Chemical Modelling -- Contents -- Chapter 1 Simulation of the Liquid State -- 1 Introduction -- 2 Simple Liquids -- 2.1 Dynamics -- 2.2 Thermodynamics -- 2.3 Mixtures -- 3 Water and its Solutions -- 3.1 Pure Water -- 3.2 Aqueous Solutions -- 4 Organic Liquids -- 4.1 Alkanes -- 4.2 Oxygen Containing Molecules -- 5 Non-equilibrium Molecular Dynamics (NEMD) -- 6 Glasses -- 6.1 Phenomenology -- 6.2 Structural Models for Supercooled Liquids -- 6.3 Ageing -- 6.4 Rheology -- 6.5 Glasses in Confined Geometries -- 7 Liquid Surfaces -- 7.1 Liquid-Vapour Interfaces -- 7.2 Liquid-Liquid Interfaces -- 7.3 Liquid-Solid Interfaces -- 7.4 Tribology -- 7.5 Two-dimensional Liquids -- 7.6 Droplets -- 8 Dissipative Particle Dynamics -- 9 Computational Techniques -- 9.1 Introduction -- 9.2 Periodic Boundary Conditions -- 9.3 Long-range Coulomb Forces -- 9.4 Integrators and Thermostatting -- 9.5 Ergodicity and Sampling of Rare Events -- References -- Chapter 2 Enumeration in Chemistry -- 1 Introduction and Historical Review -- 1.1 Early History: Isomer Enumeration -- 1.2 Further Enumerations -- 1.3 Why Enumerate? -- 2 Enumeration Methods -- 2.1 Enumeration under Group Equivalences -- 2.2 Linear Recursive Methods - Kekule Structure Counting -- 2.3 Transfer Matrix Methods -- 2.4 Exhaustive Generation (Brute Force) Methods -- 2.5 Other Methods -- 3 Current Results -- 3.1 Isomers: Enumeration and Generation -- 3.2 Fullerenes and Related Objects -- 3.3 Counts of Resonance Structures and Related Items -- 3.4 Walks, Connected Subgraphs and Vertices at a Given Distance -- 3.5 Other Enumerations -- 4 Conclusion -- References -- Chapter 3 Density Functional Theory -- 1 Introduction -- 2 Basic Principles -- 3 Functionals -- 4 Semi-empirical Methods -- 5 Order-N Methods -- 6 Heterogeneous Catalysis -- 7 Descriptions of Chemical Reactions -- 8 Quantum Treatment of Other Particles.

9 Problems with 1/r- Potentials -- 10 Exact-exchange Methods -- 11 Time-dependent Density-functional Theory -- 12 Polarizability and Hyperpolarizability -- 13 Conclusions -- Acknowledgements -- References -- Chapter 4 Numerical Methods for the Solution of 1D, 2D, and 3D Differential Equations Arising in Chemical Problems -- 1 Introduction -- 2 Adapted, Exponentially Fitted and Trigonometrically Fitted Symplectic Integrators -- 2.1 Case m = 0 -- 2.2 Case m = 1 -- 2.3 Runge-Kutta-Nyström Method with FSAL Property -- 2.4 Trigonometrically Fitted Symplectic Intergrators -- 2.5 Exponentially Fitted Symplectic Intergrators -- 2.6 Exponentially Fitted and Trigonometrically Fitted Symplectic Linear Symmetric Multistep Methods -- 2.6.1 First Family of Methods - Case t0 = -2 -- 2.6.2 Second Family of Methods - Case t0 ≠ -2 -- 2.6.3 Stability Analysis -- 2.7 Numerical Examples -- 2.7.1 Inhomogeneous Equation -- 2.7.2 Duffin's Equation -- 2.7.3 An Orbit Problem Studied by Stiefel and Bettis -- 3 Dissipative Methods -- 3.1 Phase-lag of Non-symmetric (Dissipative) Two-step Methods -- 3.2 Dissipative Methods Developed in the Literature -- 3.3 Generator of Dissipative Numerov-type Methods -- 3.4 Exponentially Fitted Dissipative Numerov-type Methods -- 3.4.1 New Exponentially Fitted Dissipative Two-step Method. Case I -- 3.4.2 New Trigonometrically Fitted Dissipative Two-step Method. Case I -- 3.4.3 New Exponentially Fitted Dissipative Two-step Method. Case II -- 3.4.4 New Trigonometrically Fitted Dissipative Two-step Method. Case II -- 4 Numerical Illustrations for Linear Multistep Methods and Dissipative Methods -- 4.1 Resonance Problem -- 4.1.1 The Woods-Saxon Potential -- 4.1.2 Modified Woods-Saxon Potential -- 4.2 The Bound-states Problem -- 4.3 Remarks and Conclusions.

