Understanding Molecular Simulation - 2nd Edition - ISBN: 9780122673511, 9780080519982

Understanding Molecular Simulation

2nd Edition

From Algorithms to Applications

Authors: Daan Frenkel Berend Smit
eBook ISBN: 9780080519982
Hardcover ISBN: 9780122673511
Imprint: Academic Press
Published Date: 19th October 2001
Page Count: 664
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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 Hamiltonians

Examples 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.


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

Table of Contents

Preface to the Second Edition


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


Author Index



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About the Author

Daan Frenkel

Daan Frenkel is based at the FOM Institute for Atomic and Molecular Physics and at the Department of Chemistry, University of Amsterdam. His research has three central themes: prediction of phase behavior of complex liquids, modeling the (hydro) dynamics of colloids and microporous structures, and predicting the rate of activated processes. He was awarded the prestigious Spinoza Prize from the Dutch Research Council in 2000.

Affiliations and Expertise

FOM Institute for Atomic and Molecular Physics, The Netherlands

Berend Smit

Berend Smit is Professor at the Department of Chemical Engineering of the Faculty of Science, University of Amsterdam. His research focuses on novel Monte Carlo simulations. Smit applies this technique to problems that are of technological importance, particularly those of interest in chemical engineering.

Affiliations and Expertise

University of Amsterdam, Amsterdam, The Netherlands


"…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