Molecular Modelling for Beginners, 2nd Edition

Preface to the Second Edition.

Preface to the First Edition.

Chapter 1: Electric Charges and their Properties.

1.1 Point Charges.

1.2 Coulomb's Law.

1.3 Pair Wise Additivity.

1.4 Electric Field.

1.5 Work.

1.6 Charge Distributions.

1.7 The Mutual Potential Energy U.

1.8 Relationship between Force and Mutual Potential Energy.

1.9 Electric Multipoles.

1.10 Electrostatic Potential.

1.11 Polarization and Polarizability.

1.12 Dipole Polarizability.

1.13 Many-body forces.

1.14 Problem Set.

Chapter 2: The Forces between Molecules.

2.1 Pair Potential.

2.2 Multipole Expansion.

2.3 Charge-Dipole interaction.

2.4 Dipole-Dipole Interaction.

2.5 Taking Account of the Temperature.

2.6 Induction Energy.

2.7 Dispersion Energy.

2.8 Repulsive Contributions.

2.9 Combination Rules.

2.10 Comparison with Experiment.

2.11 Improved Pair Potentials.

2.12 A Numerical Potential.

2.13 Site-Site Potentials.

2.14 Problem Set.

Chapter 3: Balls on Springs.

3.1 Vibrational Motion.

3.2 The Force Law.

3.3 A Simple Diatomic.

3.4 Three Problems.

3.5 The Morse Potential.

3.6 More Advanced Potentials.

Chapter 4: Molecular Mechanics.

4.1 More about Balls on Springs.

4.2 Larger Systems of Balls on Springs.

4.3 Force Fields.

4.4 Molecular Mechanics (MM).

4.5 Modelling the Solvent.

4.6 Time-and-Money-Saving Tricks.

4.7 Modern Force Fields.

4.8 Some commercial force fields.

Chapter 5: The Molecular Potential Energy Surface.

5.1 Multiple Minima.

5.2 Saddle Points.

5.3 Characterization.

5.4 Finding Minima.

5.5 Multivariate Grid Search.

5.6 Derivative Methods.

5.7 First-Order Methods.

5.8 Second-Order Methods.

5.9 Choice of Method.

5.10 The Z Matrix.

5.11 The End of the Z-Matrix.

5.12 Redundant Internal Coordinates.

Chapter 6: Molecular Mechanics Examples.

6.1 Geometry Optimization.

6.2 Conformation Searches.

6.3 Amino Acids.

6.4 QSAR.

6.5 Problem Set.

Chapter 7: Sharing Out the Energy.

7.1 Games of Chance.

7.2 Enumeration.

7.3 Boltzmann Probability.

7.4 Safety in Numbers.

7.5 Partition Function.

7.6 Two -level Quantum System.

7.7 Lindemann's Theory of Melting.

7.8 Problem Set.

Chapter 8: Introduction to Statistical Thermodynamics.

8.1 The Ensemble.

8.2 The Internal Energy U_th.

8.3 Helmholtz Energy A.

8.4 Entropy S.

8.5 Equation of State and Pressure.

8.6 Phase Space.

8.7 Configurational Integral.

8.8 Virial of Clausius.

Chapter 9: Monte Carlo Simulations.

9.1 An Early Paper.

9.2 The First "Chemical" Monte Carlo Simulation.

9.3 Importance Sampling.

9.4 Periodic Box.

9.5 Cutoffs.

9.6 MC Simulation of Rigid Molecules.

9.7 Flexible Molecules.

Chapter 10: Molecular Dynamics.

10.1 Radial Distribution Function.

10.2 Pair Correlation Functions.

10.3 Molecular Dynamics Methodology.

10.5 Algorithms for Time Dependence.

10.6 Molten Salts.

10.7 Liquid Water.

10.8 Different Types of Molecular Dynamics.

10.9 Uses in Conformational Studies.

Chapter 11: Introduction to Quantum Modeling.

11.1 The Schrödinger Equation.

11.2 The Time-Independent Schrödinger Equation.

11.3 Particles in Potential Wells.

11.4 Correspondence Principle.

11.5 Two-Dimensional Infinite Well.

11.6 Three-Dimensional Infinite Well.

11.7 Two Non-Interacting Particles.

11.8 Finite Well.

11.9 Unbound States.

11.10 Free Particles.

11.11 Vibrational Motion.

Chapter 12: Quantum Gases.

12.1 Sharing Out the Energy.

12.2 Rayleigh Counting.

12.3 The Maxwell-Boltzmann Distribution of Atomic Kinetic Energies.

12.4 Black Body Radiation.

12.5 Modelling Metals.

12.6 Indistinguishability.

12.7 Spin.

12.8 Fermions and Bosons.

12.9 Pauli Exclusion Principle.

12.10 Boltzmann's Counting Rule.

Chapter 13: One-Electron Atoms.

