分子模拟入门 第2版 英文版 影印本PDF|Epub|txt|kindle电子书版本网盘下载

分子模拟入门 第2版 英文版 影印本PDF格式电子书版下载

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1 Introduction1

Part Ⅰ Basics7

2 Statistical Mechanics9

2.1 Entropy and Temperature9

2.2 Classical Statistical Mechanics13

2.2.1 Ergodicity15

2.3 Questions and Exercises17

3 Monte Carlo Simulations23

3.1 The Monte Carlo Method23

3.1.1 Importance Sampling24

3.1.2 The Metropolis Method27

3.2 A Basic Monte Carlo Algorithm31

3.2.1 The Algorithm31

3.2.2 Technical Details32

3.2.3 Detailed Balance versus Balance42

3.3 Trial Moves43

3.3.1 Translational Moves43

3.3.2 Orientational Moves48

3.4 Applications51

3.5 Questions and Exercises58

4 Molecular Dynamics Simulations63

4.1 Molecular Dynamics:The Idea63

4.2 Molecular Dynamics:A Program64

4.2.1 Initialization65

4.2.2 The Force Calculation67

4.2.3 Integrating the Equations of Motion69

4.3 Equations of Motion71

4.3.1 Other Algorithms74

4.3.2 Higher-Order Schemes77

4.3.3 Liouville Formulation of Time-Reversible Algorithms77

4.3.4 Lyapunov Instability81

4.3.5 One More Way to Look at the Verlet Algorithm82

4.4 Computer Experiments84

4.4.1 Diffusion87

4.4.2 Order-n Algorithm to Measure Correlations90

4.5 Some Applications97

4.6 Questions and Exercises105

Part Ⅱ Ensembles109

5 Monte Carlo Simulations in Various Ensembles111

5.1 General Approach112

5.2 Canonical Ensemble112

5.2.1 Monte Carlo Simulations113

5.2.2 Justification of the Algorithm114

5.3 Microcanonical Monte Carlo114

5.4 Isobaric-Isothermal Ensemble115

5.4.1 Statistical Mechanical Basis116

5.4.2 Monte Carlo Simulations119

5.4.3 Applications122

5.5 Isotension-Isothermal Ensemble125

5.6 Grand-Canonical Ensemble126

5.6.1 Statistical Mechanical Basis127

5.6.2 Monte Carlo Simulations130

5.6.3 Justification of the Algorithm130

5.6.4 Applications133

5.7 Questions and Exercises135

6 Molecular Dynamics in Various Ensembles139

6.1 Molecular Dynamics at Constant Temperature140

6.1.1 The Andersen Thermostat141

6.1.2 Nosé-Hoover Thermostat147

6.1.3 Nosé-Hoover Chains155

6.2 Molecular Dynamics at Constant Pressure158

6.3 Questions and Exercises160

Part Ⅲ Free Energies and Phase Equilibria165

7 Free Energy Calculations167

7.1 Thermodynamic Integration168

7.2 Chemical Potentials172

7.2.1 The Particle Insertion Method173

7.2.2 Other Ensembles176

7.2.3 Overlapping Distribution Method179

7.3 Other Free Energy Methods183

7.3.1 Multiple Histograms183

7.3.2 Acceptance Ratio Method189

7.4 Umbrella Sampling192

7.4.1 Nonequilibrium Free Energy Methods196

7.5 Questions and Exercises199

8 The Gibbs Ensemble201

8.1 The Gibbs Ensemble Technique203

8.2 The Partition Function204

8.3 Monte Carlo Simulations205

8.3.1 Particle Displacement205

8.3.2 Volume Change206

8.3.3 Particle Exchange208

8.3.4 Implementation208

8.3.5 Analyzing the Results214

8.4 Applications220

8.5 Questions and Exercises223

9 Other Methods to Study Coexistence225

9.1 Semigrand Ensemble225

9.2 Tracing Coexistence Curves233

10 Free Energies of Solids241

10.1 Thermodynamic Integration242

10.2 Free Energies of Solids243

10.2.1 Atomic Solids with Continuous Potentials244

10.3 Free Energies of Molecular Solids245

10.3.1 Atomic Solids with Discontinuous Potentials248

10.3.2 General Implementation Issues249

10.4 Vacancies and Interstitials263

10.4.1 Free Energies263

10.4.2 Numerical Calculations266

11 Free Energy of Chain Molecules269

11.1 Chemical Potential as Reversible Work269

11.2 Rosenbluth Sampling271

11.2.1 Macromolecules with Discrete Conformations271

11.2.2 Extension to Continuously Deformable Molecules276

11.2.3 Overlapping Distribution Rosenbluth Method282

11.2.4 Recursive Sampling283

