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9780122673511

Understanding Molecular Simulation

by ;
  • ISBN13:

    9780122673511

  • ISBN10:

    0122673514

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2001-10-24
  • Publisher: Elsevier Science
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Summary

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.

Table of Contents

Preface to the Second Edition xiii
Preface xv
List of Symbols
xix
Introduction
1(6)
Part I Basics 7(102)
Statistical Mechanics
9(14)
Entropy and Temperature
9(4)
Classical Statistical Mechanics
13(4)
Ergodicity
15(2)
Questions and Exercises
17(6)
Monte Carlo Simulations
23(40)
The Monte Carlo Method
23(8)
Importance Sampling
24(3)
The Metropolis Method
27(4)
A Basic Monte Carlo Algorithm
31(12)
The Algorithm
31(1)
Technical Details
32(10)
Detailed Balance versus Balance
42(1)
Trial Moves
43(8)
Translational Moves
43(5)
Orientational Moves
48(3)
Applications
51(7)
Questions and Exercises
58(5)
Molecular Dynamics Simulations
63(46)
Molecular Dynamics: The Idea
63(1)
Molecular Dynamics: A Program
64(7)
Initialization
65(2)
The Force Calculation
67(2)
Integrating the Equations of Motion
69(2)
Equations of Motion
71(13)
Other Algorithms
74(3)
Higher-Order Schemes
77(1)
Liouville Formulation of Time-Reversible Algorithms
77(4)
Lyapunov Instability
81(1)
One More Way to Look at the Verlet Algorithm
82(2)
Computer Experiments
84(13)
Diffusion
87(3)
Order-n Algorithm to Measure Correlations
90(7)
Some Applications
97(8)
Questions and Exercises
105(4)
Part II Ensembles 109(56)
Monte Carlo Simulations in Various Ensembles
111(28)
General Approach
112(1)
Canonical Ensemble
112(2)
Monte Carlo Simulations
113(1)
Justification of the Algorithm
114(1)
Microcanonical Monte Carlo
114(1)
Isobaric-Isothermal Ensemble
115(10)
Statistical Mechanical Basis
116(3)
Monte Carlo Simulations
119(3)
Applications
122(3)
Isotension-Isothermal Ensemble
125(1)
Grand-Canonical Ensemble
126(9)
Statistical Mechanical Basis
127(3)
Monte Carlo Simulations
130(1)
Justification of the Algorithm
130(3)
Applications
133(2)
Questions and Exercises
135(4)
Molecular Dynamics in Various Ensembles
139(26)
Molecular Dynamics at Constant Temperature
140(18)
The Andersen Thermostat
141(6)
Nose-Hoover Thermostat
147(8)
Nose-Hoover Chains
155(3)
Molecular Dynamics at Constant Pressure
158(2)
Questions and Exercises
160(5)
Part III Free Energies and Phase Equilibria 165(124)
Free Energy Calculations
167(34)
Thermodynamic Integration
168(4)
Chemical Potentials
172(11)
The Particle Insertion Method
173(3)
Other Ensembles
176(3)
Over lapping Distribution Method
179(4)
Other Free Energy Methods
183(9)
Multiple Histograms
183(6)
Acceptance Ratio Method
189(3)
Umbrella Sampling
192(7)
Nonequilibrium Free Energy Methods
196(3)
Questions and Exercises
199(2)
The Gibbs Ensemble
201(24)
The Gibbs Ensemble Technique
203(1)
The Partition Function
204(1)
Monte Carlo Simulations
205(15)
Particle Displacement
205(1)
Volume Change
206(2)
Particle Exchange
208(1)
Implementation
208(6)
Analyzing the Results
214(6)
Applications
220(3)
Questions and Exercises
223(2)
Other Methods to Study Coexistence
225(16)
Semigrand Ensemble
225(8)
Tracing Coexistence Curves
233(8)
Free Energies of Solids
241(28)
Thermodynamic Integration
242(1)
Free Energies of Solids
243(2)
Atomic Solids with Continuous Potentials
244(1)
Free Energies of Molecular Solids
245(18)
Atomic Solids with Discontinuous Potentials
248(1)
General Implementation Issues
249(14)
Vacancies and Interstitials
263(6)
Free Energies
263(3)
Numerical Calculations
266(3)
Free Energy of Chain Molecules
269(20)
Chemical Potential as Reversible Work
269(2)
Rosenbluth Sampling
271(18)
Macromolecules with Discrete Conformations
271(5)
Extension to Continuously Deformable Molecules
276(6)
Overlapping Distribution Rosenbluth Method
