A recently reported algorithm for representing adiabatic states coupled by conical intersections using a quasi-diabatic state Hamiltonian in four and five atom systems is extended to treat nonadiabatic processes in considerably larger molecules. The method treats all internal degrees of freedom and uses electronic structure data from ab initio multireference configuration interaction wave functions with nuclear configuration selection based on quasi-classical surface hopping trajectories. The method is shown here to be able to treat ∼30 internal degrees of freedom including dissociative and large amplitude internal motion. Two procedures are introduced which are essential to the algorithm, a null space projector which removes basis functions from the fitting process until they are needed and a partial diagonalization technique which allows for automated, but accurate, treatment of the vicinity of extended seams of conical intersections of two or more states. These procedures are described in detail. The method is illustrated using the photodissociaton of phenol, C6H5OH(⁠|${\rm \tilde X}{}^{1} A^{\prime} $|X̃1A) + hv → C6H5OH(⁠|$\tilde A{}^{1} A^{\prime} $|Ã1A, |${\rm \tilde B}{}^{\rm 1}{\rm A^{\prime \prime} }$|B̃1A) → C6H5O(⁠|${\rm \tilde X}{}^2{\rm B}_1$|X̃2B1, |${\rm \tilde A}{}^2{\rm B}_2$|Ã2B2) + H as a test case. Ab initio electronic structure data for the 1,2,31A states of phenol, which are coupled by conical intersections, are obtained from multireference first order configuration interaction wave functions. The design of bases to simultaneously treat large amplitude motion and dissociation is described, as is the ability of the fitting procedure to smooth the irregularities in the electronic energies attributable to the orbital changes that are inherent to nonadiabatic processes.

1.
K. C.
Thompson
,
M. J. T.
Jordan
, and
M. A.
Collins
,
J. Chem. Phys.
108
,
8302
(
1998
).
2.
K. C.
Thompson
,
M. J. T.
Jordan
, and
M. A.
Collins
,
J. Chem. Phys.
108
,
564
(
1998
).
3.
R. P. A.
Bettens
and
M. A.
Collins
,
J. Chem. Phys.
111
,
816
(
1999
).
4.
B. J.
Braams
and
J. M.
Bowman
,
Int. Rev. Phys. Chem.
28
,
577
(
2009
).
5.
Z.
Xie
and
J. M.
Bowman
,
J. Chem. Theory Comput.
6
,
26
(
2010
).
6.
R.
Dawes
,
A.
Passalacqua
,
T. D.
Sewell
,
A. F.
Wagner
,
M.
Minkoff
, and
D. L.
Thompson
,
J. Chem. Phys.
130
,
144107
(
2009
).
7.
R.
Dawes
,
D. L.
Thompson
,
A. F.
Wagner
, and
M.
Minkoff
,
J. Chem. Phys.
128
,
84107
(
2009
).
8.
X.
Zhu
and
D. R.
Yarkony
,
J. Chem. Phys.
136
,
174110
(
2012
).
9.
X.
Zhu
and
D. R.
Yarkony
,
J. Chem. Phys.
137
,
22A511
(
2012
).
10.
H.
Köppel
,
W.
Domcke
, and
L. S.
Cederbaum
,
Adv. Chem. Phys.
57
,
59
(
1984
).
11.
H.
Köppel
,
Adv. Ser. Phys. Chem.
15
,
175
(
2004
).
12.
T.
Pacher
,
L. S.
Cederbaum
, and
H.
Köppel
,
J. Chem. Phys.
89
,
7367
(
1988
).
13.
T.
Pacher
,
L. S.
Cederbaum
, and
H.
Köppel
,
Adv. Chem. Phys.
84
,
293
(
1993
).
14.
H.
Köppel
and
B.
Schubert
,
Mol. Phys.
104
,
1069
(
2006
).
15.
D.
Opalka
and
W.
Domcke
,
J. Chem. Phys.
138
,
224103
(
2013
).
16.
M. A.
Collins
,
O.
Godsi
,
S.
Liu
, and
D. H.
Zhang
,
J. Chem. Phys.
135
,
234307
(
2011
).
17.
C. R.
Evenhuis
and
M. A.
Collins
,
J. Chem. Phys.
121
,
2515
(
2004
).
18.
C. R.
Evenhuis
,
X.
