We have previously proposed that further improved functionals for density functional theory can be constructed based on the Armiento-Mattsson subsystem functional scheme if, in addition to the uniform electron gas and surface models used in the Armiento-Mattsson 2005 functional, a model for the strongly confined electron gas is also added. However, of central importance for this scheme is an index that identifies regions in space where the correction provided by the confined electron gas should be applied. The electron localization function (ELF) is a well-known indicator of strongly localized electrons. We use a model of a confined electron gas based on the harmonic oscillator to show that regions with high ELF directly coincide with regions where common exchange energy functionals have large errors. This suggests that the harmonic oscillator model together with an index based on the ELF provides the crucial ingredients for future improved semi-local functionals. For a practical illustration of how the proposed scheme is intended to work for a physical system we discuss monoclinic cupric oxide, CuO. A thorough discussion of this system leads us to promote the cell geometry of CuO as a useful benchmark for future semi-local functionals. Very high ELF values are found in a shell around the O ions, and take its maximum value along the Cu–O directions. An estimate of the exchange functional error from the effect of electron confinement in these regions suggests a magnitude and sign that could account for the error in cell geometry.

1.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
(
1964
).
2.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
3.
A. E.
Mattsson
and
W.
Kohn
,
J. Chem. Phys.
115
,
3441
(
2001
).
4.
A. E.
Mattsson
and
D. R.
Jennison
,
Surf. Sci. Lett.
520
,
L611
(
2002
).
5.
K.
Carling
,
G.
Wahnström
,
T. R.
Mattsson
,
A. E.
Mattsson
,
N.
Sandberg
, and
G.
Grimvall
,
Phys. Rev. Lett.
85
,
3862
(
2000
).
6.
T. R.
Mattsson
and
A. E.
Mattsson
,
Phys. Rev. B
66
,
214110
(
2002
).
7.
R.
Armiento
and
A. E.
Mattsson
,
Phys. Rev. B
72
,
085108
(
2005
).
8.
A. E.
Mattsson
and
R.
Armiento
,
Phys. Rev. B
79
,
155101
(
2009
).
9.
J. P.
Perdew
and
Y.
Wang
,
Phys. Rev. B
33
,
8800
(
1986
).
10.
W.
Kohn
and
A. E.
Mattsson
,
Phys. Rev. Lett.
81
,
3487
(
1998
).
11.
Z.
Yan
,
J. P.
Perdew
, and
S.
Kurth
,
Phys. Rev. B
61
,
16430
(
2000
).
12.
A. E.
Mattsson
,
R.
Armiento
, and
T. R.
Mattsson
,
Phys. Rev. Lett.
101
,
239701
(
2008
).
13.
A. E.
Mattsson
,
R.
Armiento
,
J.
Paier
,
G.
Kresse
,
J. M.
Wills
, and
T. R.
Mattsson
,
J. Chem. Phys.
128
,
084714
(
2008
).
14.
F.
Tran
,
R.
Laskowski
,
P.
Blaha
, and
K.
Schwarz
,
Phys. Rev. B
75
,
115131
(
2007
).
15.
R. P.
Muller
,
A. E.
Mattsson
, and
C. L.
Janssen
,
J. Comp. Chem.
31
,
1860
(
2010
).
16.
A. E.
Mattsson
and
R.
Armiento
,
Int. J. Quantum Chem.
110
,
2274
(
2010
).
17.
R.
Armiento
and
A. E.
Mattsson
,
Phys. Rev. B
66
,
165117
(
2002
).
18.
F.
Hao
,
R.
Armiento
, and
A. E.
Mattsson
,
Phys. Rev. B
82
,
115103
(
2010
).
19.
P.
Garcia-Gonzalez
,
Phys. Rev. B
62
,
2321
(
2000
).
20.
P.
Garcia-Gonzalez
and
R. W.
Godby
,
Phys. Rev. Lett.
88
,
056406
(
2002
).
21.
L. A.
Constantin
,
J. P.
Perdew
, and
J. M.
Pitarke
,
Phys. Rev. Lett.
101
,
016406
(
2008
).
22.
Y. H.
Kim
,
I. H.
Lee
,
S.
Nagaraja
,
J. P.
Leburton
,
R. Q.
Hood
, and
R. M.
Martin
,
Phys. Rev. B
61
,
5202
(
2000
).
23.
L.
Pollack
and
J. P.
Perdew
,
J. Phys.: Condens. Matter
12
,
1239
(
2000
).
24.
25.
J. P.
Perdew
and
A.
Zunger
,
Phys. Rev. B
23
,
5048
(
1981
).
26.
R. O.
Jones
and
O.
Gunnarsson
,
Rev. Mod. Phys.
61
,
689
(
1989
).
27.
M.
Städele
,
M.
Moukara
,
J. A.
Majewski
,
P.
