We present a systematic test of four general semiclassical procedures for the theoretical treatment of multistate molecular processes such as electronically nonadiabatic photochemical reactions. The methods are tested by comparing their predictions to accurate quantal results for three two-state model reactions involving conical intersections. The four methods tested are Tully’s fewest-switches version of trajectory surface hopping (1990), the Blais–Truhlar trajectory surface hopping method (1983), the Ehrenfest scheme (1975–1979), and the Meyer–Miller method (1979). We test the ability of the classical path methods to predict both electronic probabilities and product rovibrational distributions. For each of the four basic approaches we test six options for extracting final-state information from the calculated dynamics. We find that, although in most cases there is qualitative agreement between average quantum mechanical and trajectory results, the overall average error is about 50% for Tully’s fewest-switches method, the Ehrenfest method, and the Meyer–Miller method, and even higher, about 60%, for the Blais–Truhlar method. These values do not include additional errors in the below-threshold regions, which are especially large for the Meyer–Miller method because of the electronic zero-point energy in the Meyer–Miller classical analog Hamiltonian.

1.
R. B. Woodward and R. Hoffmann, The Conservation of Orbital Symmetry (Verlag Chemie, Weinheim, 1970);
M. J. S. Dewar and R. C. Dougherty, The PMO Theory of Organic Chemistry (Plenum, New York, 1975);
L. Salem, Electrons in Chemical Reactions: First Principles (Wiley, New York, 1982);
J. Simons, Energetic Principles of Chemical Reactions (Jones and Bartlett, Boston, 1983).
2.
D. R.
Yarkony
,
J. Phys. Chem.
100
,
18612
(
1996
).
3.
M.
Zhao
,
D. G.
Truhlar
,
N. C.
Blais
,
D. W.
Schwenke
, and
D. J.
Kouri
,
J. Phys. Chem.
94
,
6696
(
1990
), and references therein.
4.
W. H.
Miller
,
Adv. Chem. Phys.
30
,
77
(
1975
);
see also
J. W.
Duff
and
D. G.
Truhlar
,
Chem. Phys.
9
,
243
(
1975
), and references therein.
5.
E. J.
Heller
,
J. Chem. Phys.
62
,
1544
(
1975
);
see also
R. T.
Skodje
and
D. G.
Truhlar
,
J. Chem. Phys.
80
,
3123
(
1984
), and references therein.
6.
M. S.
Topaler
,
M. D.
Hack
,
T. C.
Allison
,
Y.-P.
Liu
,
S. L.
Mielke
,
D. W.
Schwenke
, and
D. G.
Truhlar
,
J. Chem. Phys.
106
,
8699
(
1997
).
7.
M. S.
Topaler
,
T. C.
Allison
,
D. W.
Schwenke
, and
D. G.
Truhlar
,
J. Phys. Chem.
102
,
1666
(
1998
).
8.
E. E. Nikitin, Theory of Elementary Atomic and Molecular Processes (Oxford University Press, London, 1974).
9.
J. C.
Tully
and
R. K.
Preston
,
J. Chem. Phys.
55
,
562
(
1971
).
10.
P.
Pechukas
,
Phys. Rev.
181
,
174
(
1969
).
11.
N. C.
Blais
and
D. G.
Truhlar
,
J. Chem. Phys.
79
,
1334
(
1983
).
12.
J. C.
Tully
,
J. Chem. Phys.
93
,
1061
(
1990
).
13.
S.
Chapman
,
Adv. Chem. Phys.
82
,
423
(
1992
).
14.
M. F.
Herman
,
Annu. Rev. Phys. Chem.
45
,
83
(
1994
).
15.
H.-D.
Meyer
and
W. H.
Miller
,
J. Chem. Phys.
70
,
3214
(
1979
).
16.
P.
Ehrenfest
,
Z. Phys.
45
,
455
(
1927
).
Ehrenfest showed that Newton’s classical equations of motion are valid if both the force and the momentum are replaced by their quantum mechanical average values.
17.
S. C.
Mehrota
and
J. E.
Boggs
,
J. Chem. Phys.
63
,
4618
(
1975
).
18.
G. D.
Billing
,
Chem. Phys.
9
,
359
(
1975
).
19.
K. J.
McCann
and
M. R.
Flannery
,
Chem. Phys. Lett.
35
,
124
(
1975
).
20.
J.
