We present a physically motivated correlation functional belonging to the meta-generalized gradient approximation (meta-GGA) rung, which can be supplemented with long-range dispersion corrections without introducing double-counting of correlation contributions. The functional is derived by the method of constraint satisfaction, starting from an analytical expression for a real-space spin-resolved correlation hole. The model contains a position-dependent function that controls the range of the interelectronic correlations described by the semilocal functional. With minimal empiricism, this function may be adjusted so that the correlation model blends with a specific dispersion correction describing long-range contributions. For a preliminary assessment, our functional has been combined with an atom-pairwise dispersion correction and full Hartree-Fock (HF)-like exchange. Despite the HF-exchange approximation, its predictions compare favorably with reference interaction energies in an extensive set of non-covalently bound dimers.
REFERENCES
1.
J.
Dobson
, in Fundamentals of Time-Dependent Density Functional Theory
, Lecture Notes in Physics
, Vol. 837
, edited by M. A.
Marques
, N. T.
Maitra
, F. M.
Nogueira
, E.
Gross
, and A.
Rubio
(Springer
, Berlin/Heidelberg
, 2012
), p. 417
.2.
J. F.
Dobson
, J.
Wang
, B. P.
Dinte
, K.
McLennan
, and H. M.
Le
, Int. J. Quantum Chem.
101
, 579
(2005
).3.
A. J.
Cohen
, P.
Mori-Sánchez
, and W.
Yang
, Chem. Rev.
112
, 289
(2012
).4.
J.
Dobson
and T.
Gould
, J. Phys.: Condens. Matter
24
, 073201
(2012
).5.
A.
Becke
and E.
Johnson
, J. Chem. Phys.
122
, 154104
(2005
).6.
A.
Becke
and E.
Johnson
, J. Chem. Phys.
123
, 154101
(2005
).7.
A.
Becke
and E.
Johnson
, J. Chem. Phys.
127
, 124108
(2007
).8.
A.
Heßelmann
, J. Chem. Phys.
130
, 084104
(2009
).9.
J.
Ángyán
, J. Chem. Phys.
127
, 024108
(2007
).10.
S.
Grimme
, J.
Antony
, S.
Ehrlich
, and H.
Krieg
, J. Chem. Phys.
132
, 154104
(2010
).11.
A.
Tkatchenko
and M.
Scheffler
, Phys. Rev. Lett.
102
, 073005
(2009
).12.
M.
Dion
, H.
Rydberg
, E.
Schröder
, D.
Langreth
, and B.
Lundqvist
, Phys. Rev. Lett.
92
, 246401
(2004
).13.
K.
Lee
, É.
Murray
, L.
Kong
, B.
Lundqvist
, and D.
Langreth
, Phys. Rev. B
82
, 081101
(2010
).14.
O.
Vydrov
and T.
Van Voorhis
, J. Chem. Phys.
130
, 104105
(2009
).15.
O.
Vydrov
and T.
Van Voorhis
, Phys. Rev. Lett.
103
, 63004
(2009
).16.
O.
Vydrov
and T.
Van Voorhis
, J. Chem. Phys.
133
, 244103
(2010
).17.
O.
Vydrov
, and T.
Voorhis
, in Fundamentals of Time-Dependent Density Functional Theory
, Lecture Notes in Physics
, Vol. 837
, edited by M. A.
Marques
, N. T.
Maitra
, F. M.
Nogueira
, E.
Gross
, and A.
Rubio
(Springer
, Berlin/Heidelberg
, 2012
), pp. 443
–456
.18.
K.
Pernal
, R.
Podeszwa
, K.
Patkowski
, and K.
Szalewicz
, Phys. Rev. Lett.
103
, 263201
(2009
).19.
Ł.
Rajchel
, P.
Żuchowski
, M. M.
Szczęśniak
, and G.
Chałasiński
, Chem. Phys. Lett.
486
, 160
(2010
).20.
M.
Kamiya
, T.
Tsuneda
, and K.
Hirao
, J. Chem. Phys.
117
, 6010
(2002
).21.
E. D.
Murray
, K.
Lee
, and D. C.
Langreth
, J. Chem. Theory Comput.
5
, 2754
(2009
).22.
J.
Perdew
, K.
Burke
, and M.
Ernzerhof
, Phys. Rev. Lett.
