The time-dependent density functional theory (TDDFT) has been broadly used to investigate the excited-state properties of various molecular systems. However, the current TDDFT heavily relies on outcomes from the corresponding ground-state DFT calculations, which may be prone to errors due to the lack of proper treatment in the non-dynamical correlation effects. Recently, thermally assisted-occupation DFT (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)], a DFT with fractional orbital occupations, was proposed, explicitly incorporating the non-dynamical correlation effects in the ground-state calculations with low computational complexity. In this work, we develop TDTAO-DFT, which is a TD, linear-response theory for excited states within the framework of TAO-DFT. With tests on the excited states of H2, the first triplet excited state (13Σu+) was described well, with non-imaginary excitation energies. TDTAO-DFT also yields zero singlet–triplet gap in the dissociation limit for the ground singlet (11Σg+) and the first triplet state (13Σu+). In addition, as compared to traditional TDDFT, the overall excited-state potential energy surfaces obtained from TDTAO-DFT are generally improved and better agree with results from the equation-of-motion coupled-cluster singles and doubles.

1.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
(
1964
).
2.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
3.
R. O.
Jones
,
Rev. Mod. Phys.
87
,
897
(
2015
).
4.
A. D.
Becke
,
J. Chem. Phys.
140
,
18A301
(
2014
).
5.
N.
Mardirossian
and
M.
Head-Gordon
,
Mol. Phys.
115
,
2315
(
2017
).
6.
E.
Runge
and
E. K. U.
Gross
,
Phys. Rev. Lett.
52
,
997
(
1984
).
7.
M.
Petersilka
,
U. J.
Gossmann
, and
E. K. U.
Gross
,
Phys. Rev. Lett.
76
,
1212
(
1996
).
8.
M. E.
Casida
, “
Time-dependent density functional response theory for molecules
,” in
Recent Advances in Density Functional Methods
(
World Scientific
,
1995
), pp.
155
192
.
9.
A.
Dreuw
and
M.
Head-Gordon
,
Chem. Rev.
105
,
4009
(
2005
).
10.
M. P.
Deskevich
,
M. Y.
Hayes
,
K.
Takahashi
,
R. T.
Skodje
, and
D. J.
Nesbitt
,
J. Chem. Phys.
124
,
224303
(
2006
).
11.
I.
Tavernelli
,
U. F.
Röhrig
, and
U.
Rothlisberger
,
Mol. Phys.
103
,
963
(
2005
).
12.
T. L. J.
Toivonen
,
T. I.
Hukka
,
O.
Cramariuc
,
T. T.
Rantala
, and
H.
Lemmetyinen
,
J. Phys. Chem. A
110
,
12213
(
2006
).
13.
S.
Hirata
and
M.
Head-Gordon
,
Chem. Phys. Lett.
314
,
291
(
1999
).
14.
R. E.
Stratmann
,
G. E.
Scuseria
, and
M. J.
Frisch
,
J. Chem. Phys.
109
,
8218
(
1998
).
15.
C.-P.
Hsu
,
S.
Hirata
, and
M.
Head-Gordon
,
J. Phys. Chem. A
105
,
451
(
2001
).
16.
B. G.
Levine
,
C.
Ko
,
J.
Quenneville
, and
T. J.
Martínez
,
Mol. Phys.
104
,
1039
(
2006
).
17.
M.
Filatov
,
J. Chem. Theory Comput.
9
,
4526
(
2013
).
18.
O. V.
Gritsenko
,
S. J. A.
van Gisbergen
,
A.
Görling
, and
E. J.
Baerends
,
J. Chem. Phys.
113
,
8478
(
2000
).
19.
M. E.
Casida
,
F.
Gutierrez
,
J.
Guan
,
F.-X.
Gadea
,
D.
Salahub
, and
J.-P.
Daudey
,
J. Chem. Phys.
113
,
7062
(
2000
).
20.
A. D.
Becke
,
J. Chem. Phys.
122
,
064101
(
2005
).
21.
A. D.
Becke
,
J. Chem. Phys.
138
,
074109
(
2013
).
