We consider the general problem of vibrational analysis at nonglobally optimized points on a reduced dimensional reaction surface. We discuss the importance of the use of curvilinear internal coordinates to describe molecular motion and derive a curvilinear projection operator to remove the contribution of nonzero gradients from the Hessian matrix. Our projection scheme is tested in the context of a two-dimensional quantum scattering calculation for the reaction H+CH4H2+CH3 and its reverse H2+CH3H+CH4. Using zero-point energies calculated via rectilinear and curvilinear projections we construct two two-dimensional, adiabatically corrected, ab initio reaction surfaces for this system. It is shown that the use of curvilinear coordinates removes unphysical imaginary frequencies observed with rectilinear projection and leads to significantly improved thermal rate constants for both the forward and reverse reactions.

1.
J. E.
Bright-Wilson
,
J. C.
Decius
, and
P. C.
Cross
,
Molecular Vibrations
(
Dover
,
New York
,
1980
).
2.
J. M.
Bowman
,
Theor. Chem. Acc.
108
,
125
(
2002
).
3.
J. M.
Bowman
and
A. F.
Wagner
, in
The Theory of Chemical Reaction Dynamics
, edited by
D. C.
Clary
(
Reidel
,
Dordrecht
,
1985
), p.
47
.
4.
W. H.
Miller
,
N. C.
Handy
, and
J. E.
Adams
,
J. Chem. Phys.
72
,
99
(
1980
).
5.
Q.
Sun
and
J. M.
Bowman
,
Int. J. Quantum Chem., Symp.
23
,
115
(
1989
).
6.
Q.
Sun
and
J. M.
Bowman
,
J. Chem. Phys.
92
,
5201
(
1990
).
7.
R. B.
Walker
and
E. F.
Hayes
, in
The Theory of Chemical Reaction Dynamics
, edited by
D. C.
Clary
(
Reidel
,
Dordrecht
,
1985
), p.
105
.
8.
9.
G. A.
Natanson
,
B. C.
Garrett
,
T. N.
Truong
,
T.
Joseph
, and
D. G.
Truhlar
,
J. Chem. Phys.
94
,
7875
(
1991
).
10.
C. F.
Jackels
,
Z.
Gu
, and
D. G.
Truhlar
,
J. Chem. Phys.
102
,
3188
(
1995
).
11.
Y. -Y.
Chuang
and
D.
Truhlar
,
J. Phys. Chem. A
102
,
242
(
1998
).
12.
J. C.
Corchado
and
J.
Espinosa-García
,
J. Chem. Phys.
106
,
4013
(
1997
).
13.
J. T.
Carrington
, Jr.
and
W. H.
Miller
,
J. Chem. Phys.
81
,
3942
(
1984
).
14.
B.
Kerkeni
and
D. C.
Clary
,
J. Chem. Phys.
120
,
2308
(
2004
).
15.
B.
Kerkeni
and
D. C.
Clary
,
J. Chem. Phys.
121
,
6809
(
2004
).
16.
B.
Kerkeni
and
D. C.
Clary
,
Phys. Chem. Chem. Phys.
8
,
917
(
2006
).
17.
B.
Kerkeni
and
D. C.
Clary
,
Chem. Phys. Lett.
421
,
499
(
2006
).
18.
S. T.
Banks
and
D. C.
Clary
,
Phys. Chem. Chem. Phys.
9
,
933
(
2007
).
19.
D.
Lu
and
D. G.
Truhlar
,
J. Chem. Phys.
99
,
2723
(
1993
).
20.
K.
Fukui
,
Acc. Chem. Res.
14
,
363
(
1981
).
21.
P.
Pulay
and
G.
Fogarasi
,
J. Chem. Phys.
96
,
2856
(
1992
).
22.
J. W.
Sutherland
,
M. C.
Su
, and
J. V.
Michael
,
Int. J. Chem. Kinet.
33
,
669
(
2001
).
23.
M.
Berlie
and
D.
LeRoy
,
Can. J. Chem.
32
,
650
(
1954
).
24.
P. -M.
Marquaire
,
A. G.
Dastidar
,
K. C.
Manthorne
, and
P. D.
Pacey
,
Can. J. Chem.
72
,
600
(
1994
).
25.
M. J.
Kurylo
,
G. A.
Hollinden
, and
R. B.
Timmons
,
J. Chem. Phys.
52
,
1773
(
1970
).
26.
H.
Arai
,
S.
Nagai
,
K.
Matsuda
, and
M.
Hatada
,
Radiat. Phys. Chem.
17
,
151
(
1981
).
27.
T.
Takayanagi
,
J. Chem. Phys.
104
,
2237
(
1996
).
28.
H. -G.
Yu
and
G.
Nyman
,
J. Chem. Phys.
111
,
3508
(
1999
).
29.
M. L.
Wang
,
Y.
Li
,
J. Z. H.
Zhang
, and
D. H.
Zhang
,
J. Chem. Phys.
113
,
1802
(
2000
).
30.
D.
Wang
and
J. M.
Bowman
,
J. Chem. Phys.
115
,
2055
(
2001
).
