Restricted open-shell Kohn-Sham (ROKS) theory provides a powerful computational tool for calculating singlet excited state energies and dynamics. However, the possibility of multiple solutions to the ROKS equations — with the associated difficulty of automatically selecting the physically meaningful solution — limits its usefulness for intensive applications such as long-time Born-Oppenheimer molecular dynamics. We present an implementation of ROKS for excited states which prescribes the physically correct solution from an overlap criterion and guarantees that this solution is stationary, allowing for straightforward evaluation of nuclear gradients. The method is used to benchmark ROKS for vertical excitation energies of small and large organic dyes and for the calculation of Stokes shifts. With common density functional approximations, ROKS vertical excitation energies, and Stokes shifts show similar accuracy to those from time-dependent density functional theory and Δ-self-consistent-field approaches. Advantages of the ROKS approach for excited state structure and molecular dynamics are discussed.

1.
J.
Hachmann
,
R.
Olivares-Amaya
,
S.
Atahan-Evrenk
,
C.
Amador-Bedolla
,
R. S.
Sanchez-Carrera
,
A.
Gold-Parker
,
L.
Vogt
,
A. M.
Brockway
, and
A.
Aspuru-Guzik
,
J. Phys. Chem. Lett.
2
,
2241
(
2011
).
2.
B.
Baumeier
,
F.
May
,
C.
Lennartz
, and
D.
Andrienko
,
J. Mater. Chem.
22
,
10971
(
2012
).
3.
M. E.
Casida
and
M.
Huix-Rotllant
,
Annu. Rev. Phys. Chem.
63
,
287
(
2012
).
4.
B.
Kaduk
,
T.
Kowalczyk
, and
T.
Van Voorhis
,
Chem. Rev.
112
,
321
(
2012
).
5.
T.
Ziegler
,
A.
Rauk
, and
E. J.
Baerends
,
Theor. Chim. Acta
43
,
261
(
1977
).
6.
T.
Ziegler
,
M.
Seth
,
M.
Krykunov
,
J.
Autschbach
, and
F.
Wang
,
J. Chem. Phys.
130
,
154102
(
2009
).
7.
J.
Cullen
,
M.
Krykunov
, and
T.
Ziegler
,
Chem. Phys.
391
,
11
(
2011
).
8.
T.
Ziegler
,
M.
Krykunov
, and
J.
Cullen
,
J. Chem. Theory Comput.
7
,
2485
(
2011
).
9.
T.
Kowalczyk
,
S. R.
Yost
, and
T.
Van Voorhis
,
J. Chem. Phys.
134
,
054128
(
2011
).
10.
E. R.
Davidson
and
L. Z.
Stenkamp
,
Int. J. Quantum Chem., Symp.
10
(
S10
),
21
(
1976
).
11.
A.
Balkova
and
R. J.
Bartlett
,
Chem. Phys. Lett.
193
,
364
(
1992
).
12.
B. O.
Roos
,
K.
Andersson
,
M. P.
Fulscher
,
P. A.
Malmqvist
,
L.
SerranoAndres
,
K.
Pierloot
, and
M.
Merchan
,
Adv. Chem. Phys.
93
,
219
(
1996
).
13.
A. T. B.
Gilbert
,
N. A.
Besley
, and
P. M. W.
Gill
,
J. Phys. Chem. A
112
,
13164
(
2008
).
14.
N. A.
Besley
,
A. T. B.
Gilbert
, and
P. M. W.
Gill
,
J. Chem. Phys.
130
,
124308
(
2009
).
15.
M.
Filatov
and
S.
Shaik
,
Chem. Phys. Lett.
304
,
429
(
1999
).
16.
I.
Frank
,
J.
Hutter
,
D.
Marx
, and
M.
Parrinello
,
J. Chem. Phys.
108
,
4060
(
1998
).
17.
I.
Okazaki
,
F.
Sato
,
T.
