The alternative separation of exchange and correlation energies proposed by Toulouse et al [Theor. Chem. Acc.114, 305 (2005)] is explored in the context of multi-configuration range-separated density-functional theory. The new decomposition of the short-range exchange–correlation energy relies on the auxiliary long-range interacting wavefunction rather than the Kohn–Sham (KS) determinant. The advantage, relative to the traditional KS decomposition, is that the wavefunction part of the energy is now computed with the regular (fully interacting) Hamiltonian. One potential drawback is that, because of double counting, the wavefunction used to compute the energy cannot be obtained by minimizing the energy expression with respect to the wavefunction parameters. The problem is overcome by using short-range optimized effective potentials (OEPs). The resulting combination of OEP techniques with wavefunction theory has been investigated in this work, at the Hartree-Fock (HF) and multi-configuration self-consistent-field (MCSCF) levels. In the HF case, an analytical expression for the energy gradient has been derived and implemented. Calculations have been performed within the short-range local density approximation on H2, N2, Li2, and H2O. Significant improvements in binding energies are obtained with the new decomposition of the short-range energy. The importance of optimizing the short-range OEP at the MCSCF level when static correlation becomes significant has also been demonstrated for H2, using a finite-difference gradient. The implementation of the analytical gradient for MCSCF wavefunctions is currently in progress.

1.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
2.
F.
Malet
and
P.
Gori-Giorgi
,
Phys. Rev. Lett.
109
,
246402
(
2012
).
3.
A. D.
Becke
,
J. Chem. Phys.
138
,
074109
(
2013
).
4.
P. R. T.
Schipper
,
O. V.
Gritsenko
, and
E. J.
Baerends
,
Theor. Chem. Acc.
99
,
329
(
1998
).
5.
M.
Filatov
and
S.
Shaik
,
Chem. Phys. Lett.
304
,
429
(
1999
).
6.
J.-D.
Chai
,
J. Chem. Phys.
136
,
154104
(
2012
).
7.
C. R.
Nygaard
and
J.
Olsen
,
J. Chem. Phys.
138
,
094109
(
2013
).
8.
R.
Colle
and
O.
Salvetti
,
J. Chem. Phys.
93
,
534
(
1990
).
9.
A.
Savin
,
Int. J. Quantum Chem.
34
,
59
(
1988
).
10.
A.
Savin
,
J. Chim. Phys.
86
,
757
(
1989
).
11.
B.
Miehlich
,
H.
Stoll
, and
A.
Savin
,
Mol. Phys.
91
,
527
(
1997
).
12.
J.
Gräffenstein
and
D.
Cremer
,
Chem. Phys. Lett.
316
,
569
(
2000
).
13.
14.
F.
Ying
,
P.
Su
,
Z.
Chen
,
S.
Shaik
, and
W.
Wu
,
J. Chem. Theory Comput.
8
,
1608
(
2012
).
15.
N. O. J.
Malcolm
and
J. J. W.
McDouall
,
Chem. Phys. Lett.
282
,
121
(
1998
).
16.
J. J. W.
McDouall
,
Mol. Phys.
101
,
361
(
2003
).
17.
J.
Gräffenstein
and
D.
Cremer
,
Mol. Phys.
103
,
279
(
2005
).
18.
S.
Gusarov
,
P.-Å.
Malmqvist
,
R.
Lindh
, and
B. O.
Roos
,
Theor. Chem. Acc.
112
,
84
(
2004
).
19.
K.
Nakata
,
T.
Ukai
,
S.
Yamanaka
,
T.
Takada
, and
K.
Yamaguchi
,
Int. J. Quantum Chem.
106
,
3325
(
2006
).
20.
S.
Yamanaka
,
K.
Nakata
,
T.
Ukai
,
T.
Takada
, and
K.
Yamaguchi
,
Int. J. Quantum Chem.
106
,
3312
(
2006
).
21.
T.
Ukai
,
K.
Nakata
,
S.
Yamanaka
,
T.
Takada
, and
K.
Yamaguchi
,
Mol. Phys.
105
,
2667
(
2007
).
22.
A. J.
Pérez-Jiménez
and
J. M.
Pérez-Jordá
,
Phys. Rev. A
75
,
012503
(
2007
).
23.
M.
Weimer
,
F.
Della Sala
, and
A.
Görling
,
J. Chem. Phys.
128
,
144109
(
2008
).
24.
Y.
Kurzweil
,
K. V.
Lawler
, and
M.
Head-Gordon
,
Mol. Phys.
107
,
2103
(
2009
).
25.
A.
