A solution to the long-standing problem of developing numerically stable optimized effective potential (OEP) methods based on Gaussian basis sets is presented by introducing an approach consisting of an exact exchange OEP method with an accompanying construction and balancing scheme for the involved auxiliary and orbital Gaussian basis sets that is numerically stable and that properly represents an exact exchange Kohn-Sham method. The method is a purely analytical method that does not require any numerical grid, scales like Hartree-Fock or B3LYP procedures, is straightforward to implement, and is easily generalized to take into account orbital-dependent density functionals other than the exact exchange considered in this work. Thus, the presented OEP approach opens the way to the development and application of novel orbital-dependent exchange-correlation functionals. It is shown that adequately taking into account the continuum part of the Kohn-Sham orbital spectrum is crucial for numerically stable Gaussian basis set OEP methods. Moreover, it is mandatory to employ orbital basis sets that are converged with respect to the used auxiliary basis representing the exchange potential. OEP calculations in the past often did not meet the latter requirement and therefore may have led to erroneously low total energies.

1.
R. G.
Parr
and
W.
Yang
,
Density-Functional Theory of Atoms and Molecules
(
Oxford University Press
,
Oxford
,
1989
).
2.
R. M.
Dreizler
and
E. K. U.
Gross
,
Density Functional Theory
(
Springer
,
Heidelberg
,
1990
).
3.
W.
Koch
and
M. C.
Holthausen
,
A Chemist’s Guide to Density Functional Theory
(
Wiley-VCH
,
New York
,
2000
).
4.
A.
Görling
,
J. Chem. Phys.
123
,
062203
(
2005
), and references therein.
5.
A. D.
Becke
,
J. Chem. Phys.
98
,
5648
(
1993
).
6.
T. V.
Voorhis
and
G. E.
Scuseria
,
J. Chem. Phys.
109
,
400
(
1998
).
7.
M.
Ernzerhof
and
G. E.
Scuseria
,
J. Chem. Phys.
111
,
911
(
1999
).
8.
J. P.
Perdew
,
S.
Kurth
,
A.
Zupan
, and
P.
Blaha
,
Phys. Rev. Lett.
82
,
2544
(
1999
).
9.
A. V.
Arbuznikov
and
M.
Kaupp
,
Chem. Phys. Lett.
381
,
495
(
2003
).
10.
A.
Görling
and
M.
Levy
,
Phys. Rev. A
50
,
196
(
1994
).
11.
A.
Görling
and
M.
Levy
,
Int. J. Quantum Chem., Quantum Chem. Symp.
29
,
93
(
1995
).
12.
R. T.
Sharp
and
G. K.
Horton
,
Phys. Rev.
90
,
317
(
1953
).
13.
J. D.
Talman
and
W. F.
Shadwick
,
Phys. Rev. A
14
,
36
(
1976
).
14.
T.
Grabo
,
T.
Kreibich
,
S.
Kurth
, and
E. K. U.
Gross
,
Strong Coulomb Correlations in Electronic Structure: Beyond the Local Density Approximatio
(
Gordon and Breach
,
Tokyo
,
1998
).
15.
V.
Sahni
,
J.
Gruenbaum
, and
J. P.
Perdew
,
Phys. Rev. B
26
,
4371
(
1982
).
16.
A.
Görling
,
Phys. Rev. B
59
,
10370
(E) (
1999
).
17.
M.
Städele
,
J. A.
Majewski
,
P.
Vogl
, and
A.
Görling
,
Phys. Rev. Lett.
79
,
2089
(
1997
).
18.
M.
Städele
,
M.
Moukara
,
J. A.
Majewski
,
P.
Vogl
, and
A.
Görling
,
Phys. Rev. B
59
,
10031
(
1999
).
19.
A.
Görling
,
Phys. Rev. Lett.
83
,
5459
(
1999
).
20.
S.
Ivanov
,
S.
Hirata
, and
R. J.
Bartlett
,
Phys. Rev. Lett.
83
,
5455
(
1999
).
21.
S.
Hamel
,
M. E.
Casida
, and
D. R.
Salahub
,
J. Chem. Phys.
114
,
7342
(
2001
).
22.
S.
Hirata
,
S.
Ivanov
,
I.
Grabowski
,
R.
Bartlett
,
K.
Burke
, and
J. D.
Talman
,
J. Chem. Phys.
115
,
1635
(
2001
).
23.
L.
Veseth
,
J. Chem. Phys.
114
,
8789
(
2001
).
24.
W.
Yang
and
Q.
Wu
,
Phys. Rev. Lett.
89
,
143002
(
2002
).
25.
D. R.
Rohr
,
O. V.
Gritsenko
, and
E. J.
Baerends
,
J. Mol. Struct.: THEOCHEM
762
,
193
(
2006
).
26.
S.
Kümmel
and
J. P.
Perdew
,
Phys. Rev. Lett.
90
,
043004
(
2003
).
27.
A.
Görling
,
A.
Heßelmann
,
M.
Jones
, and
M.
