分子模拟入门 第2版 英文版 影印本PDF电子书下载

1 Introduction 1

Part Ⅰ Basics 7

2 Statistical Mechanics 9

2.1 Entropy and Temperature 9

2.2 Classical Statistical Mechanics 13

2.2.1 Ergodicity 15

2.3 Questions and Exercises 17

3 Monte Carlo Simulations 23

3.1 The Monte Carlo Method 23

3.1.1 Importance Sampling 24

3.1.2 The Metropolis Method 27

3.2 A Basic Monte Carlo Algorithm 31

3.2.1 The Algorithm 31

3.2.2 Technical Details 32

3.2.3 Detailed Balance versus Balance 42

3.3 Trial Moves 43

3.3.1 Translational Moves 43

3.3.2 Orientational Moves 48

3.4 Applications 51

3.5 Questions and Exercises 58

4 Molecular Dynamics Simulations 63

4.1 Molecular Dynamics:The Idea 63

4.2 Molecular Dynamics:A Program 64

4.2.1 Initialization 65

4.2.2 The Force Calculation 67

4.2.3 Integrating the Equations of Motion 69

4.3 Equations of Motion 71

4.3.1 Other Algorithms 74

4.3.2 Higher-Order Schemes 77

4.3.3 Liouville Formulation of Time-Reversible Algorithms 77

4.3.4 Lyapunov Instability 81

4.3.5 One More Way to Look at the Verlet Algorithm 82

4.4 Computer Experiments 84

4.4.1 Diffusion 87

4.4.2 Order-n Algorithm to Measure Correlations 90

4.5 Some Applications 97

4.6 Questions and Exercises 105

Part Ⅱ Ensembles 109

5 Monte Carlo Simulations in Various Ensembles 111

5.1 General Approach 112

5.2 Canonical Ensemble 112

5.2.1 Monte Carlo Simulations 113

5.2.2 Justification of the Algorithm 114

5.3 Microcanonical Monte Carlo 114

5.4 Isobaric-Isothermal Ensemble 115

5.4.1 Statistical Mechanical Basis 116

5.4.2 Monte Carlo Simulations 119

5.4.3 Applications 122

5.5 Isotension-Isothermal Ensemble 125

5.6 Grand-Canonical Ensemble 126

5.6.1 Statistical Mechanical Basis 127

5.6.2 Monte Carlo Simulations 130

5.6.3 Justification of the Algorithm 130

5.6.4 Applications 133

5.7 Questions and Exercises 135

6 Molecular Dynamics in Various Ensembles 139

6.1 Molecular Dynamics at Constant Temperature 140

6.1.1 The Andersen Thermostat 141

6.1.2 Nosé-Hoover Thermostat 147

6.1.3 Nosé-Hoover Chains 155

6.2 Molecular Dynamics at Constant Pressure 158

6.3 Questions and Exercises 160

Part Ⅲ Free Energies and Phase Equilibria 165

7 Free Energy Calculations 167

7.1 Thermodynamic Integration 168

7.2 Chemical Potentials 172

7.2.1 The Particle Insertion Method 173

7.2.2 Other Ensembles 176

7.2.3 Overlapping Distribution Method 179

7.3 Other Free Energy Methods 183

7.3.1 Multiple Histograms 183

7.3.2 Acceptance Ratio Method 189

7.4 Umbrella Sampling 192

7.4.1 Nonequilibrium Free Energy Methods 196

7.5 Questions and Exercises 199

8 The Gibbs Ensemble 201

8.1 The Gibbs Ensemble Technique 203

8.2 The Partition Function 204

8.3 Monte Carlo Simulations 205

8.3.1 Particle Displacement 205

8.3.2 Volume Change 206

8.3.3 Particle Exchange 208

8.3.4 Implementation 208

8.3.5 Analyzing the Results 214

8.4 Applications 220

8.5 Questions and Exercises 223

9 Other Methods to Study Coexistence 225

9.1 Semigrand Ensemble 225

9.2 Tracing Coexistence Curves 233

10 Free Energies of Solids 241

10.1 Thermodynamic Integration 242

10.2 Free Energies of Solids 243

10.2.1 Atomic Solids with Continuous Potentials 244

10.3 Free Energies of Molecular Solids 245

10.3.1 Atomic Solids with Discontinuous Potentials 248

10.3.2 General Implementation Issues 249

10.4 Vacancies and Interstitials 263

10.4.1 Free Energies 263

10.4.2 Numerical Calculations 266

11 Free Energy of Chain Molecules 269

11.1 Chemical Potential as Reversible Work 269

11.2 Rosenbluth Sampling 271

11.2.1 Macromolecules with Discrete Conformations 271

11.2.2 Extension to Continuously Deformable Molecules 276

11.2.3 Overlapping Distribution Rosenbluth Method 282

11.2.4 Recursive Sampling 283

11.2.5 Pruned-Enriched Rosenbluth Method 285

Part Ⅳ Advanced Techniques 289

