Monte Carlo Methods in Chemical Physics

562 Pages·1998·28.25 MB·English

by  David M. Ferguson

MONTE CARL0 METHODS IN CHEMICAL PHYSICS
ADVANCES IN CHEMICAL PHYSICS
VOLUME 105
EDITORIAL BOARD
BRUCEJ, . BERNED, epartment of Chemistry, Columbia University, New York, New
York, U.S.A.
KURTB INDERI,n stitut fur Physik, Johannes Gutenberg-Universitat Mainz, Mainz,
Germany
A. WELFORDC ASTLEMAJNR, ., Department of Chemistry, The Pennsylvania State
University, University Park, Pennsylvania, U.S.A.
DAVIDC HANDLERD, epartment of Chemistry, University of California, Berkeley,
California, U.S.A.
M. S. CHILD,D epartment of Theoretical Chemistry, University of Oxford, Oxford,
U.K.
WILLIAMT . COFFEYD, epartment of Microelectronics and Electrical Engineering,
Trinity College, University of Dublin, Dublin, Ireland
F. FLEMINCGR IM, Department of Chemistry, University of Wisconsin, Madison,
Wisconsin, U.S.A.
ERNESTR . DAVIDSOND, epartment of Chemistry, Indiana University, Bloomington,
Indiana, U.S.A.
GRAHAMR . FLEMINGD,e partment of Chemistry, The University of Chicago,
Chicago, Illinois, U.S.A.
KARLF . FREED,T he James Franck Institute, The University of Chicago, Chicago,
Illinois, U.S.A
PIERRGEA SPARDC, enter for Nonlinear Phenomena and Complex Systems, Brussels,
Belgium
ERIC J. HELLERI,n stitute for Theoretical Atomic and Molecular Physics, Harvard-
Smithsonian Center for Astrophysics, Cambridge, Massachuetts, U.S.A.
ROBINM . HOCHSTRASSEDRe,p artment of Chemistry, The University of Pennsyl-
vania, Philadelphia, Pennsylvania, U.S.A
R. KOSLOFFT,h e Fritz Haber Research Center for Molecular Dynamics and Depart-
ment of Physical Chemistry, The Hebrew University of Jerusalem, Jerusalem,
Israel
RUDOLPHA . MARCUSD, epartment of Chemistry, California Institute of Technology,
Pasadena, California, U.S.A.
G. NICOLIS,C enter for Nonlinear Phenomena and Complex Systems, UniversitC
Libre de Bruxelles, Brussels, Belgium
THOMAPS . RUSSELLD, epartment of Polymer Science, University of Massachusetts.
Amherst, Massachusets
DONALDG . TRUHLARD, epartment of Chemistry, University of Minnesota, Min-
neapolis, Minnesota, U.S.A.
JOHND . WEEKSI,n stitute for Physical and Technology and Department of Chem-
istry, University of Maryland, College Park, Maryland, U.S.A.
PETERG, . WOLYNESD, epartment of Chemistry, School of Chemical Sciences, Uni-
versity of Illinois, Urbana, Illinois, U.S.A.
MONTE CARL0 METHODS
IN CHEMICAL PHYSICS
Edited by
DAVID M. FERGUSON
Department of Medicinal Chemistry
University of Minnesota
Minneapolis, Minnesota
J. ILJA SIEPMANN
Department of Chemistry
University of Minnesota
Minneapolis, Minnesota
DONALD G. TRUHLAR
Department of Chemistry
University of Minnesota
Minneapolis, Minnesota
ADVANCES IN CHEMICAL PHYSICS
VOLUME 105
Series Editors
I. PRIGOGINE STUART A. RICE
Center for Studies in Statistical 'Mechanics Department of Chemistry
and Complex Systems and
The University of Texas The James Franck Institute
Austin, Texas The University of Chicago
and Chicago, Illinois
International Solvay Institutes
Universitk Libre de Bruxelles
Brussels, Belgium
An Interscience@P ublication
JOHN WILEY & SONS, INC.
