A hybrid quantum/classical molecular dynamics approach is applied to a proton transfer reaction represented by a symmetric double well system coupled to a dissipative bath. In this approach, the proton is treated quantum mechanically and all bath modes are treated classically. The transition state theory rate constant is obtained from the potential of mean force, which is generated along a collective reaction coordinate with umbrella sampling techniques. The transmission coefficient, which accounts for dynamical recrossings of the dividing surface, is calculated with a reactive flux approach combined with the molecular dynamics with quantum transitions surface hopping method. The hybrid quantum/classical results agree well with numerically exact results in the spatial-diffusion-controlled regime, which is most relevant for proton transfer in proteins. This hybrid quantum/classical approach has already been shown to be computationally practical for studying proton transfer in large biological systems. These results have important implications for future applications to hydrogen transfer reactions in solution and proteins.
REFERENCES
1.
D.
Li
and G. A.
Voth
, J. Phys. Chem.
95
, 10425
(1991
).2.
H.
Azzouz
and D.
Borgis
, J. Chem. Phys.
98
, 7361
(1993
).3.
R.
Pomes
and B.
Roux
, Chem. Phys. Lett.
234
, 416
(1995
).4.
M. E.
Tuckerman
, D.
Marx
, M. L.
Klein
, and M.
Parrinello
, Science
275
, 817
(1997
).5.
A.
Warshel
and Z. T.
Chu
, J. Chem. Phys.
93
, 4003
(1990
).6.
J.-K.
Hwang
, Z. T.
Chu
, A.
Yadav
, and A.
Warshel
, J. Phys. Chem.
95
, 8445
(1991
).7.
A.
Yadav
, R. M.
Jackson
, J. J.
Holbrook
, and A.
Warshel
, J. Am. Chem. Soc.
113
, 4800
(1991
).8.
J.-K.
Hwang
and A.
Warshel
, J. Am. Chem. Soc.
118
, 11745
(1996
).9.
M.
Garcia-Viloca
, J.
Gao
, M.
Karplus
, and D. G.
Truhlar
, Science
303
, 186
(2004
).10.
J.
Gao
and D. G.
Truhlar
, Annu. Rev. Phys. Chem.
53
, 467
(2002
).11.
D. G.
Truhlar
, J.
Gao
, C.
Alhambra
, M.
Garcia-Viloca
, J. C.
Corchado
, M. L.
Sanchez
, and J.
Villa
, Acc. Chem. Res.
35
, 341
(2002
).12.
G.
Hanna
and R.
Kapral
, J. Chem. Phys.
122
, 244505
(2005
).13.
D.
Borgis
, G.
Tarjus
, and H.
Azzouz
, J. Phys. Chem.
96
, 3188
(1992
).14.
D.
Laria
, G.
Ciccotti
, M.
Ferrario
, and R.
Kapral
, J. Chem. Phys.
97
, 378
(1992
).15.
A.
Staib
, D.
Borgis
, and J. T.
Hynes
, J. Chem. Phys.
102
, 2487
(1995
).16.
K.
Ando
and J. T.
Hynes
, J. Phys. Chem. B
101
, 10464
(1997
).17.
S. R.
Billeter
, S. P.
Webb
, P. K.
Agarwal
, T.
Iordanov
, and S.
Hammes-Schiffer
, J. Am. Chem. Soc.
123
, 11262
(2001
).18.
S. R.
Billeter
, S. P.
Webb
, T.
Iordanov
, P. K.
Agarwal
, and S.
Hammes-Schiffer
, J. Chem. Phys.
114
, 6925
(2001
).19.
S.
Hammes-Schiffer
and S.
Billeter
, Int. Rev. Phys. Chem.
20
, 591
(2001
).20.
P.
Bala
, P.
Grochowski
, B.
Lesyng
, and J. A.
McCammon
, J. Phys. Chem.
100
, 2535
(1996
).21.
P.
Bala
, P.
Grochowski
, K.
Nowinski
, B.
Lesyng
, and J. A.
McCammon
, Biophys. J.
79
, 1253
(2000
).22.
P.
Bala
, B.
Lesyng
, and J. A.
McCammon
, Chem. Phys.
180
, 271
(1994
).23.
S.
Hammes-Schiffer
and J. C.
Tully
, J. Chem. Phys.
101
, 4657
(1994
).24.
S. Y.
Kim
and S.
Hammes-Schiffer
, J. Chem. Phys.
119
, 4389
(2003
).25.
P. K.
Agarwal
, S. R.
Billeter
, and S.
Hammes-Schiffer
, J. Phys. Chem. B
106
, 3283
(2002
).26.
P. K.
Agarwal
, S. R.
Billeter
, P. T. R.
Rajagopalan
, S. J.
Benkovic
, and S.
Hammes-Schiffer
, Proc. Natl. Acad. Sci. U.S.A.
99
, 2794
(2002
).27.
J. B.
Watney
, P. K.
Agarwal
, and S.
Hammes-Schiffer
, J. Am. Chem. Soc.
125
, 3745
(2003
).28.