12 Long-Range Interactions 291

12.1 Ewald Sums 292

12.1.1 Point Charges 292

12.1.2 Dipolar Particles 300

12.1.3 Dielectric Constant 301

12.1.4 Boundary Conditions 303

12.1.5 Accuracy and Computational Complexity 304

12.2 Fast Multipole Method 306

12.3 Particle Mesh Approaches 310

12.4 Ewald Summation in a Slab Geometry 316

13 Biased Monte Carlo Schemes 321

13.1 Biased Sampling Techniques 322

13.1.1 Beyond Metropolis 323

13.1.2 Orientational Bias 323

13.2 Chain Molecules 331

13.2.1 Configurational-Bias Monte Carlo 331

13.2.2 Lattice Models 332

13.2.3 Off-lattice Case 336

13.3 Generation of Trial Orientations 341

13.3.1 Strong Intramolecular Interactions 342

13.3.2 Generation of Branched Molecules 350

13.4 Fixed Endpoints 353

13.4.1 Lattice Models 353

13.4.2 Fully Flexible Chain 355

13.4.3 Strong Intramolecular Interactions 357

13.4.4 Rebridging Monte Carlo 357

13.5 Beyond Polymers 360

13.6 Other Ensembles 365

13.6.1 Grand-Canonical Ensemble 365

13.6.2 Gibbs Ensemble Simulations 370

13.7 Recoil Growth 374

13.7.1 Algorithm 376

13.7.2 Justification of the Method 379

13.8 Questions and Exercises 383

14 Accelerating Monte Carlo Sampling 389

14.1 Parallel Tempering 389

14.2 Hybrid Monte Carlo 397

14.3 Cluster Moves 399

14.3.1 Clusters 399

14.3.2 Early Rejection Scheme 405

15 Tackling Time-Scale Problems 409

15.1 Constraints 410

15.1.1 Constrained and Unconstrained Averages 415

15.2 On-the-Fly Optimization:Car-Parrinello Approach 421

15.3 Multiple Time Steps 424

16 Rare Events 431

16.1 Theoretical Background 432

16.2 Bennett-Chandler Approach 436

16.2.1 Computational Aspects 438

16.3 Diffusive Barrier Crossing 443

16.4 Transition Path Ensemble 450

16.4.1 Path Ensemble 451

16.4.2 Monte Carlo Simulations 454

16.5 Searching for the Saddle Point 462

17 Dissipative Particle Dynamics 465

17.1 Description of the Technique 466

17.1.1 Justification of the Method 467

17.1.2 Implementation of the Method 469

17.1.3 DPD and Energy Conservation 473

17.2 Other Coarse-Grained Techniques 476

Part Ⅴ Appendices 479

A Lagrangian and Hamiltonian 481

A.1 Lagrangian 483

A.2 Hamiltonian 486

A.3 Hamilton Dynamics and Statistical Mechanics 488

A.3.1 Canonical Transformation 489

A.3.2 Symplectic Condition 490

A.3.3 Statistical Mechanics 492

B Non-Hamiltonian Dynamics 495

B.1 Theoretical Background 495

B.2 Non-Hamiltonian Simulation of the N,V,T Ensemble 497

B.2.1 The Nosé-Hoover Algorithm 498

B.2.2 Nosé-Hoover Chains 502

B.3 The N,P,T Ensemble 505

C Linear Response Theory 509

C.1 Static Response 509

C.2 Dynamic Response 511

C.3 Dissipation 513

C.3.1 Electrical Conductivity 516

C.3.2 Viscosity 518

C.4 Elastic Constants 519

D Statistical Errors 525

D.1 Static Properties:System Size 525

D.2 Correlation Functions 527

D.3 Block Averages 529

E Integration Schemes 533

E.1 Higher-Order Schemes 533

E.2 Nosé-Hoover Algorithms 535

E.2.1 Canonical Ensemble 536

E.2.2 The Isothermal-Isobaric Ensemble 540

F Saving CPU Time 545

F.1 Verlet List 545

F.2 Cell Lists 550

F.3 Combining the Verlet and Cell Lists 550

F.4 Efficiency 552

G Reference States 559

G.1 Grand-Canonical Ensemble Simulation 559

H Statistical Mechanics of the Gibbs“Ensemble” 563

H.1 Free Energy of the Gibbs Ensemble 563

H.1.1 Basic Definitions 563

H.1.2 Free Energy Density 565

H.2 Chemical Potential in the Gibbs Ensemble 570

I Overlapping Distribution for Polymers 573

J Some General Purpose Algorithms 577

K Small Research Projects 581

K.1 Adsorption in Porous Media 581

K.2 Transport Properties in Liquids 582

K.3 Diffusion in a Porous Media 583

K.4 Multiple-Time-Step Integrators 584

K.5 Thermodynamic Integration 585

L Hints for Programming 587

Bibliography 589

Author Index 619

Index 628