The method for the analytic calculation of the nonadiabatic coupling vector at the multireference configuration-interaction (MR-CI) level and its program implementation into the COLUMBUS program system described in the preceding paper [Lischka et al., J. Chem. Phys. 120, 7322 (2004)] has been combined with automatic searches for minima on the crossing seam (MXS). Based on a perturbative description of the vicinity of a conical intersection, a Lagrange formalism for the determination of MXS has been derived. Geometry optimization by direct inversion in the iterative subspace extrapolation is used to improve the convergence properties of the corresponding Newton-Raphson procedure. Three examples have been investigated: the crossing between the 1 1B1/2 1A1 valence states in formaldehyde, the crossing between the 2 1A1/3 1A1π-π* valence and ny-3py Rydberg states in formaldehyde, and three crossings in the case of the photodimerization of ethylene. The methods developed allow MXS searches of significantly larger systems at the MR-CI level than have been possible before and significantly more accurate calculations as compared to previous complete-active space self-consistent field approaches.

1.
D. R. Yarkony, in Modern Electronic Structure Theory, Part I, edited by D. R. Yarkony (World Scientific, Singapore, 1995), p. 642.
2.
F.
Bernardi
,
M.
Olivucci
, and
M. A.
Robb
,
Chem. Soc. Rev.
1996
,
321
.
3.
H.
Köppel
,
W.
Domcke
, and
L. S.
Cederbaum
,
Adv. Chem. Phys.
57
,
59
(
1984
).
4.
C. A.
Mead
and
D. G.
Truhlar
,
J. Chem. Phys.
70
,
2284
(
1979
).
5.
C. A.
Mead
,
J. Chem. Phys.
78
,
807
(
1983
).
6.
M. V.
Berry
,
Proc. R. Soc. London, Ser. A
392
,
45
(
1984
).
7.
D. R.
Yarkony
,
J. Phys. Chem. A
101
,
4263
(
1997
).
8.
G. J.
Atchity
,
S. S.
Xantheas
, and
K.
Ruedenberg
,
J. Chem. Phys.
95
,
1862
(
1991
).
9.
M.
Baer
,
J. Phys. Chem. A
105
,
2198
(
2001
).
10.
M.
Baer
,
Chem. Phys.
259
,
123
(
2000
).
11.
J. v.
Neumann
and
E.
Wigner
,
Phys. Z.
30
,
467
(
1929
).
12.
E.
Teller
,
J. Chem. Phys.
41
,
109
(
1937
).
13.
G.
Herzberg
and
H. C.
Longuet-Higgins
,
Discuss. Faraday Soc.
35
,
77
(
1963
).
14.
N.
Koga
and
K.
Morokuma
,
Chem. Phys. Lett.
119
,
371
(
1985
).
15.
A.
Farazdel
and
M.
Dupuis
,
J. Comput. Chem.
12
,
276
(
1991
).
16.
D. R.
Yarkony
,
J. Phys. Chem.
97
,
4407
(
1993
).
17.
M. R.
Manaa
and
D. R.
Yarkony
,
J. Chem. Phys.
99
,
5251
(
1993
).
18.
I. N.
Ragazos
,
M. A.
Robb
,
F.
Bernardi
, and
M.
Olivucci
,
Chem. Phys. Lett.
197
,
217
(
1992
).
19.
M. J.
Bearpark
,
M. A.
Robb
, and
H. B.
Schlegel
,
Chem. Phys. Lett.
223
,
269
(
1994
).
20.
B. H.
Lengsfield
III
,
P.
Saxe
, and
D. R.
Yarkony
,
J. Phys. Chem.
81
,
4549
(
1984
).
21.
P.
Saxe
,
B. H.
Lengsfield
, and
D. R.
Yarkony
,
Chem. Phys. Lett.
113
,
159
(
1985
).
22.
H. Lischka, M. Dallos, P. G. Szalay, David R. Yarkony, and R. Shepard, J. Chem. Phys. 120, 7322 (2004), preceding paper.
23.
R.
Shepard
,
Int. J. Quantum Chem.
31
,
33
(
1987
).
24.
R.
Shepard
,
H.
Lischka
,
P. G.
Szalay
,
T.
Kovar
, and
M.
Ernzerhof
,
J. Chem. Phys.
96
,
2085
(
1992
).
25.
R. Shepard, in Modern Electronic Structure Theory, Part I, edited by D. R. Yarkony (World Scientific, Singapore, 1995), p. 345.
