Following some recent ideas on the construction of kinetic energy density functionals that reproduce the linear response function of the homogeneous electron gas, a family of them with a nonlocal term based on the von Weizsäcker functional and with a dependence on the logarithm of the density is presented. As localized systems are the most difficult to study with explicit kinetic functionals, in this paper we apply to atomic systems a number of families of fully nonlocal kinetic functionals. We have put our attention in both the total kinetic energy and the local behavior of the kinetic energy density, and the results clearly show the quality of these fully nonlocal functionals. They make a good description of the local behavior of the kinetic energy density and maintain good results for the total kinetic energies. We must remark that almost all the functionals discussed in the paper, when using an adequate reference density, can be evaluated as a single integral in momentum space, with a quasilinear scaling for the computational cost.

1.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
(
1964
).
2.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
3.
J.
Lindhard
,
Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd.
28
, No.
8
(
1954
).
4.
S.
Liu
and
P. W.
Ayers
,
Phys. Rev. A
70
,
022501
(
2004
).
5.
D.
García-Aldea
and
J. E.
Alvarellos
,
Phys. Rev. A
77
,
022502
(
2008
).
6.
C. F. V.
Weizsacker
,
Z. Phys.
96
,
431
(
1935
).
7.
E. S.
Kryachko
and
E. V.
Ludeña
,
Energy Density Functional Theory of Many-Electron Systems
(
Kluwer
,
London
,
1990
).
8.
M.
Levy
,
J. P.
Perdew
, and
V.
Sahni
,
Phys. Rev. A
30
,
2745
(
1984
).
9.
E.
Chacón
,
J. E.
Alvarellos
, and
P.
Tarazona
,
Phys. Rev. B
32
,
7868
(
1985
).
10.
P.
García-González
,
J. E.
Alvarellos
, and
E.
Chacón
,
Phys. Rev. B
53
,
9509
(
1996
).
11.
P.
García-González
,
J. E.
Alvarellos
, and
E.
Chacón
,
Phys. Rev. A
54
,
1897
(
1996
b).
12.
N. H.
March
,
Phys. Lett.
113A
,
66
(
1985
).
13.
A.
Holas
and
N. H.
March
,
Phys. Rev. A
44
,
5521
(
1991
).
14.
D.
García-Aldea
and
J. E.
Alvarellos
,
Phys. Rev. A
76
,
052504
(
2007
).
15.
L. H.
Thomas
,
Proc. Cambridge Philos. Soc.
23
,
542
(
1927
).
16.
E.
Fermi
,
Rend. Accad. Naz. Lincei
6
,
602
(
1927
).
17.
L. W.
Wang
and
M. P.
Teter
,
Phys. Rev. B
45
,
13196
(
1992
).
18.
E.
Smargiassi
and
P. A.
Madden
,
Phys. Rev. B
49
,
5220
(
1994
).
19.
Y. A.
Wang
,
N.
Govind
, and
E. A.
Carter
,
Phys. Rev. B
58
,
13465
(
1998
).
20.
P.
García-González
,
J. E.
Alvarellos
, and
E.
Chacón
,
Phys. Rev. B
57
,
4857
(
1998
).
21.
P.
García-González
,
J. E.
Alvarellos
, and
E.
Chacón
,
Phys. Rev. A
57
,
4192
(
1998
).
22.
Y. A.
Wang
,
N.
Govind
, and
E. A.
Carter
,
Phys. Rev. B
60
,
16350
(
1999
).
23.
Y. A.
Wang
and
E. A.
Carter
, in
Theoretical Methods in Condensed Phase Chemistry
,
Progress in Theoretical Chemistry and Physics
, edited by
S. D.
Schwartz
(
Kluwer
,
Dordrecht
,
2000
), pp.
117
184
.
24.
B.
Zhou
,
V. L.
Ligneres
, and
E. A.
Carter
,
J. Chem. Phys.
122
,
044103
(
2005
).
25.
J. A.
Alonso
and
L. A.
Girifalco
,
Solid State Commun.
24
,
135
(
1977
).
26.
J. A.
Alonso
and
L. A.
Girifalco
,
Phys. Rev. B
17
,
3735
(
1978
).
27.
O.
Gunnarsson
,
M.
Jonson
, and
B. I.
Lundqvist
,
Phys. Rev. B
20
,
3136
(
1979
).
28.
P.
García-González
,
J. E.
Alvarellos
, and
E.
Chacón
,
Phys. Rev. A
62
,
014501
(
2000
).
29.
A.
Nagy
and
N. H.
March
,
Mol. Phys.
90
,
271
(
1997
).
30.
A.
Nagy
and
S.
Liu
,
Phys. Lett. A
372
,
1654
(
2008
).
31.
D.
García-Aldea
and
J. E.
Alvarellos
,
J. Chem. Phys.
127
,
144109
(
2007
).
32.
A. M.
Navarrete-López
,
J.
Garza
, and
R.
Vargas
,
J. Chem. Phys.
128
,
104110
(
2008
).
33.
S.
Liu
,
J. Chem. Phys.
126
,
191107
(
2007
).
34.
R. G.
Parr
and
W.
Yang
,
Density Functional Theory of Atoms and Molecules
(
Oxford University Press
,
New York
,
1989
).
35.
W.
Yang
,
R. G.
Parr
, and
C.
Lee
,
Phys. Rev. A
34
,
4586
(
1986
).
36.
M. J.
Frisch
,
G. W.
Trucks
,
H. B.
Schlegel
 et al, GAUSSIAN 98, Revision A.6, Gaussian, Inc., Pittsburgh, PA,
1998
.
37.
P. W.
Atkins
,
Molecular Quantum Mechanics
, 3rd ed. (
Oxford University Press
,
Oxford
,
1997
).
38.
E.
Clementi
and
D. L.
Raimondi
,
J. Chem. Phys.
38
,
2686
(
1963
).
39.
J. P.
Perdew
and
L. A.
Constantin
,
Phys. Rev. B
75
,
155109
(
2007
).
40.
A. D.
Bochevarov
and
R. A.
Friesnerb
,
J. Chem. Phys.
128
,
034102
(
2008
).
41.
Z. -Z.
Yang
,
S.
Liu
, and
Y. A.
Wang
,
Chem. Phys. Lett.
258
,
30
(
1996
).
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