Understanding molecular simulation: from algorithms to applications
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
San Diego, Calif. [u.a.]
Acad. Press
2009
|
| Ausgabe: | 2. ed., [Nachdr.] |
| Schriftenreihe: | Computational science series
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [589] - 617 |
| Beschreibung: | XXII, 638 S. Ill., graph. Darst. |
| ISBN: | 0122673514 9780122673511 |
Internformat
MARC
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| 245 | 1 | 0 | |a Understanding molecular simulation |b from algorithms to applications |c Daan Frenkel ; Berend Smit |
| 250 | |a 2. ed., [Nachdr.] | ||
| 264 | 1 | |a San Diego, Calif. [u.a.] |b Acad. Press |c 2009 | |
| 300 | |a XXII, 638 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Computational science series |v 1 | |
| 500 | |a Literaturverz. S. [589] - 617 | ||
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Datensatz im Suchindex
| _version_ | 1804140730981023744 |
|---|---|
| adam_text | Contents
Preface
to the Second Edition
xiii
Preface
xv
List of Symbols
xix
1
Introduction
1
Part I Basics
7
2
Statistical Mechanics
9
2.1
Entropy and Temperature
..................... 9
2.2
Classical Statistical Mechanics
................... 13
2.2.1
Ergodicity
.......................... 15
2.3
Questions and Exercises
...................... 17
3
Monte Carlo Simulations
23
3.1
The Monte Carlo Method
..................... 23
3.1.1
Importance Sampling
................... 24
3.1.2
The Metropolis Method
.................. 27
3.2
A Basic Monte Carlo Algorithm
.................. 31
3.2.1
The Algorithm
....................... 31
3.2.2
Technical Details
...................... 32
3.2.3
Detailed Balance versus Balance
............. 42
3.3
Trial Moves
............................. 43
3.3.1
Translational Moves
.................... 43
3.3.2
Orientational Moves
.................... 48
3.4
Applications
............................. 51
3.5
Questions and Exercises
...................... 58
vi
__________________________Contents
4
Molecular Dynamics
Simulations
63
4.1
Molecular Dynamics:
The Idea
.................. 63
4.2
Molecular Dynamics:
A Program
................. 64
4.2.1
Initialization.........................
65
4.2.2
The Force
Calculation
................... 67
4.2.3
Integrating the Equations of Motion
........... 69
4.3
Equations of Motion
........................ 71
4.3.1
Other Algorithms
...................... 74
4.3.2
Higher-Order Schemes
................... 77
4.3.3
Liouville Formulation of lime-Reversible Algorithms
. 77
4.3.4
Lyapunov Instability
.................... 81
4.3.5
One More Way to Look at the
Verlet
Algorithm
....... 82
4.4
Computer Experiments
....................... 84
4.4.1
Diffusion
........................... 87
4.4.2
Order
-η
Algorithm to Measure Correlations
...... 90
4.5
Some Applications
......................... 97
4.6
Questions and Exercises
...................... 105
Part II Ensembles
109
5
Monte Carlo Simulations in Various Ensembles 111
5.1
General Approach
.......................... 112
5.2
Canonical Ensemble
........................ 112
5.2.1
Monte Carlo Simulations
................. 113
5.2.2
Justification of the Algorithm
............... 114
5.3
Microcanonical Monte Carlo
.................... 114
5.4
Isobaric-Isothermal Ensemble
................... 115
5.4.1
Statistical Mechanical Basis
................ 116
5.4.2
Monte Carlo Simulations
................. 119
5.4.3
Applications
......................... 122
5.5
Isotension-Isothermal Ensemble
.................. 125
5.6
Grand-Canonical Ensemble
.................... 126
5.6.1
Statistical Mechanical Basis
................ 127
5.6.2
Monte Carlo Simulations
................. 130
5.6.3
Justification of the Algorithm
............... 130
5.6.4
Applications
......................... 133
5.7
Questions and Exercises
...................... 135
6
Molecular Dynamics in Various Ensembles
139
6.1
Molecular Dynamics at Constant Temperature
......... 140
6.1.1
The Andersen Thermostat
................. 141
6.1.2
Nosé-Hoover
Thermostat
................. 147
Contents
vii
6.1.3
Nosé-Hoover
Chains
....................155
6.2
