Understanding Molecular Simulation book cover

Understanding Molecular Simulation

From Algorithms to Applications

Understanding Molecular Simulation: From Algorithms to Applications explains the physics behind the "recipes" of molecular simulation for materials science. Computer simulators are continuously confronted with questions concerning the choice of a particular technique for a given application. A wide variety of tools exist, so the choice of technique requires a good understanding of the basic principles. More importantly, such understanding may greatly improve the efficiency of a simulation program. The implementation of simulation methods is illustrated in pseudocodes and their practical use in the case studies used in the text.Since the first edition only five years ago, the simulation world has changed significantly -- current techniques have matured and new ones have appeared. This new edition deals with these new developments; in particular, there are sections on:· Transition path sampling and diffusive barrier crossing to simulaterare events· Dissipative particle dynamic as a course-grained simulation technique· Novel schemes to compute the long-ranged forces· Hamiltonian and non-Hamiltonian dynamics in the context constant-temperature and constant-pressure molecular dynamics simulations· Multiple-time step algorithms as an alternative for constraints· Defects in solids· The pruned-enriched Rosenbluth sampling, recoil-growth, and concerted rotations for complex molecules· Parallel tempering for glassy HamiltoniansExamples are included that highlight current applications and the codes of case studies are available on the World Wide Web. Several new examples have been added since the first edition to illustrate recent applications. Questions are included in this new edition. No prior knowledge of computer simulation is assumed.

Audience
Graduate students in physics and materials science departments studying molecular simulation techniques; scientists in the fields of polymers, materials science, and applied physics.

Hardbound, 664 Pages

Published: October 2001

Imprint: Academic Press

ISBN: 978-0-12-267351-1

Reviews

  • "…brilliantly maintains a balance between explaining the physical phenomena and performing computations. Its marvelous writing style invites scientists and students to deepen their knowledge of MD simulations."--ComputingReviews.com, January 11, 2013
    "... this book brilliantly lays down the scientific foundations of the simulational approach ..."--
    Prof. Kurt Binder in Physics World, 1997
    "... a treasure. The book is a marvellous mix of just enough formalism with an informal and readable style, sufficient detail to understand methodological advances, appropriate mathematics ..."--Prof. Mark A. Ratner in Physics Today, 1997


Contents


  • Preface to the Second Edition

    Preface

    List of Symbols

    1 Introduction

    Part I Basics

    2 Statistical Mechanics

    2.1 Entropy and Temperature

    2.2 Classical Statistical Mechanics

    2.3 Questions and Exercises

    3 Monte Carlo Simulations

    3.1 The Monte Carlo Method

    3.2 A Basic Monte Carlo Algorithm

    3.3 Trial Moves

    3.4 Applications

    3.5 Questions and Exercises

    4 Molecular Dynamics Simulations

    4.1 Molecular Dynamics: the Idea

    4.2 Molecular Dynamics: a Program

    4.3 Equations of Motion

    4.4 Computer Experiments

    4.5 Some Applications

    4.6 Questions and Exercises

    Part II Ensembles

    5 Monte Carlo Simulations in Various Ensembles

    5.1 General Approach

    5.2 Canonical Ensemble

    5.3 Microcanonical Monte Carlo

    5.4 Isobaric-Isothermal Ensemble

    5.5 Isotension-Isothermal Ensemble

    5.6 Grand-Canonical Ensemble

    5.7 Questions and Exercises

    6 Molecular Dynamics in Various Ensembles

    6.1 Molecular Dynamics at Constant Temperature

    6.2 Molecular Dynamics at Constant Pressure

    6.3 Questions and Exercises

    Part III Free Energies and Phase Equilibria

    7 Free Energy Calculations

    7.1 Thermodynamic Integration

    7.2 Chemical Potentials

    7.3 Other Free Energy Methods

    7.4 Umbrella Sampling

    7.5 Questions and Exercises

    8 The Gibbs Ensemble

    8.1 The Gibbs Ensemble Technique

    8.2 The Partition Function

    8.3 Monte Carlo Simulations

    8.4 Applications

    8.5 Questions and Exercises

    9 Other Methods to Study Coexistence

    9.1 Semigrand Ensemble

    9.2 Tracing Coexistence Curves

    10 Free Energies of Solids

    10.1 Thermodynamic Integration

    10.2 Free Energies of Solids

    10.3 Free Energies of Molecular Solids

    10.4 Vacancies and Interstitials

    11 Free Energy of Chain Molecules

    11.1 Chemical Potential as Reversible Work

    11.2 Rosenbluth Sampling

    Part IV Advanced Techniques

    12 Long-Range Interactions

    12.1 Ewald Sums

    12.2 Fast Multipole Method

    12.3 Particle Mesh Approaches

    12.4 Ewald Summation in a Slab Geometry

    13 Biased Monte Carlo Schemes

    13.1 Biased Sampling Techniques

    13.2 Chain Molecules

    13.3 Generation of Trial Orientations

    13.4 Fixed Endpoints

    13.5 Beyond Polymers

    13.6 Other Ensembles

    13.7 Recoil Growth

    13.8 Questions and Exercises

    14 Accelerating Monte Carlo Sampling

    14.1 Parallel Tempering

    14.2 Hybrid Monte Carlo

    14.3 Cluster Moves

    15 Tackling Time-Scale Problems

    15.1 Constraints

    15.2 On-the-Fly Optimization: Car-Parrinello Approach

    15.3 Multiple Time Steps

    16 Rare Events

    16.1 Theoretical Background

    16.2 Bennett-Chandler Approach

    16.3 Diffusive Barrier Crossing

    16.4 Transition Path Ensemble

    16.5 Searching for the Saddle Point

    17 Dissipative Particle Dynamics

    17.1 Description of the Technique

    17.2 Other Coarse-Grained Techniques

    Part V Appendices

    A Lagrangian and Hamiltonian

    A.1 Lagrangian

    A.2 Hamiltonian

    A.3 Hamilton Dynamics and Statistical Mechanics

    B Non-Hamiltonian Dynamics

    B.1 Theoretical Background

    B.2 Non-Hamiltonian Simulation of the N, V, T Ensemble

    B.3 The N, P, T Ensemble

    C Linear Response Theory

    C.1 Static Response

    C.2 Dynamic Response

    C.3 Dissipation

    C.4 Elastic Constants

    D Statistical Errors

    D.1 Static Properties: System Size

    D.2 Correlation Functions

    D.3 Block Averages

    E Integration Schemes

    E.1 Higher-Order Schemes

    E.2 Nosé-Hoover Algorithms

    F Saving CPU Time

    F.1 Verlet List

    F.2 Cell Lists

    F.3 Combining the Verlet and Cell Lists

    F.4 Efficiency

    G Reference States

    G.1 Grand-Canonical Ensemble Simulation

    H Statistical Mechanics of the Gibbs Ensemble

    H.1 Free Energy of the Gibbs Ensemble

    H.2 Chemical Potential in the Gibbs Ensemble

    I Overlapping Distribution for Polymers

    J Some General Purpose Algorithms

    K Small Research Projects

    K.1 Adsorption in Porous Media

    K.2 Transport Properties in Liquids

    K.3 Diffusion in a Porous Media

    K.4 Multiple-Time-Step Integrators

    K.5 Thermodynamic Integration

    L Hints for Programming

    Bibliography

    Author Index

    Index

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