Levy
, arXiv:physics/0705.1717v1.
28.
V. K.
Staroverov
,
G. E.
Scuseria
, and
E. R.
Davidson
,
J. Chem. Phys.
124
,
141103
(
2006
).
29.
A.
Ben-Haj-Yedder
,
E.
Cancés
, and
C. L.
Bris
,
Diff. Integral Eq.
17
,
331
(
2004
).
30.
J. B.
Krieger
,
Y.
Li
, and
G. J.
Iafrate
,
Phys. Rev. A
46
,
5453
(
1992
).
31.
F.
Della Sala
and
A.
Görling
,
J. Chem. Phys.
115
,
5718
(
2001
).
32.
O. V.
Gritsenko
and
E. J.
Baerends
,
Phys. Rev. A
64
,
042506
(
2001
).
33.
A.
Holas
and
M.
Cinal
,
Phys. Rev. A
72
,
032504
(
2005
).
34.
F.
Della Sala
and
A.
Görling
,
J. Chem. Phys.
116
,
5374
(
2002
).
35.
F.
Della Sala
and
A.
Görling
,
Phys. Rev. Lett.
89
,
033003
(
2002
).
36.
V. K.
Staroverov
,
G. E.
Scuseria
, and
E. R.
Davidson
,
J. Chem. Phys.
125
,
081104
(
2006
).
37.
Q.
Wu
and
W.
Yang
,
J. Theor. Comput. Chem.
2
,
627
(
2003
).
38.
T.
Heaton-Burgess
,
F. A.
Bulat
, and
W.
Yang
,
Phys. Rev. Lett.
98
,
256401
(
2007
).
39.
.
Liu
,
P. W.
Ayers
, and
R. G.
Parr
,
J. Chem. Phys.
111
,
6197
(
1999
).
40.
P. W.
Ayers
and
M.
Levy
,
J. Chem. Phys.
115
,
4438
(
2001
).
41.
M.
Levy
,
J. P.
Perdew
, and
V.
Sahni
,
Phys. Rev. A
31
,
3231
(
1984
).
42.
C.-O.
Almbladh
and
U.
von Barth
,
Phys. Rev. B
31
,
3231
(
1985
).
43.
S.
Ivanov
,
S.
Hirata
, and
R. J.
Bartlett
,
J. Chem. Phys.
116
,
1269
(
2002
).
44.
J. T. H.
Dunning
,
J. Chem. Phys.
90
,
1007
(
1989
).
45.
H.
Partridge
,
J. Chem. Phys.
90
,
1043
(
1989
).
46.
R.
Kendall
,
J. T. H.
Dunning
, and
R.
Harrison
,
J. Chem. Phys.
96
,
6769
(
1992
).
47.
A.
Heßelmann
and
F.
Manby
,
J. Chem. Phys.
123
,
164116
(
2005
).
48.
R. R.
Toczylowski
and
S. M.
Cybulski
,
J. Phys. Chem. A
107
,
418
(
2003
).
49.
H.-J.
Werner
,
P. J.
Knowles
,
R.
Lindh
 et al, MOLPRO, Version 2006.2, a package of ab initio programs,
2006
(see http://www.molpro.net).
50.
R.
Ahlrichs
,
M.
Bär
,
M.
Häser
,
H.
Horn
, and
C.
Kölmel
,
Chem. Phys. Lett.
162
,
165
(
1989
).
51.
E.
Engel
,
S.
Keller
,
A. F.
Bonetti
,
H.
Müller
, and
R. M.
Dreizler
,
Phys. Rev. A
52
,
2750
(
1995
).
52.
E.
Engel
,
S.
Keller
, and
R. M.
Dreizler
,
Phys. Rev. A
53
,
1367
(
1996
).
53.
E.
Engel
,
A. F.
Bonetti
,
S.
Keller
,
I.
Andrejkovics
, and
R. M.
Dreizler
,
Phys. Rev. A
58
,
964
(
1998
).
54.
F.
Weigend
,
Phys. Chem. Chem. Phys.
4
,
4285
(
2002
).
55.
A.
Görling
and
A.
Heßelmann
(unpublished).
56.
A. F.
Bonetti
,
E.
Engel
,
R. N.
Schmid
, and
R. M.
Dreizler
,
Phys. Rev. Lett.
86
,
2241
(
2001
).
57.
P.
Mori-Sánchez
,
Q.
Wu
, and
W.
Yang
,
J. Chem. Phys.
123
,
062204
(
2005
).
58.
R. J.
Bartlett
,
V. F.
Lotrich
, and
I. V.
Schweigert
,
J. Chem. Phys.
123
,
062205
(
2005
).
59.
H.
Jiang
and
E.
Engel
,
J. Chem. Phys.
125
,
184108
(
2006
).
60.
A.
Heßelmann
,
Phys. Chem. Chem. Phys.
8
,
563
(
2006
).
61.
A. K.
Wilson
,
T. v.
Mourik
, and
J. T. H.
Dunning
,
J. Mol. Struct.: THEOCHEM
388
,
339
(
1997
).
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