Frenkel / Smit Understanding Molecular Simulation

From Algorithms to Applications
2. Auflage 2001
ISBN: 978-0-08-051998-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 664 Seiten, Web PDF

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.

Daan Frenkel is based at the FOM Institute for Atomic and Molecular Physics and at the Department of Chemistry, University of Amsterdam. His research has three central themes: prediction of phase behavior of complex liquids, modeling the (hydro) dynamics of colloids and microporous structures, and predicting the rate of activated processes. He was awarded the prestigious Spinoza Prize from the Dutch Research Council in 2000.

Autoren/Hrsg.

Frenkel, Daan

Smit, Berend

Inhaltsverzeichnis

1;Cover;1
2;Copyright Page;5
3;Contents;6
4;Preface to the Second Edition;14
5;Preface;16
6;List of Symbols;20
7;Chapter 1. Introduction;24
8;Part I: Basics;30
8.1;Chapter 2. Statistical Mechanics;32
8.1.1;2.1 Entropy and Temperature;32
8.1.2;2.2 Classical Statistical Mechanics;36
8.1.3;2.3 Questions and Exercises;40
8.2;Chapter 3. Monte Carlo Simulations;46
8.2.1;3.1 The Monte Carlo Method;46
8.2.2;3.2 A Basic Monte Carlo Algorithm;54
8.2.3;3.3 Trial Moves;66
8.2.4;3.4 Applications;74
8.2.5;3.5 Questions and Exercises;81
8.3;Chapter 4. Molecular Dynamics Simulations;86
8.3.1;4.1 Molecular Dynamics: The Idea;86
8.3.2;4.2 Molecular Dynamics: A Program;87
8.3.3;4.3 Equations of Motion;94
8.3.4;4.4 Computer Experiments;107
8.3.5;4.5 Some Applications;120
8.3.6;4.6 Questions and Exercises;128
9;Part II: Ensembles;132
9.1;Chapter 5. Monte Carlo Simulations in Various Ensembles;134
9.1.1;5.1 General Approach;135
9.1.2;5.2 Canonical Ensemble;135
9.1.3;5.3 Microcanonical Monte Carlo;137
9.1.4;5.4 Isobaric-Isothermal Ensemble;138
9.1.5;5.5 Isotension-Isothermal Ensemble;148
9.1.6;5.6 Grand-Canonical Ensemble;149
9.1.7;5.7 Questions and Exercises;158
9.2;Chapter 6. Molecular Dynamics in Various Ensembles;162
9.2.1;6.1 Molecular Dynamics at Constant Temperature;163
9.2.2;6.2 Molecular Dynamics at Constant Pressure;181
9.2.3;6.3 Questions and Exercises;183
10;Part III: Free Energies and Phase Equilibria;188
10.1;Chapter 7. Free Energy Calculations;190
10.1.1;7.1 Thermodynamic Integration;191
10.1.2;7.2 Chemical Potentials;195
10.1.3;7.3 Other Free Energy Methods;206
10.1.4;7.4 Umbrella Sampling;215
10.1.5;7.5 Questions and Exercises;222
10.2;Chapter 8. The Gibbs Ensemble;224
10.2.1;8.1 The Gibbs Ensemble Technique;226
10.2.2;8.2 The Partition Function;227
10.2.3;8.3 Monte Carlo Simulations;228
10.2.4;8.4 Applications;243
10.2.5;8.5 Questions and Exercises;246
10.3;Chapter 9. Other Methods to Study Coexistence;248
10.3.1;9.1 Semigrand Ensemble;248
10.3.2;9.2 Tracing Coexistence Curves;256
10.4;Chapter 10. Free Energies of Solids;264
10.4.1;10.1 Thermodynamic Integration;265
10.4.2;10.2 Free Energies of Solids;266
10.4.3;10.3 Free Energies of Molecular Solids;268
10.4.4;10.4 Vacancies and Interstitials;286
10.5;Chapter 11. Free Energy of Chain Molecules;292
10.5.1;11.1 Chemical Potential as Reversible Work;292
10.5.2;11.2 Rosenbluth Sampling;294
11;Part IV: Advanced Techniques;312
11.1;Chapter 12. Long-Range Interactions;314
11.1.1;12.1 Ewald Sums;315
11.1.2;12.2 Fast Multipole Method;329
11.1.3;12.3 Particle Mesh Approaches;333
11.1.4;12.4 Ewald Summation in a Slab Geometry;339
11.2;Chapter 13. Biased Monte Carlo Schemes;344
11.2.1;13.1 Biased Sampling Techniques;345
11.2.2;13.2 Chain Molecules;354
11.2.3;13.3 Generation of Trial Orientations;364
11.2.4;13.4 Fixed Endpoints;376
11.2.5;13.5 Beyond Polymers;383
11.2.6;13.6 Other Ensembles;388
11.2.7;13.7 Recoil Growth;397
11.2.8;13.8 Questions and Exercises;406
11.3;Chapter 14. Accelerating Monte Carlo Sampling;412
11.3.1;14.1 Parallel Tempering;412
11.3.2;14.2 Hybrid Monte Carlo;420
11.3.3;14.3 Cluster Moves;422
11.4;Chapter 15. Tackling Time-Scale Problems;432
11.4.1;15.1 Constraints;433
11.4.2;15.2 On-the-Fly Optimization: Car-Parrinello Approach;444
11.4.3;15.3 Multiple Time Steps;447
11.5;Chapter 16. Rare Events;454
11.5.1;16.1 Theoretical Background;455
11.5.2;16.2 Bennett-Chandler Approach;459
11.5.3;16.3 Diffusive Barrier Crossing;466
11.5.4;16.4 Transition Path Ensemble;473
11.5.5;16.5 Searching for the Saddle Point;485
11.6;Chapter 17. Dissipative Particle Dynamics;488
11.6.1;17.1 Description of the Technique;489
11.6.2;17.2 Other Coarse-Grained Techniques;499
12;Part V: Appendices;502
12.1;A Lagrangian and Hamiltonian;504
12.1.1;A.1 Lagrangian;506
12.1.2;A.2 Hamiltonian;509
12.1.3;A.3 Hamilton Dynamics and Statistical Mechanics;511
12.2;B Non-Hamiltonian Dynamics;518
12.2.1;B.1 Theoretical Background;518
12.2.2;B.2 Non-Hamiltonian Simulation of the N,V,T Ensemble;520
12.2.3;B.3 The N,P,T Ensemble;528
12.3;C Linear Response Theory;532
12.3.1;C.1 Static Response;532
12.3.2;C.2 Dynamic Response;534
12.3.3;C.3 Dissipation;536
12.3.4;C.4 Elastic Constants;542
12.4;D Statistical Errors;548
12.4.1;D.1 Static Properties: System Size;548
12.4.2;D.2 Correlation Functions;550
12.4.3;D.3 Block Averages;552
12.5;E Integration Schemes;556
12.5.1;E.1 Higher-Order Schemes;556
12.5.2;E.2 Nosé-Hoover Algorithms;558
12.6;F Saving CPU Time;568
12.6.1;F.1 Verlet List;568
12.6.2;F.2 Cell Lists;573
12.6.3;F.3 Combining the Verlet and Cell Lists;573
12.6.4;F.4 Efficiency;575
12.7;G Reference States;582
12.7.1;G.1 Grand-Canonical Ensemble Simulation;582
12.8;H Statistical Mechanics of the Gibbs Ensemble;586
12.8.1;H.1 Free Energy of the Gibbs Ensemble;586
12.8.2;H.2 Chemical Potential in the Gibbs Ensemble;593
12.9;I Overlapping Distribution for Polymers;596
12.10;J Some General Purpose Algorithms;600
12.11;K Small Research Projects;604
12.11.1;K.1 Adsorption in Porous Media;604
12.11.2;K.2 Transport Properties in Liquids;605
12.11.3;K.3 Diffusion in a Porous Media;606
12.11.4;K.4 Multiple-Time-Step Integrators;607
12.11.5;K.5 Thermodynamic Integration;608
12.12;L Hints for Programming;610
13;Bibliography;612
14;Author Index;642
15;Index;651