Lin
,
D. H.
Zhang
,
D. R.
Yarkony
, and
M. A.
Collins
,
J. Chem. Phys.
123
,
134110
(
2005
).
19.
O.
Godsi
,
C. R.
Evenhuis
, and
M. A.
Collins
,
J. Chem. Phys.
125
,
104105
(
2006
).
20.
C.
Evenhuis
and
T. J.
Martínez
,
J. Chem. Phys.
135
,
224110
(
2011
).
21.
H.
Nakamura
and
D. G.
Truhlar
,
J. Chem. Phys.
117
,
5576
(
2002
).
22.
H.
Nakamura
and
D. G.
Truhlar
,
J. Chem. Phys.
118
,
6816
(
2003
).
23.
A. W.
Jasper
,
B. K.
Kendrick
,
C. A.
Mead
, and
D. G.
Truhlar
, in
Modern Trends in Chemical Reaction Dynamics. Experiment and Theory (Part I)
, edited by
X.
Yang
and
K.
Liu
(
World Scientific
,
New Jersey
,
2004
), p.
329
.
24.
S.
Nangia
and
D. G.
Truhlar
,
J. Chem. Phys.
124
,
124309
(
2006
).
25.
Z. H.
Li
,
R.
Valero
, and
D. G.
Truhlar
,
Theor. Chem. Acc.
118
,
9
(
2007
).
26.
A. J. C.
Varandas
,
F. B.
Brown
,
C. A.
Mead
,
D. G.
Truhlar
, and
N. C.
Blais
,
J. Chem. Phys.
86
,
6258
(
1987
).
27.
V. C.
Mota
and
A. J. C.
Varandas
,
J. Phys. Chem. A
112
,
3768
(
2008
).
28.
W.
Eisfeld
and
A.
Viel
,
J. Chem. Phys.
122
,
204317
(
2005
).
29.
J.
Jornet-Somoza
,
B.
Lasorne
,
M. A.
Robb
,
H.-D.
Meyer
,
D.
Lauvergnat
, and
F.
Gatti
,
J. Chem. Phys.
137
,
084304
(
2012
).
30.
H. C.
Longuet-Higgins
,
Mol. Phys.
6
,
445
(
1963
).
31.
P. R.
Bunker
and
P.
Jensen
,
Molecular Symmetry and Spectroscopy
, 2nd ed. (
NRC Research Press
,
Ottawa
,
1998
).
32.
X.
Zhu
,
J.
Ma
,
D. R.
Yarkony
, and
H.
Guo
,
J. Chem. Phys.
136
,
234301
(
2012
).
33.
J.
Ma
,
X.
Zhu
,
H.
Guo
, and
D. R.
Yarkony
,
J. Chem. Phys.
137
,
22A541
(
2012
).
34.
M.
Ben-Nun
and
T. J.
Martínez
,
Adv. Chem. Phys.
121
,
439
(
2002
).
35.
G. A.
Worth
,
M. A.
Robb
, and
I.
Burghardt
,
Faraday Discuss.
127
,
307
(
2004
).
36.
G. A.
Worth
,
M. A.
Robb
, and
B.
Lasorne
,
Mol. Phys.
106
,
2077
(
2008
).
37.
M.
Barbatti
,
A. J. A.
Aquino
,
J.
Szymczak
,
D.
Nachtigallova
, and
H.
Lischka
,
Phys. Chem. Chem. Phys.
13
,
6145
(
2011
).
38.
A. F.
Izmaylov
,
J. Chem. Phys.
138
,
104115
(
2013
).
39.
M. P.
Deskevich
,
D. J.
Nesbit
, and
H.-J.
Werner
,
J. Chem. Phys.
120
,
7281
(
2004
).
40.
S. G.
Ramesh
and
W.
Domcke
,
Faraday Discuss.
163
,
73
(
2013
).
41.
H. R.
Hudock
,
B. G.
Levine
,
A. L.
Thompson
,
H.
Satzger
,
D.
Townsend
,
N.
Gador
,
S.
Ullrich
,
A.
Stolow
, and
T. J.
Martínez
,
J. Phys. Chem. A
111
,
8500
(
2007
).
42.
H. R.
Hudock
and
T.
Martinez
,
ChemPhysChem
9
,
2486
(
2008
).
43.
J. J.
Szymczak
,
M.
Barbatti
,
J. T. S.
Hoo
,
J. A.
Adkins
,
T. L.
Windus
,
D.
