Understanding Molecular Simulation: From Algorithms to Applications / Edition 1

Understanding Molecular Simulation: From Algorithms to Applications / Edition 1

by Daan Frenkel, Berend Smit
     
 

ISBN-10: 0122673700

ISBN-13: 9780122673702

Pub. Date: 01/28/1996

Publisher: Elsevier Science & Technology Books

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

Overview

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 illustrate recent applications. Questions are included in this new edition. No prior knowledge of computer simulation is assumed.

Product Details

ISBN-13:
9780122673702
Publisher:
Elsevier Science & Technology Books
Publication date:
01/28/1996
Edition description:
Older Edition
Pages:
443
Product dimensions:
6.00(w) x 9.00(h) x 1.07(d)

Table of Contents

Preface to the Second Editionxiii
Prefacexv
List of Symbolsxix
1Introduction1
Part IBasics7
2Statistical Mechanics9
2.1Entropy and Temperature9
2.2Classical Statistical Mechanics13
2.2.1Ergodicity15
2.3Questions and Exercises17
3Monte Carlo Simulations23
3.1The Monte Carlo Method23
3.1.1Importance Sampling24
3.1.2The Metropolis Method27
3.2A Basic Monte Carlo Algorithm31
3.2.1The Algorithm31
3.2.2Technical Details32
3.2.3Detailed Balance versus Balance42
3.3Trial Moves43
3.3.1Translational Moves43
3.3.2Orientational Moves48
3.4Applications51
3.5Questions and Exercises58
4Molecular Dynamics Simulations63
4.1Molecular Dynamics: The Idea63
4.2Molecular Dynamics: A Program64
4.2.1Initialization65
4.2.2The Force Calculation67
4.2.3Integrating the Equations of Motion69
4.3Equations of Motion71
4.3.1Other Algorithms74
4.3.2Higher-Order Schemes77
4.3.3Liouville Formulation of Time-Reversible Algorithms77
4.3.4Lyapunov Instability81
4.3.5One More Way to Look at the Verlet Algorithm82
4.4Computer Experiments84
4.4.1Diffusion87
4.4.2Order-n Algorithm to Measure Correlations90
4.5Some Applications97
4.6Questions and Exercises105
Part IIEnsembles109
5Monte Carlo Simulations in Various Ensembles111
5.1General Approach112
5.2Canonical Ensemble112
5.2.1Monte Carlo Simulations113
5.2.2Justification of the Algorithm114
5.3Microcanonical Monte Carlo114
5.4Isobaric-Isothermal Ensemble115
5.4.1Statistical Mechanical Basis116
5.4.2Monte Carlo Simulations119
5.4.3Applications122
5.5Isotension-Isothermal Ensemble125
5.6Grand-Canonical Ensemble126
5.6.1Statistical Mechanical Basis127
5.6.2Monte Carlo Simulations130
5.6.3Justification of the Algorithm130
5.6.4Applications133
5.7Questions and Exercises135
6Molecular Dynamics in Various Ensembles139
6.1Molecular Dynamics at Constant Temperature140
6.1.1The Andersen Thermostat141
6.1.2Nose-Hoover Thermostat147
6.1.3Nose-Hoover Chains155
6.2Molecular Dynamics at Constant Pressure158
6.3Questions and Exercises160
Part IIIFree Energies and Phase Equilibria165
7Free Energy Calculations167
7.1Thermodynamic Integration168
7.2Chemical Potentials172
7.2.1The Particle Insertion Method173
7.2.2Other Ensembles176
7.2.3Overlapping Distribution Method179
7.3Other Free Energy Methods183
7.3.1Multiple Histograms183
7.3.2Acceptance Ratio Method189
7.4Umbrella Sampling192
7.4.1Nonequilibrium Free Energy Methods196
7.5Questions and Exercises199
8The Gibbs Ensemble201
8.1The Gibbs Ensemble Technique203
8.2The Partition Function204
8.3Monte Carlo Simulations205
8.3.1Particle Displacement205
8.3.2Volume Change206
8.3.3Particle Exchange208
8.3.4Implementation208
8.3.5Analyzing the Results214
8.4Applications220
8.5Questions and Exercises223
9Other Methods to Study Coexistence225
9.1Semigrand Ensemble225
9.2Tracing Coexistence Curves233
10Free Energies of Solids241
10.1Thermodynamic Integration242
10.2Free Energies of Solids243
10.2.1Atomic Solids with Continuous Potentials244
10.3Free Energies of Molecular Solids245
10.3.1Atomic Solids with Discontinuous Potentials248
10.3.2General Implementation Issues249
10.4Vacancies and Interstitials263
10.4.1Free Energies263