31.
J.
Palma
,
J.
Echave
, and
D.
Clary
,
J. Phys. Chem. A
106
,
8256
(
2002
).
32.
M. L.
Wang
and
J. Z. H.
Zhang
,
J. Chem. Phys.
117
,
3081
(
2002
).
33.
J.
Pu
and
D. G.
Truhlar
,
J. Chem. Phys.
117
,
1479
(
2002
).
34.
M.
Yang
,
D. H.
Zhang
, and
S. -Y.
Lee
,
J. Chem. Phys.
117
,
9539
(
2002
).
35.
M. L.
Wang
and
J. Z. H.
Zhang
,
J. Chem. Phys.
117
,
10426
(
2002
).
36.
Y.
Zhao
,
T.
Yamamoto
, and
W. H.
Miller
,
J. Chem. Phys.
120
,
3100
(
2004
).
37.
F.
Huarte-Larranaga
and
U.
Manthe
,
J. Chem. Phys.
116
,
2863
(
2002
).
38.
T.
Wu
,
H. -J.
Werner
, and
U.
Manthe
,
J. Chem. Phys.
124
,
164307
(
2006
).
39.
J. P.
Layfield
,
M. D.
Owens
, and
D.
Troya
,
J. Chem. Phys.
128
,
194302
(
2008
).
40.
L.
Zhang
,
Y.
Lu
,
S. -Y.
Lee
, and
D. H.
Zhang
,
J. Chem. Phys.
127
,
234313
(
2007
).
41.
Z.
Xie
,
J. M.
Bowman
, and
X.
Zhang
,
J. Chem. Phys.
125
,
133120
(
2006
).
42.
C.
Rangel
,
J.
Corchado
, and
J.
Espinosa-Garcia
,
J. Phys. Chem. A
110
,
10375
(
2006
).
43.
L.
Zhang
,
S. -Y.
Lee
, and
D.
Zhang
,
J. Phys. Chem. A
110
,
5513
(
2006
).
44.
D.
Wang
,
J. Chem. Phys.
117
,
9806
(
2002
).
45.
G.
Nyman
,
R.
van Harrevelt
, and
U.
Manthe
,
J. Phys. Chem. A
111
,
10331
(
2007
).
46.
C.
Evenhuis
,
G.
Nyman
, and
U.
Manthe
,
J. Chem. Phys.
127
,
144302
(
2007
).
47.
B.
Kerkeni
and
D. C.
Clary
,
J. Phys. Chem. A
107
,
10851
(
2003
).
48.
B.
Kerkeni
and
D. C.
Clary
,
J. Chem. Phys.
108
,
8966
(
2004
).
49.
M. J.
Frisch
,
G. W.
Trucks
,
H. B.
Schlegel
 et al., GAUSSIAN 03, Revision C.02, Gaussian, Inc., Wallingford, CT,
2004
.
50.
MATLAB, 2 August
2005
, copyright 1984–2005, The MathWorks, Inc., Version 7.1.0.183 (R14) SERVICE PACK 3.
51.
E. B.
Stechel
,
R. B.
Walker
, and
J. C.
Light
,
J. Chem. Phys.
69
,
3518
(
1978
).
52.
O. I.
Tolstikhin
and
H.
Nakamura
,
J. Chem. Phys.
108
,
8899
(
1998
).
53.
R. E.
Wyatt
,
J. Chem. Phys.
51
,
3489
(
1969
).
54.
J. N. L.
Connor
and
M. S.
Child
,
Mol. Phys.
18
,
653
(
1970
).
55.
J.
Romelt
, in
The Theory of Chemical Reaction Dynamics
, edited by
D. C.
Clary
(
Reidel
,
Dordrecht
,
1985
), p.
77
.
56.
D. C.
Clary
,
J. Chem. Phys.
95
,
7298
(
1991
).
57.
J. M.
Bowman
,
Reaction and Molecular Dynamics
(
Springer
,
New York
,
2000
).
58.
M. J. T.
Jordan
and
R. G.
Gilbert
,
J. Chem. Phys.
102
,
5669
(
1995
).
59.
R. M.
Marshall
and
G.
Shahkar
,
J. Chem. Soc., Faraday Trans. 1
77
,
2271
(
1981
).
60.
P. C.
Kobrinsky
and
P. D.
Pacey
,
Can. J. Chem.
52
,
3665
(
1974
).
61.
V.
Knyazev
,
A.
Bencsura
,
S.
Stoliarov
, and
I.
Slagle
,
J. Phys. Chem.
100
,
11346
(
1996
).
62.
M. J.
Rabinowitz
,
J. W.
Sutherland
,
P. M.
Patterson
, and
R. B.
Klemm
,
J. Phys. Chem.
95
,
674
(
1991
).
63.
T. G.
Majury
and
E. W. R.
Steacie
,
Can. J. Chem.
30
,
800
(
1952
).
64.
H.
Gesser
and
E. W. R.
Steacie
,
Can. J. Chem.
34
,
113
(
1956
).
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