Understanding Molecular Simulation or Machine Transcription Dictation Text CD Package

Understanding Molecular Simulation: From Algorithms to Applications

Author: Daan Frenkel

Understanding Molecular Simulation: From Algorithms to Applications explains the physics behind the "recipes" of molecular simulation for materials science. Computer simulators are continuously confronted with questions concerning the choice of a particular technique for a given application. A wide variety of tools exist, so the choice of technique requires a good understanding of the basic principles. More importantly, such understanding may greatly improve the efficiency of a simulation program. The implementation of simulation methods is illustrated in pseudocodes and their practical use in the case studies used in the text.

Since the first edition only five years ago, the simulation world has changed significantly -- current techniques have matured and new ones have appeared. This new edition deals with these new developments; in particular, there are sections on:

· Transition path sampling and diffusive barrier crossing to simulaterare events
· Dissipative particle dynamic as a course-grained simulation technique
· Novel schemes to compute the long-ranged forces
· Hamiltonian and non-Hamiltonian dynamics in the context constant-temperature and constant-pressure molecular dynamics simulations
· Multiple-time step algorithms as an alternative for constraints
· Defects in solids
· The pruned-enriched Rosenbluth sampling, recoil-growth, and concerted rotations for complex molecules
· Parallel tempering for glassy Hamiltonians

Examples are included that highlight current applications and the codes of case studies are available on the World Wide Web. Several new examples have been added since the first edition to illustraterecent applications. Questions are included in this new edition. No prior knowledge of computer simulation is assumed.

Booknews

This work for nonexperts involved in computer simulation explains the physics behind the techniques of molecular simulation in materials science, allowing those using simulation to choose appropriate techniques and improve the efficiency of a simulation program. The implementation of simulation methods is illustrated in pseudocodes and their practical use is demonstrated in case studies. This edition presents new material on areas such as transition path sampling and diffusive barrier crossing to simulate rare events, dissipative particle dynamics as a course-grained simulation technique, and parallel tempering for glassy Hamiltonians. Frenkel is affiliated with the FOM Institute for Atomic and Molecular Physics and teaches chemical engineering at the University of Amsterdam, The Netherlands. Smit teaches chemical engineering at the University of Amsterdam. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Table of Contents:

	Preface to the Second Edition	xiii
	Preface	xv
	List of Symbols	xix
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	Nose-Hoover Thermostat	147
6.1.3	Nose-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 Nose-Hoover Algorithm	498
B.2.2	Nose-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	Nose-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

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