Why did we write a second edition？ A minor revision of the first edition would have been adequate to correct the（admittedly many）typographicalmistakes. However, many of the nice comments that we received from stu-dents and colleagues alike, ended with a remark of the type："unfortunately,you don't discuss topic x".

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

 2.2.1 Ergodicity

2.3 Questions and Exercises

 3 Monte Carlo Simulations

3.1 The Monte Carlo Method

 3.1.1 Importance Sampling

 3.1.2 The Metropolis Method

3.2 A Basic Monte Carlo Algorithm

 3.2.1 The Algorithm

 3.2.2 Technical Details

 3.2.3 Detailed Balance versus Balance

3.3 Trial Moves

 3.3.1 Translational Moves

 3.3.2 Orientational 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

 4.2.1 Initialization

 4.2.2 The Force Calculation

 4.2.3 Integrating the Equations of Motion

4.3 Equations of Motion

 4.3.1 Other Algorithms

 4.3.2 Higher-Order Schemes

 4.3.3 LiouviUe Formulation of Time-Reversible Algorithms

 4.3.4 Lyapunov Instability

 4.3.5 One More Way to Look at the Verlet Algorithm

4.4 Computer Experiments

 4.4.1 Diffusion

 4.4.2 Order-Algorithm to Measure Correlations

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

 5.2.1 Monte Carlo Simulations

 5.2.2 Justification of the Algorithm

5.3 Microcanonical Monte Carlo

5.4 Isobaric-Isothermal Ensemble

 5.4.1 Statistical Mechanical Basis

 5.4.2 Monte Carlo Simulations

 5.4.3 Applications

5.5 Isotension-Isothermal Ensemble

5.6 Grand-Canonical Ensemble

 5.6.1 Statistical Mechanical Basis

 5.6.2 Monte Carlo Simulations

 5.6.3 Justification of the Algorithm

 5.6.4 Applications

5.7 Questions and Exercises

 6 Molecular Dynamics in Various Ensembles

6.1 Molecular Dynamics at Constant Temperature

 6.1.1 The Andersen Thermostat 4

 6.1.2 Nos Hoover Thermostat

 6.1.3 Nose-Hoover Chains

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

 7.2.1 The Particle Insertion Method

 7.2.2 Other Ensembles

 7.2.3 Overlapping Distribution Method

7.3 Other Free Energy Methods

 7.3.1 Multiple Histograms

 7.3.2 Acceptance Ratio Method

7.4 Umbrella Sampling

 7.4.1 Nonequilibrium Free Energy Methods

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

 8.3.1 Particle Displacement

 8.3.2 Volume Change

 8.3.3 Particle Exchange

 8.3.4 Implementation

 8.3.5 Analyzing the Results

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

 10.2.1 Atomic Solids with Continuous Potentials

10.3 Free Energies of Molecular Solids

 10.3.1 Atomic Solids with Discontinuous Potentials

 10.3.2 General Implementation Issues

10.4 Vacancies and Interstitials

 10.4.1 Free Energies

 10.4.2 Numerical Calculations

 11 Free Energy of Chain Molecules

11.1 Chemical Potential as Reversible Work

11.2 Rosenbluth Sampling

 11.2.1 Macromolecules with Discrete Conformations

 11.2.2 Extension to Continuously Deformable Molecules

 11.2.3 Overlapping Distribution Rosenbluth Method

 11.2.4 Recnrsive Sampling

 11.2.5 Pruned-Enriched Rosenbluth Method

Part Ⅳ Advanced Techniques

 12 Long-Range Interactions

12.1 Ewald Sums

 12.1.1 Point Charges

 12.1.2 Dipolar Particles

 12.1.3 Dielectric Constant

 12.1.4 Boundary Conditions

 12.1.5 Accuracy and Computational Complexity

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

 13.1.1 Beyond Metropolis

 13.1.2 0rientational Bias

13.2 Chain Molecules

 13.2.1 Configurational-Bias Monte Carlo

 13.2.2 Lattice Models

 13.2.3 Off-lattice Case

13.3 Generation of Trial Orientations

 13.3.1 Strong Intramolecular Interactions

 13.3.2 Generation of Branched Molecules

13.4 Fixed Endpoints

 13.4.1 Lattice Models

 13.4.2 Fully Flexible Chain

 13.4.3 Strong Intramolecular Interactions

 13.4.4 Rebridging Monte Carlo

13.5 Beyond Polymers

13.6 Other Ensembles

 13.6.1 Grand-Canonical Ensemble

 13.6.2 Gibbs Ensemble Simulations

13.7 Recoil Growth

 13.7.1 Algorithm

 13.7.2 Justification of the Method

13.8 Questions and Exercises

 14 Accelerating Monte Carlo Sampling

14.1 Parallel Tempering

14.2 Hybrid Monte Carlo

14.3 Cluster Moves

 14.3.1 Clusters

 14.3.2 Early Rejection Scheme

 15 Tackling Time-Scale Problems

15.1 Constraints

 15.1.1 Constrained and Unconstrained Averages

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

 16.2.1 Computational Aspects

16.3 Diffusive Barrier Crossing

16.4 Transition Path Ensemble

 16.4.1 Path Ensemble

 16.4.2 Monte Carlo Simulations

16.5 Searching for the Saddle Point

 17 Dissipative Particle Dynamics

17.1 Description of the Technique

 17.1.1 Justification of the Method

 17.1.2 Implementation of the Method

 17.1.3 DPD andEnergy Conservation

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

 A.3.1 Canonical Transformation

 A.3.2 Symplectic Condition

 A.3.3 Statistical Mechanics

 B Non-Hamiltonian Dynamics

B.1 Theoretical Background

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

 B.2.1 The Nose-Hoover Algorithm

 B.2.2 Nose-Hoover Chains

 B.3 The N,P,T Ensemble

 C Linear Response Theory

C.1 Static Response

C.2 Dynamic Response

C.3 Dissipation

 C.3.1 Electrical Conductivity

 C.3.2 Viscosity

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 Nose-Hoover Algorithms

 E.2.1 Canonical Ensemble

 E.2.2 The Isothermal-Isobaric Ensemble

 F Saving CPU Time

F.1 VerletList

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.1.1 Basic Definitions

 H.1.2 Free Energy Density

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