Molecular Dynamics at Constant Pressure
............158
6.3
Questions and Exercises
......................160
Part III Free Energies and Phase Equilibria
165
7
Free Energy Calculations
167
7.1
Thermodynamic Integration
.................... 168
7.2
Chemical Potentials
......................... 172
7.2.1
The Particle Insertion Method
............... 173
7.2.2
Other Ensembles
...................... 176
7.2.3
Overlapping Distribution Method
............ 179
7.3
Other Free Energy Methods
.................... 183
7.3.1
Multiple Histograms
.................... 183
7.3.2
Acceptance Ratio Method
................. 189
7.4
Umbrella Sampling
......................... 192
7.4.1
Nonequilibrium Free Energy Methods
.......... 196
7.5
Questions and Exercises
...................... 199
8
The Gibbs Ensemble
201
8.1
The Gibbs Ensemble Technique
.................. 203
8.2
The Partition Function
....................... 204
8.3
Monte Carlo Simulations
...................... 205
8.3.1
Particle Displacement
................... 205
8.3.2
Volume Change
....................... 206
8.3.3
Particle Exchange
...................... 208
8.3.4
Implementation
....................... 208
8.3.5
Analyzing the Results
................... 214
8.4
Applications
............................. 220
8.5
Questions and Exercises
...................... 223
9
Other Methods to Study Coexistence
225
9.1
Semigrand
Ensemble
........................ 225
9.2
Tracing Coexistence Curves
.................... 233
10
Free Energies of Solids
241
10.1
Thermodynamic Integration
.................... 242
10.2
Free Energies of Solids
....................... 243
10.2.1
Atomic Solids with Continuous Potentials
....... 244
10.3
Free Energies of Molecular Solids
................. 245
10.3.1
Atomic Solids with Discontinuous Potentials
...... 248
10.3.2
General Implementation Issues
.............. 249
10.4
Vacancies and Interstitials
..................... 263
Contents
10.4.1
Free Energies
........................ 263
10.4.2
Numerical Calculations
.................. 266
11
Free Energy of Chain Molecules
269
11.1
Chemical Potential as Reversible Work
.............. 269
11.2
Rosenbluth Sampling
........................ 271
11.2.1
Macromolecules with Discrete Conformations
..... 271
11.2.2
Extension to Continuously Deformable Molecules
. . . 276
11.2.3
Overlapping Distribution Rosenbluth Method
..... 282
11.2.4
Recursive Sampling
.................... 283
11.2.5
Pruned-Enriched Rosenbluth Method
.......... 285
Part IV Advanced Techniques
289
12
Long-Range Interactions
291
12.1 Ewald
Sums
............................. 292
12.1.1
Point Charges
........................ 292
12.1.2
Dipolar Particles
...................... 300
12.1.3
Dielectric Constant
..................... 301
12.1.4
Boundary Conditions
................... 303
12.1.5
Accuracy and Computational Complexity
....... 304
12.2
Fast Multipole Method
....................... 306
12.3
Particle Mesh Approaches
..................... 310
12.4 Ewald
Summation in a Slab Geometry
.............. 316
13
Biased Monte Carlo Schemes
321
13.1
Biased Sampling Techniques
.................... 322
13.1.1
Beyond Metropolis
..................... 323
13.1.2
Orientational Bias
...................... 323
13.2
Chain Molecules
........................... 331
13.2.1
Configurational-Bias Monte Carlo
............ 331
13.2.2
LatticeModels
....................... 332
13.2.3
Off-lattice Case
....................... 336
13.3
Generation of Trial Orientations
.................. 341
13.3.1
Strong Intramolecular Interactions
............ 342
13.3.2
Generation of Branched Molecules
............ 350
13.4
Fixed
Endpoints........................... 353
13.4.1
LatticeModels
....................... 353
13.4.2
Fully Flexible Chain
.................... 355
13.4.3
Strong Intramolecular Interactions
............ 357
13.4.4
Rebridging Monte Carlo
.................. 357
13.5
Beyond Polymers
.......................... 360
13.6
Other Ensembles
.......................... 365
Contents ix
13.6.1 Grand-Canonical Ensemble..............
ι
. 365
13.6.2 Gibbs Ensemble
Simulations
............... 370
13.7
Recoil Growth............................