Nachtigallová
, and
H.
Lischka
,
J. Phys. Chem. A
113
,
12686
(
2009
).
44.
M.
Barbatti
and
H.
Lischka
,
J. Am. Chem. Soc.
130
,
6831
(
2008
).
45.
D.
Nachtigallova
,
A. J. A.
Aquino
,
J.
Szymczak
,
M.
Barbatti
,
P.
Hobza
, and
H.
Lischka
,
J. Phys. Chem. A
115
,
5247
(
2011
).
46.
M.
Barbatti
,
Z.
Lan
,
R.
Crespo-Otero
,
J. J.
Szymczak
,
H.
Lischka
, and
W.
Thiel
,
J. Chem. Phys.
137
,
22A514
(
2012
).
47.
M.
Barbatti
,
A. J. A.
Aquino
,
J. J.
Szymczak
,
D.
Nachtigallova
,
P.
Hobza
, and
H.
LIschka
,
Proc. Natl. Acad. Sci. U.S.A.
107
,
21453
(
2010
).
48.
J. C.
Tully
,
J. Chem. Phys.
93
,
1061
(
1990
).
49.
J. C.
Tully
,
Faraday Discuss.
127
,
463
(
2004
).
50.
M. N. R.
Ashfold
,
G. A.
King
,
D.
Murdock
,
M. G. D.
Nix
,
T. A. A.
Olivera
, and
A. G.
Sagea
,
Phys. Chem. Chem. Phys.
12
,
1218
(
2012
).
51.
A. L.
Devine
,
B.
Cronin
,
M. G. D.
Nix
, and
M. N. R.
Ashfold
,
J. Chem. Phys.
125
,
1184302
(
2006
).
52.
G. A.
King
,
T. A. A.
Oliver
,
M. G. D.
Nix
, and
M. N. R.
Ashfold
,
J. Phys. Chem. A
113
,
7984
(
2009
).
53.
K.
Daigoku
,
S.
Ichiuchi
,
M.
Sakai
,
M.
Fujii
, and
K.
Hashimoto
,
J. Chem. Phys.
119
,
5194
(
2003
).
54.
O. P.
Vieuxmaire
,
Z.
Lan
,
A. L.
Sobolewski
, and
W.
Domcke
,
J. Chem. Phys.
129
,
224307
(
2008
).
55.
Z.
Lan
,
W.
Domcke
,
V.
Vallet
,
A. L.
Sobolewski
, and
S.
Mahapatra
,
J. Chem. Phys.
122
,
224315
(
2005
).
56.
Michael G. D.
Nix
,
A. L.
Devine
,
B.
Cronin
,
R. N.
Dixon
, and
M. N. R.
Ashfold
,
J. Chem. Phys.
125
,
133318
(
2006
).
57.
A. L.
Devine
,
M. G. D.
Nix
,
B.
Cronin
, and
M. N. R.
Ashfold
,
Phys. Chem. Chem. Phys.
9
,
3749
(
2007
).
58.
M.
Nix
,
A.
Devine
,
R.
Dixon
, and
M.
Ashfold
,
Chem. Phys. Lett.
463
,
305
(
2008
).
59.
G. A.
King
,
A. L.
Devine
,
M. G. D.
Nix
,
D. E.
Kelly
, and
M. N. R.
Ashfold
,
Phys. Chem. Chem. Phys.
10
,
6417
(
2008
).
60.
G. A.
Pino
,
A. N.
Oldani
,
E.
Marceca
,
M.
Fujii
,
S.
Ishiuchi
,
M.
Miyazaki
,
M.
Broquier
,
C.
Dedonder
, and
C.
Jouvet
,
J. Chem. Phys.
133
,
124313
(
2010
).
61.
R. N.
Dixon
,
T. A. A.
Oliver
, and
M. N. R.
Ashfold
,
J. Chem. Phys.
134
,
194303
(
2011
).
62.
R.
Crespo-Otero
,
M.
Barbatti
,
H.
Yu
,
N. L.
Evans
, and
S.
Ulrich
,
ChemPhysChem
17
,
3365
(
2011
).
63.
H.
Yu
,
N. L.
Evans
,
V. G.
Stavros
, and
S.
Ulrich
,
Phys. Chem. Chem. Phys.
14
,
6266
(
2012
).
64.
M.
Barbatti
,
M.
