Tunneling energy splittings of vibrationally excited states are calculated quantum mechanically using several models of two‐dimensional symmetric double well potentials. Various effects of vibrational excitation on tunneling are found to appear, depending on the topography of potential energy surface; the symmetry of the mode coupling plays an essential role. Especially, oscillation of tunneling splitting with respect to vibrational quantum number can occur and is interpreted by a clear physical picture based on the semiclassical theory formulated recently [Takada and Nakamura, J. Chem. Phys. 100, 98 (1994)]. The mixedtunneling in the C region found there allows the wave functions to have nodal lines in classically inaccessible region and can cause the suppression of the tunneling. The above analysis is followed by the interpretation of recent experiments of proton tunneling in tropolone. Abinitio molecular orbital calculations are carried out for the electronically ground state. A simple three‐dimensional model potential is constructed and employed to analyze the proton tunneling dynamics. Some of the experimentally observed intriguing features can be explained by the typical mechanisms discussed above.

1.
Special issue on Tunneling in Chemical Reactions, edited by
V. A.
Benderskii
,
V. I.
Goldanskii
, and
J.
Jortner
[
Chem. Phys.
170
,
265
(
1993
)];
V. A.
Benderskii
,
D. E.
Makarov
and
C. A.
Wight
,
Adv. Chem. Phys.
88
,
1
(
1994
);
J. Jortner and B. Pullman, Tunneling (Reidel, Dordrecht, 1986);
B. Chance, D. C. Devault, H. Frauenfelder, R. A. Marcus, J. R. Schrieffer, and N. Sutin, Tunneling in Biological Systems (Academic, New York, 1979).
2.
T.
Banks
,
C. M.
Bender
, and
T. T.
Wu
,
Phys. Rev. D
8
,
3346
(
1973
);
T.
Banks
and
C. M.
Bender
,
Phys. Rev. D
8
,
3366
(
1973
).,
Phys. Rev. D
3.
J. L.
Gervais
and
B.
Sakita
,
Phys. Rev. D
16
,
3507
(
1977
).
4.
S. Coleman, in The Whys of Subnuclear Physics, edited by A. Zichichi (Plenum, New York, 1979).
5.
C. G.
Callan
, Jr.
and
S.
Coleman
,
Phys. Rev. D
16
,
1762
(
1977
).
6.
J. P.
Sethna
,
Phys. Rev. B
24
,
692
(
1981
).
7.
A.
Auerbach
and
S.
Kivelson
,
Nucl. Phys. B
257
,
FS14
],
799
(
1985
).
8.
N.
Takigawa
,
K.
Hagino
,
M.
Abe
, and
A. B.
Balantekin
,
Phys. Rev. C
49
,
2636
(
1994
).
9.
T. F.
George
and
W. H.
Miller
,
J. Chem. Phys.
56
,
5722
(
1972
);
T. F.
George
and
W. H.
Miller
,
57
,
2458
(
1972
).,
J. Chem. Phys.
10.
R. A.
Marcus
and
M. E.
Coltrin
,
J. Chem. Phys.
67
,
2609
(
1977
).
11.
M. Ya.
Ovchinnikova
,
Chem. Phys.
36
,
85
(
1979
).
12.
V. K.
Babamov
and
R. A.
Marcus
,
J. Chem. Phys.
74
,
1790
(
1981
);
H.
Nakamura
and
A.
Ohsaki
,
J. Chem. Phys.
83
,
1599
(
1985
); ,
J. Chem. Phys.
H.
Nakamura
,
Chem. Phys. Lett.
141
,
77
(
1987
);
A.
Ohsaki
and
H.
Nakamura
,
Chem. Phys. Lett.
142
,
37
(
1987
).,
Chem. Phys. Lett.
13.
B. C.
Garrett
,
D. G.
Truhlar
,
A. F.
Wagner
, and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
78
,
4400
(
1983
).
14.
D. G. Truhlar, A. D. Isaacson, and B. C. Garrett, Theory of Chemical Reaction Dynamics, edited by M. Baer (Chemical Rubber, Boca Raton, 1985), Vol. 4.
15.
V. A.
Benderskii
,
D. E.
Makarov
, and
P. G.
Grinevich
,
Chem. Phys.
170
,
275
(
1993
).
16.
S.
Takada
and
H.
Nakamura
,
J. Chem. Phys.
100
,
98
(
1994
), this is referred to as “paper I” in this article.
17.
S.
Takada
and
H.
Nakamura
,
Supp. Prog. Theor. Phys.
116
,
295
(
1994
).
18.
T.
Carrington
, Jr.
and
W. H.
Miller
,
J. Chem. Phys.
84
,
4364
(
1986
).
19.
N.
Shida
,
P. F.
Barbara
, and
J. E.
Almlöf
,
J. Chem. Phys.
91
,
4061
(
1989
).
20.
E.
Bosch
,
M.
Moreno
,
J. M.
Lluch
, and
J.
Bertrán
,
J. Chem. Phys.
93
,
5685
(
1990
).
21.
S. L.
Baughcum
,
Z.