374
13.7.1
Algorithm
.......................... 376
13.7.2
Justification of the Method
................ 379
13.8
Questions and Exercises
...................... 383
14
Accelerating Monte Carlo Sampling
389
14.1
Parallel Tempering
......................... 389
14.2
Hybrid Monte Carlo
........................ 397
14.3
Cluster Moves
............................ 399
14.3.1
Clusters
........................... 399
14.3.2
Early Rejection Scheme
.................. 405
15
Tackling Time-Scale Problems
409
15.1
Constraints
.............................. 410
15.1.1
Constrained and Unconstrained Averages
....... 415
15.2
On-the-Fly Optimization: Car-Parrinello Approach
...... 421
15.3
Multiple Time Steps
......................... 424
16
Rare Events
431
16.1
Theoretical Background
...................... 432
16.2
Bennett-Chandler Approach
.................... 436
16.2.1
Computational Aspects
.................. 438
16.3
Diffusive Barrier Crossing
..................... 443
16.4
Transition Path Ensemble
..................... 450
16.4.1
Path Ensemble
....................... 451
16.4.2
Monte Carlo Simulations
................. 454
16.5
Searching for the Saddle Point
................... 462
17
Dissipative Particle Dynamics
465
17.1
Description of the Technique
................... 466
17.1.1
Justification of the Method
................ 467
17.1.2
Implementation of the Method
.............. 469
17.1.3
DPD and Energy Conservation
.............. 473
17.2
Other Coarse-Grained Techniques
................ 476
Part V Appendices
479
A Lagrangian and Hamiltonian
481
A.I Lagrangian
..............................483
A.2 Hamiltonian
.............................486
A.3 Hamilton Dynamics and Statistical Mechanics
.........488
Contents
A.3.1
Canonical
Transformation.................489
A.3.2 Symplectic
Condition
...................490
A.3.3
Statistical Mechanics....................
492
В
Non-Hamiltonian Dynamics 495
B.I Theoretical Background......................
495
B.2 Non-Hamiltonian Simulation
of the
N,V,T Ensemble ..... 497
8.2.1
The Nosé-Hoover
Algorithm
............... 498
8.2.2
Nosé-Hoover
Chains
.................... 502
В.З
The
Ν,Ρ,Τ
Ensemble
........................ 505
С
Linear Response Theory
509
C.I Static Response
........................... 509
C.2 Dynamic Response
......................... 511
C.3 Dissipation
.............................. 513
C.3.1 Electrical Conductivity
................... 516
C.3.2 Viscosity
........................... 518
C.4 Elastic Constants
.......................... 519
D
Statistical Errors
525
D.I Static Properties: System Size
................... 525
D.2 Correlation Functions
........................ 527
D.3 Block Averages
........................... 529
E
Integration Schemes
533
E.I Higher-Order Schemes
....................... 533
E.2
Nosé-Hoover
Algorithms
..................... 535
E.2.1 Canonical Ensemble
.................... 536
E.2.2 The Isothermal-Isobaric Ensemble
............ 540
F
Saving CPU Time
545
F.I VerletList
.............................. 545
F.2 Cell Lists
............................... 550
F.3 Combining the
Verlet
and Cell Lists
............... 550
F.4 Efficiency
............................... 552
G
Reference States
559
G.I Grand-Canonical Ensemble Simulation
.............559
H
Statistical Mechanics of the Gibbs Ensemble
563
H.1 Free Energy of the Gibbs Ensemble
................ 563
H.I.I Basic Definitions
...................... 563
H.1.2 Free Energy Density
.................... 565
H.2 Chemical Potential in the Gibbs Ensemble
............ 570
Contents xi
I Overlapping Distribution for Polymers
573
J
Some General Purpose Algorithms
577
К
Small Research Projects
581
K.1 Adsorption in Porous Media
.................... 581
K.2 Transport Properties in Liquids
.................. 582
K.3 Diffusion in a Porous Media
.................... 583
K.4 Multiple-Time-Step Integrators
.................. 584
K.5 Thermodynamic Integration
.................... 585
L
Hints for Programming
587
Bibliography
589
Author Index
619
Index
628
