Seven methods, including three van der Waals density functionals (vdW-DFs) and four different variants of the Tkatchenko-Scheffler (TS) methods, are tested on the A24, L7, and Taylor et al.’s “blind” test sets. It is found that for these systems, the vdW-DFs perform better that the TS methods. In particular, the vdW-DF-cx functional gives binding energies that are the closest to the reference values, while the many-body correction of TS does not always lead to an improvement in the description of molecular systems. In light of these results, several directions for further improvements to describe van der Waals interactions are discussed.

1.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
(
1964
).
2.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
3.
S.
Grimme
,
J. Comput. Chem.
25
,
1463
(
2004
).
4.
S.
Grimme
,
J. Comput. Chem.
27
,
1787
(
2006
).
5.
S.
Grimme
,
J.
Antony
,
S.
Ehrlich
, and
H.
Krieg
,
J. Chem. Phys.
132
,
154104
(
2010
).
6.
A.
Tkatchenko
and
M.
Scheffler
,
Phys. Rev. Lett.
102
,
073005
(
2009
).
7.
A.
Tkatchenko
,
R. A.
Di Stasio
,
R.
Car
, and
M.
Scheffler
,
Phys. Rev. Lett.
108
,
236402
(
2012
).
8.
W. J.
Kim
,
M.
Kim
,
E. K.
Lee
,
S.
Lebègue
, and
H.
Kim
,
J. Phys. Chem. Lett.
7
,
3278
(
2016
).
9.
M.
Kim
,
W. J.
Kim
,
E. K.
Lee
,
S.
Lebègue
, and
H.
Kim
,
Int. J. Quantum Chem.
116
,
598
(
2016
).
10.
M.
Dion
,
H.
Rydberg
,
E.
Schroder
,
D. C.
Langreth
, and
B. I.
Lundqvist
,
Phys. Rev. Lett.
92
,
246401
(
2004
).
11.
O. A.
Vydrov
and
T. R.
Voorhis
,
J. Chem. Phys.
133
,
244103
(
2010
).
12.
K.
Berland
and
P.
Hyldgaard
,
Phys. Rev. B
89
,
035412
(
2014
).
13.
D. C.
Langreth
and
J. P.
Perdew
,
Phys. Rev. B
15
,
2884
(
1977
).
14.
D.
Langreth
and
J.
Perdew
,
Solid State Commun.
17
,
1425
(
1975
).
15.
F.
Furche
,
Phys. Rev. B
64
,
195120
(
2001
).
16.
A.
Dixit
,
J. G.
Ángyán
, and
D.
Rocca
,
J. Chem. Phys.
145
,
104105
(
2016
).
17.
A.
Dixit
,
J.
Claudot
,
S.
Lebègue
, and
D.
Rocca
,
J. Chem. Theory Comput.
13
,
5432
(
2017
).
18.
C.
Møller
and
M. S.
Plesset
,
Phys. Rev.
46
,
618
(
1934
).
19.
R. J.
Bartlett
and
M.
Musiał
,
Rev. Mod. Phys.
79
,
291
(
2007
).
20.
B.
Jeziorski
,
R.
Moszynski
, and
K.
Szalewicz
,
Chem. Rev.
94
,
1887
(
1994
).
21.
A. J.
Misquitta
,
B.
Jeziorski
, and
K.
Szalewicz
,
Phys. Rev. Lett.
91
,
033201
(
2003
).
22.
A.
Heßelmann
and
G.
Jansen
,
Chem. Phys. Lett.
367
,
778
(
2003
).
23.
O.
Gunnarsson
and
B. I.
Lundqvist
,
Phys. Rev. B
13
,
4274
(
1976
).
24.
W. A.
Al-Saidi
,
V. K.
Voora
, and
K. D.
Jordan
,
J. Chem. Theory Comput.
8
,
1503
(
2012
).
25.
J.
Kilmeš
,
D.
Bowler
, and
A.
Michaelides
,
J. Phys.: Condens. Matter
22
,
022201
(
2010
).
26.
A.
Otero-de-la Roza
and
E. R.
Johnson
,
J. Chem. Phys.
137
,
054103
(
2012
).
27.
J.
