We assess a variant of linear-response range-separated time-dependent density-functional theory (TDDFT), combining a long-range Hartree-Fock (HF) exchange kernel with a short-range adiabatic exchange-correlation kernel in the local-density approximation (LDA) for calculating isotropic C6 dispersion coefficients of homodimers of a number of closed-shell atoms and small molecules. This range-separated TDDFT tends to give underestimated C6 coefficients of small molecules with a mean absolute percentage error of about 5%, a slight improvement over standard TDDFT in the adiabatic LDA which tends to overestimate them with a mean absolute percentage error of 8%, but close to time-dependent Hartree-Fock which has a mean absolute percentage error of about 6%. These results thus show that introduction of long-range HF exchange in TDDFT has a small but beneficial impact on the values of C6 coefficients. It also confirms that the present variant of range-separated TDDFT is a reasonably accurate method even using only a LDA-type density functional and without adding an explicit treatment of long-range correlation.
REFERENCES
1.
F.
London
, Z. Phys.
63
, 245
(1930
).2.
H. B. G.
Casimir
and D.
Polder
, Phys. Rev.
73
, 360
(1948
).3.
H. C.
Longuet-Higgins
, Discuss. Faraday Soc.
40
, 7
(1965
).4.
S. J. A.
van Gisbergen
, J. G.
Snijders
, and E. J.
Baerends
, J. Chem. Phys.
103
, 9347
(1995
).5.
M. A. L.
Marques
, A.
Castro
, G.
Malloci
, G.
Mulas
, and S.
Botti
, J. Chem. Phys.
127
, 014107
(2007
).6.
A.
Banerjee
, A.
Chakrabarti
, and T. K.
Ghanty
, J. Chem. Phys.
127
, 134103
(2007
).7.
A.
Banerjee
, J.
Autschbach
, and A.
Chakrabarti
, Phys. Rev. A
78
, 032704
(2008
).8.
V. P.
Osinga
, S. J. A.
van Gisbergen
, J. G.
Snijders
, and E. J.
Baerends
, J. Chem. Phys.
106
, 5091
(1997
).9.
M. J. T.
Oliveira
, S.
Botti
, and M. A. L.
Marques
, Phys. Chem. Chem. Phys.
13
, 15055
(2011
).10.
P.
Norman
, A.
Jiemchooroj
, and B. E.
Sernelius
, J. Chem. Phys.
118
, 9167
(2003
).11.
A.
Jiemchooroj
, P.
Norman
, and B. E.
Sernelius
, J. Chem. Phys.
123
, 124312
(2005
).12.
A.
Jiemchooroj
, P.
Norman
, and B. E.
Sernelius
, J. Chem. Phys.
125
, 124306
(2006
).13.
D.
Sulzer
, P.
Norman
, and T.
Saue
, Mol. Phys.
110
, 2535
(2012
).14.
J.
Kauczor
, P.
Norman
, and W. A.
Saidi
, J. Chem. Phys.
138
, 114107
(2013
).15.
X.
Chu
and A.
Dalgarno
, J. Chem. Phys.
121
, 4083
(2004
).16.
S.
Hirata
, J. Chem. Phys.
123
, 026101
(2005
).17.
Y.
Shigeta
, K.
Hirao
, and S.
Hirata
, Phys. Rev. A
73
, 010502
(2006
).18.
M.
Hellgren
and U.
von Barth
, Phys. Rev. B
78
, 115107
(2008
).19.
M.
Hellgren
and U.
von Barth
, J. Chem. Phys.
132
, 044101
(2010
).20.
T.
Gould
, J. Chem. Phys.
137
, 111101
(2012
).21.
A.
Heßelmann
and G.
Jansen
, Chem. Phys. Lett.
367
, 778
(2003
).22.
A. J.
Misquitta
, B.
Jeziorski
, and K.
Szalewicz
, Phys. Rev. Lett.
91
, 033201
(2003
).23.