11.2.5 Pruned-Enriched Rosenbluth Method285

Part Ⅳ Advanced Techniques289

12 Long-Range Interactions291

12.1 Ewald Sums292

12.1.1 Point Charges292

12.1.2 Dipolar Particles300

12.1.3 Dielectric Constant301

12.1.4 Boundary Conditions303

12.1.5 Accuracy and Computational Complexity304

12.2 Fast Multipole Method306

12.3 Particle Mesh Approaches310

12.4 Ewald Summation in a Slab Geometry316

13 Biased Monte Carlo Schemes321

13.1 Biased Sampling Techniques322

13.1.1 Beyond Metropolis323

13.1.2 Orientational Bias323

13.2 Chain Molecules331

13.2.1 Configurational-Bias Monte Carlo331

13.2.2 Lattice Models332

13.2.3 Off-lattice Case336

13.3 Generation of Trial Orientations341

13.3.1 Strong Intramolecular Interactions342

13.3.2 Generation of Branched Molecules350

13.4 Fixed Endpoints353

13.4.1 Lattice Models353

13.4.2 Fully Flexible Chain355

13.4.3 Strong Intramolecular Interactions357

13.4.4 Rebridging Monte Carlo357

13.5 Beyond Polymers360

13.6 Other Ensembles365

13.6.1 Grand-Canonical Ensemble365

13.6.2 Gibbs Ensemble Simulations370

13.7 Recoil Growth374

13.7.1 Algorithm376

13.7.2 Justification of the Method379

13.8 Questions and Exercises383

14 Accelerating Monte Carlo Sampling389

14.1 Parallel Tempering389

14.2 Hybrid Monte Carlo397

14.3 Cluster Moves399

14.3.1 Clusters399

14.3.2 Early Rejection Scheme405

15 Tackling Time-Scale Problems409

15.1 Constraints410

15.1.1 Constrained and Unconstrained Averages415

15.2 On-the-Fly Optimization:Car-Parrinello Approach421

15.3 Multiple Time Steps424

16 Rare Events431

16.1 Theoretical Background432

16.2 Bennett-Chandler Approach436

16.2.1 Computational Aspects438

16.3 Diffusive Barrier Crossing443

16.4 Transition Path Ensemble450

16.4.1 Path Ensemble451

16.4.2 Monte Carlo Simulations454

16.5 Searching for the Saddle Point462

17 Dissipative Particle Dynamics465

17.1 Description of the Technique466

17.1.1 Justification of the Method467

17.1.2 Implementation of the Method469

17.1.3 DPD and Energy Conservation473

17.2 Other Coarse-Grained Techniques476

Part Ⅴ Appendices479

A Lagrangian and Hamiltonian481

A.1 Lagrangian483

A.2 Hamiltonian486

A.3 Hamilton Dynamics and Statistical Mechanics488

A.3.1 Canonical Transformation489

A.3.2 Symplectic Condition490

A.3.3 Statistical Mechanics492

B Non-Hamiltonian Dynamics495

B.1 Theoretical Background495

B.2 Non-Hamiltonian Simulation of the N,V,T Ensemble497

B.2.1 The Nosé-Hoover Algorithm498

B.2.2 Nosé-Hoover Chains502

B.3 The N,P,T Ensemble505

C Linear Response Theory509

C.1 Static Response509

C.2 Dynamic Response511

C.3 Dissipation513

C.3.1 Electrical Conductivity516

C.3.2 Viscosity518

C.4 Elastic Constants519

D Statistical Errors525

D.1 Static Properties:System Size525

D.2 Correlation Functions527

D.3 Block Averages529

E Integration Schemes533

E.1 Higher-Order Schemes533

E.2 Nosé-Hoover Algorithms535

E.2.1 Canonical Ensemble536

E.2.2 The Isothermal-Isobaric Ensemble540

F Saving CPU Time545

F.1 Verlet List545

F.2 Cell Lists550

F.3 Combining the Verlet and Cell Lists550

F.4 Efficiency552

G Reference States559

G.1 Grand-Canonical Ensemble Simulation559

H Statistical Mechanics of the Gibbs“Ensemble”563

H.1 Free Energy of the Gibbs Ensemble563

H.1.1 Basic Definitions563

H.1.2 Free Energy Density565

H.2 Chemical Potential in the Gibbs Ensemble570

I Overlapping Distribution for Polymers573

J Some General Purpose Algorithms577

K Small Research Projects581

K.1 Adsorption in Porous Media581

K.2 Transport Properties in Liquids582

K.3 Diffusion in a Porous Media583

K.4 Multiple-Time-Step Integrators584

K.5 Thermodynamic Integration585

L Hints for Programming587

Bibliography589

Author Index619

Index628