Self-consistent correlation potentials for H2 and LiH for various inter-atomic separations are obtained within the random phase approximation (RPA) of density functional theory. The RPA correlation potential shows a peak at the bond midpoint, which is an exact feature of the true correlation potential, but lacks another exact feature: the step important to preserve integer charge on the atomic fragments in the dissociation limit. An analysis of the RPA energy functional in terms of fractional charge is given which confirms these observations. We find that the RPA misses the derivative discontinuity at odd integer particle numbers but explicitly eliminates the fractional spin error in the exact-exchange functional. The latter finding explains the improved total energy in the dissociation limit.
REFERENCES
1.
F.
Furche
, Phys. Rev. B
64
, 195120
(2001
).2.
F.
Furche
, J. Chem. Phys.
129
, 114105
(2008
).3.
H.
Eshuis
, J.
Yarkony
, and F.
Furche
, J. Chem. Phys.
129
, 234114
(2010
).4.
L.
Schimka
, J.
Harl
, A.
Stroppa
, A.
Grneis
, M.
Marsman
, F.
Mittendorfer
, and G.
Kresse
, Nature Mater.
9
, 741
(2010
).5.
S.
Lebègue
, J.
Harl
, T.
Gould
, J. G.
Ángyán
, G.
Kresse
, and J. F.
Dobson
, Phys. Rev. Lett.
105
, 196401
(2010
).6.
J.
Harl
and G.
Kresse
, Phys. Rev. Lett.
103
, 056401
(2009
).7.
X.
Ren
, A.
Tkatchenko
, P.
Rinke
, and M.
Scheffler
, Phys. Rev. Lett.
106
, 153003
(2011
).8.
X.
Ren
, P.
Rinke
, and M.
Scheffler
, Phys. Rev. B
80
, 045402
(2009
).9.
R. W.
Godby
, M.
Schlüter
, and L. J.
Sham
, Phys. Rev. B
36
, 6497
(1987
).10.
R. W.
Godby
, M.
Schlüter
, and L. J.
Sham
, Phys. Rev. Lett.
56
, 2415
(1986
).11.
M.
Grüning
, A.
Marini
, and A.
Rubio
, J. Chem. Phys.
124
, 154108
(2006
).12.
A. L.
Fetter
and J. D.
Walecka
, Quantum Theory of Many-Particle Systems
, 2nd ed. (Dover
, New York
, 2003
).13.
F.
Aryasetiawan
, T.
Miyake
, and K.
Terakura
, Phys. Rev. Lett.
88
, 166401
(2002
).14.
M.
Fuchs
and X.
Gonze
, Phys. Rev. B
65
, 235109
(2002
).15.
W.
Kohn
, Y.
Meir
, and D. E.
Makarov
, Phys. Rev. Lett.
80
, 4153
(1998
).16.
J.
Toulouse
, I. C.
Gerber
, G.
Jansen
, A.
Savin
, and J. G.
Ángyán
, Phys. Rev. Lett.
102
, 096404
(2009
).17.
J. F.
Dobson
, in Topics in Condensed Matter Physics
, edited by M. P.
Das
(Nova
, New York
, 1994
),e-print arXiv:cond-mat/0311371.
18.
H.-V.
Nguyen
and G.
Galli
, J. Chem. Phys.
132
, 044109
(2010
).19.
S.
Lebègue
, J.
Harl
, T.
Gould
, J. G.
Ángyán
, G.
Kresse
, and J. F.
Dobson
, Phys. Rev. Lett.
105
, 196401
(2010
).20.
N.
Helbig
, I. V.
Tokatly
, and A.
Rubio
, J. Chem. Phys.
131
, 224105
(2009
).21.
A. J.
Cohen
, P.
Mori-Sánchez
, and W.
Yang
, J. Chem. Phys.
129
, 121104
(2008
).22.
P.
Mori-Sánchez
, A. J.
Cohen
, and W.
Yang
, Phys. Rev. Lett.
102
, 066403
(2009
).23.
A. J.
Cohen
, P.
Mori-Sánchez
, and W.
Yang
, Science
321
, 792
(2008
).24.
N. E.
Dahlen
, R.
van Leeuwen
, and U.
von Barth
, Int. J. Quantum Chem.