10.4.2Numerical Calculations266
11Free Energy of Chain Molecules269
11.1Chemical Potential as Reversible Work269
11.2Rosenbluth Sampling271
11.2.1Macromolecules with Discrete Conformations271
11.2.2Extension to Continuously Deformable Molecules276
11.2.3Overlapping Distribution Rosenbluth Method282
11.2.4Recursive Sampling283
11.2.5Pruned-Enriched Rosenbluth Method285
Part IVAdvanced Techniques289
12Long-Range Interactions291
12.1Ewald Sums292
12.1.1Point Charges292
12.1.2Dipolar Particles300
12.1.3Dielectric Constant301
12.1.4Boundary Conditions303
12.1.5Accuracy and Computational Complexity304
12.2Fast Multipole Method306
12.3Particle Mesh Approaches310
12.4Ewald Summation in a Slab Geometry316
13Biased Monte Carlo Schemes321
13.1Biased Sampling Techniques322
13.1.1Beyond Metropolis323
13.1.2Orientational Bias323
13.2Chain Molecules331
13.2.1Configurational-Bias Monte Carlo331
13.2.2Lattice Models332
13.2.3Off-lattice Case336
13.3Generation of Trial Orientations341
13.3.1Strong Intramolecular Interactions342
13.3.2Generation of Branched Molecules350
13.4Fixed Endpoints353
13.4.1Lattice Models353
13.4.2Fully Flexible Chain355
13.4.3Strong Intramolecular Interactions357
13.4.4Rebridging Monte Carlo357
13.5Beyond Polymers360
13.6Other Ensembles365
13.6.1Grand-Canonical Ensemble365
13.6.2Gibbs Ensemble Simulations370
13.7Recoil Growth374
13.7.1Algorithm376
13.7.2Justification of the Method379
13.8Questions and Exercises383
14Accelerating Monte Carlo Sampling389
14.1Parallel Tempering389
14.2Hybrid Monte Carlo397
14.3Cluster Moves399
14.3.1Clusters399
14.3.2Early Rejection Scheme405
15Tackling Time-Scale Problems409
15.1Constraints410
15.1.1Constrained and Unconstrained Averages415
15.2On-the-Fly Optimization: Car-Parrinello Approach421
15.3Multiple Time Steps424
16Rare Events431
16.1Theoretical Background432
16.2Bennett-Chandler Approach436
16.2.1Computational Aspects438
16.3Diffusive Barrier Crossing443
16.4Transition Path Ensemble450
16.4.1Path Ensemble451
16.4.2Monte Carlo Simulations454
16.5Searching for the Saddle Point462
17Dissipative Particle Dynamics465
17.1Description of the Technique466
17.1.1Justification of the Method467
17.1.2Implementation of the Method469
17.1.3DPD and Energy Conservation473
17.2Other Coarse-Grained Techniques476
Part VAppendices479
ALagrangian and Hamiltonian481
A.1Lagrangian483
A.2Hamiltonian486
A.3Hamilton Dynamics and Statistical Mechanics488
A.3.1Canonical Transformation489
A.3.2Symplectic Condition490
A.3.3Statistical Mechanics492
BNon-Hamiltonian Dynamics495
B.1Theoretical Background495
B.2Non-Hamiltonian Simulation of the N, V, T Ensemble497
B.2.1The Nose-Hoover Algorithm498
B.2.2Nose-Hoover Chains502
B.3The N, P, T Ensemble505
CLinear Response Theory509
C.1Static Response509
C.2Dynamic Response511
C.3Dissipation513
C.3.1Electrical Conductivity516
C.3.2Viscosity518
C.4Elastic Constants519
DStatistical Errors525
D.1Static Properties: System Size525
D.2Correlation Functions527
D.3Block Averages529
EIntegration Schemes533
E.1Higher-Order Schemes533
E.2Nose-Hoover Algorithms535
E.2.1Canonical Ensemble536
E.2.2The Isothermal-Isobaric Ensemble540
FSaving CPU Time545
F.1Verlet List545
F.2Cell Lists550
F.3Combining the Verlet and Cell Lists550
F.4Efficiency552
GReference States559
G.1Grand-Canonical Ensemble Simulation559
HStatistical Mechanics of the Gibbs "Ensemble"563
H.1Free Energy of the Gibbs Ensemble563
H.1.1Basic Definitions563
H.1.2Free Energy Density565
H.2Chemical Potential in the Gibbs Ensemble570
IOverlapping Distribution for Polymers573
JSome General Purpose Algorithms577
KSmall Research Projects581
K.1Adsorption in Porous Media581
K.2Transport Properties in Liquids582
K.3Diffusion in a Porous Media583
K.4Multiple-Time-Step Integrators584
K.5Thermodynamic Integration585
LHints for Programming587
Bibliography589
Author Index619
Index628

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