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Özet
Özet
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 HamiltoniansExamples 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.
Author Notes
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.
Berend Smit is Professor at the Department of Chemical Engineering of the Faculty of Science, University of Amsterdam. His research focuses on novel Monte Carlo simulations. Smit applies this technique to problems that are of technological importance, particularly those of interest in chemical engineering.
Table of Contents
| Preface to the Second Edition |
| Preface |
| List of Symbols |
| 1 Introduction |
| Part I Basics |
| 2 Statistical Mechanics |
| 2.1 Entropy and Temperature |
| 2.2 Classical Statistical Mechanics |
| 2.3 Questions and Exercises |
| 3 Monte Carlo Simulations |
| 3.1 The Monte Carlo Method |
| 3.2 A Basic Monte Carlo Algorithm |
| 3.3 Trial Moves |
| 3.4 Applications |
| 3.5 Questions and Exercises |
| 4 Molecular Dynamics Simulations |
| 4.1 Molecular Dynamics: the Idea |
| 4.2 Molecular Dynamics: a Program |
| 4.3 Equations of Motion |
| 4.4 Computer Experiments |
| 4.5 Some Applications |
| 4.6 Questions and Exercises |
| Part II Ensembles |
| 5 Monte Carlo Simulations in Various Ensembles |
| 5.1 General Approach |
| 5.2 Canonical Ensemble |
| 5.3 Microcanonical Monte Carlo |
| 5.4 Isobaric-Isothermal Ensemble |
| 5.5 Isotension-Isothermal Ensemble |
| 5.6 Grand-Canonical Ensemble |
| 5.7 Questions and Exercises |
| 6 Molecular Dynamics in Various Ensembles |
| 6.1 Molecular Dynamics at Constant Temperature |
| 6.2 Molecular Dynamics at Constant Pressure |
| 6.3 Questions and Exercises |
| Part III Free Energies and Phase Equilibria |
| 7 Free Energy Calculations |
| 7.1 Thermodynamic Integration |
| 7.2 Chemical Potentials |
| 7.3 Other Free Energy Methods |
| 7.4 Umbrella Sampling |
| 7.5 Questions and Exercises |
| 8 The Gibbs Ensemble |
| 8.1 The Gibbs Ensemble Technique |
| 8.2 The Partition Function |
| 8.3 Monte Carlo Simulations |
| 8.4 Applications |
| 8.5 Questions and Exercises |
| 9 Other Methods to Study Coexistence |
| 9.1 Semigrand Ensemble |
| 9.2 Tracing Coexistence Curves |
| 10 Free Energies of Solids |
| 10.1 Thermodynamic Integration |
| 10.2 Free Energies of Solids |
| 10.3 Free Energies of Molecular Solids |
| 10.4 Vacancies and Interstitials |
| 11 Free Energy of Chain Molecules |
| 11.1 Chemical Potential as Reversible Work |
| 11.2 Rosenbluth Sampling |
| Part IV Advanced Techniques |
| 12 Long-Range Interactions |
| 12.1 Ewald Sums |
| 12.2 Fast Multipole Method |
| 12.3 Particle Mesh Approaches |
| 12.4 Ewald Summation in a Slab Geometry |
| 13 Biased Monte Carlo Schemes |
| 13.1 Biased Sampling Techniques |
| 13.2 Chain Molecules |
| 13.3 Generation of Trial Orientations |
| 13.4 Fixed Endpoints |
| 13.5 Beyond Polymers |
| 13.6 Other Ensembles |
| 13.7 Recoil Growth |
| 13.8 Questions and Exercises |
| 14 Accelerating Monte Carlo Sampling |
| 14.1 Parallel Tempering |
| 14.2 Hybrid Monte Carlo |
| 14.3 Cluster Moves |
| 15 Tackling Time-Scale Problems |
| 15.1 Constraints |
| 15.2 On-the-Fly Optimization: Car-Parrinello Approach |
| 15.3 Multiple Time Steps |
| 16 Rare Events |
| 16.1 Theoretical Background |
| 16.2 Bennett-Chandler Approach |
| 16.3 Diffusive Barrier Crossing |
| 16.4 Transition Path Ensemble |
| 16.5 Searching for the Saddle Point |
| 17 Dissipative Particle Dynamics |
| 17.1 Description of the Technique |
| 17.2 Other Coarse-Grained Techniques |
| Part V Appendices |
| A Lagrangian and Hamiltonian |
| A.1 Lagrangian |
| A.2 Hamiltonian |
| A.3 Hamilton Dynamics and Statistical Mechanics |
| B Non-Hamiltonian Dynamics |
| B.1 Theoretical Background |
| B.2 Non-Hamiltonian Simulation of the N, V, T Ensemble |
| B.3 The N, P, T Ensemble |
| C Linear Response Theory |
| C.1 Static Response |
| C.2 Dynamic Response |
| C.3 Dissipation |
| C.4 Elastic Constants |
| D Statistical Errors |
| D.1 Static Properties: System Size |
| D.2 Correlation Functions |
| D.3 Block Averages |
| E Integration Schemes |
| E.1 Higher-Order Schemes |
| E.2 Nosé-Hoover Algorithms |
| F Saving CPU Time |
| F.1 Verlet List |
| F.2 Cell Lists |
| F.3 Combining the Verlet and Cell Lists |
| F.4 Efficiency |
| G Reference States |
| G.1 Grand-Canonical Ensemble Simulation |
| H Statistical Mechanics of the Gibbs Ensemble |
| H.1 Free Energy of the Gibbs Ensemble |
| H.2 Chemical Potential in the Gibbs Ensemble |
| I Overlapping Distribution for Polymers |
| J Some General Purpose Algorithms |
| K Small Research Projects |
| K.1 Adsorption in Porous Media |
| K.2 Transport Properties in Liquids |
| K.3 Diffusion in a Porous Media |
| K.4 Multiple-Time-Step Integrators |
| K.5 Thermodynamic Integration |
| L Hints for Programming |
| Bibliography |
| Author Index |
| Index |
