Molecular Modelling for Beginners

Alan Hinchliffe, Department of Chemistry, UMIST, Manchester, UK.

• Chapter 1: Electric charges and their properties. 1.1 Point Charges.1.2 Coulomb's Law.1.3 Pair wise additivity.1.4 The 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 The 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 The Pair Potential.2.2 The multipole expansion.2.3 The Charge-Dipole interaction.2.4 The dipole-dipole interaction.2.5 Taking account of the temperature.2.6 The 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 (MM).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 (PES).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 Aminoacids.6.4 QSAR.6.5 Problem Set.Chapter 7: Sharing out the energy.7.1 Games of Chance.7.2 Enumeration.7.3 The Boltzmann Probability.7.4 Safety in Numbers.7.5 The Partition Function.7.6 A two-level quantum system.7.7 Lindemann's Theory of Melting.7.8 Problem Set.Chapter 8: Quick guide to Statistical Thermodynamics.8.1 The Ensemble.8.2 The Internal Energy Uth.8.3 The Helmholtz energy A.8.4 The entropy S.8.5 Equation of state and pressure.8.6 Phase space.8.7 The Configurational Integral.8.8 The Virial of Clausius.Chapter 9: Monte Carlo Simulations.9.1 Introduction.9.2 An Early Paper.9.3 The First "Chemical" Monte Carlo Simulation.9.4 Importance Sampling.9.5 The Periodic Box.9.6 Cutoffs.9.7 MC Simulation of Rigid Molecules.9.8 Flexible Molecules.Chapter 10: Molecular Dynamics.10.1 The 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 The Correspondence Principle.11.5 The two-dimensional infinite well.11.6 The three-dimensional infinite well.11.7 Two non-interacting particles.11.8 The 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 The Pauli exclusion principle.12.10 Boltzmann's counting rule.Chapter 13: One-electron atoms.13.1 Atomic Spectra.13.2 The Correspondence Principle.13.3 The infinite nucleus approximation.13.4 Hartree's atomic units.13.5 Schrödinger treatment of the H atom..13.6 The Radial Solutions.13.7 The 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 The Many-Body Problem.14.3 The Orbital model.14.4 Perturbation Theory.14.5 The Variation Method.14.6 The linear variation method.14.7 Slater Determinants.14.8 The Slater-Condon-Shortley Rules.14.9 The Hartree Model.14.10 Atomic Shielding Constants.14.11 Koopmans' Theorem.Chapter 15: Simple molecules..15.1 The Hydrogen molecule-ion H2+.15.2 The LCAO model.15.3 Elliptic orbitals.15.4 The Heilter-London Treatment of Dihydrogen.15.5 The dihydrogen MO treatment.15.6 The James and Coolidge treatment.15.7 Population Analysis.Chapter 16: The HF-LCAO model.16.1 Roothaan's 1951 Landmark Paper.16.2 The and operators.16.3 The HF-LCAO equations.16.4 The electronic energy.16.5 Koopmans? Theorem.16.6 Open Shell systems.16.7 The 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 ã-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 Müller-Plesset Perturbation Theory.19.5 Multiconfiguration SCF.Chapter 20: Density functional theory and the Kohn-Sham LCAO equations.20.1 The Pauli and Thomas-Fermi models.20.2 The Hohenberg Kohn Theorems.20.3 The 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.24.1 Link atoms.24.2 IMOMM.24.3 IMOMO.24.4 ONIOM (Our own N-layered Integrated molecular Orbital and Molecular mechanics).

"This book has been written as an introduction to molecular modeling and is particularly useful to students new to the field. It is particularly good as a reference material as it explains many commonly used terms and equations in a clear and concise manner." (Chromatographia, January 2010)"A useful and comprehensive introduction to the field of molecular modeling for those who wish to understand the theory behind many of the methods in use today." (Reviews, May 2009)