Double, Rydberg, and charge transfer (CT) excitations have been great challenges for time-dependent density functional theory (TDDFT). Starting from an (N ± 2)-electron single-determinant reference, we investigate excitations for the N-electron system through the pairing matrix fluctuation, which contains information on two-electron addition/removal processes. We adopt the particle-particle random phase approximation (pp-RPA) and the particle-particle Tamm-Dancoff approximation (pp-TDA) to approximate the pairing matrix fluctuation and then determine excitation energies by the differences of two-electron addition/removal energies. This approach captures all types of interesting excitations: single and double excitations are described accurately, Rydberg excitations are in good agreement with experimental data and CT excitations display correct 1/R dependence. Furthermore, the pp-RPA and the pp-TDA have a computational cost similar to TDDFT and consequently are promising for practical calculations.

1.
J. B.
Foresman
,
M.
Head-Gordon
,
J. A.
Pople
, and
M. J.
Frisch
,
J. Phys. Chem.
96
,
135
(
1992
).
2.
M.
Head-Gordon
,
R. J.
Rico
,
M.
Oumi
, and
T. J.
Lee
,
Chem. Phys. Lett.
219
,
21
(
1994
).
3.
B. O.
Roos
,
The Complete Active Space Self-Consistent Field Method and its Applications in Electronic Structure Calculations
(
John Wiley and Sons
,
Inc.
,
2007
), pp.
399
445
.
4.
K.
Emrich
,
Nucl. Phys. A
351
,
379
(
1981
).
5.
H. J.
Monkhorst
,
Int. J. Quantum Chem.
12
,
421
(
1977
).
6.
J. E. D.
Bene
,
R.
Ditchfield
, and
J. A.
Pople
,
J. Chem. Phys.
55
,
2236
(
1971
).
7.
A. D.
Mclachlan
and
M. A.
Ball
,
Rev. Mod. Phys.
36
,
844
(
1964
).
8.
E.
Runge
and
E. K. U.
Gross
,
Phys. Rev. Lett.
52
,
997
(
1984
).
9.
M. E.
Casida
, “
Time-dependent density functional response theory of molecular systems: Theory, computational methods, and functionals
,” in
Recent Developments and Applications of Modern Density Functional Theory
, edited by
J.
Seminario
, Theoretical and Computational Chemistry (
Elsevier
,
1996
), Vol.
4
, pp.
391
439
.
10.
M.
Petersilka
,
U. J.
Gossmann
, and
E. K. U.
Gross
,
Phys. Rev. Lett.
76
,
1212
(
1996
).
11.
C.
Ullrich
,
Time-Dependent Density-Functional Theory: Concepts and Applications
,
Oxford Graduate Texts
(
Oxford University Press
,
Oxford
,
2012
).
12.
A.
Dreuw
and
M.
Head-Gordon
,
Chem. Rev.
105
,
4009
(
2005
).
13.
J.
Čížek
and
J.
Paldus
,
J. Chem. Phys.
47
,
3976
(
1967
).
14.
D. J.
Tozer
and
N. C.
Handy
,
Phys. Chem. Chem. Phys.
2
,
2117
(
2000
).
15.
R. J.
Cave
,
F.
Zhang
,
N. T.
Maitra
, and
K.
Burke
,
Chem. Phys. Lett.
389
,
39
(
2004
).
16.
D. J.
Tozer
,
R. D.
Amos
,
N. C.
Handy
,
B. O.
Roos
, and
L.
Serrano-Andres
,
Mol. Phys.
97
,
859
(
1999
).
17.
A.
Dreuw
,
J. L.
Weisman
, and
M.
Head-Gordon
,
J. Chem. Phys.
119
,
2943
(
2003
).
18.
A. I.
Krylov
,
Annu. Rev. Phys. Chem.
59
,
433
(
2008
).
19.
A. I.
Krylov
,
Chem. Phys. Lett.
338
,
375
(
2001
).
20.
A. I.
Krylov
,
Acc. Chem. Res.
39
,
83
(
2006
).
21.
J. F.
Stanton
and
J.
Gauss
,
J. Chem. Phys.
101
,
8938
(
1994
).
22.
M.
Nooijen
and
R. J.
Bartlett
,
J. Chem. Phys.
102
,
3629
(
1995
).
23.
K. W.
Sattelmeyer
,
H. F.
Schaefer
 III
, and
J. F.
Stanton
,
Chem. Phys. Lett.
378
,
42
(
2003
).
24.
J.
Shen
and
P.
Piecuch
,
J. Chem. Phys.
138
,
194102
(
2013
).