Smith
,
E. B.
Wilson
, and
R. W.
Duerst
,
J. Am. Chem. Soc.
106
,
2260
(
1984
);
P.
Turner
,
S. L.
Baughcum
,
S. L.
Coy
, and
Z.
Smith
,
J. Am. Chem. Soc.
106
,
2265
(
1984
).,
J. Am. Chem. Soc.
22.
A. C. P.
Alves
and
J. M.
Hollas
,
Mol. Phys.
23
,
927
(
1972
);
A. C. P.
Alves
and
J. M.
Hollas
,
25
,
1305
(
1973
).,
Mol. Phys.
23.
R.
Rossetti
and
L. E.
Brus
,
J. Chem. Phys.
73
,
1546
(
1980
).
24.
Y.
Tomioka
,
M.
Ito
, and
N.
Mikami
,
J. Phys. Chem.
87
,
4401
(
1983
).
25.
R. L.
Redington
,
Y.
Chen
,
G. J.
Scherer
, and
R. W.
Field
,
J. Chem. Phys.
88
,
627
(
1988
).
26.
R. L.
Redington
,
T. E.
Redington
,
M. A.
Hunter
, and
R. W.
Field
,
J. Chem. Phys.
92
,
6456
(
1990
).
27.
H.
Sekiya
,
Y.
Nagashima
, and
Y.
Nishimura
,
J. Chem. Phys.
92
,
5761
(
1990
);
H.
Sekiya
,
Y.
Nagashima
, and
Y.
Nishimura
,
Bull. Chem. Soc. Jpn.
62
,
3229
(
1989
).
28.
H.
Sekiya
,
K.
Sasaki
,
Y.
Nishimura
,
Z.
Li
,
A.
Mori
, and
H.
Takeshita
,
Chem. Phys. Lett.
173
,
285
(
1990
).
29.
H.
Sekiya
,
Y.
Nagashima
,
T.
Tsuji
,
Y.
Nishimura
,
A.
Mori
, and
H.
Takeshita
,
J. Phys. Chem.
95
,
10311
(
1991
).
30.
Y.
Ikegami
,
Bull. Chem. Soc. Jpn.
34
,
94
(
1960
);
Y.
Ikegami
,
36
,
1118
(
1963
).,
Bull. Chem. Soc. Jpn.
31.
R. L.
Redington
and
T. E.
Redington
,
J. Mol. Spectrosc.
78
,
229
(
1979
).
32.
A. C. P.
Alves
,
J. M.
Hollas
,
H.
Musa
, and
T.
Ridley
,
J. Mol. Spectrosc.
109
,
99
(
1985
).
33.
R. L.
Redington
,
J. Chem. Phys.
92
,
6447
(
1990
).
34.
R. L.
Redington
and
C. W.
Bock
,
J. Phys. Chem.
95
,
10284
(
1991
).
35.
K. Tanaka, H. Honjyo, T. Tanaka, H. Takaguchi, Y. Ohshima, and Y. Endo, Abstracts of the Meeting of the Molecular Structure, Yokohama, Japan, 1991 (unpublished), p. 223.
36.
V. A.
Benderskii
,
S. Yu.
Grebenshchikov
,
E. V.
Vetoshkin
,
G. V.
Mil’nikov
, and
D. E.
Makarov
,
J. Phys. Chem.
98
,
3300
(
1994
);
V. A.
Benderskii
,
S. Yu.
Grebenshchikov
,
G. V.
Mil’nikov
, and
E. V.
Vetoshkin
,
Chem. Phys.
188
,
19
(
1994
);
V. A. Benderskii, S. Yu. Grebenshchikov, and G. V. Mil’nikov, ibid. (submitted).
37.
C.
Herring
,
Rev. Mod. Phys.
34
,
631
(
1962
).
38.
L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1975).
39.
V. P. Maslov and M. V. Fedoriuk, Semi-Classical Approximation in Quan tum Mechanics (Reidel, Dordrecht, 1981).
40.
M.
Wilkinson
,
Physica. D
21
,
341
(
1986
).
41.
K.
Fukui
,
J. Phys. Chem.
74
,
4161
(
1970
);
K.
Fukui
,
S.
Kato
, and
H.
Fujimoto
,
J. Am. Chem. Soc.
97
,
1
(
1975
).
42.
J. C.
Light
,
I. P.
Hamilton
, and
J. V.
Lill
,
J. Chem. Phys.
82
,
1400
(
1985
);
R. M.
Whitnell
and
J. C.
Light
,
J. Chem. Phys.
90
,
1774
(
1989
).,
J. Chem. Phys.
43.
GAUSSIAN 92, Revision A. M. J. Frisch, G. W. Trucks, M. Head-Gordon, P. M. W. Gill, M. W. Wong, J. B. Foresman, B. G. Johnson, H. B. Schlegel, M. A. Robb, E. S. Replogle, R. Gomperts, J. L. Andres, K. Raghavachari, J. S. Binkley, C. Gonzalez, R. L. Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P. Stewart, and J. A. Pople, Gaussian, Inc., Pittsburgh PA, 1992.
This content is only available via PDF.
You do not currently have access to this content.