We consider a general class of hybrid density functionals with decomposition of the exchange component into short-range and long-range parts. The admixture of Hartree-Fock (HF) exchange is controlled by three parameters: short-range mixing, long-range mixing, and range separation. We study how the variation of these parameters affects the accuracy of hybrid functionals for thermochemistry and kinetics. For the density functional component of the hybrids, we test three nonempirical approximations: local spin-density approximation, generalized gradient approximation (GGA), and meta-GGA. We find a great degree of flexibility in choosing the mixing parameters in range-separated hybrids. For the studied properties, short-range and long-range HF exchange seem to have a similar effect on the errors. One may choose to treat the long-range portion of the exchange by HF to recover the correct asymptotic behavior of the exchange potential and improve the description of density tail regions. If this asymptote is not important, as in solids, one may use screened hybrids, where long-range HF exchange is excluded. Screened hybrids retain most of the benefits of global hybrids but significantly reduce the computational cost in extended systems.

1.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
2.
A. D.
Becke
,
J. Chem. Phys.
98
,
1372
(
1993
).
3.
A. D.
Becke
,
J. Chem. Phys.
98
,
5648
(
1993
).
4.
A. D.
Becke
,
J. Chem. Phys.
104
,
1040
(
1996
).
5.
J. P.
Perdew
,
M.
Ernzerhof
, and
K.
Burke
,
J. Chem. Phys.
105
,
9982
(
1996
).
6.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
);
[PubMed]
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
78
,
1396
(
1997
).
7.
M.
Ernzerhof
and
G. E.
Scuseria
,
J. Chem. Phys.
110
,
5029
(
1999
).
8.
C.
Adamo
and
V.
Barone
,
J. Chem. Phys.
110
,
6158
(
1999
).
9.
J.
Tao
,
J. P.
Perdew
,
V. N.
Staroverov
, and
G. E.
Scuseria
,
Phys. Rev. Lett.
91
,
146401
(
2003
).
10.
V. N.
Staroverov
,
G. E.
Scuseria
,
J.
Tao
, and
J. P.
Perdew
,
J. Chem. Phys.
119
,
12129
(
2003
);
V. N.
Staroverov
,
G. E.
Scuseria
,
J.
Tao
, and
J. P.
Perdew
,
J. Chem. Phys.
121
,
11507
(
2004
).
11.
J. P.
Perdew
,
A.
Ruzsinszky
,
J.
Tao
,
V. N.
Staroverov
,
G. E.
Scuseria
, and
G. I.
Csonka
,
J. Chem. Phys.
123
,
062201
(
2005
).
12.
A. D.
Boese
and
J. M. L.
Martin
,
J. Chem. Phys.
121
,
3405
(
2004
).
13.
Y.
Zhao
,
B. J.
Lynch
, and
D. G.
Truhlar
,
J. Phys. Chem. A
108
,
2715
(
2004
).
14.
J.
Jaramillo
,
G. E.
Scuseria
, and
M.
Ernzerhof
,
J. Chem. Phys.
118
,
1068
(
2003
).
15.
A.
Savin
, in
Recent Developments and Applications of Modern Density Functional Theory
, edited by
J. M.
Seminario
(
Elsevier
,
Amsterdam
,
1996
), pp.
327
357
.
16.
J.
Toulouse
,
F.
Colonna
, and
A.
Savin
,
Phys. Rev. A
70
,
062505
(
2004
).
17.
J.
Heyd
,
G. E.
Scuseria
, and
M.
Ernzerhof
,
J. Chem. Phys.
118
,
8207
(
2003
);
J.
Heyd
,
G. E.
Scuseria
, and
M.
Ernzerhof
,
J. Chem. Phys.
124
,
219906
(
2006
).
18.
J.
Heyd
and
G. E.
Scuseria
,
J. Chem. Phys.
120
,
7274
(
2004
).
19.
J.
Heyd
and
G. E.
Scuseria
,
J. Chem. Phys.
121
,
1187
(
2004
).
20.

In Refs. 17–19, two errors were made in interpreting the value of the parameter ω. In the HF part of the code, the value of ω2 was inadvertently used instead of ω. In the DFT part, ω was multiplied by 213 by mistake. Thus, instead of the reported ω=0.15, the value of 0.106 was used in the HF part, and 0.189 was used in the DFT part. These mistakes are corrected in the present work.

