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Computer Simulation of Liquids 2017.pdf
Cover
Preface
Contents
1 Introduction
1.1 A short history of computer simulation
1.2 Computer simulation: motivation and applications
1.3 Model systems and interaction potentials
1.4 Constructing an intermolecular potential from first principles
1.5 Force fields
1.6 Studying small systems
2 Statistical mechanics
2.1 Sampling from ensembles
2.2 Common statistical ensembles
2.3 Transforming between ensembles
2.4 Simple thermodynamic averages
2.5 Fluctuations
2.6 Structural quantities
2.7 Time correlation functions and transport coefficients
2.8 Long-range corrections
2.9 Quantum corrections
2.10 Constraints
2.11 Landau free energy
2.12 Inhomogeneous systems
2.13 Fluid membranes
2.14 Liquid crystals
3 Molecular dynamics
3.1 Equations of motion for atomic systems
3.2 Finite-difference methods
3.3 Molecular dynamics of rigid non-spherical bodies
3.4 Constraint dynamics
3.5 Multiple-timestep algorithms
3.6 Checks on accuracy
3.7 Molecular dynamics of hard particles
3.8 Constant-temperature molecular dynamics
3.9 Constant-pressure molecular dynamics
3.10 Grand canonical molecular dynamics
3.11 Molecular dynamics of polarizable systems
4 Monte Carlo methods
4.1 Introduction
4.2 Monte Carlo integration
4.3 Importance sampling
4.4 The Metropolis method
4.5 Isothermal–isobaric Monte Carlo
4.6 Grand canonical Monte Carlo
4.7 Semi-grand Monte Carlo
4.8 Molecular liquids
4.9 Parallel tempering
4.10 Other ensembles
5 Some tricks of the trade
5.1 Introduction
5.2 The heart of the matter
5.3 Neighbour lists
5.4 Non-bonded interactions and multiple timesteps
5.5 When the dust has settled
5.6 Starting up
5.7 Organization of the simulation
5.8 Checks on self-consistency
6 Long-range forces
6.1 Introduction
6.2 The Ewald sum
6.3 The particle–particle particle–mesh method
6.4 Spherical truncation
6.5 Reaction field
6.6 Fast multipole methods
6.7 The multilevel summation method
6.8 Maxwell equation molecular dynamics
6.9 Long-range potentials in slab geometry
6.10 Which scheme to use?
7 Parallel simulation
7.1 Introduction
7.2 Parallel loops
7.3 Parallel replica exchange
7.4 Parallel domain decomposition
7.5 Parallel constraints
8 How to analyse the results
8.1 Introduction
8.2 Liquid structure
8.3 Time correlation functions
8.4 Estimating errors
8.5 Correcting the results
9 Advanced Monte Carlo methods
9.1 Introduction
9.2 Estimation of the free energy
9.3 Smarter Monte Carlo
9.4 Simulation of phase equilibria
9.5 Reactive Monte Carlo
10 Rare event simulation
10.1 Introduction
10.2 Transition state approximation
10.3 Bennett–Chandler approach
10.4 Identifying reaction coordinates and paths
10.5 Transition path sampling
10.6 Forward flux and transition interface sampling
10.7 Conclusions
11 Nonequilibrium molecular dynamics
11.1 Introduction
11.2 Spatially oscillating perturbations
11.3 Spatially homogeneous perturbations
11.4 Inhomogeneous systems
11.5 Flow in confined geometry
11.6 Nonequilibrium free-energy measurements
11.7 Practical points
11.8 Conclusions
12 Mesoscale methods
12.1 Introduction
12.2 Langevin and Brownian dynamics
12.3 Brownian dynamics, molecular dynamics, and Monte Carlo
12.4 Dissipative particle dynamics
12.5 Multiparticle collision dynamics
12.6 The lattice-Boltzmann method
12.7 Developing coarse-grained potentials
13 Quantum simulations
13.1 Introduction
13.2 Ab-initio molecular dynamics
13.3 Combining quantum and classical force-field simulations
13.4 Path-integral simulations
13.5 Quantum random walk simulations
13.6 Over our horizon
14 Inhomogeneous fluids
14.1 The planar gas–liquid interface
14.2 The gas–liquid interface of a molecular fluid
14.3 The liquid–liquid interface
14.4 The solid–liquid interface
14.5 The liquid drop
14.6 Fluid membranes
14.7 Liquid crystals
Appendix A Computers and computer simulation
A.1 Computer hardware
A.2 Programming languages
A.3 Fortran programming considerations
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
C.5 Charged particles using Ewald sum
C.6 The Gay–Berne potential
C.7 Numerically testing forces and torques
Appendix D Fourier transforms and series
D.1 The Fourier transform
D.2 Spatial Fourier transforms and series
D.3 The discrete Fourier transform
D.4 Numerical Fourier transforms
Appendix E Random numbers
E.1 Random number generators
E.2 Uniformly distributed random numbers
E.3 Generating non-uniform distributions
E.4 Random vectors on the surface of a sphere
E.5 Choosing randomly and uniformly from complicated regions
E.6 Generating a random permutation
Appendix F Configurational temperature
F.1 Expression for configurational temperature
F.2 Implementation details
List of Acronyms
List of Greek Symbols
List of Roman Symbols
List of Examples
List of Codes
Bibliography
Index
COMPUTER SIMULATION OF LIQUIDS
Computer Simulation of Liquids
Second Edition
Michael P. Allen
Department of Physics, University of Warwick, UK
H. H. Wills Physics Laboratory, University of Bristol, UK
Dominic J. Tildesley
Centre Européen de Calcul Atomique et Moléculaire (CECAM),
EPFL, Switzerland
3
3
Great Clarendon Street, Oxford, OX2 6DP,
United Kingdom
Oxford University Press is a department of the University of Oxford.