5 New Developments on Numerical Methods with Constant Coefficients and on the Methods with Coefficients Dependent on the Frequency of the Problem -- 5.1 Methods with Constant Coefficients (Generators of Numerical Methods) -- 5.2 Methods with Coeficients Dependent on the Frequency of the Problem -- 5.2.1 Exponentially Fitted Hybrid Methods -- 5.2.2 Bessel-fitted and Neumann-fitted Methods -- 5.3 Runge-Kutta Exponentially Fitted Methods -- 5.4 Modified Runge-Kutta Phase-fitted Methods -- 5.5 Modified Runge-Kutta-Nyström Phase-fitted Methods -- 6 Numerical Illustration on Variable-step Methods -- 6.1 Coupled Differential Equations -- 7 General Comments -- Appendix A -- Appendix B -- Appendix C -- References -- Chapter 5 Computer-aided Drug Design 2000-2001 -- 1 Introduction -- 2 3D-QSAR -- 3 Pharmacophores -- 4 Library Design -- 5 ADME/Tox -- 6 Docking and Scoring -- 7 Cheminformatics -- 8 Structure-based Drug Design -- 9 Reviews -- 10 Conclusions -- References -- Chapter 6 Electric Multipoles, Polarizabilities, Hyperpolarizabilities and Analogous Magnetic Properties -- 1 Introduction -- 2 Response of Closed Shell Molecules to Magnetic Fields -- 2.1 Magnetic Susceptibility -- 2.2 Nuclear Shielding -- 2.3 Interaction of Molecules with Electromagnetic Fields: Higher Order Terms -- 2.4 Gauge Invariance -- 2.4.1 Change of Origin -- 2.4.2 Gauge Invariant Atomic Orbitals (London Atomic Orbitals) (GIAOs or LAOs) -- 2.4.3 Other Approaches to Gauge Invariance -- 2.5 Ab initio Calculations of Magnetic Response to 1999 -- 2.6 Current Density Functional Theory (CDFT) -- 3 Review of Literature on Response of Molecules to Magnetic Fields: June 1999-May 2001 -- 3.1 Ab initio Calculations -- 3.2 Density Functional Calculations -- 4 Review of Literature on Response of Molecules to Electric Fields: June 1999-May 2001.