NEW YORK 0 CHICHESTER 0 WEINHEIM 0 BRISBANE 0 SINGAPORE 0 TORONTO
This book is printed on acid-free paper. @ I
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Library of Congress Catalog Number 58-9935
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CONTRIBUTORS TO VOLUME 105
GERARTD BARKEMAIT, P, Utrecht University, Utrecht, The Netherlands
DARIOB RESSANINIsIt,i tuto di Scienze Matematiche Fisiche e Chimiche, Uni-
versita di, Milano, sede di Como, Como, Italy
DAVIDM . CEPERLEYN, ational Center for Supercomputing Applications
and Department of Physics, University of Illinois at Urbana-
Champaign, Urbana, Illinois
BRUCEW . CHURCHB, iophysics Program, Section of Biochemistry, Molecu-
lar and Cell Biology, Cornell University, Ithaca, New York
JUANJ . DE PABLO,D epartment of Chemical Engineering, University of
Wisconsin-Madison, Madison, Wisconsin
FERNANDAO. E SCOBEDOD,e partment of Chemical Engineering, University
of Wisconsin-Madison, Madison, Wisconsin
DAVIDM . FERGUSOND,e partment of Medicinal Chemistry and Minnesota
Supercomputer Institute, University of Minnesota, Minneapolis,
Minnesota
DAVIDG . GARRETTL,o ckheed Martin TDS Eagan, St. Paul, Minnesota
MING-HONGH AO, Baker Laboratory of Chemistry, Cornell University,
Ithaca, New York
WILLIAML . HASE, Department of Chemistry, Wayne State University,
Detroit, Michigan
J. KARLJ OHNSOND, epartment of Chemical and Petroleum Engineering,
University of Pittsburg, Pittsburg, Pennsylvania
DAVIDA . KOFKED, epartment of Chemical Engineering, State University of
New York at Buffalo, Buffalo, New York
ANDRZEJK OLINSKID, epartment of Chemistry, University of Warsaw,
Warsaw, Poland
MICHAELM ASCAGNPI,r ogram in Scientific Computing and Department of
Mathematics, University of Southern Mississippi, Hattiesburg, Mis-
sissippi
MARKE . J. NEWMANS,a nta Fe Institute, Santa Fe, New Mexico
M. P. NIGHTINGALDE,e partment of Physics, University of Rhode Island,
Kingston, Rhode Island
V
vi CONTRIBUTORS TO VOLUME 105
GILLEHS . PESLHERBDE,e partment of Chemistry and Biochemistry, Uni-
versity of Colorado at Boulder, Boulder, Colorado
PETERJ. REYNOLDPSh, ysical Sciences Division, Office of Naval Research,
Arlington, Virginia
HAROLDA . SCHERAGBAa, ker Laboratory of Chemistry, Cornell University,
Ithaca, New York
DAVIDS HALLOWABYi,o physics Program, Section of Biochemistry, Molecu-
lar and Cell Biology, Cornell University, Ithaca, New York
J. ILJAS IEPMANND,e partment of Chemistry and Department of Chemical
Engineering and Materials Science, University of Minnesota, Min-
neapolis, Minnesota
JEFFREYS KOLNICKD, epartment of Molecular Biology, The Scripps
Research Institute, La Jolla, California
ASHOK SRINIVASANN,a tional Center for Supercomputing Applications,
University of Illinois at Urbana-Champaign, Illinois.
ROBERTQ . TOPPERD, epartment of Chemistry, School of Engineering, The
Cooper Union for the Advancement of Science and Art, New York,
New York
ALEXU LITSKYB, iophysics Program, Section of Biochemistry, Molecular
and Cell Biology, Cornell University, Ithaca, New York
CYRUSJ . UMRIGARC ornell Theory Center and Laboratory of Atomic and
Solid State Physics, Cornell University, Ithaca, New York
JOHNP . VALLEAUC,h emical Physics Theory Group, Department of Chem-
istry, University of Toronto, Toronto, Canada
HAOBINW ANG,D epartment of Chemistry, University of California, Berke-
ley, Berkeley, California
PREFACE
The Monte Carlo method is pervasive in computational approaches to
many-dimensional problems in chemical physics, but there have been few if
any attempts to bring all the dominant themes together in a single volume.
This volume attempts to do just that-at a state-of-art level focusing on the
main application areas. More detailed general introductions to the Monte
Carlo method can be found in the excellent textbooks by Hammersley and
Handscomb (1964) and Kalos and Whitlock (1986).
The term Monte Carlo, which refers to the famous gambling city and
arises from the role that random numbers play in the Monte Carlo method
(see the second chapter in this volume, by Srinivasan et al.), was suggested
by Metropolis, and the method itself was first used in 1949 (Metropolis and
Ulam, 1949). Von Neumann and Ulam (1945) had earlier realized that it is
possible to solve a deterministic mathematical problem, such as the evalu-
ation of a multidimensional integral, with the help of a stochastic sampling
experiment. In fact, it turns out that if the dimensionality of an integal is of
order of 10 or larger, the Monte Carlo method becomes the preferred tech-
nique of numerical integration. Such multidimensional integrals play an
important role in many branches of physics and chemistry, especially in
statistical mechanics.