21.
J.
Heyd
,
J. E.
Peralta
,
G. E.
Scuseria
, and
R. L.
Martin
,
J. Chem. Phys.
123
,
174101
(
2005
).
22.
J.
Paier
,
M.
Marsman
,
K.
Hummer
,
G.
Kresse
,
I. C.
Gerber
, and
J. G.
Ángyán
,
J. Chem. Phys.
124
,
154709
(
2006
).
23.
A. V.
Krukau
and
G. E.
Scuseria
(unpublished).
24.
H.
Iikura
,
T.
Tsuneda
,
T.
Yanai
, and
K.
Hirao
,
J. Chem. Phys.
115
,
3540
(
2001
).
25.
Y.
Tawada
,
T.
Tsuneda
,
S.
Yanagisawa
,
T.
Yanai
, and
K.
Hirao
,
J. Chem. Phys.
120
,
8425
(
2004
).
26.
I. C.
Gerber
and
J. G.
Ángyán
,
Chem. Phys. Lett.
415
,
100
(
2005
).
27.
H.
Sekino
,
Y.
Maeda
, and
M.
Kamiya
,
Mol. Phys.
103
,
2183
(
2005
).
28.
M.
Kamiya
,
H.
Sekino
,
T.
Tsuneda
, and
K.
Hirao
,
J. Chem. Phys.
122
,
234111
(
2005
).
29.
M.
Kamiya
,
T.
Tsuneda
, and
K.
Hirao
,
J. Chem. Phys.
117
,
6010
(
2002
).
30.
T.
Sato
,
T.
Tsuneda
, and
K.
Hirao
,
Mol. Phys.
103
,
1151
(
2005
).
31.
T.
Sato
,
T.
Tsuneda
, and
K.
Hirao
,
J. Chem. Phys.
123
,
104307
(
2005
).
32.
J. G.
Ángyán
,
I. C.
Gerber
,
A.
Savin
, and
J.
Toulouse
,
Phys. Rev. A
72
,
012510
(
2005
).
33.
I. C.
Gerber
and
J. G.
Ángyán
,
Chem. Phys. Lett.
416
,
370
(
2005
).
34.
E.
Goll
,
H.-J.
Werner
, and
H.
Stoll
,
Phys. Chem. Chem. Phys.
7
,
3917
(
2005
).
35.
T.
Yanai
,
D. P.
Tew
, and
N. C.
Handy
,
Chem. Phys. Lett.
393
,
51
(
2004
).
36.
M. J. G.
Peach
,
T.
Helgaker
,
P.
Sałek
,
T. W.
Keal
,
O. B.
Lutnæs
,
D. J.
Tozer
, and
N. C.
Handy
,
Phys. Chem. Chem. Phys.
8
,
558
(
2006
).
37.
T.
Leininger
,
H.
Stoll
,
H.-J.
Werner
, and
A.
Savin
,
Chem. Phys. Lett.
275
,
151
(
1997
).
38.
R.
Pollet
,
A.
Savin
,
T.
Leininger
, and
H.
Stoll
,
J. Chem. Phys.
116
,
1250
(
2002
).
39.
J.
Toulouse
,
F.
Colonna
, and
A.
Savin
,
J. Chem. Phys.
122
,
014110
(
2005
).
40.
P. M. W.
Gill
and
R. D.
Adamson
,
Chem. Phys. Lett.
261
,
105
(
1996
).
41.
P. M. W.
Gill
,
R. D.
Adamson
, and
J. A.
Pople
,
Mol. Phys.
88
,
1005
(
1996
).
42.
M.
Ernzerhof
and
J. P.
Perdew
,
J. Chem. Phys.
109
,
3313
(
1998
).
43.
L. A.
Constantin
,
J. P.
Perdew
, and
J.
Tao
,
Phys. Rev. B
73
,
205104
(
2006
).
44.
O. A.
Vydrov
and
G. E.
Scuseria
(unpublished).
45.
J. P.
Perdew
and
Y.
Wang
,
Phys. Rev. B
45
,
13244
(
1992
).
46.
M. J.
Frisch
,
G. W.
Trucks
,
H. B.
Schlegel
 et al, GAUSSIAN Development Version, Revision D.02, Gaussian, Wallingford, CT,
2004
.
47.
L. A.
Curtiss
,
K.
Raghavachari
,
P. C.
Redfern
, and
J. A.
Pople
,
J. Chem. Phys.
106
,
1063
(
1997
).
48.
Y.
Zhang
and
W.
Yang
,
J. Chem. Phys.
109
,
2604
(
1998
).
49.
Y.
Zhao
,
N.
González-García
, and
D. G.
Truhlar
,
J. Phys. Chem. A
109
,
2012
(
2005
);
[PubMed]
Y.
Zhao
,
N.
González-García
, and
D. G.
Truhlar
,
J. Phys. Chem. A
110
,
4942
(
2006
).
50.
B. J.
Lynch
,
Y.
Zhao
, and
D. G.
Truhlar
, http://comp.chem.umn.edu/database
51.
L. A.
Curtiss
,
P. C.
Redfern
,
K.
Raghavachari
, and
J. A.
Pople
,
J. Chem. Phys.
109
,
42
(
1998
).
52.
N.
Rösch
and
S. B.
Trickey
,
J. Chem. Phys.
106
,
8940
(
1997
).
53.

In Ref. 18, we observed that the HSE functional is somewhat less accurate in predicting IPs and EAs than PBE or PBEh functionals. However, this behavior seems to be entirely attributed to the errors described in Ref. 20.

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