The augmented potential introduced by Levy and Zahariev [Phys. Rev. Lett. 113, 113002 (2014)] is shifted with respect to the standard exchange-correlation potential of the Kohn-Sham density functional theory by a density-dependent constant that makes the total energy become equal to the sum of the occupied orbital energies. In this work, we analyze several features of this approach, focusing on the limit of infinite coupling strength and studying the shift and the corresponding energy density at different correlation regimes. We present and discuss coordinate scaling properties of the augmented potential, study its connection to the response potential, and use the shift to analyze the classical jellium and uniform gas models. We also study other definitions of the energy densities in relation to the functional construction by local interpolations along the adiabatic connection. Our findings indicate that the energy density that is defined in terms of the electrostatic potential of the exchange-correlation hole is particularly well suited for this purpose.

1.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
2.
F.
Colonna
and
A.
Savin
,
J. Chem. Phys.
110
,
2828
(
1999
).
3.
A. M.
Teale
,
S.
Coriani
, and
T.
Helgaker
,
J. Chem. Phys.
130
,
104111
(
2009
).
4.
K.
Burke
,
J. Chem. Phys.
136
,
150901
(
2012
).
5.
A. D.
Becke
,
J. Chem. Phys.
140
,
18A301
(
2014
).
6.
Y.
Zhao
and
D. G.
Truhlar
,
Acc. Chem. Res.
41
,
157
(
2008
).
7.
J.
Sun
,
R. C.
Remsing
,
Y.
Zhang
,
Z.
Sun
,
A.
Ruzsinszky
,
H.
Peng
,
Z.
Yang
,
A.
Paul
,
U.
Waghmare
,
X.
Wu
,
M. L.
Klein
, and
J.
Perdew
,
Nat. Chem.
8
,
831
(
2016
).
8.
J.
Erhard
,
P.
Bleiziffer
, and
A.
Görling
,
Phys. Rev. Lett.
117
,
143002
(
2016
).
9.
S.
Vuckovic
,
T. J.
Irons
,
A.
Savin
,
A. M.
Teale
, and
P.
Gori-Giorgi
,
J. Chem. Theory Comput.
12
,
2598
(
2016
).
10.
Y.
Zhou
,
H.
Bahmann
, and
M.
Ernzerhof
,
J. Chem. Phys.
143
,
124103
(
2015
).
11.
H.
Bahmann
,
Y.
Zhou
, and
M.
Ernzerhof
,
J. Chem. Phys.
145
,
124104
(
2016
).
12.
S.
Vuckovic
,
T. J. P.
Irons
,
L. O.
Wagner
,
A. M.
Teale
, and
P.
Gori-Giorgi
,
Phys. Chem. Chem. Phys.
19
,
6169
(
2017
).
13.
S.
Vuckovic
and
P.
Gori-Giorgi
,
J. Phys. Chem. Lett.
8
,
2799
(
2017
).
14.
M.
Ernzerhof
,
Chem. Phys. Lett.
263
,
499
(
1996
).
15.
M.
Seidl
,
J. P.
Perdew
, and
M.
Levy
,
Phys. Rev. A
59
,
51
(
1999
).
16.
P.
Mori-Sánchez
,
A. J.
Cohen
, and
W.
Yang
,
J. Chem. Phys.
125
,
201102
(
2006
).
17.
A. M.
Teale
,
S.
Coriani
, and
T.
Helgaker
,
J. Chem. Phys.
132
,
164115
(
2010
).
18.
M.
Levy
and
F.
Zahariev
,
Phys. Rev. Lett.
113
,
113002
(
2014
).
19.
M.
Levy
and
F.
Zahariev
,
Mol. Phys.
114
,
1162
(
2016
).
20.
F.
Zahariev
and
M.
Levy
,
Phys. Chem. A
121
,
342
(
2017
).
21.
R.
van Leeuwen
and
E. J.
Baerends
,
Phys. Rev. A
51
,
170
(
1995
).
22.
A. P.
Gaiduk
,
S. K.
Chulkov
, and
V. N.
Staroverov
,
J. Chem. Theory Comput.
5
,
699
(
2009
).
23.
A. P.
Gaiduk
and
V. N.
Staroverov
,
J. Chem. Phys.
133
,
101104
(
2010
).
24.
P. D.
Elkind
and
V. N.
Staroverov
,
J. Chem. Phys.
136
,
124115
(
2012
).
25.
J. P.
Perdew
,
R. G.
Parr
,
M.
Levy
, and
J. L.
Balduz
,
Phys. Rev. Lett.
49
,
1691
(
1982
).
26.
W.
Yang
,
Y.
Zhang
, and
P. W.
Ayers
,
Phys. Rev. Lett.
84
,
5172
(
2000
).
27.
S.
Vuckovic
,
L.
Wagner
,
A.
Mirtschink
, and
P.
Gori-Giorgi
,
J. Chem. Theory Comput.
11
,
3153
(
2015
).
28.
M.
Levy
and
J. P.
Perdew
,
Phys. Rev. A
32
,
2010
(
1985
).
29.
M.
Seidl
,
Phys. Rev. A
60
,
4387
(
1999
).
30.
X.
Andrade
and
A.
Aspuru-Guzik
,
Phys. Rev. Lett.
107
,
183002
(
2011
).
31.
N. I.
Gidopoulos
and
N. N.
Lathiotakis
,
J. Chem. Phys.
136
,
224109
(
2012
).
32.
M.
Levy
,
Proc. Natl. Acad. Sci. U. S. A.
76
,
6062
(
1979
).
33.
D. C.
Langreth
and
J. P.
Perdew
,
Solid State Commun.
17
,
1425
(
1975
).
34.
O.