Yoshihiro
,
T.
Ueno
, and
H.
Kashiwagi
,
J. Mol. Struct.: THEOCHEM
451
,
109
(
1998
).
18.
M.
Schulte
and
I.
Frank
,
Chem. Phys.
373
,
283
(
2010
).
19.
V. N.
Glushkov
,
N. I.
Gidopoulos
, and
S.
Wilson
,
Frontiers in Quantum Systems in Chemistry and Physics
(
Springer
,
2008
), pp.
451
489
.
20.
S.
Grimm
,
C.
Nonnenberg
, and
I.
Frank
,
J. Chem. Phys.
119
,
11574
(
2003
).
21.
U. F.
Röhrig
,
I.
Frank
,
J.
Hutter
,
A.
Laio
,
J.
VandeVondele
, and
U.
Rothlisberger
,
ChemPhysChem
4
,
1177
(
2003
).
22.
C.
Nonnenberg
,
C.
Bräuchle
, and
I.
Frank
,
J. Chem. Phys.
122
,
014311
(
2005
).
23.
S. R.
Billeter
and
D.
Egli
,
J. Chem. Phys.
125
,
224103
(
2006
).
24.
J.
Toulouse
,
F.
Colonna
, and
A.
Savin
,
Phys. Rev. A
70
,
062505
(
2004
).
25.
M.
Filatov
and
S.
Shaik
,
J. Chem. Phys.
110
,
116
(
1999
).
26.
M.
Odelius
,
D.
Laikov
, and
J.
Hutter
,
J. Mol. Struct.: THEOCHEM
630
,
163
(
2003
).
27.
J.
Friedrichs
,
K.
Damianos
, and
I.
Frank
,
Chem. Phys.
347
,
17
(
2008
).
28.
K.
Hirao
and
H.
Nakatsuji
,
J. Chem. Phys.
59
,
1457
(
1973
).
29.
C.
Roothaan
,
Rev. Mod. Phys.
32
,
179
(
1960
).
30.
U.
von Barth
,
Phys. Rev. A
20
,
1693
(
1979
).
32.
M.
Levy
and
A.
Nagy
,
Phys. Rev. Lett.
83
,
4361
(
1999
).
33.
J. A.
Pople
,
R.
Krishnan
,
H. B.
Schlegel
, and
J. S.
Binkley
,
Int. J. Quantum Chem.
16
(
S13
),
225
(
1979
).
34.
P.
Pulay
, in
Modern Theoretical Chemistry
, edited by
H. F.
Schaefer
 III
(
Plenum Press
,
New York
,
1977
), Vol.
4
.
35.
J. A.
Pople
,
P. M. W.
Gill
, and
B. G.
Johnson
,
Chem. Phys. Lett.
199
,
557
(
1992
).
36.
Y.
Shao
,
L. F.
Molnar
,
Y.
Jung
,
J.
Kussmann
,
C.
Ochsenfeld
,
S. T.
Brown
,
A. T. B.
Gilbert
,
L. V.
Slipchenko
,
S. V.
Levchenko
,
D. P.
O’Neill
,
R. A.
DiStasio
 Jr.
,
R. C.
Lochan
,
T.
Wang
,
G. J. O.
Beran
,
N. A.
Besley
,
J. M.
Herbert
,
C. Y.
Lin
,
T.
Van Voorhis
,
S. H.
Chien
,
A.
Sodt
,
R. P.
Steele
,
V. A.
Rassolov
,
P. E.
Maslen
,
P. P.
Korambath
,
R. D.
Adamson
,
B.
Austin
,
J.
Baker
,
E. F. C.
Byrd
,
H.
Dachsel
,
R. J.
Doerksen
,
A.
Dreuw
,
B. D.
Dunietz
,
A. D.
Dutoi
,
T. R.
Furlani
,
S. R.
Gwaltney
,
A.
Heyden
,
S.
Hirata
,
C.-P.
