|
|
1 | (45) |
|
1.1 A short history of computer simulation |
|
|
1 | (3) |
|
1.2 Computer simulation: motivation and applications |
|
|
4 | (1) |
|
1.3 Model systems and interaction potentials |
|
|
5 | (20) |
|
1.4 Constructing an intermolecular potential from first principles |
|
|
25 | (4) |
|
|
29 | (6) |
|
1.6 Studying small systems |
|
|
35 | (11) |
|
|
46 | (49) |
|
2.1 Sampling from ensembles |
|
|
46 | (6) |
|
2.2 Common statistical ensembles |
|
|
52 | (6) |
|
2.3 Transforming between ensembles |
|
|
58 | (2) |
|
2.4 Simple thermodynamic averages |
|
|
60 | (6) |
|
|
66 | (3) |
|
2.6 Structural quantities |
|
|
69 | (4) |
|
2.7 Time correlation functions and transport coefficients |
|
|
73 | (6) |
|
2.8 Long-range corrections |
|
|
79 | (2) |
|
|
81 | (2) |
|
|
83 | (2) |
|
|
85 | (1) |
|
2.12 Inhomogeneous systems |
|
|
86 | (4) |
|
|
90 | (2) |
|
|
92 | (3) |
|
|
95 | (52) |
|
3.1 Equations of motion for atomic systems |
|
|
95 | (2) |
|
3.2 Finite-difference methods |
|
|
97 | (9) |
|
3.3 Molecular dynamics of rigid non-spherical bodies |
|
|
106 | (7) |
|
|
113 | (7) |
|
3.5 Multiple-timestep algorithms |
|
|
120 | (1) |
|
|
121 | (4) |
|
3.7 Molecular dynamics of hard particles |
|
|
125 | (5) |
|
3.8 Constant-temperature molecular dynamics |
|
|
130 | (10) |
|
3.9 Constant-pressure molecular dynamics |
|
|
140 | (4) |
|
3.10 Grand canonical molecular dynamics |
|
|
144 | (1) |
|
3.11 Molecular dynamics of polarizable systems |
|
|
145 | (2) |
|
|
147 | (38) |
|
|
147 | (1) |
|
4.2 Monte Carlo integration |
|
|
147 | (4) |
|
|
151 | (4) |
|
4.4 The Metropolis method |
|
|
155 | (5) |
|
4.5 Isothermal-isobaric Monte Carlo |
|
|
160 | (4) |
|
4.6 Grand canonical Monte Carlo |
|
|
164 | (4) |
|
4.7 Semi-grand Monte Carlo |
|
|
168 | (1) |
|
|
169 | (8) |
|
|
177 | (6) |
|
|
183 | (2) |
|
5 Some tricks of the trade |
|
|
185 | (31) |
|
|
185 | (1) |
|
5.2 The heart of the matter |
|
|
185 | (8) |
|
|
193 | (7) |
|
5.4 Non-bonded interactions and multiple timesteps |
|
|
200 | (1) |
|
5.5 When the dust has settled |
|
|
201 | (3) |
|
|
204 | (6) |
|
5.7 Organization of the simulation |
|
|
210 | (4) |
|
5.8 Checks on self-consistency |
|
|
214 | (2) |
|
|
216 | (42) |
|
|
216 | (1) |
|
|
217 | (7) |
|
6.3 The particle-particle particle-mesh method |
|
|
224 | (7) |
|
|
231 | (4) |
|
|
235 | (4) |
|
6.6 Fast multipole methods |
|
|
239 | (4) |
|
6.7 The multilevel summation method |
|
|
243 | (4) |
|
6.8 Maxwell equation molecular dynamics |
|
|
247 | (3) |
|
6.9 Long-range potentials in slab geometry |
|
|
250 | (4) |
|
6.10 Which scheme to use? |
|
|
254 | (4) |
|
|
258 | (13) |
|
|
258 | (2) |
|
|
260 | (2) |
|
7.3 Parallel replica exchange |
|
|
262 | (3) |
|
7.4 Parallel domain decomposition |
|
|
265 | (4) |
|
|
269 | (2) |
|
8 How to analyse the results |
|
|
271 | (26) |
|
|
271 | (1) |
|
|
272 | (2) |
|
8.3 Time correlation functions |
|
|
274 | (7) |
|
|
281 | (8) |
|
8.5 Correcting the results |
|
|
289 | (8) |
|
9 Advanced Monte Carlo methods |
|
|
297 | (45) |
|
|
297 | (1) |
|
9.2 Estimation of the free energy |
|
|
298 | (19) |
|
|
317 | (16) |
|
9.4 Simulation of phase equilibria |
|
|
333 | (5) |
|
|
338 | (4) |
|
|
342 | (13) |
|
|
342 | (1) |
|
10.2 Transition state approximation |
|
|
343 | (2) |
|
10.3 Bennett-Chandler approach |
