Bridging the Time Scales

by Nielaba, P.; Mareschal, Michel; Ciccotti, Giovanni

• ISBN13: 9783540443179
• ISBN10: 3540443177
• Format: Hardcover
• Copyright: 2002-11-01
• Publisher: Springer Verlag

Summary

The behaviour of many complex materials extends over time- and lengthscales well beyond those that can normally be described using standard molecular dynamics or Monte Carlo simulation techniques. As progress is coming more through refined simulation methods than from increased computer power, this volume is intended as both an introduction and a review of all relevant modern methods that will shape molecular simulation in the forthcoming decade. Written as a set of tutorial reviews, the book will be of use to specialists and nonspecialists alike.

Table of Contents

Protein Folding
Sidechain Dynamics and Protein Folding	p. 3
Introduction	p. 3
Results	p. 5
Discussion	p. 18
Methods	p. 21
References	p. 23
Applications of Statistical Mechanics to Biological Systems
A Coarse Grain Model for Lipid Monolayer and Bilayer Studies	p. 27
Introduction	p. 27
Challenges	p. 28
Models	p. 30
Previous Work	p. 30
Towards the Current CG Model	p. 32
A First Attempt	p. 34
Applications	p. 41
Fluctuation Modes	p. 41
Bulk Alkane and Water Surface Tension	p. 43
Self-assembly	p. 43
Transmembrane Peptide Induced Domain Formation	p. 46
Transmembrane Peptide Induced L¿ to HII Phase Transition	p. 52
Buckling Instabilities in Langmuir Monolayers	p. 54
Future Perspectives	p. 58
References	p. 60
Polymer Structure and Dynamics
Variable-Connectivity Monte Carlo Algorithms for the Atomistic Simulation of Long-Chain Polymer Systems	p. 67
Introduction	p. 67
The Bridging Construction	p. 71
Monte Carlo Algorithms Based on the Bridging Construction	p. 77
Concerted Rotation	p. 77
Directed Internal Bridging	p. 80
End-Bridging in the Nn¿* PT Ensemble	p. 81
Directed End-Bridging	p. 89
Sampling of Oriented Chains: NnbT¿*¿ MC Simulations	p. 90
Scission and Fusion Algorithms for Phase Equilibria	p. 92
Double Bridging and Intramolecular Double Rebridging	p. 96
Connectivity-Altering Monte Carlo and Parallel Tempering	p. 100
Applications	p. 103
Structure and Volumetric Properties of Long-Chain Polyethylene Melts	p. 103
Simulations of Polypropylene Melts of Various Tacticities	p. 107
Simulation of Polydienes	p. 110
Prediction of Melt Elasticity	p. 113
Sorption Equilibria of Alkanes in Polyethylene	p. 119
Polymers at Interfaces	p. 121
Conclusions and Outlook	p. 124
References	p. 125
Bridging the Time Scale Gap: How Does Foldable Polymer Navigate Its Conformation Space?	p. 129
Introducing the Characters	p. 129
Setting Up the Stage: Conformation Space and Reaction Coordinate	p. 130
Conformation Space: Lattice Polymer	p. 130
Conformation Space: Off-lattice Polymer	p. 131
Reaction Coordinate Problem	p. 132
Unfolding the Drama: Commitor, pfold, and the Reaction Coordinate	p. 134
Commitor	p. 134
Direct Current Analogy	p. 135
Diffusion Equation and Continuous (Off-lattice) Models	p. 136
Stationary and Transient Regimes	p. 137
Direct Current Formulation of the First Return Problem: Casino Problem and Its Easy Solution	p. 138
Direct Current Formulation of the Commitor	p. 139
Direct Current Formulation of the Landscape	p. 139
Culmination: So What?	p. 141
References	p. 141
Multiscale Computer Simulations for Polymeric Materials in Bulk and Near Surfaces	p. 143
Introduction	p. 143
Length and Time Scales for Polymer Simulations	p. 144
Dual-Scale Modelling Ansatz	p. 148
Mesoscopic Models in Bulk and Near Surfaces	p. 148
Systematic Molecular Coarse-Graining	p. 153
Mapping Schemes	p. 153
Coarse Grained Liquid Structure	p. 154
Specific Surface Effects: BPA-PC Near a Ni Surface	p. 156
Other Approaches: Automatic Coarse-Graining	p. 159
Conclusions, Outlook	p. 162
References	p. 163
Complex and Mesoscopic Fluids
Effective Interactions for Large-Scale Simulations of Complex Fluids	p. 167
Introduction	p. 167
Efficient Coarse-Graining Through Effective Interactions	p. 168
