In this work, degenerate perturbation theory through second order is used to characterize the vicinity of a three state conical intersection. This report extends our recent demonstration that it is possible to describe the branching space (in which the degeneracy is lifted linearly) and seam space (in which the degeneracy is preserved) in the vicinity of a two state conical intersection using second order perturbation theory. The general analysis developed here is based on a group homomorphism approach. Second order perturbation theory, in conjunction with high quality ab initio electronic structure data, produces an approximately diabatic Hamiltonian whose eigenenergies and eigenstates can accurately describe the three adiabatic potential energy surfaces, the interstate derivative couplings, and the branching and seam spaces in their full dimensionality. The application of this approach to the minimum energy three state conical intersection of the pyrazolyl radical demonstrates the potential of this method. A Hamiltonian comprised of the ten characteristic (linear) parameters and over 300second order parameters is constructed to describe the branching space associated with a point of conical intersection. The second order parameters are determined using data at only 30 points. In the vicinity of the conical intersection the energy and derivative couplings are well reproduced and the singularity in the derivative coupling is analyzed.

1.
S.
Matsika
and
D. R.
Yarkony
,
J. Am. Chem. Soc.
125
,
12428
(
2003
).
2.
S.
Matsika
and
D. R.
Yarkony
,
J. Am. Chem. Soc.
125
,
10672
(
2003
);
[PubMed]
S.
Matsika
,
J. Phys. Chem. A
109
,
7538
(
2005
);
[PubMed]
J. D.
Coe
and
T. J.
Martinez
,
J. Am. Chem. Soc.
127
,
4560
(
2005
);
[PubMed]
L.
Blancafort
and
M.
Robb
,
J. Phys. Chem. A
108
,
10609
(
2004
).
3.
S.
Han
and
D. R.
Yarkony
,
J. Chem. Phys.
119
,
5058
(
2003
).
4.
S. P.
Keating
and
C. A.
Mead
,
J. Chem. Phys.
82
,
5102
(
1985
).
5.
S.
Han
and
D. R.
Yarkony
,
J. Chem. Phys.
119
,
11561
(
2003
).
6.
D. R.
Yarkony
,
J. Chem. Phys.
123
,
134106
(
2005
).
7.
D. R.
Yarkony
,
J. Chem. Phys.
123
,
204101
(
2005
).
8.
S.
Han
and
D. R.
Yarkony
,
J. Chem. Phys.
118
,
9952
(
2003
).
9.
C. A.
Mead
,
J. Chem. Phys.
78
,
807
(
1983
).
10.
D. R.
Yarkony
,
J. Phys. Chem. A
101
,
4263
(
1997
).
11.
M. R.
Hoffman
,
D. J.
Fox
,
J. F.
Gaw
,
Y.
Osamura
,
Y.
Yamaguchi
,
R. S.
Grev
,
G.
Fitzgerald
,
H. F.
Schaefer
,
P. J.
Knowles
, and
N. C.
Handy
,
J. Chem. Phys.
80
,
2660
(
1984
).
12.
H.
Goldstein
,
Classical Mechanics
(
Addison-Wesley
,
Massachusetts
,
1950
).
13.
G. J.
Atchity
,
S. S.
Xantheas
, and
K.
Ruedenberg
,
J. Chem. Phys.
95
,
1862
(
1991
).
14.
D. R.
Yarkony
,
J. Chem. Phys.
112
,
2111
(
2000
).
15.
S.
Han
and
D. R.
Yarkony
,
J. Chem. Phys.
118
,
9952
(
2003
).
16.
D. R.
Yarkony
,
Acc. Chem. Res.
31
,
511
(
1998
).
17.
P.
Saxe
,
B. H.
Lengsfield
, and
D. R.
Yarkony
,
Chem. Phys. Lett.
113
,
159
(
1985
).
18.
C. A.
Mead
and
D. G.
Truhlar
,
J. Chem. Phys.
77
,
6090
(
1982
).
19.
B. H.
Lengsfield
and
D. R.
Yarkony
, in
State-Selected and State to State Ion-Molecule Reaction Dynamics: Part 2 Theory
, edited by
M.
Baer
and
C.-Y.
Ng
(
Wiley
,
New York
,
1992
), Vol.
82
, pp.
1
;
H.
Lischka
,
M.
Dallos
,
P.
Szalay
,
D. R.
Yarkony
, and
R.
Shepard
,
J. Chem. Phys.
120
,
7322
(
2004
).
[PubMed]
20.
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
90
,
1007
(
1989
).
21.
H.
Lischka
,
R.
Shepard
,
I.
Shavitt
 et al, COLUMBUS, An ab initio Electronic Structure Program (
University of Vienna
, Vienna,
2003
).
22.
MATHEMATICA
Wolfram Research, Inc.
, Champaign, Illinois,
2003
.
You do not currently have access to this content.