Savin
,
Recent Developments and Applications of Modern Density Functional Theory
(
Elsevier
,
Amsterdam
,
1996
), p.
327
.
26.
H.
Stoll
and
A.
Savin
,
Density Functional Methods in Physics
(
Plenum
,
New York
,
1985
), p.
177
.
27.
J. K.
Pedersen
, Ph.D. thesis,
University of Southern Denmark
,
2004
.
28.
E.
Fromager
,
J.
Toulouse
, and
H. J. Aa.
Jensen
,
J. Chem. Phys.
126
,
074111
(
2007
).
29.
E.
Fromager
,
F.
Réal
,
P.
Wåhlin
,
U.
Wahlgren
, and
H. J. Aa.
Jensen
,
J. Chem. Phys.
131
,
054107
(
2009
).
30.
J. G.
Ángyán
,
I. C.
Gerber
,
A.
Savin
, and
J.
Toulouse
,
Phys. Rev. A
72
,
012510
(
2005
).
31.
E.
Goll
,
H. J.
Werner
, and
H.
Stoll
,
Phys. Chem. Chem. Phys.
7
,
3917
(
2005
).
32.
J.
Toulouse
,
I. C.
Gerber
,
G.
Jansen
,
A.
Savin
, and
J. G.
Ángyán
,
Phys. Rev. Lett.
102
,
096404
(
2009
).
33.
E.
Fromager
,
R.
Cimiraglia
, and
H. J. Aa.
Jensen
,
Phys. Rev. A
81
,
024502
(
2010
).
34.
B. G.
Janesko
,
T. M.
Henderson
, and
G. E.
Scuseria
,
J. Chem. Phys.
130
,
081105
(
2009
).
35.
J.
Toulouse
,
W.
Zhu
,
A.
Savin
,
G.
Jansen
, and
J. G.
Ángyán
,
J. Chem. Phys.
135
,
084119
(
2011
).
36.
M. D.
Strømsheim
,
N.
Kumar
,
S.
Coriani
,
E.
Sagvolden
,
A. M.
Teale
, and
T.
Helgaker
,
J. Chem. Phys.
135
,
194109
(
2011
).
37.
A. M.
Teale
,
S.
Coriani
, and
T.
Helgaker
,
J. Chem. Phys.
133
,
164112
(
2010
).
38.
K.
Sharkas
,
A.
Savin
,
H. J. Aa.
Jensen
, and
J.
Toulouse
,
J. Chem. Phys.
137
,
044104
(
2012
).
39.
J.
Toulouse
,
P.
Gori-Giorgi
, and
A.
Savin
,
Theor. Chem. Acc.
114
,
305
(
2005
).
40.
A.
Savin
,
Recent Advances in Density Functional Methods
(
World Scientific
,
Singapore
,
1995
), Vol.
1
, pp.
129
153
.
41.
M.
Levy
,
Proc. Natl. Acad. Sci. U.S.A.
76
,
6062
(
1979
).
42.
E. H.
Lieb
,
Int. J. Quantum Chem.
24
,
243
(
1983
).
43.
W.
Yang
,
J. Chem. Phys.
109
,
10107
(
1998
).
44.
A.
Savin
,
F.
Colonna
, and
R.
Pollet
,
Int. J. Quantum Chem.
93
,
166
(
2003
).
45.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
(
1964
).
46.
J.
Toulouse
,
F.
Colonna
, and
A.
Savin
,
Phys. Rev. A
70
,
062505
(
2004
).
47.
J.
Toulouse
and
A.
Savin
,
J. Mol. Struct.: THEOCHEM
762
,
147
(
2006
).
48.
J.
Toulouse
,
A.
Savin
, and
H. J.
Flad
,
Int. J. Quantum Chem.
100
,
1047
(
2004
).
49.
S.
Paziani
,
S.
Moroni
,
P.
Gori-Giorgi
, and
G. B.
Bachelet
,
Phys. Rev. B
73
,
155111
(
2006
).
50.
J.
Heyd
,
G. E.
Scuseria
, and
M.
Ernzerhof
,
J. Chem. Phys.
118
,
8207
(
2003
).
51.
J.
Heyd
and
G. E.
Scuseria
,
J. Chem. Phys.
120
,
7274
(
2004
).
52.
E.
Goll
,
H. J.
Werner
,
H.
Stoll
,
T.
Leininger
,
P.
Gori-Giorgi
, and
A.
Savin
,
Chem. Phys.
329
,
276
(
2006
).
53.
J.
Toulouse
,
F.
Colonna
, and
A.