Gunnarsson
and
B. I.
Lundqvist
,
Phys. Rev. B
13
,
4274
(
1976
).
35.
A. D.
Becke
,
J. Chem. Phys.
122
,
064101
(
2005
).
36.
A. D.
Becke
and
E. R.
Johnson
,
J. Chem. Phys.
127
,
124108
(
2007
).
37.
J. P.
Perdew
,
V. N.
Staroverov
,
J.
Tao
, and
G. E.
Scuseria
,
Phys. Rev. A
78
,
052513
(
2008
).
38.
A.
Mirtschink
,
M.
Seidl
, and
P.
Gori-Giorgi
,
J. Chem. Theory Comput.
8
,
3097
(
2012
).
39.
K.
Burke
,
F. G.
Cruz
, and
K.-C.
Lam
,
J. Chem. Phys.
109
,
8161
(
1998
).
40.
F. G.
Cruz
,
K.-C.
Lam
, and
K.
Burke
,
J. Phys. Chem. A
102
,
4911
(
1998
).
41.
R.
van Leeuwen
,
O.
Gritsenko
, and
E. J.
Baerends
,
Z. Phys. D: At., Mol. Clusters
33
,
229
(
1995
).
42.
O. V.
Gritsenko
and
E. J.
Baerends
,
Phys. Rev. A
54
,
1957
(
1996
).
43.
O.
Gritsenko
,
Ł.
Mentel
, and
E.
Baerends
,
J. Chem. Phys.
144
,
204114
(
2016
).
44.
S. V.
Kohut
,
A. M.
Polgar
, and
V. N.
Staroverov
,
Phys. Chem. Chem. Phys.
18
,
20938
(
2016
).
45.
M.
Seidl
,
P.
Gori-Giorgi
, and
A.
Savin
,
Phys. Rev. A
75
,
042511
(
2007
).
46.
P.
Gori-Giorgi
,
M.
Seidl
, and
G.
Vignale
,
Phys. Rev. Lett.
103
,
166402
(
2009
).
47.
M.
Seidl
,
S.
Vuckovic
, and
P.
Gori-Giorgi
,
Mol. Phys.
114
,
1076
(
2016
).
48.
M.
Seidl
,
S.
Di Marino
,
A.
Gerolin
,
L.
Nenna
,
K. J.
Giesbertz
, and
P.
Gori-Giorgi
, preprint arXiv:1702.05022 (
2017
).
49.
M.
Colombo
and
S.
Di Marino
,
Annali di Matematica Pura ad Applicata
(
Springer
,
Berlin, Heidelberg
,
2013
), pp.
1
14
.
50.
F.
Malet
and
P.
Gori-Giorgi
,
Phys. Rev. Lett.
109
,
246402
(
2012
).
51.
G.
Buttazzo
,
L.
De Pascale
, and
P.
Gori-Giorgi
,
Phys. Rev. A
85
,
062502
(
2012
).
52.
F.
Malet
,
A.
Mirtschink
,
J. C.
Cremon
,
S. M.
Reimann
, and
P.
Gori-Giorgi
,
Phys. Rev. B
87
,
115146
(
2013
).
53.
C. B.
Mendl
,
F.
Malet
, and
P.
Gori-Giorgi
,
Phys. Rev. B
89
,
125106
(
2014
).
54.
P.
Gori-Giorgi
,
G.
Vignale
, and
M.
Seidl
,
J. Chem. Theory Comput.
5
,
743
(
2009
).
55.
M.
Levy
and
J. P.
Perdew
,
Phys. Rev. B
48
,
11638
(
1993
).
56.
P.
Gori-Giorgi
and
M.
Seidl
,
Phys. Chem. Chem. Phys.
12
,
14405
(
2010
).
57.
C. J.
Umrigar
and
X.
Gonze
,
Phys. Rev. A
50
,
3827
(
1994
).
58.
C.
Filippi
,
C.
Umrigar
, and
X.
Gonze
,
Phys. Rev. A
54
,
4810
(
1996
).
59.
M.
Lewin
and
E. H.
Lieb
,
Phys. Rev. A
91
,
022507
(
2015
).
60.
E. H.
Lieb
,
Phys. Lett. A
70
,
444
(
1979
).
61.
E. H.
Lieb
and
S.
Oxford
,
Int. J. Quantum Chem.
19
,
427
(
1981
).
62.
E.
Räsänen
,
M.
Seidl
, and
P.
Gori-Giorgi
,
Phys. Rev. B
83
,
195111
(
2011
).
63.
M.
Lewin
,
E. H.
Lieb
, and
R.
Seiringer
, e-print arXiv:1705.10676.
64.
H.
Ou-Yang
and
M.
Levy
,
Phys. Rev. Lett.
65
,
1036
(
1990
).
65.
M.
Levy
,
Density Functional Theory
(
Springer
,
1995
), pp.
11
31
.
66.
E.
Engel
and
S. H.
Vosko
,
Phys. Rev. B
47
,
13164
(
1993
).
67.
M.
Seidl
,
J. P.
Perdew
, and
S.
Kurth
,
Phys. Rev. Lett.
84
,
5070
(
2000
).
68.
A.
Görling
,
Phys. Rev. Lett.
83
,
5459
(
1999
).
69.
P. W.
Ayers
and
M.
Levy
,
J. Chem. Phys.
115
,
4438
(
2001
).
70.
N. H.
March
,
Phys. Rev. A
65
,
034501
(
2002
).
71.
S. V.
Kohut
and
V. N.
Staroverov
,
J. Chem. Phys.
139
,
164117
(
2013
).
72.
S.
De Gironcoli
, private communication (2017).
73.
F. G.
Eich
, private communication (2017).
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