We present a study of the variation of total energies and excitation energies along a range-separated adiabatic connection. This connection links the non-interacting Kohn–Sham electronic system to the physical interacting system by progressively switching on the electron–electron interactions whilst simultaneously adjusting a one-electron effective potential so as to keep the ground-state density constant. The interactions are introduced in a range-dependent manner, first introducing predominantly long-range, and then all-range, interactions as the physical system is approached, as opposed to the conventional adiabatic connection where the interactions are introduced by globally scaling the standard Coulomb interaction. Reference data are reported for the He and Be atoms and the H2 molecule, obtained by calculating the short-range effective potential at the full configuration-interaction level using Lieb's Legendre-transform approach. As the strength of the electron–electron interactions increases, the excitation energies, calculated for the partially interacting systems along the adiabatic connection, offer increasingly accurate approximations to the exact excitation energies. Importantly, the excitation energies calculated at an intermediate point of the adiabatic connection are much better approximations to the exact excitation energies than are the corresponding Kohn–Sham excitation energies. This is particularly evident in situations involving strong static correlation effects and states with multiple excitation character, such as the dissociating H2 molecule. These results highlight the utility of long-range interacting reference systems as a starting point for the calculation of excitation energies and are of interest for developing and analyzing practical approximate range-separated density-functional methodologies.

1.
J.
Toulouse
,
F.
Colonna
, and
A.
Savin
,
Phys. Rev. A
70
,
062505
(
2004
).
2.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
(
1964
).
3.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
4.
A.
Savin
in
Recent Development and Applications of Modern Density Functional Theory
, edited by
J. M.
Seminario
(
Elsevier
,
Amsterdam
,
1996
), pp.
327
357
.
5.
W.
Yang
,
J. Chem. Phys.
109
,
10107
(
1998
).
6.
R.
Pollet
,
F.
Colonna
,
T.
Leininger
,
H.
Stoll
,
H.-J.
Werner
, and
A.
Savin
,
Int. J. Quantum Chem.
91
,
84
(
2003
).
7.
A.
Savin
,
F.
Colonna
, and
R.
Pollet
,
Int. J. Quantum Chem.
93
,
166
(
2003
).
8.
J.
Toulouse
,
A.
Savin
, and
H.-J.
Flad
,
Int. J. Quantum Chem.
100
,
1047
(
2004
).
9.
J.
Toulouse
,
F.
Colonna
, and
A.
Savin
,
J. Chem. Phys.
122
,
014110
(
2005
).
10.
J.
Toulouse
,
P.
Gori-Giorgi
, and
A.
Savin
,
Theor. Chem. Acc.
114
,
305
(
2005
).
11.
E.
Goll
,
H.-J.
Werner
, and
H.
Stoll
,
Phys. Chem. Chem. Phys.
7
,
3917
(
2005
).
12.
S.
Paziani
,
S.
Moroni
,
P.
Gori-Giorgi
, and
G. B.
Bachelet
,
Phys. Rev. B
73
,
155111
(
2006
).
13.
E.
Goll
,
M.
Ernst
,
F.
Moegle-Hofacker
, and
H.
Stoll
,
J. Chem. Phys.
130
,
234112
(
2009
).
14.
A.
Savin
and
H.-J.
Flad
,
Int. J. Quantum Chem.
56
,
327
(
1995
).
15.
A.
Savin
in
Recent Advances in Density Functional Theory
, edited by
D. P.
Chong
(
World Scientific
,
1996
).
16.
T.
Leininger
,
H.
Stoll
,
H.-J.
Werner
, and
A.
Savin
,
Chem. Phys. Lett.
275
,
151
(
1997
).
17.
R.
Pollet
,
A.
Savin
,
T.
Leininger
, and
H.
Stoll
,
J. Chem. Phys.
116
,
1250
(
2002
).
18.
E.
Fromager
,
J.
Toulouse
, and
H. J. A.
Jensen
,
J. Chem. Phys.
126
,
074111
(
2007
).
19.
E.
Fromager
,
F.
Réal
,
P.
Wåhlin
,
U.
Wahlgren
, and
H. J. A.
Jensen
,
J. Chem. Phys.
131
,
054107
(
2009
).
20.
A.
Stoyanova
,
A. M.
Teale
,
J.
Toulouse
,
T.
Helgaker
, and
E.
Fromager
,
J. Chem. Phys.
139
,
134113
(
2013
).
21.
22.
D. R.
Rohr
,
J.
Toulouse
, and
K.
Pernal
,
Phys. Rev. A
82
,
052502
(
2010
).
23.
D. R.
Rohr
and
K.
Pernal
,
J. Chem. Phys.
135
,
074104
(
2011
).
24.
T.
Tsuchimochi
,
G. E.
Scuseria
, and
A.
Savin
,
J. Chem. Phys.
132
,
024111
(
2010
).
