Semiclassical approximations for quantum time correlation functions are presented for both electronically adiabatic and nonadiabatic dynamics along with discussions of the operator ordering and the classical limit. With the combined use of the initial‐value representation of the semiclassical propagator, a discrete algorithm to evaluate the Jacobi matrices, semiclassical operator ordering rules, and the stationary‐phase filter technique, a practical algorithm is developed to calculate quantum time correlation functions. This approach holds considerable promise for simulating the quantum dynamics of realistic many‐body systems. Some simple illustrative examples are used to demonstrate the feasibility and accuracy of the algorithm.

1.
R. Kubo, N. Toda, and N. Hashitsume, Statistical Physics II (Springer, Berlin, 1985).
2.
B. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley-Interscience, New York, 1976).
3.
G. C. Schatz and M. A. Ratner, Quantum Mechanics in Chemistry (Prentice-Hall, Englewood Cliffs, NJ, 1993).
4.
R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
5.
B. J.
Berne
,
J. Stat. Phys.
43
,
911
(
1986
).
6.
L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1986).
7.
Quantum Simulations of Condensed Matter Phenomena, edited by J. D. Doll and J. E. Gubernatis (World Scientific, Singapore, 1990).
8.
D. Chandler, in Liquides, Cristallisation et Transition Vitreuse Les Houches, Session LI, edited by D. Levesque, J. Hansen, and J. Zinn-Justin (Elsevier, New York, 1991).
9.
M. S. Swanson, Path Integrals and Quantum Processes (Academic, San Diego, 1992).
10.
M. F.
Herman
,
Annu. Rev. Phys. Chem.
45
,
83
(
1994
).
11.
R. P. Feynman, Statistical Mechanics (Addison-Wesley, Reading, MA, 1972), Chap. 3.
12.
D.
Thirumalai
,
E. J.
Bruskin
, and
B. J.
Berne
,
J. Chem. Phys.
79
,
5063
(
1983
).
13.
D.
Thirumlai
and
B. J.
Berne
,
J. Chem. Phys.
81
,
2512
(
1984
).
14.
V. S.
Filinov
,
Nucl. Phys. B
271
,
717
(
1986
).
15.
J. D.
Doll
,
D. L.
Freeman
, and
M. J.
Gillan
,
Chem. Phys. Lett.
143
,
277
(
1988
).
16.
J. D.
Doll
and
D. E.
Freeman
,
Adv. Chem. Phys.
73
,
289
(
1989
).
17.
J. D.
Doll
,
D. E.
Freeman
, and
T. L.
Beck
,
Adv. Chem. Phys.
78
,
61
(
1990
).
18.
N.
Makri
and
W. H.
Miller
,
Chem. Phys. Lett.
139
,
10
(
1987
).
19.
N.
Makri
and
W. H.
Miller
,
J. Chem. Phys.
89
,
2170
(
1988
).
20.
C. H.
Mak
and
D.
Chandler
,
Phys. Rev. A
41
,
5709
(
1990
).
21.
C. H.
Mak
and
D.
Chandler
,
Phys. Rev. A
44
,
2352
(
1991
).
22.
R.
Egger
and
C. H.
Mak
,
J. Chem. Phys.
99
,
2541
(
1993
).
23.
R.
Egger
,
C. H.
Mak
, and
U.
Weiss
,
J. Chem. Phys.
100
,
2651
(
1994
).
24.
D.
Makarov
and
N.
Makri
,
Phys. Rev. A
48
,
3626
(
1993
).
25.
D.
Makarov
and
N.
Makri
,
Chem. Phys. Lett.
221
,
482
(
1994
).
26.
M.
Topaler
and
N.
Makri
,
J. Chem. Phys.
101
,
7500
(
1994
).
27.
N.
Makri
and
D. E.
Makarov
,
J. Chem. Phys.
102
,
4600
(
1995
).
28.
N.
Makri
and
D. E.
Makarov
,
J. Chem. Phys.
102
,
4611
(
1995
).
29.
A. M.
Amini
and
M. F.
Herman
,
J. Chem. Phys.
99
,
5087
(
1993
).
30.
G.
Baym
and
N. D.
Mermin
,
J. Math. Phys.
2
,
232
(
1961
).
31.
D.
Thirumalai
and
B. J.
Berne
,
J. Chem. Phys.
79
,
5029
(
1983
).
32.
E. C.
Behrman
,
G. A.
Jongeward
, and
P. G.
Wolynes
,
J. Chem. Phys.
79
,
6277
(
1983
).
33.
R.
Jaquet
and
W. H.
Miller
,
J. Phys. Chem.
89
,
2139
(
1985
).
34.
K.
Yamashita
and
W. H.
Miller
,
J. Chem. Phys.
82
,
5475
(
1985
).
