In the high friction limit of Kramers’ theory, the diffusion coefficient for motion along the reaction coordinate is a crucial parameter in determining reaction rates from mean first passage times. The Einstein relation between mean squared displacement, time, and diffusivity is inaccurate at short times because of ballistic motion and inaccurate at long times because trajectories drift away from maxima in the potential of mean force. Starting from the Smoluchowski equation for a downward parabolic barrier, we show how drift induced by the potential of mean force can be included in estimating the diffusivity. A modified relation between mean squared displacement, time, and diffusivity now also includes a dependence on the barrier curvature. The new relation provides the diffusivity at the top of the barrier from a linear regression that is analogous to the procedure commonly used with Einstein's relation. The new approach has particular advantages over previous approaches when evaluations of the reaction coordinate are costly or when the reaction coordinate cannot be differentiated to compute restraining forces or velocities. We use the new method to study the dynamics of barrier crossing in a Potts lattice gas model of nucleation from solution. Our analysis shows that some current hypotheses about laser-induced nucleation mechanisms lead to a nonzero threshold laser pulse duration below which a laser pulse will not affect nucleation. We therefore propose experiments that might be used to test these hypotheses.

1.
S.
Auer
and
D.
Frenkel
,
J. Chem. Phys.
120
,
3015
(
2004
).
2.
D. K.
Klimov
and
D.
Thirumalai
,
Phys. Rev. Lett.
79
,
317
(
1997
).
3.
D. J.
Bicout
and
A.
Szabo
,
Protein Sci.
9
,
452
(
2000
).
4.
J. M.
Bui
,
R. H.
Henchman
, and
J. A.
McCammon
,
Biophys. J.
85
,
2267
(
2003
).
5.
J.
Juraszek
and
P. G.
Bolhuis
,
Biophys. J.
95
,
4246
(
2008
).
6.
C. D.
Waldburger
,
T.
Jonsson
, and
R. T.
Sauer
,
Proc. Natl. Acad. Sci. U.S.A.
93
,
2629
(
1996
).
7.
K. W.
Plaxco
and
D.
Baker
,
Proc. Natl. Acad. Sci. U.S.A.
95
,
13591
(
1998
).
8.
M.
Jacob
,
T.
Schindler
,
J.
Balbach
, and
F. X.
Schmid
,
Proc. Natl. Acad. Sci. U.S.A.
94
,
5622
(
1997
).
9.
R. P.
Bhattacharyya
and
T. R.
Sosnick
,
Biochemistry
38
,
2601
(
1999
).
10.
M.
Jacob
,
M.
Geeves
,
G.
Holtermann
, and
F. X.
Schmid
,
Nat. Struct. Biol.
6
,
923
(
1999
).
11.
M. E.
Leunissen
,
C. G.
Christova
,
A. -P.
Hynninen
,
C. P.
Royall
,
A. I.
Campbell
,
A.
Imhof
,
M.
Dijkstra
,
R.
van Roij
, and
A.
van Blaaderen
,
Nature (London)
437
,
235
(
2005
).
12.
R. D.
Barish
,
R.
Schulman
,
P. W. K.
Rothemund
, and
E.
Winfree
,
Proc. Natl. Acad. Sci. U.S.A.
106
,
6054
(
2009
).
13.
A. M.
Kalsin
,
M.
Fialkowski
,
M.
Paszewski
,
S. K.
Smoukov
,
K. J. M.
Bishop
, and
B. A.
Grzybowski
,
Science
312
,
420
(
2006
).
14.
Z. L.
Zhang
and
S. C.
Glotzer
,
Nano Lett.
4
,
1407
(
2004
).
15.
E.
Rabani
,
D. R.
Reichman
,
P. L.
Geissler
, and
L. E.
Brus
,
Nature (London)
426
,
271
(
2003
).
16.
H. A.
Kramers
,
Physica (Utrecht)
7
,
284
(
1940
).
17.
P.
Hänggi
,
P.
Talkner
, and
M.
Borkovec
,
Rev. Mod. Phys.
62
,
251
(
1990
).
18.
R. P.
Sear
,
J. Chem. Phys.
128
,
214513
(
2008
).
19.
E.
Sanz
,
C.
Valeriani
,
T.
Vissers
,
A.
Fortini
,
M. E.
Leunissen
,
A.
van Blaaderen
,
D.
Frenkel
, and
M.
Dijkstra
,
J. Phys.: Condens. Matter
20
,
494247
(
2008
).
21.
A.
Berezhkovskii
and
A.
Szabo
,
J. Chem. Phys.
122
,
014503
(
2005
).
22.
J.
Nývlt
,
Cryst. Res. Technol.
30
,
443
(
1995
).
23.
W.
Ostwald
,
Z. Phys. Chem.
22
,
289
(
1897
).
24.
A.
Ma
and
A. R.
Dinner
,
J. Phys. Chem. B
109
,
6769
(
2005
).
25.
B.
Peters
,
G. T.
Beckham
, and
B. L.
Trout
,
J. Chem. Phys.
127
,
034109
(
2007
).
26.
B.
Peters
and
B. L.
Trout
,
J. Chem. Phys.
125
,
054108
(
2006
).
27.
B.
Peters
,
J. Chem. Phys.
125
,
241101
(
2006
).
28.
E. E.
Borrero
and
F. A.
Escobedo
,
J. Chem. Phys.
127
,
164101
(
2007
).
29.
W.
Im
and
B.
Roux
,
J. Mol. Biol.
319
,
1177
(
2002
).
30.
G. E.
Uhlenbeck
and
L. S.
Ornstein
,
Phys. Rev.
36
,
823
(
1930
).
31.
32.
