Understanding Molecular Simulation. Edition No. 2 - Product Image

Understanding Molecular Simulation. Edition No. 2

  • ID: 1765371
  • Book
  • 664 Pages
  • Elsevier Science and Technology
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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.
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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
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Frenkel, Daan
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.
Smit, Berend
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.
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