We develop an efficient Monte-Carlo algorithm to sample an ensemble of stochastic transition paths between stable states. In our description, paths are represented by chains of states linked by Markovian transition probabilities. Rate constants and mechanisms characterizing the transition may be determined from the path ensemble. We have previously devised several algorithms for sampling the path ensemble. For these algorithms, the numerical effort scales with the square of the path length. In the new simulation scheme, the required computation scales linearly with the length of the transition path. This improved efficiency allows the calculation of rate constants in complex molecular systems. As an example, we study rearrangement processes in a cluster consisting of seven Lennard-Jones particles in two dimensions. Using a quenching technique we are able to identify the relevant transition mechanisms and to locate the related transition states. We furthermore calculate transition rate constants for various isomerization processes.

1.
C. H. Bennett, in Algorithms for Chemical Computations, ACS Symp. Ser. No. 46, ed. R. E. Christofferson (American Chemical Society, Washington, D. C., 1977), p. 63.
2.
D.
Chandler
,
J. Chem. Phys.
68
,
2959
(
1978
).
3.
J.
Keck
,
J. Chem. Phys.
32
,
1035
(
1960
).
4.
J. B.
Anderson
,
J. Chem. Phys.
58
,
4684
(
1973
).
5.
C.
Dellago
,
P.
Bolhuis
,
F. S.
Csajka
, and
D.
Chandler
,
J. Chem. Phys.
108
,
1964
(
1998
).
6.
L. R.
Pratt
,
J. Chem. Phys.
85
,
5045
(
1986
).
7.
F. S. Csajka and D. Chandler, J. Chem. Phys. (to be published).
8.
P. G. Bolhuis, C. Dellago, and D. Chandler, Faraday Discuss. 110 (in press, 1998).
9.
M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1987).
10.
S.
Chandrasekhar
,
Rev. Mod. Phys.
15
,
1
(
1943
).
11.
P.
de Gennes
,
J. Chem. Phys.
55
,
572
(
1971
).
12.
F. H.
Stillinger
and
T. A.
Weber
,
Science
225
,
983
(
1984
);
F. H.
Stillinger
and
T. A.
Weber
,
Science
28
,
2408
(
1983
).
13.
D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, New York, 1987).
14.
G. M.
Torrie
and
J. P.
Valleau
,
J. Comput. Phys.
23
,
187
(
1977
).
15.
D. Frenkel and B. Smit, Understanding Molecular Simulation (Academic, San Diego, 1996).
16.
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, Cambridge, 1992).
17.
M. A.
Miller
and
D. J.
Wales
,
J. Chem. Phys.
107
,
8568
(
1997
).
This content is only available via PDF.
You do not currently have access to this content.