77
, 3865
(1996
).23.
A. D.
Becke
, Phys. Rev. A
38
, 3098
(1988
).24.
J. P.
Perdew
and W.
Yue
, Phys. Rev. B
33
, 8800
(1986
).25.
O.
Vydrov
and T.
Van Voorhis
, J. Chem. Phys.
132
, 164113
(2010
).26.
S.
Grimme
and S.
Ehrlich
, J. Comput. Chem.
32
, 1456
(2011
).27.
J.
Dobson
, K.
McLennan
, A.
Rubio
, J.
Wang
, T.
Gould
, H.
Le
, and B.
Dinte
, Aust. J. Chem.
54
, 513
(2002
).28.
A.
Hesselmann
and G.
Jansen
, Chem. Phys. Lett.
367
, 778
(2003
).29.
A.
Misquitta
, R.
Podeszwa
, B.
Jeziorski
, and K.
Szalewicz
, J. Chem. Phys.
123
, 214103
(2005
).30.
31.
R.
Burcl
, G.
Chałasiński
, R.
Bukowski
, and M. M.
Szczęśniak
, J. Chem. Phys.
103
, 1498
(1995
).32.
A.
Koide
, W. J.
Meath
, and A.
Allnatt
, Chem. Phys.
58
, 105
(1981
).33.
L. A.
Burns
, A.
Vazquez-Mayagoitia
, B. G.
Sumpter
, and C. D.
Sherrill
, J. Chem. Phys.
134
, 084107
(2011
).34.
L.
Goerigk
and S.
Grimme
, Phys. Chem. Chem. Phys.
13
, 6670
(2011
).35.
W.
Hujo
and S.
Grimme
, J. Chem. Theory Comput.
7
, 3866
(2011
).36.
A.
Vazquez-Mayagoitia
, C. D.
Sherrill
, E.
Apra
, and B. G.
Sumpter
, J. Chem. Theory Comput.
6
, 727
(2010
).37.
K. S.
Thanthiriwatte
, E. G.
Hohenstein
, L. A.
Burns
, and C. D.
Sherrill
, J. Chem. Theory Comput.
7
, 88
(2011
).38.
S.
Grimme
, J. Comput. Chem.
27
, 1787
(2006
).39.
J.
Chai
and M.
Head-Gordon
, Phys. Chem. Chem. Phys.
10
, 6615
(2008
).40.
J.
Chai
and M.
Head-Gordon
, J. Chem. Phys.
128
, 084106
(2008
).41.
E.
Ruiz
, D.
Salahub
, and A.
Vela
, J. Phys. Chem.
100
, 12265
(1996
).42.
G.
Sini
, J. S.
Sears
, and J.-L.
Bredas
, J. Chem. Theory Comput.
7
, 602
(2011
).43.
R.
Podeszwa
, K.
Pernal
, K.
Patkowski
, and K.
Szalewicz
, J. Phys. Chem. Lett.
1
, 550
(2010
).44.
M.
Swart
, M.
Solà
, and F.
Bickelhaupt
, J. Chem. Phys.
131
, 094103
(2009
).45.
46.
M.
Levy
, Proc. Natl. Acad. Sci. U.S.A.
76
, 6062
(1979
).47.
P.
Hohenberg
and W.
Kohn
, Phys. Rev.
136
, B864
(1964
).48.
W.
Kohn
and L. J.
Sham
, Phys. Rev.
140
, A1133
(1965
).49.
M.
Levy
, in Theoretical and Computational Chemistry
, edited by J.
Seminario
(Elsevier
, 1996
), Vol. 4
.50.
E.
Baerends
and O.
Gritsenko
, J. Phys. Chem. A
101
, 5383
(1997
).51.
K.
Burke
, J.
Perdew
, and M.
Ernzerhof
, J. Chem. Phys.
109
, 3760
(1998
).52.
A.
Sarsa
, F.
Gálvez
, and E.
Buendia
, J. Chem. Phys.
109
, 7075
(1998
).53.
J.
Hollett
, L.
McKemmish
, and P.
Gill
, J. Chem. Phys.
134
, 224103
(2011
).54.
A.
Rajagopal
, J.
Kimball
, and M.
Banerjee
, Phys. Rev. B
18
, 2339
(1978
).55.
56.
C.
