Table Of ContentTHE ART OF MOLECULAR DYNAMICS SIMULATION
Theextremelypowerfultechniqueofmoleculardynamicssimulationinvolvessolv-
ing the classical many-body problem in contexts relevantto the studyof matter at
theatomisticlevel.Sincethereisnoalternativeapproachcapableofhandlingthis
broadrangeofproblemsattherequiredlevelofdetail,moleculardynamicsmeth-
odshaveprovedthemselvesindispensableinbothpureandappliedresearch.This
bookisablendoftutorialandrecipecollection,providingbothanintroductionto
the subject for beginners and a reference manual for more experienced practition-
ers. It is organized as a series of case studies that take the reader through each of
the steps from formulating the problem, developing the necessary software, and
thenusingtheprogramstomakeactualmeasurements.
This second edition has been extensively revised and enlarged. It contains a sub-
stantialamountofnewmaterialandthesoftwareusedinthecasestudieshasbeen
completelyrewritten.
Dennis Rapaport received his B.Sc. and M.Sc. degrees in physics from the Uni-
versity of Melbourne, and his Ph.D. in theoretical physics from King’s College,
University of London. He is a Professor of Physics at Bar-Ilan University and is
currentlydepartmentalchairman.HehasheldvisitingappointmentsatCornellUni-
versityandIBMinNewYork,isanAdjunctProfessorattheUniversityofGeorgia
andaFellowoftheAmericanPhysicalSociety.Hisinterestincomputermodeling
emerged during his undergraduate years and his present research interests include
both the methodology of molecular dynamics simulation and its application to a
varietyoffields.
THE ART OF MOLECULAR
DYNAMICS SIMULATION
Second Edition
D. C. RAPAPORT
cambridge university press
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge cb2 2ru, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521825689
© Cambridge University Press 1995, Dennis Rapaport 2004
This publication is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
First published in print format 2004
isbn-13 978-0-511-19232-6 eBook (Adobe Reader)
isbn-10 0-511-19232-0
eBook (Adobe Reader)
isbn-13 978-0-521-82568-9 hardback
isbn-10 0-521-82568-7 hardback
Cambridge University Press has no responsibility for the persistence or accuracy of urls
for external or third-party internet websites referred to in this publication, and does not
guarantee that any content on such websites is, or will remain, accurate or appropriate.
Contents
Prefacetothefirstedition pageix
Prefacetothesecondedition xii
Aboutthesoftware xiii
1 Introduction 1
1.1 Historicalbackground 1
1.2 Computersimulation 2
1.3 Moleculardynamics 4
1.4 Organization 8
1.5 Furtherreading 10
2 Basicmoleculardynamics 11
2.1 Introduction 11
2.2 Soft-diskfluid 11
2.3 Methodology 18
2.4 Programming 20
2.5 Results 34
2.6 Furtherstudy 43
3 Simulatingsimplesystems 44
3.1 Introduction 44
3.2 Equationsofmotion 44
3.3 Potentialfunctions 46
3.4 Interactioncomputations 49
3.5 Integrationmethods 60
3.6 Initialstate 67
3.7 Performancemeasurements 74
3.8 Trajectorysensitivity 77
3.9 Furtherstudy 82
v
vi Contents
4 Equilibriumpropertiesofsimplefluids 83
4.1 Introduction 83
4.2 Thermodynamicmeasurements 84
4.3 Structure 90
4.4 Packingstudies 96
4.5 Clusteranalysis 112
4.6 Furtherstudy 118
5 Dynamicalpropertiesofsimplefluids 120
5.1 Introduction 120
5.2 Transportcoefficients 120
5.3 Measuringtransportcoefficients 124
5.4 Space–timecorrelationfunctions 134
5.5 Measurements 145
5.6 Furtherstudy 152
6 Alternativeensembles 153
6.1 Introduction 153
6.2 Feedbackmethods 154
6.3 Constraintmethods 165
6.4 Furtherstudy 174
7 Nonequilibriumdynamics 176
7.1 Introduction 176
7.2 Homogeneousandinhomogeneoussystems 176
7.3 Directmeasurement 177
7.4 Modifieddynamics 188
7.5 Furtherstudy 198
8 Rigidmolecules 199
8.1 Introduction 199
8.2 Dynamics 200
8.3 Molecularconstruction 216
8.4 Measurements 222
8.5 Rotationmatrixrepresentation 232
8.6 Furtherstudy 243
9 Flexiblemolecules 245
9.1 Introduction 245
9.2 Descriptionofmolecule 245
9.3 Implementationdetails 247
9.4 Properties 251
9.5 Modelingstructureformation 256
Contents vii
9.6 Surfactantmodels 257
9.7 Surfactantbehavior 262
9.8 Furtherstudy 266
10 Geometricallyconstrainedmolecules 267
