, Matrices and Tensors.
16.2 Change of Coordinate System.
16.2.1 Examples of changing the coordinate
system.
16.2.2 Vibrational
normal coordinates.
16.2.3 Energy of a
Slater determinant.
16.2.4 Energy of a CI
wave function.
16.3 Coordinates, Functions, Functionals,
Operators and Superoperators.
16.3.1 Differential operators.
16.4 Normalization,
Orthogonalization and Projection.
16.5 Differential Equations.
16.5.1 Simple first-order differential
equations.
16.5.2 Less simple first-order differential
equations.
16.5.3 Simple second-order differential
equations.
16.5.4 Less simple second-order differential
equations.
16.5.5 Second-order differential equations
depending on the function itself.
16.6 Approximating Functions.
16.6.1
16.6.2 Basis set expansion.
16.7
Fourier and
References
Chapter 17: Statistics
and QSAR.
17.2
Elementary Statistical Measures.
17.3
Correlation Between Two Sets of Data.
17.4 Correlation between Many Sets
of Data.
17.4.1 Multiple descriptor sets and
quality analysis.
17.4.2 Multiple Linear Regression.
17.4.3 Principal Component and Partial Least
Squares analysis.
17.4.4 Illustrative example.
17.5 Quantitative Structure Activity
Relationships (QSAR).
References
Chapter 18: Concluding Remarks.
Appendix A. Notation.
Appendix B. The Variational Principle.
The Hohenberg-Kohn
Theorems.
The Adiabatic Connection
Formula.
Appendix C. Atomic Units.
Appendix D. Z-matrix Construction.
Index.