35.
R. N.
Silver
,
D. S.
Sivia
, and
J. E.
Gubernatis
,
Phys. Rev. B
41
,
2380
(
1990
).
36.
J. E.
Gubernatis
,
M.
Jarrell
,
R. N.
Silver
, and
D. S.
Sivia
,
Phys. Rev. B
44
,
6011
(
1991
).
37.
E.
Gallicchio
and
B. J.
Berne
,
J. Chem. Phys.
101
,
9909
(
1994
).
38.
J.
Cao
and
G. A.
Voth
,
J. Chem. Phys.
99
,
10070
(
1993
).
39.
J.
Cao
and
G. A.
Voth
,
J. Chem. Phys.
100
,
5106
(
1994
).
40.
J.
Cao
and
G. A.
Voth
,
J. Chem. Phys.
101
,
6157
(
1994
).
41.
J.
Cao
and
G. A.
Voth
,
J. Chem. Phys.
101
,
6168
(
1994
).
42.
J. Cao and G. Martyna, J. Chem. Phys. (to be published).
43.
J. Lobaugh and G. A. Voth, J. Chem. Phys. (to be published). This paper describes a CMD simulation of excess proton transport in liquid water.
44.
M. Pavese and G. A. Voth, Chem. Phys. Lett. (submitted). This paper describes a CMD simulation of self-diffusion in liquid para-hydrogen.
45.
J. Lobaugh, M. Pavese, and G. A. Voth (unpublished). This paper describes a CMD simulation of quantum water.
46.
W. H.
Miller
,
J. Chem. Phys.
53
,
1949
(
1970
).
47.
R. A.
Marcus
,
Chem. Phys. Lett.
7
,
525
(
1970
).
48.
W. H.
Miller
,
Adv. Chem. Phys.
25
,
69
(
1974
).
49.
J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, New York, 1985).
50.
J. H.
Van Vleck
,
Proc. Natl. Acad. Sci. U.S.A.
14
,
178
(
1928
).
51.
V. P. Maslov and M. V. Fedoryuk, Semiclassical Approximation in Quantum Mechanics (Reidel, Boston, MA, 1981).
52.
M. C.
Gutzwiller
,
J. Math. Phys.
8
,
1979
(
1967
).
53.
P.
Pechukas
,
Phys. Rev.
181
,
166
(
1969
).
54.
P.
Pechukas
,
Phys. Rev.
181
,
174
(
1969
).
55.
R. G.
Littlejohn
,
J. Stat. Phys.
68
,
7
(
1992
).
56.
G.
Campolieti
and
P.
Brumer
,
Phys. Rev. A
50
,
997
(
1994
).
57.
E. J.
Heller
,
J. Chem. Phys.
94
,
2723
(
1991
).
58.
W. H.
Miller
,
J. Chem. Phys.
95
,
9428
(
1991
).
59.
E.
Heller
,
J. Chem. Phys.
95
,
9431
(
1991
).
60.
M. Morse, Variational Analysis (Wiley, New York, 1972).
61.
N. Fröman and P. O. Fröman, JWKB Approximation (North-Holland, Amsterdam, 1965).
62.
H.
Weyl
,
Z. Phys.
46
,
1
(
1927
).
63.
J. E.
Moyal
,
Proc. Camb. Philos. Soc.
45
,
99
(
1949
).
64.
R. Hernandez (private communication).
65.
E. P.
Wigner
,
Phys. Rev.
40
,
749
(
1932
).
66.
F. J.
Webster
,
P. J.
Rossky
, and
R. A.
Friesner
,
Comp. Phys. Commun.
63
,
494
(
1991
).
67.
J. C.
Tully
and
R. K.
Preston
,
J. Chem. Phys.
55
,
562
(
1972
).
68.
J. C.
Tully
,
J. Chem. Phys.
93
,
1061
(
1990
).
69.
D. F. Coker, in Computer Simulation in Chemical Physics, edited by M. P. Allen and D. J. Tildesley (Kluwer, Dordrecht, The Netherlands, 1993).
70.
L.
Xiao
and
D. F.
Coker
,
J. Chem. Phys.
100
,
8646
(
1994
).
71.
L.
Xiao
and
D. F.
Coker
,
J. Chem. Phys.
102
,
1107
(
1994
).
72.
W. H.
Miller
,
S. D.
Schwartz
, and
J. W.
Tromp
,
J. Chem. Phys.
79
,
4889
(
1983
).
73.
J. Cao and G. A. Voth, J. Chem. Phys. (submitted).
74.
A.
Schmid
,
J. Low. Temp. Phys.
49
,
609
(
1982
).
75.
K.
Husimi
,
Proc. Phys. Math. Soc. Jpn.
22
,
264
(
1940
).
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