Y.
Tawada
, T.
Tsuneda
, S.
Yanagisawa
, T.
Yanai
, and K.
Hirao
, J. Chem. Phys.
120
, 8425
(2004
).24.
H.
Iikura
, T.
Tsuneda
, T.
Yanai
, and K.
Hirao
, J. Chem. Phys.
115
, 3540
(2001
).25.
M.
Kamiya
, H.
Sekino
, T.
Tsuneda
, and K.
Hirao
, J. Chem. Phys.
122
, 234111
(2005
).26.
H.
Sekino
, Y.
Maeda
, and M.
Kamiya
, Mol. Phys.
103
, 2183
(2005
).27.
H.
Sekino
, Y.
Maeda
, M.
Kamiya
, and K.
Hirao
, J. Chem. Phys.
126
, 014107
(2007
).28.
D.
Jacquemin
, E. A.
Perpète
, G.
Scalmani
, M. J.
Frisch
, R.
Kobayashi
, and C.
Adamo
, J. Chem. Phys.
126
, 144105
(2007
).29.
D.
Jacquemin
, E. A.
Perpète
, I.
Ciofini
, and C.
Adamo
, J. Comput. Chem.
29
, 921
(2008
).30.
B.
Kirtman
, S.
Bonness
, A.
Ramirez-Solis
, B.
Champagne
, H.
Matsumoto
, and H.
Sekino
, J. Chem. Phys.
128
, 114108
(2008
).31.
J.-W.
Song
, M. A.
Watson
, H.
Sekino
, and K.
Hirao
, J. Chem. Phys.
129
, 024117
(2008
).32.
E.
Livshits
and R.
Baer
, Phys. Chem. Chem. Phys.
9
, 2932
(2007
).33.
T.
Yanai
, D. P.
Tew
, and N. C.
Handy
, Chem. Phys. Lett.
393
, 51
(2004
).34.
J.-W.
Song
, S.
Tokura
, T.
Sato
, M. A.
Watson
, and K.
Hirao
, J. Chem. Phys.
127
, 154109
(2007
).35.
J.-D.
Chai
and M.
Head-Gordon
, J. Chem. Phys.
128
, 084106
(2008
).36.
A. W.
Lange
, M. A.
Rohrdanz
, and J. M.
Hubert
, J. Phys. Chem. B
112
, 6304
(2008
).37.
M. A.
Rohrdanz
and J. M.
Herbert
, J. Chem. Phys.
129
, 034107
(2008
).38.
Y.
Akinaga
and S.
Ten-no
, Chem. Phys. Lett.
462
, 348
(2008
).39.
J.-W.
Song
, M. A.
Watson
, A.
Nakata
, and K.
Hirao
, J. Chem. Phys.
129
, 184113
(2008
).40.
M. A.
Rohrdanz
, K. M.
Martins
, and J. M.
Herbert
, J. Chem. Phys.
130
, 054112
(2009
).41.
Y.
Akinaga
and S.
Ten-no
, Int. J. Quantum Chem.
109
, 1905
(2009
).42.
J.-W.
Song
, M. A.
Watson
, and K.
Hirao
, J. Chem. Phys.
131
, 144108
(2009
).43.
R.
Peverati
and D. G.
Truhlar
, J. Phys. Chem. Lett.
2
, 2810
(2011
).44.
K. A.
Nguyen
, P. N.
Day
, and R.
Pachter
, J. Chem. Phys.
135
, 074109
(2011
).45.
Y.-S.
Lin
, C.-W.
Tsai
, G.-D.
Li
, and J.-D.
Chai
, J. Chem. Phys.
136
, 154109
(2012
).46.
E.
Rebolini
, A.
Savin
, and J.
Toulouse
, “Electronic excitations from a linear-response range-separated hybrid scheme
” (unpublished).47.
J. G.
Ángyán
, I. C.
Gerber
, A.
Savin
, and J.
