Description:
A first in its field, this book is both an introduction to computer simulation of liquids for upper level undergraduates and a how-to guide for specialists. The authors discuss the latest simulation techniques of molecular dynamics and the Monte Carlo methods as well as how to avoid common programming pitfalls. Theoretical concepts and practical programming advice are amply reinforced with examples of computer simulation in action and samples of Fortran code. The authors have also included a wide selection of programs and routines on microfiche to aid chemists, physicists, chemical engineers, and computer scientists, as well as graduate and advanced students in chemistry.
Table Of Contents

                           List of Symbols

       Introduction

             A short history of computer simulation

             Computer simulation: motivation and applications

             Model systems and interaction potentials

                    Introduction

                    Atomic systems

                    Molecular Systems

                    Lattice Systems

                    Calculating the Potential

             Constructing an intermolecular potential

                    Introduction

                    Building the Model Potential

                    Adjusting the model potential

             Studying small systems

                    Introduction

                    Periodic boundary conditions

                    Potential truncation

                    Computer code for periodic boundaries

                    Spherical Boundary conditions

       Statistical Mechanics

             Sampling from ensembles

             Common statistical ensembles

             Transforming between ensembles

             Simple thermodynamic average

             Fluctuations

             Structural quantities

             Time Correlation functions and transport coefficients

             Long-range corrections

             Quantum corrections

             Constraints

       Molecular Dynamics

             Equations of motion for atomic systems

             Finite difference methods

                    The Verlet algorithm

                    The Gear predictor-corrector

                    Other methods

             Molecular dynamics of rigid non-spherical bodies

                    Non-linear molecules

                    Linear molecules

             Constraint Dynamics

             Checks on Accuracy

             Molecular dynamics of hard systems

                    Hard spheres

                    Hard non-spherical bodies

       Monte Carlo Methods

             Introduction

             Monte Carlo integration

                    Hit and miss

                    Sample mean integration

             Importance sampling

             The Metropolis Method

             Isothermal-isobaric Monte Carlo

             Grand canonical Monte Carlo

             Molecular Liquids

                    Rigid molecules

                    Non-rigid molecules

       Some Tricks of The Trade

             Introduction

             The heart of the matter

                    Efficient calculation of forces, energies, and pressures

                    Avoiding the square root

                    Table look-up and spline-fit potentials

                    Shifted and shifted-force potentials

             Neighbour lists

                    The Verlet neighbour list

                    Cell structures and linked lists

             Multiple time step methods

             How to handle long-range forces

                    Introduction

                    The Ewald sum

                    The reaction field method

                    Other methods

                    Summary

             When the dust has settled

             Starting up

                    The initial configuration

                    The initial velocities

                    Equilibration

             Organization of the simulation

                    Input/output and file handling

                    Program structure

                    The Scheme in action

       How to Analyse the Results

             Introduction

             Liquid structure

             Time correlation functions

                    The direct approach

                    The fast Fourier transform method

             Estimating errors

                    Errors in equilibrium averages

                    Errors in fluctuations

                    Errors in structural quantities

                    Errors in time correlation functions

             Correcting the results

                    Correcting thermodynamic averages

                    Extending g(r) to large r

                    Extrapolating g(r) to contact

                    Smoothing g(r)

                    Calculating transport coefficients

                    Smoothing a spectrum

       Advanced Simulation Techniques

             Introduction

             Free Energy Estimation

                    Introduction

                    Non-Boltzmann sampling

                    Acceptance ratio method

                    Summary

             Smarter Monte Carlo

                    Preferential sampling

                    Force-bias Monte Carlo

                    Smart Monte Carlo

                    Virial-bias Monte Carlo

             Constant-temperature molecular dynamics

                    Stochastic methods

                    Extended system methods

                    Constraint methods

                    Other methods

             Constant-pressure molecular dynamics

                    Extended system methods

                    Constraint methods

                    Other methods

                    Changing box shape

             Practical points

             The Gibbs Monte Carlo method

       Non-Equilibrium Molecular Dynamics

             Introduction

             Shear flow

             Expansion and contraction

             Heat flow

             Diffusion

             Other perturbations

             Practical points

       Brownian Dynamics

             Introduction

             Projection operators

             Brownian dynamics

             Hydrodynamic and memory effects

       Quantum Simulations

             Introduction

             Semiclassical path-integral simulations

             Semiclassical Gaussian wavepackets

             Quantum random walk simulations

       Some Applications

             Introduction

             The liquid drop

             Melting

             Molten salts

             Liquid crystals

             Rotational dynamics

             Long-time tails

             Interfaces

APPENDIX A COMPUTERS AND COMPUTER SIMULATION

             A.1 Computer hardware

             A.2 Programming hardware

             A.3 Efficient programming in FORTRAN-77

APPENDIX B REDUCED UNITS

             B.1 Reduced units

APPENDIX C CALCULATION OF FORCES AND TORQUES

             C.1 Introduction

             C.2 The polymer chain

             C.3 The molecular fluid with multipoles

             C.4 The triple-dipole potential

APPENDIX D FOURIER TRANSFORMS

             D.1 The Fourier transform

             D.2 The discrete Fourier transform

             D.3 Numerical Fourier transforms

APPENDIX E THE GEAR PREDICTOR-CORRECTOR

             E.1 The Gear predictor-corrector

APPENDIX F PROGRAM AVAILABILITY

APPENDIX G RANDOM NUMBERS

             G.1 Random number generators

             G.2 Random numbers uniform on (0,1)

             G.3 Generating non-uniform distributions

             G.4 Random vectors on the surface of a sphere

             G.5 Choosing randomly and uniformly from complicated regions

             G.6 Sampling from an arbitrary distribution

References

Index