The implementation of an efficient program of the algebraic diagrammatic construction method for the polarisation propagator in third-order perturbation theory (ADC(3)) for the computation of excited states is reported. The accuracies of ADC(2) and ADC(3) schemes have been investigated with respect to Thiel's recently established benchmark set for excitation energies and oscillator strengths. The calculation of 141 vertical excited singlet and 71 triplet states of 28 small to medium-sized organic molecules has revealed that ADC(3) exhibits mean error and standard deviation of 0.12 ± 0.28 eV for singlet states and −0.18 ± 0.16 eV for triplet states when the provided theoretical best estimates are used as benchmark. Accordingly, the ADC(2)-s and ADC(2)-x calculations revealed accuracies of 0.22 ± 0.38 eV and −0.70 ± 0.37 eV for singlets and 0.12 ± 0.16 eV and −0.55 ± 0.20 eV for triplets, respectively. For a comparison of CC3 and ADC(3), only non-CC3 benchmark values were considered, which comprise 84 singlet states and 19 triplet states. For these singlet states CC3 exhibits an accuracy of 0.23 ± 0.21 eV and ADC(3) an accuracy of 0.08 ± 0.27 eV, and accordingly for the triplet states of 0.12 ± 0.10 eV and −0.10 ± 0.13 eV, respectively. Hence, based on the quality of the existing benchmark set it is practically not possible to judge whether ADC(3) or CC3 is more accurate, however, ADC(3) has a much larger range of applicability due to its more favourable scaling of O(N6) with system size.

1.
L.
Gonzalez
,
D.
Escudero
, and
L.
Serrano-Andres
,
Chem. Phys. Chem.
13
,
28
(
2012
).
2.
P. H. P.
Harbach
and
A.
Dreuw
, in
Modeling of Molecular Properties
, edited by
P.
Comba
(
Wiley-VCH
,
Weinheim
,
2011
), p.
29
.
3.
M.
Wormit
and
A.
Dreuw
,
Phys. Chem. Chem. Phys.
9
,
2917
(
2007
).
4.
A.
Dreuw
,
Chem. Phys. Chem.
7
,
2259
(
2006
).
5.
S.
Grimme
,
Rev. Comput. Chem.
20
,
153
(
2004
).
6.
J. E.
Ridley
and
M. C.
Zerner
,
Theor. Chim. Acta
32
,
111
(
1973
).
7.
M. C.
Zerner
,
G. H.
Loew
,
R. K.
Kirchner
, and
U. T.
Mueller-Westerhoff
,
J. Am. Chem. Soc.
102
,
589
(
1980
).
8.
W.
Weber
and
W.
Thiel
,
Theor. Chem. Acc.
103
,
495
(
2000
).
9.
A.
Koslowski
,
M. E.
Beck
, and
W.
Thiel
,
J. Comput. Chem.
24
,
714
(
2003
).
10.
E.
Runge
and
E. K. U.
Gross
,
Phys. Rev. Lett.
52
,
997
(
1984
).
11.
M. E.
Casida
,
Recent Advances in Density Functional Methods. Part I
(
World Scientific
,
Singapore
,
1995
), pp.
155
192
.
12.
A.
Dreuw
and
M.
Head-Gordon
,
Chem. Rev.
105
,
4009
(
2005
).
13.
S.
Grimme
,
Chem. Phys. Lett.
259
,
128
(
1996
).
14.
S.
Grimme
and
M.
Waletzke
,
J. Chem. Phys.
111
,
5645
(
1999
).
15.
C. M.
Marian
and
N.
Gilka
,
J. Chem. Theor. Comput.
4
,
1501
(
2008
).
16.
P. J.
Bruna
and
S. D.
Peyerimhoff
, “
Excited-state potentials
,” in
Advances in Chemical Physics
(
Wiley
,
2007
), pp.
1
97
.
17.
R.
McWeeny
and
B. T.
Sutcliffe
,
Methods of Molecular Quantum Mechanics
(
Academic Press
,
London
,
1969
).
18.
O.
Christiansen
,
H.
Koch
, and
P.
Jørgensen
,
Chem. Phys. Lett.
243
,
409
(
1995
).
19.
C.
Haettig
and
K.
Hald
,
Phys. Chem. Chem. Phys.
4
,
2111
(
2002
).
20.
C.
Haettig
,
Adv. Quantum Chem.
50
,
37
(
2005
).
21.
H.
Sekino
and
R. J.
Bartlett
,
Int. J. Quantum Chem. Symp.
18
,
255
(
1984
).
22.
J. F.
Stanton
and
R. J.
Bartlett
,
J. Chem. Phys.
98
,
7029
(
1993
).
23.
E.
Dalgaard
and
H. J.
Monkhorst
,
Phys. Rev.
A28
,
1217
(
1983
).
24.
H.
Koch
and
P.