|
|
345 | (1) |
|
10.4 Identifying reaction coordinates and paths |
|
|
346 | (1) |
|
10.5 Transition path sampling |
|
|
347 | (3) |
|
10.6 Forward flux and transition interface sampling |
|
|
350 | (4) |
|
|
354 | (1) |
|
11 Nonequilibrium molecular dynamics |
|
|
355 | (27) |
|
|
355 | (2) |
|
11.2 Spatially oscillating perturbations |
|
|
357 | (4) |
|
11.3 Spatially homogeneous perturbations |
|
|
361 | (9) |
|
11.4 Inhomogeneous systems |
|
|
370 | (1) |
|
11.5 Flow in confined geometry |
|
|
371 | (5) |
|
11.6 Nonequilibrium free-energy measurements |
|
|
376 | (3) |
|
|
379 | (2) |
|
|
381 | (1) |
|
|
382 | (24) |
|
|
382 | (1) |
|
12.2 Langevin and Brownian dynamics |
|
|
383 | (4) |
|
12.3 Brownian dynamics, molecular dynamics, and Monte Carlo |
|
|
387 | (3) |
|
12.4 Dissipative particle dynamics |
|
|
390 | (2) |
|
12.5 Multiparticle collision dynamics |
|
|
392 | (2) |
|
12.6 The lattice-Boltzmann method |
|
|
394 | (3) |
|
12.7 Developing coarse-grained potentials |
|
|
397 | (9) |
|
|
406 | (40) |
|
|
406 | (2) |
|
13.2 Ab-initio molecular dynamics |
|
|
408 | (12) |
|
13.3 Combining quantum and classical force-field simulations |
|
|
420 | (6) |
|
13.4 Path-integral simulations |
|
|
426 | (11) |
|
13.5 Quantum random walk simulations |
|
|
437 | (5) |
|
|
442 | (4) |
|
|
446 | (35) |
|
14.1 The planar gas-liquid interface |
|
|
446 | (16) |
|
14.2 The gas-liquid interface of a molecular fluid |
|
|
462 | (2) |
|
14.3 The liquid-liquid interface |
|
|
464 | (1) |
|
14.4 The solid-liquid interface |
|
|
464 | (5) |
|
|
469 | (6) |
|
|
475 | (4) |
|
|
479 | (2) |
|
Appendix A Computers and computer simulation |
|
|
481 | (6) |
|
|
481 | (1) |
|
A.2 Programming languages |
|
|
482 | (1) |
|
A.3 Fortran programming considerations |
|
|
483 | (4) |
|
|
487 | (4) |
|
|
487 | (4) |
|
Appendix C Calculation of forces and torques |
|
|
491 | (10) |
|
|
491 | (1) |
|
|
491 | (3) |
|
C.3 The molecular fluid with multipoles |
|
|
494 | (2) |
|
C.4 The triple-dipole potential |
|
|
496 | (1) |
|
C.5 Charged particles using Ewald sum |
|
|
497 | (1) |
|
C.6 The Gay-Berne potential |
|
|
498 | (2) |
|
C.7 Numerically testing forces and torques |
|
|
500 | (1) |
|
Appendix D Fourier transforms and series |
|
|
501 | (8) |
|
D.1 The Fourier transform |
|
|
501 | (1) |
|
D.2 Spatial Fourier transforms and series |
|
|
502 | (2) |
|
D.3 The discrete Fourier transform |
|
|
504 | (1) |
|
D.4 Numerical Fourier transforms |
|
|
505 | (4) |
|
Appendix E Random numbers |
|
|
509 | (8) |
|
E.1 Random number generators |
|
|
509 | (1) |
|
E.2 Uniformly distributed random numbers |
|
|
510 | (1) |
|
E.3 Generating non-uniform distributions |
|
|
511 | (3) |
|
E.4 Random vectors on the surface of a sphere |
|
|
514 | (1) |
|
E.5 Choosing randomly and uniformly from complicated regions |
|
|
515 | (1) |
|
E.6 Generating a random permutation |
|
|
516 | (1) |
|
Appendix F Configurational temperature |
|
|
517 | (4) |
|
F.1 Expression for configurational temperature |
|
|
517 | (1) |
|
F.2 Implementation details |
|
|
517 | (4) |
List of Acronyms |
|
521 | (6) |
List of Greek Symbols |
|
527 | (2) |
List of Roman Symbols |
|
529 | (4) |
List of Examples |
|
533 | (1) |
List of Codes |
|
534 | (2) |
Bibliography |
|
536 | (86) |
Index |
|
622 | |