K. F.
Wong
, T.
Selzer
, S. J.
Benkovic
, and S.
Hammes-Schiffer
, Proc. Natl. Acad. Sci. U.S.A.
102
, 6807
(2005
).29.
S.
Hammes-Schiffer
, Biochemistry
41
, 13335
(2002
).30.
S. J.
Benkovic
and S.
Hammes-Schiffer
, Science
301
, 1196
(2003
).31.
J.
Morelli
and S.
Hammes-Schiffer
, Chem. Phys. Lett.
269
, 161
(1997
).32.
J.-Y.
Fang
and S.
Hammes-Schiffer
, J. Chem. Phys.
107
, 8933
(1997
).33.
J.-Y.
Fang
and S.
Hammes-Schiffer
, J. Chem. Phys.
110
, 11166
(1999
).34.
M.
Topaler
and N.
Makri
, J. Chem. Phys.
101
, 7500
(1994
).35.
P.
Hänggi
, P.
Talkner
, and M.
Borkovec
, Rev. Mod. Phys.
62
, 251
(1990
).36.
H.
Wang
, X.
Sun
, and W. H.
Miller
, J. Chem. Phys.
108
, 9726
(1998
).37.
W. H.
Thompson
, J. Chem. Phys.
110
, 4221
(1999
).38.
H.
Wang
, M.
Thoss
, and W. H.
Miller
, J. Chem. Phys.
112
, 47
(2000
).39.
M. V.
Basilevsky
and G. V.
Davidovitch
, J. Chem. Phys.
115
, 6072
(2001
).40.
E.
Geva
, Q.
Shi
, and G. A.
Voth
, J. Chem. Phys.
115
, 9209
(2001
).41.
Q.
Shi
and E.
Geva
, J. Chem. Phys.
116
, 3223
(2002
).42.
T.
Yamamoto
, H.
Wang
, and W. H.
Miller
, J. Chem. Phys.
116
, 7335
(2002
).43.
J.-L.
Liao
and E.
Pollak
, J. Chem. Phys.
116
, 2718
(2002
).44.
45.
D.
Barik
, S. K.
Banik
, and D. S.
Ray
, J. Chem. Phys.
119
, 680
(2003
).46.
D.
Barik
, B. C.
Bag
, and D. S.
Ray
, J. Chem. Phys.
119
, 12973
(2004
).47.
A.
Pomyalov
and D.
Tannor
, J. Chem. Phys.
123
, 204111
(2005
).48.
J.-L.
Liao
and E.
Pollak
, Chem. Phys.
268
, 295
(2001
).49.
E. S.
Sim
, G.
Krilov
, and B. J.
Berne
, J. Phys. Chem. A
105
, 2824
(2001
).50.
G.
Krilov
, E. S.
Sim
, and B. J.
Berne
, Chem. Phys.
268
, 21
(2001
).51.
E.
Rabani
, G.
Krilov
, and B. J.
Berne
, J. Chem. Phys.
112
, 2605
(2002
).52.
A. O.
Caldeira
and A. J.
Leggett
, Ann. Phys. (N.Y.)
149
, 374
(1983
).53.
A. J.
Leggett
, S.
Chakravorty
, A. T.
Dorsey
, M. P.
Fisher
, A.
Garg
, and W.
Zwerger
, Rev. Mod. Phys.
59
, 1
(1987
).54.
D.
Chandler
, J. Chem. Phys.
68
, 2959
(1978
).55.
W. H.
Miller
, J. Chem. Phys.
61
, 1823
(1974
).56.
J. T.
Hynes
, in Theory of Chemical Reaction Dynamics
, edited by M.
Baer
(CRC
, Boca Raton, FL
, 1985
), Vol. 4
, p. 171
.57.
E.
Wigner
, J. Chem. Phys.
5
, 720
(1937
).58.
E.
Wigner
, Trans. Faraday Soc.
34
, 29
(1938
).59.
J. C.
Keck
, J. Chem. Phys.
32
, 1035
(1960
).60.
J. C.
Keck
, Discuss. Faraday Soc.
33
, 173
(1962
).61.
C. H.
Bennett
, Algorithms for Chemical Computation
(American Chemical Society
, Washington, DC
, 1977
).62.
J. B.
Anderson
, J. Chem. Phys.
58
, 4684
(1973
).63.
D.
Chandler
, in Classical and Quantum Dynamics in Condensed Phase Simulations
, edited by B. J.
Berne
, G.
Ciccotti
, and D. F.
Coker
(World Scientific
, Singapore
, 1998
), p. 3
.64.
J. B.
Watney
, A. V.
Soudackov
, K. F.
Wong
, and S.
Hammes-Schiffer
, Chem. Phys. Lett.
418
, 268
(2006
).65.
E. A.
Carter
, G.
Ciccotti
, J. T.
Hynes
, and R.
Kapral
, Chem. Phys. Lett.
156
, 472
(1989
).66.
G. K.
Schenter
, B. C.
Garrett
, and D. G.
Truhlar
, J. Chem. Phys.