22.
E.
Proynov
,
Y.
Shao
, and
J.
Kong
,
Chem. Phys. Lett.
493
,
381
(
2010
).
23.
E.
Proynov
,
F.
Liu
,
Y.
Shao
, and
J.
Kong
,
J. Chem. Phys.
136
,
034102
(
2012
).
24.
J.
Kong
and
E.
Proynov
,
J. Chem. Theory Comput.
12
,
133
(
2016
).
25.
J.
Gräfenstein
and
D.
Cremer
,
Chem. Phys. Lett.
316
,
569
(
2000
).
26.
G.
Li Manni
,
R. K.
Carlson
,
S.
Luo
,
D.
Ma
,
J.
Olsen
,
D. G.
Truhlar
, and
L.
Gagliardi
,
J. Chem. Theory Comput.
10
,
3669
(
2014
).
27.
G.
Li Manni
,
R. K.
Carlson
,
S.
Luo
,
D.
Ma
,
J.
Olsen
,
D. G.
Truhlar
, and
L.
Gagliardi
,
J. Chem. Theory Comput.
12
,
458
(
2016
).
28.
E.
Fromager
,
S.
Knecht
, and
H. J. A.
Jensen
,
J. Chem. Phys.
138
,
084101
(
2013
).
29.
K.
Sharkas
,
A.
Savin
,
H. J. A.
Jensen
, and
J.
Toulouse
,
J. Chem. Phys.
137
,
044104
(
2012
).
30.
J. F.
Stanton
and
J.
Gauss
,
J. Chem. Phys.
101
,
8938
(
1994
).
31.
M.
Nooijen
and
R. J.
Bartlett
,
J. Chem. Phys.
102
,
3629
(
1998
).
32.
Y.
Shao
,
M.
Head-Gordon
, and
A. I.
Krylov
,
J. Chem. Phys.
118
,
4807
(
2003
).
33.
J.-D.
Chai
,
J. Chem. Phys.
136
,
154104
(
2012
).
34.
J.-D.
Chai
,
J. Chem. Phys.
140
,
18A521
(
2014
).
35.
J.-D.
Chai
,
J. Chem. Phys.
146
,
044102
(
2017
).
36.
F.
Xuan
,
J.-D.
Chai
, and
H.
Su
,
ACS Omega
4
,
7675
(
2019
).
37.
C.-Y.
Lin
,
K.
Hui
,
J.-H.
Chung
, and
J.-D.
Chai
,
RSC Adv.
7
,
50496
(
2017
).
38.
C.-S.
Wu
and
J.-D.
Chai
,
J. Chem. Theory Comput.
11
,
2003
(
2015
).
39.
C.-N.
Yeh
and
J.-D.
Chai
,
Sci. Rep.
6
,
30562
(
2016
).
40.
S.
Seenithurai
and
J.-D.
Chai
,
Sci. Rep.
6
,
33081
(
2016
).
41.
C.-S.
Wu
,
P.-Y.
Lee
, and
J.-D.
Chai
,
Sci. Rep.
6
,
37249
(
2016
).
42.
S.
Seenithurai
and
J.-D.
Chai
,
Sci. Rep.
7
,
4966
(
2017
).
43.
S.
Seenithurai
and
J.-D.
Chai
,
Sci. Rep.
8
,
13538
(
2018
).
44.
C.-N.
Yeh
,
C.
Wu
,
H.
Su
, and
J.-D.
Chai
,
RSC Adv.
8
,
34350
(
2018
).
45.
J.-H.
Chung
and
J.-D.
Chai
,
Sci. Rep.
9
,
2907
(
2019
).
46.
Y.
Yang
,
E. R.
Davidson
, and
W.
Yang
,
Proc. Natl. Acad. Sci. U. S. A.
113
,
E5098
(
2016
).
47.
J.
Hachmann
,
J. J.
Dorando
,
M.
Avilés
, and
G. K.-L.
Chan
,
J. Chem. Phys.
127
,
134309
(
2007
).
48.
W.
Mizukami
,
Y.