282(1)
Recursive Sampling
283(2)
Pruned-Enriched Rosenbluth Method
285(4)
Part IV Advanced Techniques 289(190)
Long-Range Interactions
291(30)
Ewald Sums
292(14)
Point Charges
292(8)
Dipolar Particles
300(1)
Dielectric Constant
301(2)
Boundary Conditions
303(1)
Accuracy and Computational Complexity
304(2)
Fast Multipole Method
306(4)
Particle Mesh Approaches
310(6)
Ewald Summation in a Slab Geometry
316(5)
Biased Monte Carlo Schemes
321(68)
Biased Sampling Techniques
322(9)
Beyond Metropolis
323(1)
Orientational Bias
323(8)
Chain Molecules
331(10)
Configurational-Bias Monte Carlo
331(1)
Lattice Models
332(4)
Off-lattice Case
336(5)
Generation of Trial Orientations
341(12)
Strong Intramolecular Interactions
342(8)
Generation of Branched Molecules
350(3)
Fixed Endpoints
353(7)
Lattice Models
353(2)
Fully Flexible Chain
355(2)
Strong Intramolecular Interactions
357(1)
Rebridging Monte Carlo
357(3)
Beyond Polymers
360(5)
Other Ensembles
365(9)
Grand-Canonical Ensemble
365(5)
Gibbs Ensemble Simulations
370(4)
Recoil Growth
374(9)
Algorithm
376(3)
Justification of the Method
379(4)
Questions and Exercises
383(6)
Accelerating Monte Carlo Sampling
389(20)
Parallel Tempering
389(8)
Hybrid Monte Carlo
397(2)
Cluster Moves
399(10)
Clusters
399(6)
Early Rejection Scheme
405(4)
Tackling Time-Scale Problems
409(22)
Constraints
410(11)
Constrained and Unconstrained Averages
415(6)
On-the-Fly Optimization: Car-Parrinello Approach
421(3)
Multiple Time Steps
424(7)
Rare Events
431(34)
Theoretical Background
432(4)
Bennett-Chandler Approach
436(7)
Computational Aspects
438(5)
Diffusive Barrier Crossing
443(7)
Transition Path Ensemble
450(12)
Path Ensemble
451(3)
Monte Carlo Simulations
454(8)
Searching for the Saddle Point
462(3)
Dissipative Particle Dynamics
465(14)
Description of the Technique
466(10)
Justification of the Method
467(2)
Implementation of the Method
469(4)
DPD and Energy Conservation
473(3)
Other Coarse-Grained Techniques
476(3)
Part V Appendices 479(110)
A Lagrangian and Hamiltonian
481(14)
A.1 Lagrangian
483(3)
A.2 Hamiltonian
486(2)
A.3 Hamilton Dynamics and Statistical Mechanics
488(1)
A.3.1 Canonical Transformation
489(1)
A.3.2 Symplectic Condition
490(2)
A.3.3 Statistical Mechanics
492(3)
B. Non-Hamiltonian Dynamics
495(14)
B.1 Theoretical Background
495(2)
B.2 Non-Hamiltonian Simulation of the N, V, T Ensemble
497(1)
B.2.1 The Nose-Hoover Algorithm
498(4)
B.2.2 Nose-Hoover Chains
502(3)
B.3 The N, P, T Ensemble
505(4)
C. Linear Response Theory
509(16)
C.1 Static Response
509(2)
C.2 Dynamic Response
511(2)
C.3 Dissipation
513(3)
C.3.1 Electrical Conductivity
516(2)
C.3.2 Viscosity
518(1)
C.4 Elastic Constants
519(6)
D. Statistical Errors
525(8)
D.1 Static Properties: System Size
525(2)
D.2 Correlation Functions
527(2)
D.3 Block Averages
529(4)
E Integration Schemes
533(12)
E.1 Higher-Order Schemes
533(2)
E.2 Nose-Hoover Algorithms
535(1)
E.2.1 Canonical Ensemble
536(4)
E.2.2 The Isothermal-Isobaric Ensemble
540(5)
F Saving CPU Time
545(14)
F.1 Verlet List
545(5)
F.2 Cell Lists
550(1)
F.3 Combining the Verlet and Cell Lists
550(2)
F.4 Efficiency
552(7)
G Reference States
559(4)
G.1 Grand-Canonical Ensemble Simulation
559(4)
H Statistical Mechanics of the Gibbs ``Ensemble''
563(10)
H.1 Free Energy of the Gibbs Ensemble
563(1)
H.1.1 Basic Definitions
563(2)
H.1.2 Free Energy Density
565(5)
H.2 Chemical Potential in the Gibbs Ensemble
570(3)
I Overlapping Distribution for Polymers
573(4)
J Some General Purpose Algorithms
577(4)
K Small Research Projects
581(6)
K.1 Adsorption in Porous Media
581(1)
K.2 Transport Properties in Liquids
582(1)
K.3 Diffusion in a Porous Media
583(1)
K.4 Multiple-Time-Step Integrators
584(1)
K.5 Thermodynamic Integration
585(2)
L Hints for Programming
587(2)
Bibliography 589(30)
Author Index 619(9)
Index 628

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