Durup
,
Chem. Phys. Lett.
132
,
299
(
1986
).
21.
M.
Amarouche
,
F. X.
Gadea
, and
J.
Durup
,
Chem. Phys.
130
,
145
(
1989
).
22.
W. H.
Miller
and
C. W.
McCurdy
,
J. Chem. Phys.
69
,
5163
(
1978
).
23.
X.
Sun
and
W. H.
Miller
,
J. Chem. Phys.
106
,
916
(
1997
).
24.
B. C.
Garrett
and
D. G.
Truhlar
,
Theor. Chem. Adv. Perspectives
6A
,
216
(
1981
). [This publication is also referred to as B. C. Garrett abnd D. G. Truhlar, in Theoretical Chemistry: Theory of Scattering: Papers in Honor of Henry Eyring, edited by D. Henderson. Vol. 6, Part A (Academic, New York, 1981), pp. 216–289. Library of Congress Catalog Card Number 75-21963, ISBN 0-12-681906-8.]
25.
C. A.
Mead
and
D. G.
Truhlar
,
J. Chem. Phys.
77
,
6090
(
1982
).
26.
P.
Halvick
and
D. G.
Truhlar
,
J. Chem. Phys.
96
,
2895
(
1992
);
P.
Halvick
and
D. G.
Truhlar
,
J. Chem. Phys.
100
,
4718
(E) (
1994
).
27.
D. W.
Schwenke
,
S. L.
Mielke
,
G. J.
Tawa
,
R. S.
Friedman
,
P.
Halvick
, and
D. G.
Truhlar
,
Chem. Phys. Lett.
203
,
565
(
1993
).
28.
M. F.
Herman
,
J. Chem. Phys.
81
,
754
(
1984
).
29.
D. F.
Coker
and
L.
Xiao
,
J. Chem. Phys.
102
,
496
(
1995
).
30.
U.
Müller
and
G.
Stock
,
J. Chem. Phys.
107
,
6230
(
1997
).
31.
F.
Strocchi
,
Rev. Mod. Phys.
38
,
36
(
1966
);
W.-M.
Zheng
and
D. H.
Feng
,
Phys. Rep.
252
,
1
(
1995
).
32.
A.
Garciá-Vela
,
R. B.
Gerber
, and
D. G.
Imre
,
J. Chem. Phys.
97
,
7242
(
1992
).
33.
R. B.
Gerber
,
V.
Buch
, and
M. A.
Ratner
,
J. Chem. Phys.
77
,
3022
(
1982
);
V.
Buch
,
R. B.
Gerber
, and
M. A.
Ratner
,
Chem. Phys. Lett.
101
,
44
(
1983
).
34.
R.
Alimi
,
R. B.
Gerber
,
A. D.
Hammerich
,
R.
Kosloff
, and
M. A.
Ratner
,
J. Chem. Phys.
93
,
6484
(
1990
).
35.
R. E.
Langer
,
Phys. Rev.
51
,
669
(
1937
).
36.
W. H.
Miller
,
J. Chem. Phys.
53
,
3578
(
1970
);
see also Refs. 4 and 14 and the following references and references therein,
R. A.
Marcus
,
J. Chem. Phys.
56
,
311
(
1972
);
R. A.
Marcus
,
J. Chem. Phys.
59
,
5135
(
1973
);
J. W.
Duff
and
D. G.
Truhlar
,
Chem. Phys.
4
,
1
(
1974
);
J. W.
Duff
and
D. G.
Truhlar
,
Chem. Phys.
17
,
249
(
1976
);
M. F.
Herman
and
E.
Kluk
,
Chem. Phys.
91
,
27
(
1984
);
E. J.
Heller
,
Chem. Phys.
94
,
2723
(
1991
);
K. G.
Kay
,
J. Chem. Phys.
107
,
2313
(
1997
).
37.
X.
Sun
and
W. H.
Miller
,
J. Chem. Phys.
106
,
6346
(
1997
);
see also
G.
Stock
and
M.
Thoss
,
Phys. Rev. Lett.
78
,
578
(
1997
);
V. S.
Batista
and
W. H.
Miller
,
Chem. Phys.
108
,
498
(
1998
).
38.
S. L.
Mielke
,
G. J.
Tawa
,
D. G.
Truhlar
, and
D. W.
Schwenke
,
J. Am. Chem. Soc.
115
,
6436
(
1993
).