Electric Double-Layers	p. 172
Simulating the Polarization of Dielectric Media	p. 174
Coarse-Graining Linear Polymer Solutions	p. 176
Star Polymers and Dendrimers	p. 178
Colloids and Polymers: Depletion Interactions	p. 183
Binary Colloidal "Alloys"	p. 185
From Colloidal to Nanoscales	p. 187
Conclusions	p. 190
References	p. 192
Slow Dynamics and Reactivity
Simulation of Models for the Glass Transition: Is There Progress?	p. 199
Introduction	p. 199
Towards the Simulation of Real Glassy Materials: The Case of SiO2	p. 204
Parallel Tempering	p. 209
An Abstract Model for Static and Dynamic Glass Transitions: The 10-State Mean Field Potts Glass	p. 212
The Bead-Spring Model: A Coarse-Grained Model for the Study of the Glass Transition of Polymer Melts	p. 217
The Bond Fluctuation Model Approach to Glassforming Polymer Melts	p. 219
Can One Map Coarse-Grained Models onto Atomistically Realistic Ones?	p. 222
Concluding Remarks	p. 224
References	p. 226
Lattice Models
Monte Carlo Methods for Bridging the Timescale Gap	p. 231
General Introduction	p. 231
Problems and Challenges	p. 232
Introduction to Metropolis Importance Sampling	p. 232
Origin of Time-Scale Problems	p. 234
Traditional Computational Solutions	p. 235
Some "Recent" Developments	p. 236
Second Order Transitions	p. 236
Cluster Flipping	p. 236
The N-fold Way and Extensions	p. 237
"Wang-Landau" Sampling	p. 239
First Order Transitions	p. 240
Free Energy Comparison: The Statistical Mechanics Perspective	p. 241
Multicanonical Monte Carlo	p. 244
Tracking Phase Boundaries: Histogram Extrapolation	p. 245
Phase Switch Monte Carlo	p. 247
First Order Transitions and Wang-Landau Sampling	p. 253
Systems with Complex Order	p. 256
"Dynamic" Behavior: Spin Dynamics with Decompositions of Exponential Operators	p. 258
Summary and Outlook	p. 263
References	p. 265
Go-with-the-Flow Lattice Boltzmann Methods for Tracer Dynamics	p. 267
Introduction	p. 267
LBE Schemes with Tracer Dynamics	p. 269
Extra-dimensional Methods	p. 269
Hybrid Grid-Grid	p. 269
Hybrid Grid-Particle	p. 270
Go-with-the-Flow Kinetic Methods	p. 270
Hydrodynamic Dispersion	p. 270
The Moment Propagation Method	p. 272
Galilean Invariance	p. 276
Varying the Peclet Number	p. 276
The VACF at Infinite Time	p. 277
Generalization	p. 278
Applications of the Model	p. 279
Dispersion in a Tube	p. 279
Dispersion in Cubic Periodic Arrays	p. 282
Conclusions	p. 283
References	p. 284
Multiscale Modelling in Materials Science
Atomistic Simulations of Solid Friction	p. 289
Introduction	p. 289
The Relevance of Details: A Simple Case Study	p. 291
Solid Friction Versus Stokes Friction	p. 294
Dry Friction	p. 297
Rigid Walls and Geometric Interlocking	p. 297
Elastic Deformations: Role of Disorder and Dimensions	p. 298
Extreme Conditions and Non-elastic Deformations	p. 299
Lubrication	p. 301
Boundary Lubrication	p. 303
Hydrodynamic Lubrication and Its Breakdown	p. 305
Setting Up a Tribological Simulation	p. 305
The Essential Ingredients	p. 305
Physo-chemical Properties	p. 307
Initial Geometry	p. 308
Driving Device	p. 310
Thermostating	p. 311
Methods to Treat the Wall's Elasticity	p. 311
Calculation of the Friction Force	p. 313
Interpretation of Time Scales and Velocities	p. 313
Conclusions	p. 314
References	p. 316
Methodological Developments in MD and MC
Bridging the Time Scale Gapwith Transition Path Sampling	p. 321
Why Transition Path Sampling Is Needed	p. 321
How Transition Path Sampling Works	p. 323
Probabilities of Trajectories	p. 323
Defining the Transition Path Ensemble	p. 324
Sampling the Transition Path Ensemble	p. 325
What Transition Path Sampling Can Do	p. 326
The Rare Event Problem	p. 327
Solving the Rare Event Problem with Transition Path Sampling	p. 327
Interpreting the Ensemble of Harvested Paths	p. 329
Rate Constants	p. 330
What Transition Path Sampling Cannot Do (Yet)	p. 330
One and Two Point Boundary Problems	p. 330
Chains of States with Long Time Steps	p. 331
Pattern Recognition	p. 332
References	p. 332
