Exact relations are derived between scaling to the high-density limit of density functional theory and taking to infinity for nondegenerate atoms. Görling–Levy perturbation results are deduced for hydrogenic densities. The kinetic contribution to the correlation energy is also studied, and estimates given for its value for neutral atoms. Popular approximate functionals are tested against these benchmarks.
REFERENCES
1.
R. G.
Parr
and W.
Yang
, Density Functional Theory of Atoms and Molecules
(Oxford
, New York, 1989
).2.
W.
Koch
and M. C.
Holthausen
, A Chemist’s Guide to Density Functional Theory
(Wiley-VCH
, Weinheim, 2000
).3.
J. P.
Perdew
and S.
Kurth
, in Density Functionals: Theory and Applications
, edited by D.
Joubert
(Springer
, Berlin, 1998
).4.
M.
Levy
and J. P.
Perdew
, Phys. Rev. A
32
, 2010
(1985
).5.
K.
Burke
, in Electronic Density Functional Theory: Recent Progress and New Directions
, edited by J. F.
Dobson
, G.
Vignale
, and M. P.
Das
(Plenum
, New York, 1997
), p. 19
.6.
Y. A.
Wang
, Phys. Rev. A
56
, 1646
(1997
).7.
A. D.
Becke
, J. Chem. Phys.
98
, 5648
(1993
).8.
J. P.
Perdew
, M.
Ernzerhof
, and K.
Burke
, J. Chem. Phys.
105
, 9982
(1996
).9.
K.
Burke
, M.
Ernzerhof
, and J. P.
Perdew
, Chem. Phys. Lett.
265
, 115
(1997
).10.
E. R.
Davidson
, S. A.
Hagstrom
, S. J.
Chakravorty
, V. Meiser
Umar
, and C. Froese
Fischer
, Phys. Rev. A
44
, 7071
(1991
).11.
S. J.
Chakravorty
, S. R.
Gwaltney
, E. R.
Davidson
, F. A.
Parpia
, and C. Froese
Fischer
, Phys. Rev. A
47
, 3649
(1993
).12.
E.
Engel
and R. M.
Dreizler
, J. Comput. Chem.
20
, 31
(1999
).13.
C. J.
Umrigar
and X.
Gonze
, Phys. Rev. A
50
, 3827
(1994
).14.
C. J.
Huang
and C. J.
Umrigar
, Phys. Rev. A
56
, 290
(1997
).15.
M.
Levy
, Phys. Rev. A
43
, 4637
(1991
).16.
J. P.
Perdew
and Y.
Wang
, Phys. Rev. B
45
, 13244
(1992
).17.
J. P.
Perdew
, E. R.
McMullen
, and A.
Zunger
, Phys. Rev. A
23
, 2785
(1981
).18.
J. P.
Perdew
, K.
Burke
, and M.
Ernzerhof
, Phys. Rev. Lett.
78
, 1396
(1997
).19.
J. P.
Perdew
, in Electronic Structure of Solids ’91
, edited by P.
Ziesche
and H.
Eschrig
(Akademie
, Berlin, 1991
), p. 11
.20.
J.
Harris
and R. O.
Jones
, J. Phys. F: Met. Phys.
4
, 1170
(1974
).21.
D. C.
Langreth
and J. P.
Perdew
, Solid State Commun.
17
, 1425
(1975
).22.
O.
Gunnarsson
and B. I.
Lundqvist
, Phys. Rev. B
13
, 4274
(1976
).23.
D. C.
Langreth
and J. P.
Perdew
, Phys. Rev. B
15
, 2884
(1977
).24.
A.
Görling
and M.
Levy
, Phys. Rev. B
47
, 13105
(1993
).25.
S. J.
Chakravorty
and E. R.
Davidson
, J. Phys. Chem.
100
, 6167
(1996
).26.
J.
Linderberg
and H.
Shull
, J. Mol. Spectrosc.
5
, 1
(1960
).27.
E. K. U.
Gross
, M.
Petersilka
, and T.
Grabo
, in Chemical Applications of Density Functional Theory
, edited by B. B.
Laird
, R. B.
Ross
, and T.
Ziegler
(American Chemical Society
, Washington, DC, 1996
), p. 42
.28.
A.
Görling
and M.
Ernzerhof
, Phys. Rev. A
51
, 4501
(1995
).29.
E. P.
Ivanova
and U. I.
Safronova
, J. Phys. B
8
, 1591
(1975
).30.
S.
Ivanov
and M.
Levy
, J. Phys. Chem. A
102
, 3151
(1998
).31.
S.
Ivanov
and M.
Levy
, Theor. Chem. Acc.
103
, 117
(1999
).32.
D.
Frydel
, W. H.
Terilla
, and K.
Burke
, J. Chem. Phys.
112
, 5292
(2000
).33.
C.
Filippi
, X.
Gonze
, and C. J.
Umrigar
, in Recent Developments and Applications of Density Functional Theory
, edited by J. M.
Seminario
(Elsevier
, Amsterdam, 1996
).34.
R. C.
Morrison
and Q.
Zhao
, Phys. Rev. A
51
, 1980
(1995
).35.
E.
Clementi
and C.
Roetti
, At. Data Nucl. Data Tables
14
, 177
(1974
).36.
O.
Jitrik
and C. F.
Bunge
, Phys. Rev. A
43
, 5804
(1991
).37.
Q.
Zhao
and R. G.
Parr
, Phys. Rev. A
46
, 2337
(1992
).38.
Q.
Zhao
and R. G.
Parr
, J. Chem. Phys.
98
, 543
(1992
).39.
Q.
Zhao
, R. C.
Morrison
, and R. G.
Parr
, Phys. Rev. A
50
, 2138
(1994
).40.
41.
V. N.
Staroverov
, G. E.
Scuseria
, J. P.
Perdew
, J.
Tao
, and E. R.
Davidson
, Phys. Rev. A
70
, 012502
(2004
).© 2005 American Institute of Physics.
2005
American Institute of Physics
You do not currently have access to this content.