119
, 5828
(2003
).67.
J. A.
Montgomery
, D.
Chandler
, and B. J.
Berne
, J. Chem. Phys.
70
, 4056
(1979
).68.
B. J.
Berne
, in Multiple Time Scales
, edited by J. U.
Brackbill
and B. I.
Cohen
(Academic
, New York
, 1985
), p. 419
.69.
S.
Hammes-Schiffer
and J. C.
Tully
, J. Chem. Phys.
103
, 8528
(1995
).70.
J. C.
Tully
, J. Chem. Phys.
93
, 1061
(1990
).71.
P. V.
Parandekar
and J. C.
Tully
, J. Chem. Phys.
122
, 094102
(2005
).72.
N.
Metropolis
, A. W.
Rosenbluth
, M. N.
Rosenbluth
, A. N.
Teller
, and E.
Teller
, J. Chem. Phys.
21
, 1087
(1953
).73.
M. P.
Allen
and D. J.
Tildesley
, Computer Simulation of Liquids
(Clarendon
, Oxford
, 1989
).74.
C. C.
Marston
and G. G.
Balint-Kurti
, J. Chem. Phys.
91
, 3571
(1989
).75.
S. P.
Webb
and S.
Hammes-Schiffer
, J. Chem. Phys.
113
, 5214
(2000
).76.
S.
Kumar
, J. M.
Rosenberg
, D.
Bouzida
, R. H.
Swendsen
, and P. A.
Kollman
, J. Comput. Chem.
13
, 1011
(1992
).77.
B.
Roux
, Comput. Phys. Commun.
91
, 275
(1995
).78.
W. H.
Press
, B. P.
Flannery
, S. A.
Teukolsky
, and W. T.
Vetterling
, Numerical Recipes in C
(Cambridge University
, Cambridge
, 1988
).79.
D. F.
Coker
, in Computer Simulations in Chemical Physics
, edited by M. P.
Allen
and D. J.
Tildesley
(Kluwer Academic
, Netherlands
, 1993
), p. 315
.80.
J.-Y.
Fang
and S.
Hammes-Schiffer
, J. Phys. Chem. A
103
, 9399
(1999
).81.
A. W.
Jasper
, S. N.
Stechmann
, and D. G.
Truhlar
, J. Chem. Phys.
116
, 5424
(2002
).82.
A. W.
Jasper
and D. G.
Truhlar
, Chem. Phys. Lett.
369
, 60
(2003
).83.
U.
Muller
and G.
Stock
, J. Chem. Phys.
107
, 6230
(1997
).84.
P. M.
Kiefer
and J. T.
Hynes
, Solid State Ionics
168
, 219
(2004
).85.
A.
Warshel
, Computer Modeling of Chemical Reactions in Enzymes and Solutions
(Wiley
, New York
, 1991
).86.
J. C.
Tully
, Faraday Discuss.
110
, 1
(1998
).87.
D.
Kohen
, F. H.
Stillinger
, and J. C.
Tully
, J. Chem. Phys.
109
, 4713
(1998
).88.
M.
Thachuk
, M. Y.
Ivanov
, and D. M.
Wardlaw
, J. Chem. Phys.
109
, 5747
(1998
).89.
E. R.
Bittner
and P. J.
Rossky
, J. Chem. Phys.
103
, 8130
(1995
).90.
B. J.
Schwartz
, E. R.
Bittner
, O. V.
Prezhdo
, and P. J.
Rossky
, J. Chem. Phys.
104
, 5942
(1996
).91.
O. V.
Prezhdo
and P. J.
Rossky
, J. Chem. Phys.
107
, 825
(1997
).92.
O. V.
Prezhdo
and P. J.
Rossky
, J. Chem. Phys.
107
, 5863
(1997
).93.
C. Y.
Zhu
, S.
Nangia
, A. W.
Jasper
, and D. G.
Truhlar
, J. Chem. Phys.
121
, 7658
(2004
).94.
E. P.
Wigner
, Phys. Rev.
40
, 749
(1932
).95.
D. G.
Truhlar
, in Isotope Effects in Chemistry and Biology
, edited by A.
Kohen
and H.-H.
Limbach
(Taylor & Francis
, LLC, Boca Raton
, 2006
), p. 592
.96.
R. F.
Grote
and J. T.
Hynes
, J. Chem. Phys.
73
, 2715
(1980
).97.
E.
Pollak
, J. Chem. Phys.
85
, 865
(1986
).98.
E.
Pollak
, H.
Grabert
, and P.
Hänggi
, J. Chem. Phys.
91
, 4073
(1989
).99.
P. G.
Wolynes
, Phys. Rev. Lett.
47
, 968
(1981
).100.
P.
Hänggi
, E.
Pollak
, and H.
Grabert
, University of Augsburg
, Report No. 215, 1989
.101.
I.
Rips
and E.
Pollak
, Phys. Rev. A
41
, 5366
(1990
).© 2006 American Institute of Physics.
2006
American Institute of Physics
You do not currently have access to this content.