Leseproben

Chapter 2 Statistical Mechanics (p. 10-11)

The topic of this book is computer simulation. Computer simulation allows us to study properties of many-particle systems. However, not all properties can be directly measured in a simulation. Conversely, most of the quantities that can be measured in a simulation do not correspond to properties that aremeasured in real experiments. To give a specific example: in aMolecular Dynamics simulation of liquid water, we could measure the instantaneous positions and velocities of all molecules in the liquid. However, this kind of information cannot be compared to experimental data, because no real experiment provides us with such detailed information. Rather, a typical experiment measures an average property, averaged over a large number of particles and, usually, also averaged over the time of the measurement. If we wish to use computer simulation as the numerical counterpart of experiments, we must know what kind of averages we should aim to compute. In order to explain this, we need to introduce the language of statistical mechanics. This we shall do here. We provide the reader with a quick (and slightly dirty) derivation of the basic expressions of statistical mechanics. The aimof these derivations is only to show that there is nothing mysterious about concepts such as phase space, temperature and entropy and many of the other statistical mechanical objects that will appear time and again in the remainder of this book.

2.1 Entropy and Temperature

Most of the computer simulations that we discuss are based on the assumption that classical mechanics can be used to describe the motions of atoms and molecules. This assumption leads to a great simplification in almost all calculations, and it is therefore most fortunate that it is justified in many cases of practical interest. Surprisingly, it turns out to be easier to derive the basic laws of statistical mechanics using the language of quantum mechanics. We will follow this route of least resistance. In fact, for our derivation, we need only little quantum mechanics. Specifically, we need the fact that a quantum mechanical system can be found in different states.