4.1 New Schemes for Calculation and Analysis of Properties -- 4.2 Ab initio Calculations on Atoms -- 4.3 Ab initio and DFT Calculations on Diatomic Molecules -- 4.4 Ab initio and DFT Calculations on Small and Medium-sized Molecules -- 4.4.1 Water -- 4.4.2 O3, SO2, SeO2 and TeO2 -- 4.4.3 Other Molecules -- 4.5 Semi-empirical Calculations on Molecules -- 4.6 Vibrational Effects -- 4.7 Calculations on Complexes, Dimers, Clusters and Excited States -- 4.8 Fullerenes -- 4.9 Polymers -- 4.10 Crystals -- References -- Chapter 7 Many-body Perturbation Theory and Its Application to the Molecular Electronic Structure Problem -- 1 Introduction -- 2 Many-body Perturbation Theory through Second Order -- 2.1 Rayleigh-Schrödinger Perturbation Theory through Second Order -- 2.2 Møller-Plesset Perturbation Theory -- 2.3 Partitioning and the Remainder Term -- 2.4 The Choice of Zero-order Hamiltonian -- 2.5 Scaling of the Zero-order Hamiltonian -- 2.6 Multireference Second-order Many-body Perturbation Theory, Intruder States and Brillouin-Wigner Perturbation Theory through Second Order -- 3 Some Applications of Second-order Many-body Perturbation Theory with a Møller-Plesset Reference Hamiltonian -- 3.1 Publications with the String 'MP2' in Their Title -- 3.2 Publications with the String 'MP2' in Their Title and/or Keywords -- 3.2.1 Journal of Chemical Physics -- 3.2.2 Chemical Physics Letters -- 3.2.3 Journal of Physical Chemistry A -- 3.2.4 Journal of Physical Chemistry B -- 4 Summary and Prospects -- Acknowledgements -- References -- Chapter 8 Quantum Topological Atoms -- 1 Introduction -- 2 Theoretical -- 2.1 Alternative Partitioning -- 2.2 Electron Correlation -- 2.3 Algorithms and Software -- 2.4 Transferability -- 2.5 Pseudopotential -- 2.6 Intermolecular Interaction -- 2.7 Transfer Probability -- 2.8 Entropy -- 2.9 General Extensions -- 2.10 Quantum Monte Carlo.

2.11 Magnetic Coupling -- 3 Chemical Bonding -- 3.1 Theory -- 3.2 Heavy Atom Group Elements -- 3.3 Surface Science -- 3.4 Fluorides -- 3.5 Transition Metals -- 3.6 van de Waals -- 3.7 Agostic -- 3.8 Radicals -- 3.9 Alkali and Alkaline Earth Oxides and Halides -- 3.10 Organic -- 3.11 Aromaticity -- 3.12 Minerals -- 3.13 Populations -- 3.14 Bond and Valence Indices -- 3.15 Solid State -- 3.16 Organometallics -- 3.17 Chemical Shift -- 3.18 Biological -- 3.19 Noble Gases -- 3.20 Zeolites -- 3.21 Hypervalency -- 3.22 Polymers -- 4 X-Ray Diffraction -- 4.1 Organic Compounds -- 4.2 Minerals -- 4.3 Metals -- 4.4 Hydrogen Bonding -- 4.5 Comparison between Theory and Experiment -- 4.6 Transition Metals -- 4.7 Biological -- 5 Laplacian of the Electron Density -- 5.1 Surface Science -- 5.2 Theory: Electron Pair Localization -- 5.3 Transition Metals -- 5.4 Heavy Metal Group -- 5.5 Non-linear Optics -- 6 Hydrogen Bonding -- 6.1 Reviews -- 6.2 Dihydrogen Bond -- 6.3 Groups 13/15 -- 6.4 C-H...X -- 6.5 Organic -- 6.6 Cooperative Effect -- 6.7 Blue-shifted -- 6.8 Biochemical -- 6.9 With Ions -- 6.10 Isotope Effects -- 6.11 Low Barrier -- 6.12 Intramolecular -- 6.13 π-Systems -- 6.14 Kinetic Energy Density -- 6.15 Organometallic -- 7 Topology of Other Functions -- 7.1 ELF -- 7.2 Electrostatic Potential -- 7.3 Intracule-Extracule -- 8 Reactions -- 8.1 Organic -- 8.2 Inorganic -- 8.3 Transition Metals -- 8.4 Mass Spectrometry -- 8.5 Rotation Barrier -- 8.6 Biological -- 9 Ionic Materials -- 9.1 Thermodynamics -- 9.2 Phase Change -- 9.3 Impurity/Doping -- 10 Spectroscopy -- 11 Opinions and Plans -- 12 Conclusion -- 13 Disclaimer -- References.