|
| any_adam_object | 1 |
| author | Frenkel, Daan 1948- Smit, Berend 1962- |
| author_GND | (DE-588)13372302X (DE-588)133723046 |
| author_facet | Frenkel, Daan 1948- Smit, Berend 1962- |
| author_role | aut aut |
| author_sort | Frenkel, Daan 1948- |
| author_variant | d f df b s bs |
| building | Verbundindex |
| bvnumber | BV035790581 |
| classification_rvk | UM 3100 VC 6300 |
| ctrlnum | (OCoLC)554151822 (DE-599)OBVAC07653826 |
| discipline | Chemie / Pharmazie Physik |
| edition | 2. ed., [Nachdr.] |
| format | Book |
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| id | DE-604.BV035790581 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:38Z |
| institution | BVB |
| isbn | 0122673514 9780122673511 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018649923 |
| oclc_num | 554151822 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR DE-188 |
| owner_facet | DE-703 DE-355 DE-BY-UBR DE-188 |
| physical | XXII, 638 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Acad. Press |
| record_format | marc |
| series | Computational science series |
| series2 | Computational science series |
| spelling | Frenkel, Daan 1948- Verfasser (DE-588)13372302X aut Understanding molecular simulation from algorithms to applications Daan Frenkel ; Berend Smit 2. ed., [Nachdr.] San Diego, Calif. [u.a.] Acad. Press 2009 XXII, 638 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computational science series 1 Literaturverz. S. [589] - 617 Statistische Physik (DE-588)4057000-9 gnd rswk-swf Zwischenmolekulare Kraft (DE-588)4191346-2 gnd rswk-swf Computersimulation (DE-588)4148259-1 gnd rswk-swf Molekül (DE-588)4039972-2 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Molekül (DE-588)4039972-2 s Monte-Carlo-Simulation (DE-588)4240945-7 s DE-604 Statistische Physik (DE-588)4057000-9 s Computersimulation (DE-588)4148259-1 s 1\p DE-604 Zwischenmolekulare Kraft (DE-588)4191346-2 s 2\p DE-604 Smit, Berend 1962- Verfasser (DE-588)133723046 aut Computational science series 1 (DE-604)BV014091179 1 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018649923&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Frenkel, Daan 1948- Smit, Berend 1962- Understanding molecular simulation from algorithms to applications Computational science series Statistische Physik (DE-588)4057000-9 gnd Zwischenmolekulare Kraft (DE-588)4191346-2 gnd Computersimulation (DE-588)4148259-1 gnd Molekül (DE-588)4039972-2 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| subject_GND | (DE-588)4057000-9 (DE-588)4191346-2 (DE-588)4148259-1 (DE-588)4039972-2 (DE-588)4240945-7 |
| title | Understanding molecular simulation from algorithms to applications |
| title_auth | Understanding molecular simulation from algorithms to applications |
| title_exact_search | Understanding molecular simulation from algorithms to applications |
| title_full | Understanding molecular simulation from algorithms to applications Daan Frenkel ; Berend Smit |
| title_fullStr | Understanding molecular simulation from algorithms to applications Daan Frenkel ; Berend Smit |
| title_full_unstemmed | Understanding molecular simulation from algorithms to applications Daan Frenkel ; Berend Smit |
| title_short | Understanding molecular simulation |
| title_sort | understanding molecular simulation from algorithms to applications |
| title_sub | from algorithms to applications |
| topic | Statistische Physik (DE-588)4057000-9 gnd Zwischenmolekulare Kraft (DE-588)4191346-2 gnd Computersimulation (DE-588)4148259-1 gnd Molekül (DE-588)4039972-2 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| topic_facet | Statistische Physik Zwischenmolekulare Kraft Computersimulation Molekül Monte-Carlo-Simulation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018649923&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV014091179 |
| work_keys_str_mv | AT frenkeldaan understandingmolecularsimulationfromalgorithmstoapplications AT smitberend understandingmolecularsimulationfromalgorithmstoapplications |