The Stochastic Difference Equation as a Tool to Compute Long Time Dynamics	p. 335
Introduction	p. 335
Molecular Dynamics	p. 335
Initial Value Formulation	p. 336
A Boundary Value Formulation in Time	p. 336
A Boundary Value Formulation in Length	p. 340
The Stochastic Difference Equation	p. 341
Stochastic Difference in Time: Definition	p. 341
A Stochastic Model for a Trajectory	p. 345
"Stabilizing" Long Time Trajectories, or Filtering High Frequency Modes	p. 347
Weights of Trajectories and Sampling Procedures	p. 350
Mean Field Approach, Fast Equilibration and Molecular Labeling	p. 353
Stochastic Difference in Length	p. 355
"Fractal" Refinement of Trajectories Parameterized by Length	p. 358
Numerical Experiments	p. 360
Concluding Remarks	p. 363
Numerical Simulations of Molecular Systems with Long Range Interactions	p. 367
Introduction	p. 367
3-D Systems	p. 367
Confined Systems	p. 373
Conclusion	p. 377
References	p. 377
Perpectives in ab initio MD
New Developments in Plane-Wave Based ab initio Calculations	p. 381
Introduction	p. 381
Methods	p. 382
Clusters, Surfaces and Solids/Liquids	p. 382
Solids/Liquids	p. 383
Clusters	p. 384
Surfaces	p. 386
Wires	p. 388
Summary	p. 389
Application to Ewald Summation	p. 390
Application to Plane-Wave Based Density Functional Theory	p. 391
Dual Length Scale Approach	p. 392
Results	p. 399
Clusters	p. 400
Hartree and Local Pseudopotential Energies for a Model Density	p. 400
Water Molecule and Hydronium Ion	p. 400
Surface Ewald Summation	p. 401
Model BCC Surface	p. 401
Ice Surface with a Defect	p. 403
Mixed ab initio/Empirical Force Fields	p. 405
Neat Water	p. 405
HCA II in Water	p. 407
Conclusion	p. 409
References	p. 410
Time and Length Scales in ab initio Molecular Dynamics	p. 413
Introduction	p. 413
Overcoming the Time Scale Barrier: Enhanced Sampling Techniques for ab initio Molecular Dynamics Simulations	p. 414
Time Scale Limitations in ab initio Molecular Dynamics Simulations	p. 414
The Use of Classical Force Fields as Bias Potentials for an Enhanced Sampling of Conformational Transitions	p. 415
Finite Electronic Temperatures as Electronic Bias Potentials	p. 417
Computation of Acid Dissociation Constants	p. 419
Time and Length Scales in Aqueous Chemistry	p. 419
Determination of Free Energy Profiles	p. 420
Statistical Thermodynamics of Gas-Phase Equilibria	p. 421
Reversible Work and Equilibrium Constants	p. 422
Controlled Dissociation in a Small Box	p. 424
Computation of the Water Dissociation Constant	p. 425
Application to Weak Acids and Evaluation of Method	p. 427
Linear Scaling Electronic Structure Methods for ab initio Molecular Dynamics	p. 428
Kohn-Sham Matrix Calculation	p. 429
Wavefunction Optimization; Solving the Kohn-Sham Equations	p. 434
References	p. 440
Quantum Simulations
A Statistical Mechanical Theory of Quantum Dynamics in Classical Environments	p. 445
Introduction	p. 445
Quantum Dynamics and Statistical Mechanics	p. 446
Mixed Representation of Quantum Statistical Mechanics	p. 448
Quantum-Classical World	p. 451
Nature of Quantum-Classical Dynamics	p. 453
Time Evolution of Dynamical Variables	p. 458
Equations for Canonical Variables	p. 461
Quantum-Classical Equilibrium Density	p. 462
Quantum-Classical Time Correlation Functions	p. 463
Simulation Schemes	p. 467
Spin-Boson Model	p. 468
Conclusion	p. 470
References	p. 471
The Coupled Electronic-Ionic Monte Carlo Simulation Method	p. 473
Introduction	p. 473
The Coupled Electronic-Ionic Monte Carlo Method	p. 476
The Penalty Method	p. 477
Energy Differences	p. 478
Direct Difference	p. 479
Reweighting	p. 479
Importance Sampling	p. 480
Choice of Trial Wave Function	p. 480
Twist Average Boundary Conditions	p. 482
Fluid Molecular Hydrogen	p. 483
The Atomic-Metallic Phase	p. 486
Trial Wave Function and Optimization	p. 486
Comparison with PIMC	p. 491
Hydrogen Equation of State and Solid-Liquid Phase Transition of the Protons	p. 494
Conclusions and Outlook	p. 497
References	p. 499
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