26.
H.
Lischka
,
M.
Dallos
, and
R.
Shepard
,
Mol. Phys.
100
,
1647
(
2002
).
27.
H.
Lischka
,
R.
Shepard
,
F. B.
Brown
, and
I.
Shavitt
,
Int. J. Quantum Chem., Quantum Chem. Symp.
S15
,
91
(
1981
).
28.
R.
Shepard
,
I.
Shavitt
,
R. M.
Pitzer
, et al.,
Int. J. Quantum Chem.
S22
,
149
(
1988
).
29.
H.
Lischka
,
R.
Shepard
,
R. M.
Pitzer
, et al.,
Phys. Chem. Chem. Phys.
3
,
664
(
2001
).
30.
COLUMBUS, An Ab Initio Electronic Structure Program, release 5.9 (2003), written by H. Lischka, R. Shepard, I. Shavitt, et al.
31.
D. R.
Yarkony
,
Rev. Mod. Phys.
68
,
985
(
1996
).
32.
D. R.
Yarkony
,
Acc. Chem. Res.
31
,
511
(
1998
).
33.
P. O.
Löwdin
,
J. Mol. Spectrosc.
10
,
12
(
1963
).
34.
D. R.
Yarkony
,
J. Chem. Phys.
112
,
2111
(
2000
).
35.
H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA, 1950).
36.
M. R.
Manaa
and
D. R.
Yarkony
,
J. Am. Chem. Soc.
116
,
11444
(
1994
).
37.
D. R.
Yarkony
,
J. Phys. Chem. A
105
,
6277
(
2001
).
38.
P.
Pulay
,
Chem. Phys. Lett.
73
,
393
(
1980
);
P.
Pulay
,
J. Comput. Chem.
3
,
556
(
1982
).
39.
P.
Császár
and
P.
Pulay
,
J. Mol. Struct.
114
,
31
(
1984
).
40.
S.
Matsika
and
D. R.
Yarkony
,
J. Chem. Phys.
117
,
6907
(
2002
).
41.
G.
Fogarasi
,
X.
Zhou
,
P. W.
Taylor
, and
P.
Pulay
,
J. Am. Chem. Soc.
114
,
8191
(
1992
).
42.
M.
Dallos
,
Th.
Müller
,
H.
Lischka
and
R.
Shepard
,
J. Chem. Phys.
114
,
746
(
2001
).
43.
M. R. J.
Hachey
,
P. J.
Bruna
, and
F.
Grein
,
J. Phys. Chem.
99
,
8050
(
1995
).
44.
R. B.
Woodward
and
R.
Hoffmann
,
Angew. Chem., Int. Ed. Engl.
8
,
781
(
1969
).
45.
J.
Michl
,
Photochem. Photobiol.
25
,
141
(
1977
).
46.
J. Michl and V. Bonačič-Koutecky, Electronic Aspects of Organic Photochemistry (Wiley, New York, 1990).
47.
F.
Bernardi
,
S.
De
,
M.
Olivucci
, and
M. A.
Robb
,
J. Am. Chem. Soc.
112
,
1737
(
1990
).
48.
F.
Bernardi
,
A.
Bottoni
,
M.
Olivucci
,
A.
Venturini
, and
M. A.
Robb
,
J. Chem. Soc.
90
,
1617
(
1994
).
49.
F.
Bernardi
,
M.
Olivucci
, and
M. A.
Robb
,
J. Photochem. Photobiol., A
105
,
365
(
1997
).
50.
A.
Bunge
,
J. Chem. Phys.
53
,
20
(
1970
).
51.
T. Helgaker, H. J. Aa. Jensen, P. Jørgensen, et al., DALTON, an ab initio electronic structure program, Release 1.0, 1997.
52.
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
90
,
1007
(
1989
).
53.
R. A.
Kendall
,
T. H.
Dunning
, Jr.
, and
R. J.
Harrison
,
J. Chem. Phys.
96
,
6796
(
1992
).
54.
D. E.
Woon
and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
100
,
2975
(
1994
).
55.
T.
van Mourik
,
A. K.
Wilson
, and
T. H.
Dunning
, Jr.
,
Mol. Phys.
96
,
529
(
1999
).
56.
Th.
Müller
,
M.
Dallos
, and
H.
Lischka
,
J. Chem. Phys.
110
,
7176
(
1999
).
This content is only available via PDF.
You do not currently have access to this content.