Lee
and R.
Parr
, Phys. Rev. A
35
, 2377
(1987
).57.
58.
P.
Gori-Giorgi
and J.
Perdew
, Phys. Rev. B
64
, 155102
(2001
).59.
60.
V.
Rassolov
, J.
Pople
, and M.
Ratner
, Phys. Rev. B
62
, 2232
(2000
).61.
M.
Levy
, Phys. Rev. A
43
, 4637
(1991
).62.
M.
Levy
and J.
Perdew
, Phys. Rev. A
32
, 2010
(1985
).63.
P.
Gori-Giorgi
, F.
Sacchetti
, and G.
Bachelet
, Phys. Rev. B
61
, 7353
(2000
).64.
G.
Ortiz
, M.
Harris
, and P.
Ballone
, Phys. Rev. Lett.
82
, 5317
(1999
).65.
M.
Gell-Mann
and K. A.
Brueckner
, Phys. Rev.
106
, 364
(1957
).66.
P.
Jurecka
, J.
Sponer
, J.
Cerny
, and P.
Hobza
, Phys. Chem. Chem. Phys.
8
, 1985
(2006
).67.
R.
Podeszwa
, K.
Patkowski
, and K.
Szalewicz
, Phys. Chem. Chem. Phys.
12
, 5974
(2010
).68.
Mathematica
, Wolfram Research, Inc.
, Champaign, Illinois
, 7th ed. (2008
).69.
M. W.
Schmidt
, K. K.
Baldridge
, J. A.
Boatz
, S. T.
Elbert
, M. S.
Gordon
, J. H.
Jensen
, S.
Koseki
, N.
Matsunaga
, K. A.
Nguyen
, S.
Su
, T. L.
Windus
, M.
Dupuis
, and J. A.
Montgomery
, J. Comput. Chem.
14
, 1347
(1993
).70.
M. S.
Gordon
, and M. W.
Schmidt
, “Advances in electronic structure theory: GAMESS a decade later
,” in Theory and Applications of Computational Chemistry: The First Forty Years
, edited by C. E.
Dykstra
, G.
Frenking
, K. S.
Kim
, and G. E.
Scuseria
(Elsevier
, Amsterdam
, 2005
), p. 1167
.71.
E. I.
Proynov
and D. R.
Salahub
, Phys. Rev. B
49
, 7874
(1994
).72.
T.
Tsuneda
, T.
Suzumura
, and K.
Hirao
, J. Chem. Phys.
110
, 10664
(1999
).73.
J.
Perdew
, A.
Ruzsinszky
, J.
Tao
, V.
Staroverov
, G.
Scuseria
, and G.
Csonka
, J. Chem. Phys.
123
, 062201
(2005
).74.
M.
Levy
, Int. J. Quantum Chem.
36
, 617
(1989
).75.
J. P.
Perdew
, S.
Kurth
, A.
Zupan
, and P.
Blaha
, Phys. Rev. Lett.
82
, 2544
(1999
).76.
Y.
Zhao
, N.
Schultz
, and D.
Truhlar
, J. Chem. Theory Comput.
2
, 364
(2006
).77.
K.
Burke
, J.
Perdew
, and D.
Langreth
, Phys. Rev. Lett.
73
, 1283
(1994
).78.
T.
Henderson
and R.
Bartlett
, Phys. Rev. A
70
, 22512
(2004
).79.
A. C.
Cancio
, C. Y.
Fong
, and J. S.
Nelson
, Phys. Rev. A
62
, 062507
(2000
).80.
W.
Kohn
, Y.
Meir
, and D. E.
Makarov
, Phys. Rev. Lett.
80
, 4153
(1998
).81.
Y.
Zhao
and D.
Truhlar
, Theor. Chem. Acc.
120
, 215
(2008
).82.
M.
Modrzejewski
, Ł.
Rajchel
, M. M.
Szczęśniak
, and G.
Chałasiński
, J. Chem. Phys.
136
, 204109
(2012
).83.
Y.
Zhao
and D.
Truhlar
, J. Phys. Chem. A
109
, 5656
(2005
).84.
Y.
Zhao
and D.
Truhlar
, J. Chem. Theory Comput.
1
, 415
(2005
).© 2012 American Institute of Physics.
2012
American Institute of Physics
You do not currently have access to this content.