39.
M. S.
Topaler
and
D. G.
Truhlar
,
J. Chem. Phys.
107
,
392
(
1997
).
40.
D. G. Truhlar and J. T. Muckerman, in Atom–Molecule Collision Theory, edited by R. B. Bernstein (Plenum, New York, 1979), pp. 505–566.
41.
R. G.
Gordon
,
J. Chem. Phys.
44
,
3083
(
1966
).
42.
N. C.
Blais
and
D. G.
Truhlar
,
J. Chem. Phys.
65
,
5335
(
1976
).
43.
D. G.
Truhlar
,
Int. J. Quantum Chem., Symp.
10
,
239
(
1976
).
44.
D. G.
Truhlar
,
B. P.
Reid
,
D. E.
Zurawski
, and
J. C.
Gray
,
J. Phys. Chem.
85
,
786
(
1981
).
45.
G.
Stock
,
J. Chem. Phys.
103
,
2888
(
1995
).
46.
Y.
Sun
,
D. J.
Kouri
,
D. G.
Truhlar
, and
D. W.
Schwenke
,
Phys. Rev. A
41
,
4857
(
1990
).
47.
G. J. Tawa, S. L. Mielke, D. G. Truhlar, and D. W. Schwenke, in Advances in Molecular Vibrations and Collisional Dynamics, edited by J. M. Bowman (JAI, Greenwich, CT, 1994), Vol. 2B, pp. 45–116.
48.
G. J.
Tawa
,
S. L.
Mielke
,
D. G.
Truhlar
, and
D. W.
Schwenke
,
J. Chem. Phys.
100
,
5751
(
1994
).
49.
D. W.
Schwenke
,
S. L.
Mielke
,
G. J.
Tawa
,
R. S.
Friedman
,
P.
Halvick
, and
D. G.
Truhlar
,
Chem. Phys. Lett.
203
,
565
(
1993
).
50.
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge University Press, Cambridge, 1994), pp. 718–725.
51.
In Ref. 47, pp. 716–718.
52.
D. G.
Schweikert
,
J. Math. Phys.
45
,
312
(
1966
).
53.
A. K.
Cline
,
Commun. ACM
17
,
218
(
1974
).
54.
See AIP Document No. E-PAPS E-JCPSA6-109-029833 for 5 tables and 5 Figures.
E-PAPS document files may be retrieved free of charge from our FTP server (http://www.aip.org/epaps/epaps.html) or from ftp.aip.org in the directory /epaps/. For further information, e-mail: paps@aip.org or fax: 516-576-2223.
55.
Y.
Guo
,
D. L.
Thompson
, and
T. D.
Sewell
,
J. Chem. Phys.
104
,
576
(
1996
).
56.
See, for example,
J. C.
Gray
,
B. C.
Garrett
, and
D. G.
Truhlar
,
J. Chem. Phys.
70
,
5921
(
1979
), and references therein.
57.
T. C.
Thompson
and
D. G.
Truhlar
,
Chem. Phys. Lett.
75
,
87
(
1980
);
N.
Makri
and
W. H.
Miller
,
J. Chem. Phys.
87
,
5781
(
1987
);
H. D.
Meyer
,
U.
Manthe
, and
L. S.
Cederbaum
,
J. Chem. Phys.
97
,
3199
(
1992
).
58.
C. C.
Martens
and
J.-Y.
Fang
,
J. Chem. Phys.
106
,
4918
(
1997
).
59.
M. S. Topaler, D. G. Truhlar, X.-Y. Chang, P. Piecuch, and J. C. Polanyi (unpublished).
60.
M. F.
Herman
and
K. F.
Freed
,
J. Chem. Phys.
78
,
6010
(
1983
).
61.
D. A.
Micha
,
J. Chem. Phys.
78
,
7138
(
1983
);
J. A.
Olson
and
D. A.
Micha
,
J. Chem. Phys.
80
,
2602
(
1984
).
62.
P. J.
Kuntz
,
J. Chem. Phys.
95
,
141
(
1991
).
63.
F.
Webster
,
P. J.
Rossky
, and
R. A.
Friesner
,
Comput. Phys. Commun.
63
,
494
(
1991
).
64.
E. R.
Bittner
and
P. J.
Rossky
,
J. Chem. Phys.
103
,
8130
(
1995
).
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