25.
M.
Musiał
,
M.
Olszówka
,
D. I.
Lyakh
, and
R. J.
Bartlett
,
J. Chem. Phys.
137
,
174102
(
2012
).
26.
I.
Lindgren
,
Int. J. Quantum Chem.
14
,
33
(
1978
).
27.
M. A.
Haque
and
D.
Mukherjee
,
J. Chem. Phys.
80
,
5058
(
1984
).
28.
L. Z.
Stolarczyk
and
H. J.
Monkhorst
,
Phys. Rev. A
32
,
725
(
1985
).
29.
L. Z.
Stolarczyk
and
H. J.
Monkhorst
,
Phys. Rev. A
32
,
743
(
1985
).
30.
L. Z.
Stolarczyk
and
H. J.
Monkhorst
,
Phys. Rev. A
37
,
1908
(
1988
).
31.
L. Z.
Stolarczyk
and
H. J.
Monkhorst
,
Phys. Rev. A
37
,
1926
(
1988
).
32.
D.
Mukherjee
and
S.
Pal
,
Adv. Quantum Chem.
20
,
291
(
1989
).
33.
U.
Kaldor
,
Theor. Chim. Acta
80
,
427
(
1991
).
34.
M.
Nooijen
and
R. J.
Bartlett
,
J. Chem. Phys.
106
,
6441
(
1997
).
35.
M.
Nooijen
and
R. J.
Bartlett
,
J. Chem. Phys.
106
,
6449
(
1997
).
36.
Y.
Shao
,
M.
Head-Gordon
, and
A. I.
Krylov
,
J. Chem. Phys.
118
,
4807
(
2003
).
37.
Z.
Rinkevicius
,
O.
Vahtras
, and
H.
Ågren
,
J. Chem. Phys.
133
,
114104
(
2010
).
38.
H.
van Aggelen
,
Y.
Yang
, and
W.
Yang
,
Phys. Rev. A
88
,
030501
(
2013
).
39.
Y.
Yang
,
H.
van Aggelen
,
S. N.
Steinmann
,
D.
Peng
, and
W.
Yang
,
J. Chem. Phys.
139
,
174110
(
2013
).
40.
C.-M.
Liegener
,
Chem. Phys. Lett.
90
,
188
(
1982
).
41.
S.
Taioli
,
S.
Simonucci
,
L.
Calliari
, and
M.
Dapor
,
Phys. Rep.
493
,
237
(
2010
).
42.
J.
Blaizot
and
G.
Ripka
,
Quantum Theory of Finite Systems
(
Cambridge
,
MA
,
1986
).
43.
D. J.
Rowe
,
Rev. Mod. Phys.
40
,
153
(
1968
).
44.
P.
Ring
and
P.
Schuck
,
The Nuclear Many-Body Problem
,
Physics and Astronomy Online Library
(
Springer
,
2004
).
45.
See supplementary material at http://dx.doi.org/10.1063/1.4834875 for complete derivation and detailed data.
46.
See http://www.qm4d.info for an in-house program for qm/mm simulations.
47.
D.
Zhang
,
S. N.
Steinmann
, and
W.
Yang
,
J. Chem. Phys.
139
,
154109
(
2013
).
48.
L. A.
Curtiss
,
K.
Raghavachari
,
P. C.
Redfern
, and
J. A.
Pople
,
J. Chem. Phys.
106
,
1063
(
1997
).
49.
T.
Helgaker
,
P.
Jørgensen
, and
J.
Olsen
,
Molecular Electronic-Structure Theory
(
Wiley
,
2000
).
50.
Q.
Wu
,
A. J.
Cohen
, and
W.
Yang
,
Mol. Phys.
103
,
711
(
2005
).
51.
D. E.
Woon
and
T. H.
Dunning
,
J. Chem. Phys.
100
,
2975
(
1994
).
52.
A. E.
Kramida
,
Y.
Ralchenko
,
J.
Reader
, and N. A. Team, NIST Atomic Spectra Database (version 5.0),
2012
.
53.
T.
Fujii
,
A.
Kamata
,
M.
Shimizu
,
Y.
Adachi
, and
S.
Maeda
,
Chem. Phys. Lett.
115
,
369
(
1985
).
54.
M.
Dallos
and
H.
Lischka
,
Theor. Chem. Acc.
112
,
16
(
2004
).
55.
D. J.
Tozer
and
N. C.
Handy
,
J. Chem. Phys.
109
,
10180
(
1998
).
56.
E. R.
Davidson
,
J. Comput. Phys.
17
,
87
(
1975
).

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