13.1 Atomic Spectra.

13.2 Correspondence Principle.

13.3 Infinite Nucleus Approximation.

13.4 Hartree's Atomic Units.

13.5 Schrödinger Treatment of the Hydrogen Atom..

13.6 Radial Solutions.

13.7 Atomic Orbitals.

13.8 The Stern-Gerlach Experiment.

13.9 Electron Spin.

13.10 Total Angular Momentum.

13.11 Dirac Theory of the Electron.

13.12 Measurement in the Quantum World.

Chapter 14: The Orbital Model.

14.1 One- and Two-Electron Operators.

14.2 Many-Body Problem.

14.3 Orbital Model.

14.4 Perturbation Theory.

14.5 Variation Method.

14.6 The Linear Variation Method.

14.7 Slater Determinants.

14.8 Slater-Condon-Shortley Rules.

14.9 Hartree Model.

14.10 Atomic Shielding Constants.

14.11 Koopmans' Theorem.

Chapter 15: Simple Molecules.

15.1 Hydrogen Molecule-ion H₂+.

15.2 LCAO Model.

15.3 Elliptic Orbitals.

15.4 Heilter-London Treatment of Dihydrogen.

15.5 Dihydrogen MO Treatment.

15.6 James and Coolidge Treatment.

15.7 Population Analysis.

Chapter 16: The HF-LCAO Model.

16.1 Roothaan's 1951 Landmark Paper.

16.2 The Ĵ and &Kcirc; Operators.

16.3 HF-LCAO Equations.

16.4 Electronic Energy.

16.5 Koopman’s Theorem.

16.6 Open Shell Systems.

16.7 Unrestricted Hartree-Fock (UHF) Model.

16.8 Basis Sets.

16.9 Gaussian Orbitals.

Chapter17: HF-LCAO Examples.

17.1 Output.

17.2 Visualization.

17.3 Properties.

17.4 Geometry Optimization.

17.5 Vibrational Analysis.

17.6 Thermodynamic Properties.

17.7 Back to L-Phenylanine.

17.8 Excited States.

17.9 Consequences of the Brillouin Theorem.

17.10 Electric Field Gradients.

17.11 Hyperfine Interactions.

17.12 Problem Set.

Chapter 18: Semiempirical Models.

18.1 Hückel π-electron Theory.

18.2 Extended Hückel Theory.

18.3 Pariser, Parr and Pople.

18.4 Zero Differential Overlap.

18.5 Which Basis Functions Are They?

18.6 All Valence Electron ZDO Models.

18.7 CNDO.

18.8 CNDO/2.

18.9 CNDO/S.

18.10 INDO.

18.11 NDDO (Neglect of Diatomic Differential Overlap).

18.12 The MINDO Family.

18.13 MNDO.

18.14 Austin Model 1 (AM1).

18.15 PM3.

18.16 SAM1.

18.17 ZINDO/1 and ZINDO/S.

18.18 Effective Core Potentials.

18.19 Problem Set.

Chapter 19: Electron Correlation.

19.1 Electron Density Functions.

19.2 Configuration Interaction.

19.3 The Coupled Cluster Method.

19.4 Møller-Plesset Perturbation Theory.

19.5 Multiconfiguration SCF.

Chapter 20: Density Functional Theory and the Kohn-Sham LCAO Equations.

20.1 Pauli and Thomas-Fermi Models.

20.2 Hohenberg Kohn Theorems.

20.3 Kohn-Sham (KS-LCAO) equations.

20.4 Numerical Integration (Quadrature).

20.5 Practical Details.

20.6 Custom and Hybrid Functionals.

20.7 An Example.

Chapter 21: Accurate Thermodynamic Properties; the Gn Models.

21.1 G1 Theory.

21.2 G2 Theory.

21.3 G3 Theory.

Chapter 22: Transition States.

22.1 An Example.

22.2 The Reaction Path.

Chapter 23: Dealing with the Solvent.

23.1 Solvent Models.

23.2 Langevin Dynamics.

23.3 Continuum Solvation Models.

23.4 The Periodic Solvent Box.

Chapter 24: Hybrid Models; the QM/MM Approach.

24.1 Link Atoms.

24.2 IMOMM.

24.3 IMOMO.

24.4 ONIOM (Our own N-layered Integrated Molecular Orbital and Molecular mechanics).

References.

Appendix A.A Mathematical Aide-Memoire.

Appendix B.Glossary.

Appendix C.List of Symbols.

Index.