25.
T.
Tsuchimochi
and
G. E.
Scuseria
,
J. Chem. Phys.
134
,
064101
(
2011
).
26.
J. G.
Ángyán
,
I. C.
Gerber
,
A.
Savin
, and
J.
Toulouse
,
Phys. Rev. A
72
,
012510
(
2005
).
27.
I. C.
Gerber
and
J. G.
Ángyán
,
Chem. Phys. Lett.
416
,
370
(
2005
).
28.
I. C.
Gerber
and
J. G.
Ángyán
,
J. Chem. Phys.
126
,
044103
(
2007
).
29.
J. G.
Ángyán
,
Phys. Rev. A
78
,
022510
(
2008
).
30.
E.
Fromager
and
H. J. A.
Jensen
,
Phys. Rev. A
78
,
022504
(
2008
).
31.
E.
Goll
,
T.
Leininger
,
F. R.
Manby
,
A.
Mitrushchenkov
,
H.-J.
Werner
, and
H.
Stoll
,
Phys. Chem. Chem. Phys.
10
,
3353
(
2008
).
32.
B. G.
Janesko
and
G. E.
Scuseria
,
Phys. Chem. Chem. Phys.
11
,
9677
(
2009
).
33.
E.
Fromager
,
R.
Cimiraglia
, and
H. J. A.
Jensen
,
Phys. Rev. A
81
,
024502
(
2010
).
34.
S.
Chabbal
,
H.
Stoll
,
H.-J.
Werner
, and
T.
Leininger
,
Mol. Phys.
108
,
3373
(
2010
).
35.
S.
Chabbal
,
D.
Jacquemin
,
C.
Adamo
,
H.
Stoll
, and
T.
Leininger
,
J. Chem. Phys.
133
,
151104
(
2010
).
36.
E.
Fromager
and
H. J. A.
Jensen
,
J. Chem. Phys.
135
,
034116
(
2011
).
37.
Y.
Cornaton
,
A.
Stoyanova
,
H. J. A.
Jensen
, and
E.
Fromager
,
Phys. Rev. A
88
,
022516
(
2013
).
38.
E.
Goll
,
H.-J.
Werner
,
H.
Stoll
,
T.
Leininger
,
P.
Gori-Giorgi
, and
A.
Savin
,
Chem. Phys.
329
,
276
(
2006
).
39.
E.
Goll
,
H.
Stoll
,
C.
Thierfelder
, and
P.
Schwerdtfeger
,
Phys. Rev. A
76
,
032507
(
2007
).
40.
E.
Goll
,
H.-J.
Werner
, and
H.
Stoll
,
Chem. Phys.
346
,
257
(
2008
).
41.
J.
Toulouse
,
I. C.
Gerber
,
G.
Jansen
,
A.
Savin
, and
J. G.
Ángyán
,
Phys. Rev. Lett.
102
,
096404
(
2009
).
42.
B. G.
Janesko
,
T. M.
Henderson
, and
G. E.
Scuseria
,
J. Chem. Phys.
130
,
081105
(
2009
).
43.
B. G.
Janesko
,
T. M.
Henderson
, and
G. E.
Scuseria
,
J. Chem. Phys.
131
,
034110
(
2009
).
44.
B. G.
Janesko
and
G. E.
Scuseria
,
J. Chem. Phys.
131
,
154106
(
2009
).
45.
W.
Zhu
,
J.
Toulouse
,
A.
Savin
, and
J. G.
Ángyán
,
J. Chem. Phys.
132
,
244108
(
2010
).
46.
J.
Toulouse
,
W.
Zhu
,
J. G.
Ángyán
, and
A.
Savin
,
Phys. Rev. A
82
,
032502
(
2010
).
47.
J.
Paier
,
B. G.
Janesko
,
T. M.
Henderson
,
G. E.
Scuseria
,
A.
Grüneis
, and
G.
Kresse
,
J. Chem. Phys.
132
,
094103
(
2010
).
48.
J.
Toulouse
,
W.
Zhu
,
A.
Savin
,
G.
Jansen
, and
J. G.
Ángyán
,
J. Chem. Phys.
135
,
084119
(
2011
).
49.
J. G.
Ángyán
,
R.-F.
Liu
,
J.
Toulouse
, and
G.
Jansen
,
J. Chem. Theory Comput.
7
,
3116
(
2011
).
50.
R. M.
Irelan
,
T. M.
Henderson
, and
G. E.
Scuseria
,
J. Chem. Phys.
135
,
094105
(
2011
).
51.
T.
Gould
and
J. F.
Dobson
,
Phys. Rev. B
84
,
241108
(
2011
).
52.
E.
Fromager
,
S.
Knecht
, and
H. J. A.
Jensen
,
J. Chem. Phys.
138
,
084101
(
2013
).
53.
E.