10.1 Introduction 267
10.2 Geometricconstraints 267
10.3 Solvingtheconstraintproblem 270
10.4 Internalforces 278
10.5 Implementationdetails 286
10.6 Measurements 291
10.7 Furtherstudy 294
11 Internalcoordinates 296
11.1 Introduction 296
11.2 Chaincoordinates 296
11.3 Kinematicanddynamicrelations 298
11.4 Recursivedescriptionofdynamics 299
11.5 Solvingtherecursionequations 308
11.6 Implementationdetails 317
11.7 Measurements 322
11.8 Furtherstudy 325
12 Many-bodyinteractions 326
12.1 Introduction 326
12.2 Three-bodyforces 326
12.3 Embedded-atomapproach 332
12.4 Furtherstudy 343
13 Long-rangeinteractions 344
13.1 Introduction 344
13.2 Ewaldmethod 345
13.3 Tree-codeapproach 359
13.4 Fast-multipolemethod 365
13.5 Implementingthefast-multipolemethod 373
13.6 Results 386
13.7 Furtherstudy 389
14 Steppotentials 391
14.1 Introduction 391
14.2 Computationalapproach 392
14.3 Eventmanagement 403
14.4 Properties 411
14.5 Generalizations 414
viii Contents
14.6 Furtherstudy 417
15 Time-dependentphenomena 418
15.1 Introduction 418
15.2 Opensystems 418
15.3 Thermalconvection 420
15.4 Obstructedflow 429
15.5 Furtherstudy 435
16 Granulardynamics 436
16.1 Introduction 436
16.2 Granularmodels 436
16.3 Vibratinggranularlayer 439
16.4 Wavepatterns 443
16.5 Furtherstudy 445
17 Algorithmsforsupercomputers 446
17.1 Introduction 446
17.2 Thequestforperformance 446
17.3 Techniquesforparallelprocessing 447
17.4 Distributedcomputation 450
17.5 Shared-memoryparallelism 467
17.6 Techniquesforvectorprocessing 473
17.7 Furtherstudy 480
18 Moreaboutsoftware 481
18.1 Introduction 481
18.2 Structuresandmacrodefinitions 481
18.3 Allocatingarrays 487
18.4 Utilityfunctions 488
18.5 Organizinginputdata 495
18.6 Configurationsnapshotfiles 498
18.7 Managingextensivecomputations 500
18.8 Headerfiles 504
19 Thefuture 505
19.1 Roleofsimulation 505
19.2 Limitsofgrowth 506
19.3 Visualizationandinteractivity 507
19.4 Coda 508
Appendix 509
References 519
Functionindex 532
Index 535
Colophon 549
Preface to the first edition
Moleculardynamicssimulationprovidesthemethodologyfordetailedmicroscopic
modeling on the molecular scale. After all, the nature of matter is to be found in
the structure and motion of its constituent building blocks, and the dynamics is
contained in the solution to the N-body problem. Given that the classical N-body
problem lacks a general analytical solution, the only path open is the numerical
one.Scientistsengagedinstudyingmatteratthislevelrequirecomputationaltools
to allow them to follow the movement of individual molecules and it is this need
thatthemoleculardynamicsapproachaimstofulfill.
Theall-importantquestionthatarisesrepeatedlyinnumerouscontextsisthere-
lation between the bulk propertiesof matter – be it in the liquid, solid, or gaseous
state– and the underlying interactionsamong the constituentatoms ormolecules.
Rather than attempting to deduce microscopic behavior directly from experiment,
the molecular dynamics method – MD for short – follows the constructive ap-
proachinthatittriestoreproducethebehaviorusingmodelsystems.Thecontinu-
ally increasing power of computers makes it possible to pose questions of greater
complexity, with a realistic expectation of obtaining meaningful answers; the in-
escapableconclusionisthatMDwill–ifithasn’talready–becomeanindispens-
ablepartofthetheorist’stoolbox.ApplicationsofMDaretobefoundinphysics,
chemistry,biochemistry,materialsscience,andinbranchesofengineering.
This is a recipe book. More precisely, it is a combination of an introduction to
MD for the beginner, and a cookbook and reference manual for the more expe-
rienced practitioner. The hope is that through the use of a series of case studies,
in which real problems are studied, both goals can be achieved. The book can be
read from cover to cover to explore the principles and capabilities of MD, or it
can be used in cookbook style – with a certain amount of cross-referencing – to
obtaintherecipeforaparticularkindofcomputation.Somefamiliaritywithclas-
sical and statistical mechanics, numerical methods and computer programming is
assumed.
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