Hsu
,
G.
Kedziora
,
R. Z.
Khalliulin
,
P.
Klunzinger
,
A. M.
Lee
,
M. S.
Lee
,
W.
Liang
,
I.
Lotan
,
N.
Nair
,
B.
Peters
,
E. I.
Proynov
,
P. A.
Pieniazek
,
Y. M.
Rhee
,
J.
Ritchie
,
E.
Rosta
,
C. D.
Sherrill
,
A. C.
Simmonett
,
J. E.
Subotnik
,
H. L.
Woodcock
 III
,
W.
Zhang
,
A. T.
Bell
,
A. K.
Chakraborty
,
D. M.
Chipman
,
F. J.
Keil
,
A.
Warshel
,
W. J.
Hehre
,
H. F.
Schaefer
 III
,
J.
Kong
,
A. I.
Krylov
,
P. M. W.
Gill
, and
M.
Head-Gordon
,
Phys. Chem. Chem. Phys.
8
,
3172
(
2006
).
37.
38.
V. R.
Saunders
and
I. H.
Hillier
,
Int. J. Quantum Chem.
7
,
699
(
1973
).
39.
M.
Schreiber
,
M. R.
Silva-Junior
,
S. P. A.
Sauer
, and
W.
Thiel
,
J. Chem. Phys.
128
,
134110
(
2008
).
40.
See supplementary material at http://dx.doi.org/10.1063/1.4801790 for ROKS vertical excitation energies of the large organic dye set and for optimized ground- and excited-state geometries of the dyes in Figure 2.
41.
T.
Liu
,
W.-G.
Han
,
F.
Himo
,
G. M.
Ullmann
,
D.
Bashford
,
A.
Toutchkine
,
K. M.
Hahn
, and
L.
Noodleman
,
J. Phys. Chem. A
108
,
3545
(
2004
).
42.
X.
Peng
,
F.
Song
,
E.
Lu
,
Y.
Wang
,
W.
Zhou
,
J.
Fan
, and
Y.
Gao
,
J. Am. Chem. Soc.
127
,
4170
(
2005
).
43.
T.
Itoh
,
J. Mol. Spectrosc.
261
,
53
(
2010
).
44.
T.
Itoh
,
J. Mol. Spectrosc.
252
,
115
(
2008
).
45.
N. P.
Ernsting
,
M.
Asimov
, and
F. P.
Schafer
,
Chem. Phys. Lett.
91
,
231
(
1982
).
46.
G.
Haucke
and
G.
Graness
,
Angew. Chem., Int. Ed
34
,
67
(
1995
).
47.
W.
Freyer
,
S.
Mueller
, and
K.
Teuchner
,
J. Photochem. Photobiol., A
163
,
231
(
2004
).
48.
T. M. H.
Creemers
,
A. J.
Lock
,
V.
Subramanian
,
T. M.
Jovin
, and
S.
Völker
,
Nat. Struct. Biol.
6
,
557
(
1999
).
49.
Y.
Ma
,
M.
Rohlfing
, and
C.
Molteni
,
J. Chem. Theory Comput.
6
,
257
(
2010
).
50.
R.
Williams
and
G. J.
Goldsmith
,
J. Chem. Phys.
39
,
2008
(
1963
).
51.
D.
Eastwood
,
L.
Edwards
,
M.
Gouterman
, and
J.
Steinfeld
,
J. Mol. Spectrosc.
20
,
381
(
1966
).
52.
A.
Bèrces
,
R. M.
Dickson
,
L.
Fan
,
H.
Jacobsen
,
D.
Swerhone
, and
T.
Ziegler
,
Comput. Phys. Commun.
100
,
247
(
1997
).
53.
L.
Top
,
E.
Hontz
,
A.
Sinha
, and
T.
Van Voorhis
, “
A novel method for generating an initial-guess reaction path: The Harmonic-Interpolated Path
” (unpublished).

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