A. C.
Pan
,
D.
Sezer
, and
B.
Roux
,
J. Phys. Chem. B
112
,
3432
(
2008
).
33.
G.
Hummer
and
I. G.
Kevrekidis
,
J. Chem. Phys.
118
,
10762
(
2003
).
34.
B. J.
Berne
,
M.
Borkovec
, and
J. E.
Straub
,
J. Phys. Chem.
92
,
3711
(
1988
).
35.
T. B.
Woolf
and
B.
Roux
,
J. Am. Chem. Soc.
116
,
5916
(
1994
).
37.
G. M.
Torrie
and
J. P.
Valleau
,
Chem. Phys. Lett.
28
,
578
(
1974
).
38.
A.
Ma
,
A.
Nag
, and
A. R.
Dinner
,
J. Chem. Phys.
124
,
144911
(
2006
).
39.
L.
Farkas
,
Z. Phys. Chem.
125
,
236
(
1927
).
40.
R.
Becker
and
W.
Doring
,
Ann. Phys.
416
,
719
(
1935
).
41.
D.
Kashchiev
,
Nucleation: Basic Theory with Applications
(
Butterworth-Heinemann
,
Oxford
,
2000
).
42.
R.
Aris
,
Proc. R. Soc. London, Ser. A
235
,
67
(
1956
).
43.
K.
Schulten
,
Z.
Schulten
, and
A.
Szabo
,
J. Chem. Phys.
74
,
4426
(
1981
).
45.
P. M.
Chaikin
and
T. C.
Lubensky
,
Principles of Condensed Matter Physics
(
Cambridge University Press
,
Cambridge
,
1995
).
46.
P. R.
ten Wolde
and
D.
Frenkel
,
J. Chem. Phys.
109
,
9901
(
1998
).
47.
48.
49.
R.
Radhakrishnan
and
T.
Schlick
,
J. Chem. Phys.
121
,
2436
(
2004
).
50.
B.
Peters
,
N. E. R.
Zimmermann
,
G. T.
Beckham
,
J. W.
Tester
, and
B. L.
Trout
,
J. Am. Chem. Soc.
130
,
17342
(
2008
).
51.
N.
Duff
and
B.
Peters
,
J. Chem. Phys.
131
,
184101
(
2009
).
52.
J. E.
Ricci
,
The Phase Rule and Heterogeneous Equilibrium
(
Van Nostrand
,
New York
,
1951
).
53.
S.
Punnathanam
and
P. A.
Monson
,
J. Chem. Phys.
125
,
024508
(
2006
).
54.
R.
Pool
and
P. G.
Bolhuis
,
J. Phys. Chem. B
109
,
6650
(
2005
).
55.
T. I.
Morrow
and
E. J.
Maginn
,
J. Chem. Phys.
122
,
054504
(
2005
).
56.
T. I.
Morrow
and
E. J.
Maginn
,
J. Chem. Phys.
125
,
204712
(
2006
).
57.
D. A.
Kofke
and
E. D.
Glandt
,
Mol. Phys.
64
,
1105
(
1988
).
58.
R.
Pool
and
P. G.
Bolhuis
,
Phys. Chem. Chem. Phys.
8
,
941
(
2006
).
59.
N.
Metropolis
,
A. W.
Rosenbluth
,
M. N.
Rosenbluth
,
A. H.
Teller
, and
E.
Teller
,
J. Chem. Phys.
21
,
1087
(
1953
).
60.
J.
Zaccaro
,
J.
Matic
,
A. S.
Myerson
, and
B. A.
Garetz
,
Cryst. Growth Des.
1
,
5
(
2001
).
61.
X.
Sun
,
B. A.
Garetz
, and
A. S.
Myerson
,
Cryst. Growth Des.
6
,
684
(
2006
).
62.
B. A.
Garetz
,
J. E.
Aber
,
N. L.
Goddard
,
R. G.
Young
, and
A. S.
Myerson
,
Phys. Rev. Lett.
77
,
3475
(
1996
).
63.
J.
Matic
,
X.
Sun
,
B. A.
Garetz
, and
A. S.
Myerson
,
Cryst. Growth Des.
5
,
1565
(
2005
).
64.
I. S.
Lee
,
J. M. B.
Evans
,
D.
Erdemir
,
A. Y.
Lee
,
B. A.
Garetz
, and
A. S.
Myerson
,
Cryst. Growth Des.
8
,
4255
(
2008
).
65.
X.
Sun
,
B. A.
Garetz
, and
A. S.
Myerson
,
Cryst. Growth Des.
8
,
1720
(
2008
).
66.
A. J.
Alexander
and
P. J.
Camp
,
Cryst. Growth Des.
9
,
958
(
2009
).
67.
B. A.
Garetz
,
J.
Matic
, and
A. S.
Myerson
,
Phys. Rev. Lett.
89
,
175501
(
2002
).
68.
69.
A. C.
Pan
and
D.
Chandler
,
J. Phys. Chem. B
108
,
19681
(
2004
).
70.
P. R.
ten Wolde
and
D.
Frenkel
,
Science
277
,
1975
(
1997
).
71.
D.
Erdemir
,
A. Y.
Lee
, and
A. S.
Myerson
,
Acc. Chem. Res.
42
,
621
(
2009
).
72.
P. G.
Vekilov
,
Cryst. Growth Des.
4
,
671
(
2004
).
73.
M. J.
Ruiz-Montero
,
D.
Frenkel
, and
J. J.
Brey
,
Mol. Phys.
90
,
925
(
1997
).
74.
E.
Vanden-Eijnden
and
F. A.
Tal
,
J. Chem. Phys.
123
,
184103
(
2005
).
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