Savin
,
J. Chem. Phys.
122
,
014110
(
2005
).
54.
E.
Goll
,
M.
Ernst
,
F.
Moegle-Hofacker
, and
H.
Stoll
,
J. Chem. Phys.
130
,
234112
(
2009
).
55.
P.
Gori-Giorgi
and
A.
Savin
,
Int. J. Quantum Chem.
109
,
1950
(
2009
).
56.
W.
Yang
and
Q.
Wu
,
Phys. Rev. Lett.
89
,
143002
(
2002
).
57.
E.
Fromager
,
S.
Knecht
, and
H. J. Aa.
Jensen
,
J. Chem. Phys.
138
,
084101
(
2013
).
58.
T.
Helgaker
,
P.
Jørgensen
, and
J.
Olsen
,
Molecular Electronic-Structure Theory
(
Wiley
,
Chichester
,
2004
), pp.
433
522
.
59.
DALTON2011: An ab initio electronic structure program
,”
2001
, see http://daltonprogram.org/.
60.
Q.
Wu
and
W.
Yang
,
J. Theor. Comput. Chem.
02
,
627
(
2003
).
61.
T. H.
Dunning
,
J. Chem. Phys.
90
,
1007
(
1989
).
62.
D.
Woon
and
T. H.
Dunning
,
J. Chem. Phys.
100
,
2975
(
1994
).
63.
H.
Iikura
,
T.
Tsuneda
,
T.
Yanai
, and
K.
Hirao
,
J. Chem. Phys.
115
,
3540
(
2001
).
64.
J. W.
Song
,
T.
Hirosawa
,
T.
Tsuneda
, and
K.
Hirao
,
J. Chem. Phys.
126
,
154105
(
2007
).
65.
O. A.
Vydrov
,
J.
Heyd
,
A. V.
Krukau
, and
G. E.
Scuseria
,
J. Chem. Phys.
125
,
074106
(
2006
).
66.
O. A.
Vydrov
and
G. E.
Scuseria
,
J. Chem. Phys.
125
,
234109
(
2006
).
67.
I. C.
Gerber
and
J. G.
Ángyán
,
Chem. Phys. Lett.
415
,
100
(
2005
).
68.
J. D.
Chai
and
M.
Head-Gordon
,
J. Chem. Phys.
128
,
084106
(
2008
).
69.
M. A.
Rohrdanz
,
K. M.
Martins
, and
J. M.
Herbert
,
J. Chem. Phys.
130
,
054112
(
2009
).
70.
T.
Stein
,
H.
Eisenberg
,
L.
Kronik
, and
R.
Baer
,
Phys. Rev. Lett.
105
,
266802
(
2010
).
71.
I. C.
Gerber
and
J. G.
Ángyán
,
J. Chem. Phys.
126
,
044103
(
2007
).
72.
W.
Zhu
,
J.
Toulouse
,
A.
Savin
, and
J. G.
Ángyán
,
J. Chem. Phys.
132
,
244108
(
2010
).
73.
J.
Toulouse
,
W.
Zhu
,
J. G.
Ángyán
, and
A.
Savin
,
Phys. Rev. A
82
,
032502
(
2010
).
74.
G. C.
Lie
and
E.
Clementi
,
J. Chem. Phys.
60
,
1288
(
1974
).
75.
G. C.
Lie
and
E.
Clementi
,
J. Chem. Phys.
60
,
1275
(
1974
).
76.
J. A.
Coxon
and
T. C.
Melville
,
J. Mol. Spectrosc.
235
,
235
(
2006
).
77.
B.
Barakat
,
R.
Bacis
,
F.
Carrot
,
S.
Churassy
,
P.
Crozet
, and
F.
Martin
,
Chem. Phys.
102
,
215
(
1986
).
78.
Y.
Cornaton
,
A.
Stoyanova
,
H. J. Aa.
Jensen
, and
E.
Fromager
,
Phys. Rev. A
88
,
022516
(
2013
).
79.
J. B.
Hasted
,
Water: A Comprehensive Treatise
(
Plenum
,
New York
,
1972
), Vol.
1
, p.
255
.
80.
T.
Heaton-Burgess
,
F. A.
Bulat
, and
W.
Yang
,
Phys. Rev. Lett.
98
,
256401
(
2007
).
81.
T.
Heaton-Burgess
and
W.
Yang
,
J. Chem. Phys.
129
,
194102
(
2008
).
82.
P.
Salek
,
T.
Helgaker
, and
T.
Saue
,
Chem. Phys.
311
,
187
(
2005
).
83.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
You do not currently have access to this content.