Toulouse
, Phys. Rev. A
72
, 012510
(2005
).48.
J.
Toulouse
, F.
Colonna
, and A.
Savin
, Phys. Rev. A
70
, 062505
(2004
).49.
J.
Toulouse
, F.
Colonna
, and A.
Savin
, J. Chem. Phys.
122
, 014110
(2005
).50.
J.
Toulouse
, F.
Colonna
, and A.
Savin
, Mol. Phys.
103
, 2725
(2005
).51.
K.
Pernal
, J. Chem. Phys.
136
, 184105
(2012
).52.
E.
Fromager
, S.
Knecht
, and H. J. A.
Jensen
, J. Chem. Phys.
138
, 084101
(2013
).53.
J. N.
Byrd
, R.
Côté
, and J. A.
Montgomery
Jr., J. Chem. Phys.
135
, 244307
(2011
).54.
A. D.
Dwyer
, Ph.D. dissertation, Durham University
, Durham, 2011
.55.
M. E.
Casida
, in Recent Advances in Density Functional Methods, Part I
, edited by D. P.
Chong
(World Scientific
, Singapore
, 1995
), p. 155
.56.
A.
Derevianko
, S. G.
Porsev
, and J. F.
Babb
, At. Data Nucl. Data Tables
96
, 323
(2010
).57.
W.
Thomas
, Naturwiss.
13
, 627
(1925
).58.
W.
Kuhn
, Z. Phys.
33
, 408
(1925
).59.
F.
Reiche
and W.
Thomas
, Z. Phys.
34
, 510
(1925
).60.
F.
Furche
, J. Chem. Phys.
114
, 5982
(2001
).61.
D. J.
Thouless
, Nucl. Phys.
22
, 78
(1961
).62.
A. D.
McLachlan
and M. A.
Ball
, Rev. Mod. Phys.
36
, 844
(1964
).63.
R. A.
Harris
, J. Chem. Phys.
50
, 3947
(1969
).64.
C.
Jamorski
, M. E.
Casida
, and D. R.
Salahub
, J. Chem. Phys.
104
, 5134
(1996
).65.
H.-J.
Werner
, P. J.
Knowles
, G.
Knizia
, F. R.
Manby
, M.
Schütz
et al., MOLPRO, version 2012.1, a package of ab initio programs, 2012
, see http://www.molpro.net.66.
J. C.
Slater
, Phys. Rev.
81
, 385
(1951
).67.
J. P.
Perdew
and Y.
Wang
, Phys. Rev. B
45
, 13244
(1992
).68.
S.
Paziani
, S.
Moroni
, P.
Gori-Giorgi
, and G. B.
Bachelet
, Phys. Rev. B
73
, 155111
(2006
).69.
J.
Toulouse
, W.
Zhu
, J. G.
Ángyán
, and A.
Savin
, Phys. Rev. A
82
, 032502
(2010
).70.
J.
Toulouse
, W.
Zhu
, A.
Savin
, G.
Jansen
, and J. G.
Ángyán
, J. Chem. Phys.
135
, 084119
(2011
).71.
D.
Woon
and T.
Dunning
, J. Chem. Phys.
100
, 2975
(1994
).72.
D.
Woon
and T.
Dunning
, J. Chem. Phys.
103
, 4572
(1995
).73.
K. A.
Peterson
and T. H.
Dunning
Jr., J. Chem. Phys.
117
, 10548
(2002
).74.
N. J.
DeYonker
, K. A.
Peterson
, and A. K.
Wilson
, J. Phys. Chem. A
111
, 11383
(2007
).75.
B. P.
Prascher
, D. E.
Woon
, K. A.
Peterson
, T. H.
Dunning
Jr., and A. K.
Wilson
, Theor. Chem. Acc.
128
, 69
(2011
).76.
J.
Koput
and K. A.
Peterson
, J. Phys. Chem. A
106
, 9595
(2002
).77.
