We describe a new approach to the rare-event Monte Carlo sampling problem. This technique utilizes a symmetrization strategy to create probability distributions that are more highly connected and, thus, more easily sampled than their original, potentially sparse counterparts. After discussing the formal outline of the approach and devising techniques for its practical implementation, we illustrate the utility of the technique with a series of numerical applications to Lennard-Jones clusters of varying complexity and rare-event character.

1.
J. P.
Valleau
and
S. G.
Whittington
, in
Modern Theoretical Chemistry
, edited by
B. J.
Berne
(
Plenum
,
New York
,
1977
).
2.
J. P.
Valleau
and
G. M.
Torrie
, in
Modern Theoretical Chemistry
, edited by
B. J.
Berne
(
Plenum
,
New York
,
1977
).
3.
M.
Kalos
and
P.
Whitlock
,
Monte Carlo Methods
(
Wiley-Interscience
,
New York
,
1986
).
4.
D.
Frenkel
and
B.
Smit
,
Understanding Molecular Simulation: From Algorithms to Applications
(
Academic
,
New York
,
2002
).
5.
M. P.
Nightingale
and
C. J.
Umrigar
, “
Quantum Monte Carlo Methods in Physics and Chemistry
,”
NATO Science Series
, Vol. 525, edited by
M. P.
Nightengale
and
C. J.
Umrigar
(
Kluwer
,
Dordrecht
,
1999
).
6.
M.
de Koning
,
W.
Cai
,
B.
Sadigh
,
T.
Oppelstrup
,
M. H.
Kalos
, and
V. V.
Bulatov
,
J. Chem. Phys.
122
(
7
),
074103
(
2005
).
7.
F. H.
Stillinger
and
T. A.
Weber
,
Phys. Rev. A
28
,
2408
(
1983
).
8.
F. H.
Stillinger
and
T. A.
Weber
,
J. Phys. Chem.
87
(
15
),
2833
(
1983
).
9.
D. D.
Frantz
,
D. L.
Freeman
, and
J. D.
Doll
,
J. Chem. Phys.
93
(
4
),
2769
(
1990
).
10.
C. J.
Geyer
, in
Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface
, edited by
E. M.
Keramigas
(
Interface Foundation
,
Fairfax
,
1991
), pp.
156
163
.
11.
C. J.
Geyer
and
E. A.
Thompson
,
J. Am. Stat. Assoc.
90
,
909
(
1995
).
12.
K.
Hukushima
and
K.
Nemoto
,
J. Phys. Soc. Jpn.
65
(
6
),
1604
(
1996
).
13.
D. J.
Earl
and
M. W.
Deem
,
Phys. Chem. Chem. Phys.
7
(
23
),
3910
(
2005
).
14.
A. F.
Voter
,
J. Chem. Phys.
82
(
4
),
1890
(
1985
).
15.
N.
Plattner
,
J. D.
Doll
, and
M.
Meuwly
,
J. Chem. Phys.
133
(
4
),
044506
(
2010
).
16.
J.
Kim
and
J. E.
Straub
,
J. Chem. Phys.
130
(
14
),
144114
(
2009
).
17.
D. A.
Kofke
,
J. Chem. Phys.
117
(
15
),
6911
(
2002
).
18.
C.
Predescu
,
M.
Predescu
, and
C. V.
Ciobanu
,
J. Phys. Chem. B
109
(
9
),
4189
(
2005
).
19.
C.
Predescu
,
M.
Predescu
, and
C. V.
Ciobanu
,
J. Chem. Phys.
120
(
9
),
4119
(
2004
).
20.
D.
Sabo
,
M.
Meuwly
,
D. L.
Freeman
, and
J. D.
Doll
,
J. Chem. Phys.
128
(
17
),
174109
(
2008
).
21.
H. G.
Katzgraber
,
S.
Trebst
,
D. A.
Huse
, and
M.
Troyer
,
J. Stat. Mech.: Theory Exp.
http://stacks.iop.org/JSTAT/2006/P03018.
22.
The Classic Fairy Tales
, edited by Iona and
Peter
Opie
(
Oxford University Press
,
New York
,
1992
), p.
200
.
23.
P.
Dupuis
,
Y.
Liu
,
H.
Wang
,
N.
Plattner
, and
J. D.
Doll
, “On the Infinite Swapping Limit for Parallel Tempering,”
SIAM J. Multiscale Model. Simul.
(submitted).
24.
D.
Sindhikara
,
Y. L.
Meng
, and
A. E.
Roitberg
,
J. Chem. Phys.
128
(
2
),
024103
(
2008
).
25.
S. M.
Ulam
,
Adventures of a Mathematician
(
Scribners
,
New York
,
1976
).
26.
D. J.
Wales
,
Energy Landscapes With Applications to Clusters, Biomolecules and Glasses
(
Cambridge University Press
,
Cambridge, England
,
2003
).
27.
F. F.
Abraham
,
Homogeneous Nucleation Theory: The Pretransition Theory of Vapor Condensation
(
Academic
,
New York
,
1974
), Ch. 9.
28.
P. J.
Rossky
,
J. D.
Doll
, and
H. L.
Friedman
,
J. Chem. Phys.
69
,
5628
(
1978
).
29.
W. H.
Press
,
S. A.
Teukolsky
,
W. T.
Vetterling
, and
B. P.
Flannery
,
Numerical Recipes in Fortran 77
, 2nd ed. (
Cambridge University Press
,
Cambridge, England
,
1996
).
30.
J. P. K.
Doye
,
M. A.
Miller
, and
D. J.
Wales
,
J. Chem. Phys.
111
(
18
),
8417
(
1999
).
31.
D. B.
Faken
, “
Studying the Lennard-Jones Potential Surface: Landscapes and Optimization
,” Ph.D. dissertation, Department of Chemistry,
Brown University
,
1994
.
32.
H. B.
Liu
and
K. D.
Jordan
,
J. Phys. Chem. A
109
(
23
),
5203
(
2005
).
33.
F.
Calvo
,
J. Chem. Phys.
123
(
12
),
124106
(
2005
).
34.
J. P.
Neirotti
,
F.
Calvo
,
D. L.
Freeman
, and
J. D.
Doll
,
J. Chem. Phys.
112
,
10340
(
2000
).
35.
M.
Athenes
and
F.
Calvo
,
ChemPhysChem
9
,
2332
(
2008
).
36.
I.
Coluzza
and
D.
Frenkel
,
ChemPhysChem
6
,
1779
(
2005
).
37.
D. J.
Sindhikara
,
D. J.
Emerson
, and
A. E.
Roitberg
,
J. Chem. Theory Comput.
6
,
2804
(
2010
).
38.
D. M.
Ceperley
,
Rev. Mod. Phys.
67
,
279
(
1995
).
39.
D.
Sabo
,
J. D.
Doll
, and
D. L.
Freeman
,
J. Chem. Phys.
116
,
3509
(
2002
).
40.
Y.
Sugita
and
Y.
Okamoto
,
Chem. Phys. Lett.
314
,
141
(
1999
).
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