It furthers the University’s objective of excellence in research, scholarship,
and education by publishing worldwide. Oxford is a registered trade mark of
Oxford University Press in the UK and in certain other countries
© M. P. Allen and D. J. Tildesley 2017
The moral rights of the authors have been asserted
First Edition published in 1987
Second Edition published in 2017
Impression: 1
All rights reserved. No part of this publication may be reproduced, stored in
a retrieval system, or transmitted, in any form or by any means, without the
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and you must impose this same condition on any acquirer
Published in the United States of America by Oxford University Press
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Library of Congress Control Number: 2017936745
ISBN 978–0–19–880319–5 (hbk.)
ISBN 978–0–19–880320–1 (pbk.)
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Links to third party websites are provided by Oxford in good faith and
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To Diane, Eleanor, Pauline, and Charles
Preface
In the years following the publication of the rst edition, we have frequently discussed
producing an updated version, and indeed have been nagged on many occasions by
colleagues to do so. Despite its increasingly dated content, with quaint references to
microche, magnetic tapes, and Fortran-77 language examples, the rst edition has
continued to sell well for three decades. is is quite surprising, bearing in mind the
tremendous development of the eld and the computer technologies on which it is based.
To an extent, the material in our book has been complemented by the publication of other
books and online resources which help to understand the underlying principles. Also, it is
much easier than it used to be to nd technical details in the primary literature, in papers,
appendices, and supplementary information. New and improved techniques appear all
the time, and the problem is almost that there is too much information, and too much
rediscovery of existing methods. e widespread use of simulation packages has provided
enormous leverage in this research eld. ere is much to gain by carefully reading the
manual for your chosen package, and we strongly recommend it!
Nonetheless, it remains true that ‘geing started’ can be a signicant barrier, and there
is always the need to understand properly what is going on ‘under the hood’, so as not to
use a packaged technique beyond its range of validity. Many colleagues have rearmed
to us that there is still a need for a general guide book, concentrating on the strengths of
the rst edition: providing practical advice and examples rather than too much theory. So,
we agreed that an updated version of our book would be of value. We intended to produce
this many years ago, and it is a sad fact that the demands of academia and industry le
too lile time to make good on these aspirations. We wish to acknowledge the patience
of our editor at Oxford University Press, S¨onke Adlung, who has stuck with us over this
long period.
Although the eld has grown enormously, we resisted the temptation to change
the title of the book. It was always focused on the liquid state, and this encompasses
what are now known as complex uids, such as liquid crystals, polymers, some colloidal
suspensions, gels, so maer in general, some biological systems such as uid membranes,
and glasses. e techniques will also be of interest outside the aforementioned elds, and
there is no well-dened dividing line, but we try not to stray too far outside our expertise.
Rather than give a long list in the title, we hope that ‘Computer Simulation of Liquids’,
interpreted with some latitude, is still suciently descriptive.
e content of the book, although structured in the same way as the rst edition,
has changed to reect the above expansion in the eld, as well as technical advances.
e rst few chapters cover basic material. Molecular dynamics in various ensembles
is now regarded as basic, rather than advanced, and we devote whole chapters to the
handling of long-range forces and simulating on parallel computers, both of which are
now mainstream topics. ere are a few more chapters covering advanced simulation
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