Preface to the Second Edition | p. xiii |
Preface | p. xv |
List of Symbols | p. xix |
Introduction | p. 1 |
Basics | p. 7 |
Statistical Mechanics | p. 9 |
Entropy and Temperature | p. 9 |
Classical Statistical Mechanics | p. 13 |
Ergodicity | p. 15 |
Questions and Exercises | p. 17 |
Monte Carlo Simulations | p. 23 |
The Monte Carlo Method | p. 23 |
Importance Sampling | p. 24 |
The Metropolis Method | p. 27 |
A Basic Monte Carlo Algorithm | p. 31 |
The Algorithm | p. 31 |
Technical Details | p. 32 |
Detailed Balance versus Balance | p. 42 |
Trial Moves | p. 43 |
Translational Moves | p. 43 |
Orientational Moves | p. 48 |
Applications | p. 51 |
Questions and Exercises | p. 58 |
Molecular Dynamics Simulations | p. 63 |
Molecular Dynamics: The Idea | p. 63 |
Molecular Dynamics: A Program | p. 64 |
Initialization | p. 65 |
The Force Calculation | p. 67 |
Integrating the Equations of Motion | p. 69 |
Equations of Motion | p. 71 |
Other Algorithms | p. 74 |
Higher-Order Schemes | p. 77 |
Liouville Formulation of Time-Reversible Algorithms | p. 77 |
Lyapunov Instability | p. 81 |
One More Way to Look at the Verlet Algorithm | p. 82 |
Computer Experiments | p. 84 |
Diffusion | p. 87 |
Order-n Algorithm to Measure Correlations | p. 90 |
Some Applications | p. 97 |
Questions and Exercises | p. 105 |
Ensembles | p. 109 |
Monte Carlo Simulations in Various Ensembles | p. 111 |
General Approach | p. 112 |
Canonical Ensemble | p. 112 |
Monte Carlo Simulations | p. 113 |
Justification of the Algorithm | p. 114 |
Microcanonical Monte Carlo | p. 114 |
Isobaric-Isothermal Ensemble | p. 115 |
Statistical Mechanical Basis | p. 116 |
Monte Carlo Simulations | p. 119 |
Applications | p. 122 |
Isotension-Isothermal Ensemble | p. 125 |
Grand-Canonical Ensemble | p. 126 |
Statistical Mechanical Basis | p. 127 |
Monte Carlo Simulations | p. 130 |
Justification of the Algorithm | p. 130 |
Applications | p. 133 |
Questions and Exercises | p. 135 |
Molecular Dynamics in Various Ensembles | p. 139 |
Molecular Dynamics at Constant Temperature | p. 140 |
The Andersen Thermostat | p. 141 |
Nose-Hoover Thermostat | p. 147 |
Nose-Hoover Chains | p. 155 |
Molecular Dynamics at Constant Pressure | p. 158 |
Questions and Exercises | p. 160 |
Free Energies and Phase Equilibria | p. 165 |
Free Energy Calculations | p. 167 |
Thermodynamic Integration | p. 168 |
Chemical Potentials | p. 172 |
The Particle Insertion Method | p. 173 |
Other Ensembles | p. 176 |
Overlapping Distribution Method | p. 179 |
Other Free Energy Methods | p. 183 |
Multiple Histograms | p. 183 |
Acceptance Ratio Method | p. 189 |
Umbrella Sampling | p. 192 |
Nonequilibrium Free Energy Methods | p. 196 |
Questions and Exercises | p. 199 |
The Gibbs Ensemble | p. 201 |
The Gibbs Ensemble Technique | p. 203 |
The Partition Function | p. 204 |
Monte Carlo Simulations | p. 205 |
Particle Displacement | p. 205 |
Volume Change | p. 206 |
Particle Exchange | p. 208 |
Implementation | p. 208 |
Analyzing the Results | p. 214 |
Applications | p. 220 |
Questions and Exercises | p. 223 |
Other Methods to Study Coexistence | p. 225 |
Semigrand Ensemble | p. 225 |
Tracing Coexistence Curves | p. 233 |
Free Energies of Solids | p. 241 |
Thermodynamic Integration | p. 242 |
Free Energies of Solids | p. 243 |
Atomic Solids with Continuous Potentials | p. 244 |
Free Energies of Molecular Solids | p. 245 |
Atomic Solids with Discontinuous Potentials | p. 248 |
General Implementation Issues | p. 249 |
Vacancies and Interstitials | p. 263 |
Free Energies | p. 263 |
Numerical Calculations | p. 266 |
Free Energy of Chain Molecules | p. 269 |
Chemical Potential as Reversible Work | p. 269 |
Rosenbluth Sampling | p. 271 |
Macromolecules with Discrete Conformations | p. 271 |
Extension to Continuously Deformable Molecules | p. 276 |
Overlapping Distribution Rosenbluth Method | p. 282 |
Recursive Sampling | p. 283 |
Pruned-Enriched Rosenbluth Method | p. 285 |
Advanced Techniques | p. 289 |