Kurashige
, and
T.
Yanai
,
J. Chem. Theory Comput.
9
,
401
(
2013
).
49.
K.
Pelzer
,
L.
Greenman
,
G.
Gidofalvi
, and
D. A.
Mazziotti
,
J. Phys. Chem. A
115
,
5632
(
2011
).
50.
J.
Fosso-Tande
,
T.-S.
Nguyen
,
G.
Gidofalvi
, and
A. E.
DePrince
,
J. Chem. Theory Comput.
12
,
2260
(
2016
).
51.
M. S.
Deleuze
,
L.
Claes
,
E. S.
Kryachko
, and
J.-P.
François
,
J. Chem. Phys.
119
,
3106
(
2003
).
52.
B.
Hajgató
,
M. S.
Deleuze
,
D. J.
Tozer
, and
F.
De Proft
,
J. Chem. Phys.
129
,
084308
(
2008
).
53.
B.
Hajgató
,
D.
Szieberth
,
P.
Geerlings
,
F.
De Proft
, and
M. S.
Deleuze
,
J. Chem. Phys.
131
,
224321
(
2009
).
54.
B.
Hajgato
,
M.
Huzak
, and
M. S.
Deleuze
,
J. Phys. Chem. A
115
,
9282
(
2011
).
55.
N. D.
Mermin
,
Phys. Rev.
137
,
A1441
(
1965
).
56.
P.
Slavíček
and
T. J.
Martínez
,
J. Chem. Phys.
132
,
234102
(
2010
).
57.
C.
Ullrich
,
Time-Dependent Density-Functional Theory: Concepts and Applications
, Oxford Graduate Texts (
OUP
,
Oxford
,
2012
).
58.
A. D.
Becke
,
J. Chem. Phys.
104
,
1040
(
1996
).
59.
M. E.
Casida
and
M.
Huix-Rotllant
,
Annu. Rev. Phys. Chem.
63
,
287
(
2012
).
60.
61.
P. M. W.
Gill
,
B. G.
Johnson
, and
J. A.
Pople
,
Chem. Phys. Lett.
209
,
506
(
1993
).
62.
C. W.
Murray
,
N. C.
Handy
, and
G. J.
Laming
,
Mol. Phys.
78
,
997
(
1993
).
63.
V. I.
Lebedev
and
D.
Laikov
,
Dokl. Math.
59
,
477
481
(
1999
).
64.
Z.-L.
Cai
and
J. R.
Reimers
,
J. Chem. Phys.
112
,
527
(
2000
).
65.
N.
Kouchi
,
M.
Ukai
, and
Y.
Hatano
,
J. Phys. B: At., Mol. Opt. Phys.
30
,
2319
(
1997
).
66.
D. J.
Tozer
,
J. Chem. Phys.
119
,
12697
(
2003
).
67.
A.
Dreuw
,
J. L.
Weisman
, and
M.
Head-Gordon
,
J. Chem. Phys.
119
,
2943
(
2003
).
68.
K. J. H.
Giesbertz
,
E. J.
Baerends
, and
O. V.
Gritsenko
,
Phys. Rev. Lett.
101
,
033004
(
2008
).
69.
K. J. H.
Giesbertz
,
K.
Pernal
,
O. V.
Gritsenko
, and
E. J.
Baerends
,
J. Chem. Phys.
130
,
114104
(
2009
).
70.
K. J. H.
Giesbertz
,
O. V.
Gritsenko
, and
E. J.
Baerends
,
J. Chem. Phys.
133
,
174119
(
2010
).
71.
I. N.
Kadochnikov
,
B. I.
Loukhovitski
, and
A. M.
Starik
,
Phys. Scr.
88
,
058306
(
2013
).
72.
E.
Gross
and
W.
Kohn
, “
Density functional theory of many-fermion systems
,” in
Advances in Quantum Chemistry
, edited by
P.-O.
Löwdin
(
Academic Press
,
1990
), Vol. 21, pp.
255
291
.
73.
G.
Vignale
,
Phys. Rev. A
77
,
062511
(
2008
).

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