Rebolini
,
A.
Savin
, and
J.
Toulouse
,
Mol. Phys.
111
,
1219
(
2013
).
54.
J.
Toulouse
,
E.
Rebolini
,
T.
Gould
,
J. F.
Dobson
,
P.
Seal
, and
J. G.
Ángyán
,
J. Chem. Phys.
138
,
194106
(
2013
).
55.
E. D.
Hedegård
,
F.
Heiden
,
S.
Knecht
,
E.
Fromager
, and
H. J. A.
Jensen
,
J. Chem. Phys.
139
,
184308
(
2013
).
56.
K.
Pernal
,
J. Chem. Phys.
136
,
184105
(
2012
).
57.
O. V.
Gritsenko
,
S. J. A.
van Gisbergen
,
A.
Görling
, and
E. J.
Baerends
,
J. Chem. Phys.
113
,
8478
(
2000
).
58.
N. T.
Maitra
,
F.
Zhang
,
R. J.
Cave
, and
K.
Burke
,
J. Chem. Phys.
120
,
5932
(
2004
).
59.
M. E.
Casida
,
C.
Jamorski
,
K. C.
Casida
, and
D. R.
Salahub
,
J. Chem. Phys.
108
,
4439
(
1998
).
60.
A.
Dreuw
,
J. L.
Weisman
, and
M.
Head-Gordon
,
J. Chem. Phys.
119
,
2943
(
2003
).
61.
E. H.
Lieb
,
Int. J. Quantum Chem.
24
,
243
(
1983
).
62.
F.
Colonna
and
A.
Savin
,
J. Chem. Phys.
110
,
2828
(
1999
).
63.
A. M.
Teale
,
S.
Coriani
, and
T.
Helgaker
,
J. Chem. Phys.
130
,
104111
(
2009
).
64.
D. P.
Joubert
and
G. P.
Strivastava
,
J. Chem. Phys.
109
,
5212
(
1998
).
65.
A.
Savin
,
F.
Colonna
, and
M.
Allavena
,
J. Chem. Phys.
115
,
6827
(
2001
).
66.
A. M.
Teale
,
S.
Coriani
, and
T.
Helgaker
,
J. Chem. Phys.
132
,
164115
(
2010
).
67.
M. D.
Strømsheim
,
N.
Kumar
,
S.
Coriani
,
E.
Sagvolden
,
A. M.
Teale
, and
T.
Helgaker
,
J. Chem. Phys.
135
,
194109
(
2011
).
68.
J.
Toulouse
,
F.
Colonna
, and
A.
Savin
,
Mol. Phys.
103
,
2725
(
2005
).
69.
A. M.
Teale
,
S.
Coriani
, and
T.
Helgaker
,
J. Chem. Phys.
133
,
164112
(
2010
).
70.
F.
Zhang
and
K.
Burke
,
Phys. Rev. A
69
,
052510
(
2004
).
71.
P.
Gori-Giorgi
and
A.
Savin
,
Phys. Rev. A
73
,
032506
(
2006
).
72.
DALTON, a molecular electronic structure program, Release DALTON2013.0 (2013), seehttp://daltonprogram.org.
73.
K.
Aidas
,
C.
Angeli
,
K. L.
Bak
,
V.
Bakken
,
R.
Bast
,
L.
Boman
,
O.
Christiansen
,
R.
Cimiraglia
,
S.
Coriani
,
P.
Dahle
 et al,
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
4
,
269
(
2014
).
74.
Q.
Wu
and
W.
Yang
,
J. Theor. Comput. Chem.
02
,
627
(
2003
).
75.
K.
Kaufmann
,
J. Phys. B: At. Mol. Opt. Phys.
24
,
2277
(
1991
).
76.
T. H.
Dunning
,
J. Chem. Phys.
90
,
1007
(
1989
).
77.
See supplementary material at http://dx.doi.org/10.1063/1.4890652 for the fits of the total and excitation energies.
78.
C.
Umrigar
,
A.
Savin
, and
X.
Gonze
, in
Electronic Density Functional Theory
, edited by
J. F.
Dobson
,
G.
Vignale
, and
M. P.
Das
(
Springer
,
US
,
1998
), pp.
167
176
.
79.
C.
Filippi
,
C. J.
Umrigar
, and
X.
Gonze
,
J. Chem. Phys.
107
,
9994
(
1997
).
80.
A.
Savin
,
C. J.
Umrigar
, and
X.
Gonze
,
Chem. Phys. Lett.
288
,
391
(
1998
).
81.
I.
Gerber
and
J. G.
Ángyán
,
Chem. Phys. Lett.
415
,
100
(
2005
).
83.
A.
Savin
,
J. Chem. Phys.
134
,
214108
(
2011
).
84.
A.
Savin
,
J. Chem. Phys.
140
,
18A509
(
2014
).

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