Long-Range Interactions | p. 291 |
Ewald Sums | p. 292 |
Point Charges | p. 292 |
Dipolar Particles | p. 300 |
Dielectric Constant | p. 301 |
Boundary Conditions | p. 303 |
Accuracy and Computational Complexity | p. 304 |
Fast Multipole Method | p. 306 |
Particle Mesh Approaches | p. 310 |
Ewald Summation in a Slab Geometry | p. 316 |
Biased Monte Carlo Schemes | p. 321 |
Biased Sampling Techniques | p. 322 |
Beyond Metropolis | p. 323 |
Orientational Bias | p. 323 |
Chain Molecules | p. 331 |
Configurational-Bias Monte Carlo | p. 331 |
Lattice Models | p. 332 |
Off-lattice Case | p. 336 |
Generation of Trial Orientations | p. 341 |
Strong Intramolecular Interactions | p. 342 |
Generation of Branched Molecules | p. 350 |
Fixed Endpoints | p. 353 |
Lattice Models | p. 353 |
Fully Flexible Chain | p. 355 |
Strong Intramolecular Interactions | p. 357 |
Rebridging Monte Carlo | p. 357 |
Beyond Polymers | p. 360 |
Other Ensembles | p. 365 |
Grand-Canonical Ensemble | p. 365 |
Gibbs Ensemble Simulations | p. 370 |
Recoil Growth | p. 374 |
Algorithm | p. 376 |
Justification of the Method | p. 379 |
Questions and Exercises | p. 383 |
Accelerating Monte Carlo Sampling | p. 389 |
Parallel Tempering | p. 389 |
Hybrid Monte Carlo | p. 397 |
Cluster Moves | p. 399 |
Clusters | p. 399 |
Early Rejection Scheme | p. 405 |
Tackling Time-Scale Problems | p. 409 |
Constraints | p. 410 |
Constrained and Unconstrained Averages | p. 415 |
On-the-Fly Optimization: Car-Parrinello Approach | p. 421 |
Multiple Time Steps | p. 424 |
Rare Events | p. 431 |
Theoretical Background | p. 432 |
Bennett-Chandler Approach | p. 436 |
Computational Aspects | p. 438 |
Diffusive Barrier Crossing | p. 443 |
Transition Path Ensemble | p. 450 |
Path Ensemble | p. 451 |
Monte Carlo Simulations | p. 454 |
Searching for the Saddle Point | p. 462 |
Dissipative Particle Dynamics | p. 465 |
Description of the Technique | p. 466 |
Justification of the Method | p. 467 |
Implementation of the Method | p. 469 |
DPD and Energy Conservation | p. 473 |
Other Coarse-Grained Techniques | p. 476 |
Appendices | p. 479 |
Lagrangian and Hamiltonian | p. 481 |
Lagrangian | p. 483 |
Hamiltonian | p. 486 |
Hamilton Dynamics and Statistical Mechanics | p. 488 |
Canonical Transformation | p. 489 |
Symplectic Condition | p. 490 |
Statistical Mechanics | p. 492 |
Non-Hamiltonian Dynamics | p. 495 |
Theoretical Background | p. 495 |
Non-Hamiltonian Simulation of the N, V, T Ensemble | p. 497 |
The Nose-Hoover Algorithm | p. 498 |
Nose-Hoover Chains | p. 502 |
The N, P, T Ensemble | p. 505 |
Linear Response Theory | p. 509 |
Static Response | p. 509 |
Dynamic Response | p. 511 |
Dissipation | p. 513 |
Electrical Conductivity | p. 516 |
Viscosity | p. 518 |
Elastic Constants | p. 519 |
Statistical Errors | p. 525 |
Static Properties: System Size | p. 525 |
Correlation Functions | p. 527 |
Block Averages | p. 529 |
Integration Schemes | p. 533 |
Higher-Order Schemes | p. 533 |
Nose-Hoover Algorithms | p. 535 |
Canonical Ensemble | p. 536 |
The Isothermal-Isobaric Ensemble | p. 540 |
Saving CPU Time | p. 545 |
Verlet List | p. 545 |
Cell Lists | p. 550 |
Combining the Verlet and Cell Lists | p. 550 |
Efficiency | p. 552 |
Reference States | p. 559 |
Grand-Canonical Ensemble Simulation | p. 559 |
Statistical Mechanics of the Gibbs "Ensemble" | p. 563 |
Free Energy of the Gibbs Ensemble | p. 563 |
Basic Definitions | p. 563 |
Free Energy Density | p. 565 |
Chemical Potential in the Gibbs Ensemble | p. 570 |
Overlapping Distribution for Polymers | p. 573 |
Some General Purpose Algorithms | p. 577 |
Small Research Projects | p. 581 |
Adsorption in Porous Media | p. 581 |
Transport Properties in Liquids | p. 582 |
Diffusion in a Porous Media | p. 583 |
Multiple-Time-Step Integrators | p. 584 |
Thermodynamic Integration | p. 585 |
Hints for Programming | p. 587 |
Bibliography | p. 589 |
Author Index | p. 619 |
Index | p. 628 |
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