Vogl
, and
A.
Görling
,
Phys. Rev. B
59
,
10031
(
1999
).
28.
A. D.
Becke
,
J. Chem. Phys.
98
,
5648
(
1993
).
29.
J.
Heyd
,
G. E.
Scuseria
, and
M.
Ernzerhof
,
J. Chem. Phys.
124
,
219906
(
2006
).
31.
O. V.
Gritsenko
,
R.
van Leeuwen
,
E.
van Lenthe
, and
E. J.
Baerends
,
Phys. Rev. A
51
,
1944
(
1995
).
32.
A. D.
Becke
and
E. R.
Johnson
,
J. Chem. Phys.
124
,
221101
(
2006
).
33.
N.
Umezawa
,
Phys. Rev. A
74
,
032505
(
2006
).
34.
R.
Armiento
,
S.
Kümmel
, and
T.
Körzdörfer
,
Phys. Rev. B
77
,
165106
(
2008
).
35.
E.
Rasanen
,
S.
Pittalis
, and
C. R.
Proetto
,
J. Chem. Phys.
132
,
044112
(
2010
).
36.
F.
Tran
and
P.
Blaha
,
Phys. Rev. Lett.
102
,
226401
(
2009
).
37.
V. I.
Anisimov
,
F.
Aryasetiawan
, and
A. I.
Lichtenstein
,
J. Phys.: Condens. Matter
9
,
767
(
1997
).
38.
A.
Filippetti
and
V.
Fiorentini
,
Phys. Rev. Lett.
95
,
086405
(
2005
).
39.
D.
Wu
,
Q.
Zhang
, and
M.
Tao
,
Phys. Rev. B
73
,
235206
(
2006
).
40.
S. H.
Vosko
,
L.
Wilk
, and
M.
Nusair
,
Can. J. Phys.
58
,
1200
(
1980
).
41.
E.
Engel
and
R. N.
Schmid
,
Phys. Rev. Lett.
103
,
036404
(
2009
).
42.
A. D.
Becke
and
K. E.
Edgecombe
,
J. Chem. Phys.
92
,
5397
(
1990
).
43.
E.
Sim
,
J.
Larkin
,
K.
Burke
, and
C. W.
Bock
,
J. Chem. Phys.
118
,
8140
(
2003
).
44.
A.
Savin
,
O.
Jepsen
,
J.
Flad
,
O. K.
Andersen
,
H.
Preuss
, and
H. G.
von Schnering
,
Angew. Chem. Int. Ed. Engl.
31
,
187
(
1992
).
45.
B.
Silvi
and
A.
Savin
,
Nature (London)
371
,
683
(
1994
).
46.
A.
Savin
,
A. D.
Becke
,
J.
Flad
,
R.
Nesper
,
H.
Preuss
, and
H. G.
von Schnering
,
Angew. Chem. Int. Ed. Engl.
30
,
409
(
1991
).
47.
M.
Nekovee
,
W. M. C.
Foulkes
, and
R. J.
Needs
,
Phys. Rev. Lett.
87
,
036401
(
2001
).
48.
M.
Nekovee
,
W. M. C.
Foulkes
, and
R. J.
Needs
,
Phys. Rev. B
68
,
235108
(
2003
).
49.
S. J.
Clark
and
P. P.
Rushton
,
J. Phys.: Condens. Matter
16
,
4833
(
2004
).
50.
A. C.
Cancio
and
M. Y.
Chou
,
Phys. Rev. B
74
,
081202
(
2006
).
51.
W. Y.
Ching
,
Y.-N.
Xu
, and
K. W.
Wong
,
Phys. Rev. B
40
,
7684
(
1989
).
52.
K.
Terakura
,
T.
Oguchi
,
A. R.
Williams
, and
J.
Kübler
,
Phys. Rev. B
30
,
4734
(
1984
).
53.
T. C.
Leung
,
C. T.
Chan
, and
B. N.
Harmon
,
Phys. Rev. B
44
,
2923
(
1991
).
54.
P.
Dufek
,
P.
Blaha
,
V.
Sliwko
, and
K.
Schwarz
,
Phys. Rev. B
49
,
10170
(
1994
).
55.
S.
Åsbrink
and
L.-J.
Norrby
,
Acta Crystallogr. Sec. B
26
,
8
(
1970
).
56.
G.
Kresse
and
J.
Hafner
,
Phys. Rev. B
47
,
558
(
1993
).
57.
G.
Kresse
and
J.
Hafner
,
Phys. Rev. B
49
,
14251
(
1994
).
58.
G.
Kresse
and
J.
Furthmüller
,
Phys. Rev. B
54
,
11169
(
1996
).
59.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
60.
H. J.
Monkhorst
and
J. D.
Pack
,
Phys. Rev. B
13
,
5188
(
1976
).
You do not currently have access to this content.