Jørgensen
,
J. Chem. Phys.
93
,
3333
(
1990
).
25.
J.
Oddershede
,
Adv. Quantum Chem.
11
,
275
(
1978
).
26.
J.
Oddershede
,
Adv. Chem. Phys.
69
,
201
(
1987
).
27.
K. L.
Bak
,
H.
Koch
,
J.
Oddershede
,
O.
Christiansen
, and
S. P. A.
Sauer
,
J. Chem. Phys.
112
,
4173
(
2000
).
28.
J.
Schirmer
,
Phys. Rev. A
26
,
2395
(
1982
).
29.
A. B.
Trofimov
and
J.
Schirmer
,
J. Phys. B
28
,
2299
(
1995
).
30.
F.
Mertins
and
J.
Schirmer
,
Phys. Rev. A
53
,
2140
(
1996
).
31.
A. B.
Trofimov
,
G.
Stelter
, and
J.
Schirmer
,
J. Chem. Phys.
111
,
9982
(
1999
).
32.
H.
Koch
,
O.
Christiansen
, and
P.
Jørgensen
,
Chem. Phys. Lett.
244
,
75
(
1995
).
33.
H.
Koch
,
O.
Christiansen
,
P.
Jørgensen
,
T.
Helgaker
, and
A. S.
de Meras
,
J. Chem. Phys.
106
,
1808
(
1997
).
34.
K.
Andersson
,
P.-Å.
Malmqvist
, and
B. O.
Roos
,
J. Chem. Phys.
96
,
1218
(
1992
).
35.
J. D.
Watts
and
R. J.
Bartlett
,
J. Chem. Phys.
101
,
3073
(
1994
).
36.
P.
Piecuch
,
S. A.
Kucharski
,
K.
Kowalski
, and
M.
Musial
,
Comput. Phys. Commun.
149
,
71
(
2002
).
37.
O.
Christiansen
,
H.
Koch
, and
P.
Jørgensen
,
J. Chem. Phys.
105
,
1451
(
1996
).
38.
O.
Christiansen
,
H.
Koch
,
P.
Jørgensen
, and
J.
Olsen
,
Chem. Phys. Lett.
256
,
185
(
1996
).
39.
A. B.
Trofimov
,
G.
Stelter
, and
J.
Schirmer
,
J. Chem. Phys.
117
,
6402
(
2002
).
40.
M.
Wormit
,
D. R.
Rehn
,
P. H. P.
Harbach
,
J.
Wenzel
,
C. M.
Krauter
,
E.
Epifanovsky
, and
A.
Dreuw
,
Mol. Phys.
112
,
774
(
2014
).
41.
M.
Schreiber
,
M. R.
Silva-Junior
,
S. P. A.
Sauer
, and
W.
Thiel
,
J. Chem. Phys.
128
,
134110
(
2008
).
42.
M. R.
Silva-Junior
,
M.
Schreiber
,
S. P. A.
Sauer
, and
W.
Thiel
,
J. Chem. Phys.
129
,
104103
(
2008
).
43.
J.
Schirmer
,
Phys. Rev. A
43
,
4647
(
1991
).
44.
J.
Schirmer
and
A. B.
Trofimov
,
J. Chem. Phys.
120
,
11449
(
2004
).
45.
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. V.
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
, and
A. K.
Chakraborty
,
Phys. Chem. Chem. Phys.
8
,
3172
(
2006
).
46.
E.
Epifanovsky
,
M.
Wormit
,
T.
Kuś
,
A.
Landau
,
D.
Zuev
,
K.
Khistyaev
,
P.
Manohar
,
I.
Kaliman
,
A.
Dreuw
, and
A. I.
Krylov
,
J. Comput. Chem.
34
,
2293
(
2013
).
47.
E. R.
Davidson
,
J. Comput. Phys.
17
,
87
(
1975
).
48.
C.
Møller
and
M. S.
Plesset
,
Phys. Rev.
46
,
618
(
1934
).
49.
A.
Schäfer
,
H.
Horn
, and
R.
Ahlrichs
,
J. Chem. Phys.
97
,
2571
(
1992
).
50.
M. R.
Silva-Junior
,
M.
Schreiber
,
S. P. A.
Sauer
, and
W.
Thiel
,
J. Chem. Phys.
133
,
174318
(
2010
).
51.
J.
Schirmer
and
F.
Mertins
,
Theo. Chem. Acc.
125
,
145
(
2010
).
52.
L. S.
Cederbaum
and
W.
Domcke
,
Advances in Chemical Physics Vol. 36
(
Wiley
,
New York
,
1977
).
53.
J.
Schirmer
and
G.
Angonoa
,
J. Chem. Phys.
91
,
1754
(
1989
).
54.
J.
Schirmer
and
A.
Thiel
,
J. Chem. Phys.
115
,
10621
(
2001
).
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