Ruckenbauer
,
J. J.
Szymczak
,
A. J. A.
Aquinoa
, and
H.
Lischka
,
Phys. Chem. Chem. Phys.
10
,
482
(
2008
).
65.
R.
Montero
,
A.
Conde
,
V.
Ovejas
,
M.
Fernandez-Fernandez
,
F.
Castano
, and
A.
Longarte
,
J. Phys. Chem. A
116
,
10752
(
2012
).
66.
R.
Montero
,
A.
Conde
,
V.
Ovejas
,
M.
Fernandez-Fernandez
,
F.
Castano
, and
A.
Longarte
,
J. Chem. Phys.
137
,
064317
(
2012
).
67.
Z. H.
Li
,
Ahren W.
Jasper
,
David A.
Bonhommeau
,
R.
Valero
, and
D. G.
Truhlar
, ANT2013, a computer program,
2013
.
68.
O.
Godsi
,
M. A.
Collins
, and
U.
Peskin
,
J. Chem. Phys.
132
,
124106
(
2010
).
69.
H.
Netzloff
,
M.
Collins
, and
M.
Gordon
,
J. Chem. Phys.
124
,
154104
(
2006
).
70.
P. R.
Bunker
,
Molecular Symmetry and Spectroscopy
(
Academic Press
,
New York
,
1979
).
71.
C. A.
Mead
,
J. Chem. Phys.
78
,
807
(
1983
).
72.
Z. H.
Top
and
M.
Baer
,
Chem. Phys.
15
,
49
(
1976
).
73.
C. A.
Mead
and
D. G.
Truhlar
,
J. Chem. Phys.
77
,
6090
(
1982
).
74.
G. J.
Atchity
,
S. S.
Xantheas
, and
K.
Ruedenberg
,
J. Chem. Phys.
95
,
1862
(
1991
).
75.
D. R.
Yarkony
,
J. Chem. Phys.
112
,
2111
(
2000
).
76.
M. L.
Hause
,
Y. H.
Yoon
,
A. S.
Case
, and
F. F.
Crim
,
J. Chem. Phys.
128
,
104307
(
2008
).
77.
A.
Iqbal
,
M.
Cheung
,
M.
Nix
, and
V.
Stavros
,
J. Phys. Chem. A
113
,
8157
(
2009
).
78.
A.
Devine
,
M.
Nix
,
R.
Dixon
, and
M.
Ashfold
,
J. Phys. Chem. A
112
,
9563
(
2008
).
79.
H.
An
and
K.
Baeck
,
J. Phys. Chem. A
115
,
13309
(
2011
).
80.
J.
Lorentzon
,
P.-Å.
Malmqvist
,
M.
Fülscher
, and
B. O.
Roos
,
Theor. Chem. Acc.
91
,
91
(
1995
).
81.
G.
Czakó
and
J. M.
Bowman
,
J. Chem. Phys.
136
,
044307
(
2012
).
82.
See supplementary material at http://dx.doi.org/10.1063/1.4857335 for supplementary tables.
83.
M. D.
Hack
,
A. W.
Jasper
,
Y. L.
Volobuev
,
D. W.
Schwenke
, and
D. G.
Truhlar
,
J. Phys. Chem. A
103
,
6309
(
1999
).
84.
G. A.
Worth
,
H.-D.
Meyer
,
H.
Köppel
,
L. S.
Cederbaum
, and
I.
Burghardt
,
Int. Rev. Phys. Chem.
27
,
569
(
2008
).
85.
J.
Gonzalez-Vazquez
and
L.
Gonzalez
,
ChemPhysChem
11
,
3617
(
2010
).
86.
K. A.
Kistler
and
S.
Matsika
,
J. Chem. Phys.
128
,
215102
(
2008
).
87.
S.
Matsika
,
J. Phys. Chem. A
109
,
7538
(
2005
).
88.
J. D.
Coe
and
T. J.
Martinez
,
J. Am. Chem. Soc.
127
,
4560
(
2005
).
89.
L.
Blancafort
and
M.
Robb
,
J. Phys. Chem. A
108
,
10609
(
2004
).
90.
J. D.
Coe
,
M. T.
Ong
,
B. G.
Levine
, and
T. J.
Martinez
,
J. Phys. Chem. A
112
,
12559
(
2008
).
91.
H. C.
Longuet-Higgins
,
Proc. R. Soc. London, Ser. A
344
,
147
(
1975
).

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