101
, 512
(2005
).25.
M.
Fuchs
, Y.-M.
Niquet
, X.
Gonze
, and K.
Burke
, J. Chem. Phys.
122
, 094116
(2005
).26.
N. E.
Dahlen
, R.
van Leeuwen
, and U.
von Barth
, Phys. Rev. A
73
, 012511
(2006
).27.
A.
Heßelmann
and A.
Görling
, Phys. Rev. Lett.
106
, 093001
(2011
).28.
J. P.
Perdew
, R. G.
Parr
, M.
Levy
, and J. L.
Balduz
, Phys. Rev. Lett.
49
, 1691
(1982
).29.
P.
Mori-Sánchez
, A. J.
Cohen
, and W.
Yang
, Phys. Rev. Lett.
100
, 146401
(2008
).30.
31.
O. V.
Gritsenko
and E. J.
Baerends
, Phys. Rev. A
54
, 1957
(1996
).32.
P. R.T.
Schipper
, O. V.
Gritsenko
, and E. J.
Baerends
, Phys. Rev. A
57
, 1729
(1998
).33.
D.
Tempel
, T. J.
Martinez
, and N. T.
Maitra
, J. Chem. Theory Comput.
5
, 770
(2009
).34.
J. P.
Perdew
, in Density Functional Methods in Physics
, edited by R. M.
Dreizler
and J.
da Providencia
(Plenum
, New York
, 1985
).35.
E.
Sagvolden
and J. P.
Perdew
, Phys. Rev. A
77
, 012517
(2008
).36.
M. A.
Buijse
, E. J.
Baerends
, and J. G.
Snijders
, Phys. Rev. A
40
, 4190
(1989
).37.
M.
Hellgren
and U.
von Barth
, Phys. Rev. B
76
, 075107
(2007
).38.
M.
Hellgren
and U.
von Barth
, J. Chem. Phys.
132
, 044101
(2010
).39.
D. C.
Langreth
and J. P.
Perdew
, Solid State Commun.
17
, 1425
(1975
).40.
O.
Gunnarsson
and B. I.
Lundqvist
, Phys. Rev. B
13
, 4274
(1976
).41.
Time-Dependent Density Functional Theory
, edited by M.
Marques
, C. A.
Ullrich
, F.
Nogueira
, A.
Rubio
, K.
Burke
, and E. K. U.
Gross
(Springer
, Berlin
, 2006
).42.
E. K. U.
Gross
and W.
Kohn
, Phys. Rev. Lett.
55
, 2850
(1985
).43.
L. J.
Sham
and M.
Schlüter
, Phys. Rev. Lett.
51
, 1888
(1983
).44.
U.
von Barth
, N.
Dahlen
, R.
van Leeuwen
, and G.
Stefanucci
, Phys. Rev. B
72
, 235109
(2005
).45.
W.
Yang
and Q.
Wu
, Phys. Rev. Lett.
89
, 143002
(2002
).46.
See http://pyquante.sourceforge.net/ for the source code and description of the PyQuante module to Python.
47.
D. R.
Rohr
, O. V.
Gritsenko
, and E. J.
Baerends
, Chem. Phys. Lett.
432
, 336
(2006
).48.
D. R.
Rohr
and A.
Savin
, J. Mol. Struct.
943
, 90
(2010
).49.
A.
Heßelmann
, A. W.
Götz
, F. D.
Salla
, and A.
Görling
, J. Chem. Phys.
127
, 054102
(2007
).50.
H.
Bachau
, E.
Cormier
, P.
Decleva
, J. E.
Hansen
, and F.
Martin
, Rep. Prog. Phys.
64
, 1815
(2001
).51.
M.
Hellgren
and U.
von Barth
, J. Chem. Phys.
131
, 044110
(2009
).52.
C. J.
Umrigar
and X.
Gonze
, Phys. Rev. A
50
, 3827
(1994
).53.
S. J. A.
van Gisbergen
, P. R.T.
Schipper
, O. V.
Gritsenko
, E. J.
Baerends
, J. G.
Snijders
, B.
Champagne
, and B.
Kirtman
, Phys. Rev. Lett.
83
, 694
(1999
).© 2012 American Institute of Physics.
2012
American Institute of Physics
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