We present a flexible nonlinear reaction coordinate analysis method for the transition path ensemble based on the likelihood maximization approach developed by Peters and Trout [J. Chem. Phys.125, 054108 (2006)]. By parametrizing the reaction coordinate by a string of images in a collective variable space, we can optimize the likelihood that the string correctly models the committor data obtained from a path sampling simulation. The collective variable space with the maximum likelihood is considered to contain the best description of the reaction. The use of the reweighted path ensemble [J. Rogal et al., J. Chem. Phys.133, 174109 (2010)] allows a complete reaction coordinate description from the initial to the final state. We illustrate the method on a z-shaped two-dimensional potential. While developed for use with path sampling, this analysis method can also be applied to regular molecular dynamics trajectories.

1.
G. M.
Torrie
and
J. P.
Valleau
,
Chem. Phys. Lett.
28
,
578
(
1974
).
2.
E.
Carter
,
G.
Ciccotti
,
J. T.
Hynes
, and
R.
Kapral
,
Chem. Phys. Lett.
156
,
472
(
1989
).
3.
A.
Laio
and
M.
Parrinello
,
Proc. Natl. Acad. Sci. U.S.A.
99
,
12562
(
2002
).
4.
C.
Dellago
,
P. G.
Bolhuis
, and
P. L.
Geissler
,
Adv. Chem. Phys.
123
,
1
(
2002
).
5.
C.
Dellago
,
P. G.
Bolhuis
,
F. S.
Csajka
, and
D.
Chandler
,
J. Chem. Phys.
108
,
1964
(
1998
).
6.
W.
E
and
E.
Vanden-Eijnden
,
J. Stat. Phys.
123
,
503
(
2006
).
7.
W.
E
and
E.
Vanden-Eijnden
,
Annu. Rev. Phys. Chem.
61
,
391
(
2010
).
8.
P. G.
Bolhuis
,
C.
Dellago
, and
D.
Chandler
,
Proc. Natl. Acad. Sci. U.S.A.
97
,
5877
(
2000
).
9.
A.
Ma
and
A. R.
Dinner
,
J. Phys. Chem. B
109
,
6769
(
2005
).
10.
G.
Hummer
,
J. Chem. Phys.
120
,
516
(
2004
).
11.
R.
Best
and
G.
Hummer
,
Proc. Natl. Acad. Sci. U.S.A.
102
,
6732
(
2005
).
12.
B.
Peters
and
B. L.
Trout
,
J. Chem. Phys.
125
,
054108
(
2006
).
13.
B.
Peters
,
G. T.
Beckham
, and
B. L.
Trout
,
J. Chem. Phys.
127
,
034109
(
2007
).
14.
J.
Juraszek
and
P. G.
Bolhuis
,
Biophys. J.
95
,
4246
(
2008
).
15.
J.
Vreede
,
J.
Juraszek
, and
P. G.
Bolhuis
,
Proc. Natl. Acad. Sci. U.S.A.
107
,
2397
(
2010
).
16.
E.
Borrero
and
F.
Escobedo
,
J. Chem. Phys.
127
,
164101
(
2007
).
17.
G. T.
Beckham
,
B.
Peters
,
C.
Starbuck
,
N.
Variankaval
, and
B. L.
Trout
,
J. Am. Chem. Soc.
129
,
4714
(
2007
).
18.
B.
Pan
,
M. S.
Ricci
, and
B. L.
Trout
,
J. Phys. Chem. B
114
,
4389
(
2010
).
19.
W.
E
,
W.
Ren
, and
E.
Vanden-Eijnden
,
Phys. Rev. B
66
,
052301
(
2002
).
20.
E.
Vanden-Eijnden
and
M.
Venturoli
,
J. Chem. Phys.
130
,
194103
(
2009
).
21.
J.
Rogal
,
W.
Lechner
,
J.
Juraszek
,
B.
Ensing
, and
P. G.
Bolhuis
,
J. Chem. Phys.
133
,
17109
(
2010
).
22.
J.
Juraszek
and
P. G.
Bolhuis
,
Proc. Natl. Acad. Sci. U.S.A.
103
,
15859
(
2006
).
24.
A.
Berezhkovskii
and
A.
Szabo
,
J. Chem. Phys.
122
,
014503
(
2005
).
25.
T. S.
van Erp
,
D.
Moroni
, and
P. G.
Bolhuis
,
J. Chem. Phys.
118
,
7762
(
2003
).
26.
A. M.
Ferrenberg
and
R. H.
Swendsen
,
Phys. Rev. Lett.
63
,
1195
(
1989
).
27.
T. S.
van Erp
,
Phys. Rev. Lett.
98
,
268301
(
2007
).
28.
P. G.
Bolhuis
,
J. Chem. Phys.
129
,
114108
(
2008
).
30.
P. G.
Bolhuis
,
J. Phys.: Condens. Matter
15
,
S113
(
2003
).
31.
L.
Maragliano
,
A.
Fischer
,
E.
Vanden-Eijnden
, and
G.
Ciccotti
,
J. Chem. Phys.
125
,
024106
(
2006
).
32.
P.
Metzner
,
C.
Schütte
, and
E.
Vanden-Eijnden
,
J. Chem. Phys.
125
,
084110
(
2006
).
You do not currently have access to this content.