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 Liouville Formulation of Time-Reversible Algorithm 4.3.4 Lyapunov Instability 4.3.5 One More Way to Look at the Verlet Algorithm 4.4 Computer Experiments 4.4.1 Diffusio 4.4.2 Order-n 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-lsothermal 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 6.1.2 Nosé-Hoover Thermostat 6.1.3 Nosé-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 Isertion 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 Samplin 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 Itegration 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 Recursive 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 Orientational 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 and Energy 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.1Theoretical Background B.2 Non-Hamiltonian Simulation of the N, V, T Ensemble B.2.1 The Nosé-Hoover Algorithm B.2.2 Nosé-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 Nosé-Hoover Algorithms E.2.1 Canonical Ensemble E.2.2 The Isothermal-Isobaric Ensemble 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.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
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