A.
Tkatchenko
and M.
Scheffler
, Phys. Rev. Lett.
102
, 073005
(2009
).78.
G. D.
Zeiss
and W. J.
Meath
, Mol. Phys.
33
, 1155
(1977
).79.
D. J.
Margoliash
and W. J.
Meath
, J. Chem. Phys.
68
, 1426
(1978
).80.
T. H.
Dunning
, J. Chem. Phys.
90
, 1007
(1989
).81.
R. A.
Kendall
, T. H.
Dunning
, and R. J.
Harrison
, J. Chem. Phys.
96
, 6796
(1992
).82.
D.
Woon
and T.
Dunning
, J. Chem. Phys.
98
, 1358
(1993
).83.
A.
Wilson
, D.
Woon
, K.
Peterson
, and T. H.
Dunning
, J. Chem. Phys.
110
, 7667
(1999
).84.
A. D.
Becke
, J. Chem. Phys.
98
, 5648
(1993
).85.
V.
Barone
and C.
Adamo
, Chem. Phys. Lett.
224
, 432
(1994
).86.
P. J.
Stephens
, F. J.
Devlin
, C. F.
Chabalowski
, and M. J.
Frisch
, J. Phys. Chem.
98
, 11623
(1994
).87.
M. J.
Frisch
, G. W.
Trucks
, H. B.
Schlegel
et al., GAUSSIAN 09, Revision A.1, Gaussian Inc., Wallingford, CT, 2009
.88.
A.
Görling
, H. H.
Heinze
, and M.
Levy
, J. Mol. Struct.: THEOCHEM
501–502
, 271
(2000
).89.
A.
Szabo
and N. S.
Ostlund
, J. Chem. Phys.
67
, 4351
(1977
).90.
E.
Engel
and A. F.
Bonetti
, Int. J. Mod. Phys. B
15
, 1703
(2001
).91.
E.
Engel
, in A Primer in Density Functional Theory
, Lecture Notes in Physics
Vol. 620
, edited by C.
Fiolhais
, F.
Nogueira
, and M. A. L.
Marques
(Springer
, Berlin
, 2003
), pp. 56
–122
.92.
E.
Zaremba
and W.
Kohn
, Phys. Rev. B
13
, 2270
(1976
).93.
Y.
Dmitriev
and G.
Peinel
, Int. J. Quantum Chem.
19
, 763
(1981
).94.
95.
R.
McWeeny
, Methods of Molecular Quantum Mechanics
, 2nd ed. (Academic Press
, London
, 1992
).96.
J. F.
Dobson
, in Topics in Condensed Matter Physics
, edited by M. P.
Das
(Nova Science Publishers
, New York
, 1994
), pp. 121
–142
;e-print arXiv:cond-mat/0311371.
97.
J. F.
Dobson
, K.
McLennan
, A.
Rubio
, J.
Wang
, T.
Gould
, H. M.
Le
, and B. P.
Dinte
, Aust. J. Chem.
54
, 513
(2001
).98.
A. E.
Hansen
and T. D.
Bouman
, Mol. Phys.
37
, 1713
(1979
).99.
R. A.
Harris
, A. E.
Hansen
, and T. D.
Bouman
, J. Chem. Phys.
91
, 5856
(1989
).100.
101.
R.
van Leeuwen
and N. E.
Dahlen
, in “The Electron Liquid Paradigm in Condensed Matter Physics
,” Proceedings of the International School of Physics “Enrico Fermi” Vol. 157
, edited by G. F.
Giuliani
and G.
Vignale
(IOS Press
, Amsterdam
, 2004
).102.
D. J.
Rowe
, Rev. Mod. Phys.
40
, 153
(1968
).103.
T.
Helgaker
, P.
Jørgensen
, and J.
Olsen
, Molecular Electronic-Structure Theory
(Wiley
, Chichester
, 2002
).© 2013 AIP Publishing LLC.
2013
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