Several of the chapters in this volume are concerned with the calculation
of thermodynamic ensemble averages for systems of many particles. An
introduction to this key application area is presented in the first chapter (by
Siepmann), and advanced work is discussed in the last six chapters in this
volume (by de Pablo and Escobedo, Valleau, Kofke, Siepmann, Johnson,
and Barkema and Newmann). There are a large number of monographs
and edited volumes with a major emphasis on techniques like those
described above and their application to a wide variety of molecular simu-
lations. Allen and Tildesley (1987), Heerman (1990), Binder and Heerman
(1992), Binder (1995), and Frenkel and Smit (1996) may be consulted as a
core library in this area.
Although the simulation of ensembles of particles constitutes a huge liter-
ature, it is only one aspect of the use of Monte Carlo methods in chemical
physics. Basically, whenever one has to calculate integrals over a high-
dimensionality space, the Monte Carlo method is potentially the algorithm
of choice. Thus, for example, in few-body simulations of chemical reactions,
one must integrate over the initial conditions of the reactant molecules, and
vii
viii PREFACE
this application is covered in the sixth chapter in this volume (by Peslherbe
et al.).
Feynman’s path-integral method also involves multidimensional inte-
grals, and the dimensionality of these integrals can be much higher than the
number of actual physical degrees of freedom of the system. The application
of Monte Carlo methods to this problem is covered in the fifth chapter in
this volume (by Topper). The Monte Carlo method arises somewhat differ-
ently in applications of quantum mechanics based on the Schrodinger equa-
tion. There are two basic approaches. The first is based on a variational
approach in which parameters in a trial function are varied, and variational
expectation values over the trial function are evaluated by Monte Carlo
quadratures. The second approach is different in that one actually solves
the Schrodinger equation. The method is based on an analogy of the
Schrodinger equation to a diffusion equation or stochastic process, which
is quite natural to solve by a random walk. These approaches are discussed
in the third and fourth chapters in this volume (by Bressanini and Reynolds
and Nightingale and Umrigar).
In the simulation of ensembles of condensed-phase particles, one must
often combine the techniques used to sample over the motions of the par-
ticles as a whole (these are the same techniques used to simulate a liquid of
noble-gas atoms) with the techniques for sampling the internal motions
(vibrations and rotations) of the molecules themselves. The latter problem
becomes particularly significant for large molecules with internal rotations
and other low-frequency, wide-amplitude motions. Often there are many
local minima of the molecular potential-energy function, and one must
develop specialized techniques to ensure that these are all sampled appro-
priately. This problem is especially covered in the seventh through eleventh
chapters in this volume (by Skolnick and Kolinski, Scheraga and Hao,
Church et al., Ferguson and Garrett, and de Pablo and Escobedo).
An interesting development of the last 10 years that has made Monte
Carlo methods even more pervasive in the field of scientific computation is
the prominence of parallel computation. Often, but not always, Monte
Carlo algorithms are more amenable to parallelization than are competitive
approaches. The quest for parallelism has led to a new appreciation for the
power and advantages of uncorrelated samples, and also to many new
research questions. For example, the ever-present search for methods of
generating long strings of uncorrelated random numbers to drive the algo-
rithms presents new challenges; this is discussed in the second chapter in
this volume (by Srinivasan et al.).
The Monte Carlo method is so general, and its use is so pervasive in
chemical physics, that there will surely be further development of these
techniques in the future. Will the Monte Carlo approach to simulation be
PREFACE ix
the single most widely used paradigm in computational science in the new
millennium? Only time will tell, but the probability is high.
REFERENCES
M. P. Allen, and D. J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford,
1987.
K. Binder, Monte Carlo and Molecular Dynamics Simulations in Polymer Sciences, Oxford, New
York.
K. Binder, and D. W. Heerman, Monte Carlo Simulation in Statistical Physics: An Introduction,
2nd ed., Springer, Berlin, 1992.
D. Frenkel, and B. Smit, Understanding Molecular Simulation: From Algorithms to Applica-
tions, Academic Press, New York, 1996.
J. M. Hammersley, and D. C. Handscomb, Monte Carlo Methods, Methuen, London, 1964.
D. W. Heerman, Computer Simulation Methods in Theoretical Physics, 2nd ed., Wiley, New
York, 1990.
M. H. Kalos, and P. A. Whitlock, Monte Carlo Methods, Wiley, New York, 1986.
N. Metropolis, and S. Ulam, J. Am. Stat. Assoc. 44, 335 (1949).
J. von Neumann, and S. Ulam, Bull. Am. Math. SOC.,5 1,660 (1945).
DAVIDM . FBRGUSON
J. ILJAS IEPMANN
DONALDG .
TRUHLAR
University of Minnesota