目錄
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 Nos?-Hoover Thermostat
6.1.3 Nos?-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.1 Theoretical Background
B.2 Non-Hamiltonian Simulation of the N, V, T Ensemble
B.2.1 The Nos?-Hoover Algorithm
B.2.2 Nos?-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 Nos?-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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