Hermann
,
R. A.
DiStasio
, and
A.
Tkatchenko
,
Chem. Rev.
117
,
4714
(
2017
).
28.
K.
Berland
,
V. R.
Cooper
,
K.
Lee
,
E.
Schroder
,
T.
Thonhauser
,
P.
Hyldgaard
, and
B. I.
Lundqvist
,
Rep. Prog. Phys.
78
,
066501
(
2015
).
29.
J.
Řezáč
and
P.
Hobza
,
J. Chem. Theory Comput.
9
,
2151
(
2013
).
30.
R.
Sedlak
,
T.
Janowski
,
M.
Pitoňák
,
J.
Řezáč
,
P.
Pulay
, and
P.
Hobza
,
J. Chem. Theory Comput.
9
,
3364
(
2013
).
31.
D. E.
Taylor
,
J. G.
Ángyán
,
G.
Galli
,
C.
Zhang
,
F.
Gygi
,
K.
Hirao
,
J. W.
Song
,
K.
Rahul
,
O.
Anatole Von Lilienfeld
,
R.
Podeswa
,
I. W.
Bulik
,
T. M.
Henderson
,
G. E.
Scuseria
,
J.
Toulouse
,
R.
Peverati
,
D. G.
Truhlar
, and
K.
Szalewicz
,
J. Chem. Phys.
145
,
124105
(
2016
).
32.
A.
Tkatchenko
,
A.
Ambrosetti
, and
R. A.
DiStasio
, Jr.
,
J. Chem. Phys.
138
,
074106
(
2013
).
33.
A.
Ambrosetti
,
A. M.
Reilly
,
R. A.
DiStasio
, Jr.
, and
T.
Tkatchenko
,
J. Chem. Phys.
140
,
18A508
(
2014
).
34.
T.
Gould
,
S.
Lebègue
,
J. G.
Ángyán
, and
T.
Bučko
,
J. Chem. Theory Comput.
12
,
5920
(
2016
).
35.
J. F.
Dobson
,
Int. J. Quantum Chem.
114
,
1157
(
2014
).
36.
J. R.
Reimers
,
M.
Li
,
D.
Wan
,
T.
Gould
, and
M. J.
Ford
,
Non-Covalent Interactions in Quantum Chemistry and Physics
(
Elsevier
,
2017
), pp.
387
416
.
37.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
38.
H.
Rydberg
,
M.
Dion
,
N.
Jacobson
,
E.
Schroder
,
P.
Hyldgaard
,
S. I.
Simak
,
D. C.
Langreth
, and
B. I.
Lundqvist
,
Phys. Rev. Lett.
91
,
126402
(
2003
).
39.
A.
Puzder
,
M.
Dion
, and
D. C.
Langreth
,
J. Chem. Phys.
124
,
164105
(
2006
).
40.
K.
Lee
,
E. D.
Murray
,
L.
Kong
,
B. I.
Lundqvist
, and
D. C.
Langreth
,
Phys. Rev. B
82
,
081101
(
2010
).
41.
J. P.
Perdew
and
Y.
Wang
,
Phys. Rev. B
33
,
8800(R)
(
1986
).
42.
I.
Hamada
,
Phys. Rev. B
89
,
121103
(
2014
).
43.
A. D.
Becke
,
J. Chem. Phys.
85
,
7184
(
1986
).
44.
D. C.
Langreth
and
S.
Vosko
,
Adv. Quantum Chem.
21
,
175
(
1990
).
45.
K.
Berland
,
C. A.
Arter
,
V. R.
Cooper
,
K.
Lee
,
B. I.
Lundqvist
,
E.
Schroder
,
T.
Thonhauser
, and
P.
Hyldgaard
,
J. Chem. Phys.
140
,
18A539
(
2014
).
46.
A. D.
Becke
and
E. R.
Johnson
,
J. Chem. Phys.
127
,
154108
(
2007
).
47.
E. R.
Johnson
and
A. D.
Becke
,
J. Chem. Phys.
124
,
174104
(
2006
).
48.
S.
Grimme
,
S.
Ehrlich
, and
L.
Goerigk
,
J. Comput. Chem.
32
,
1456
(
2011
).
49.
N.
Marom
,
A.
Tkatchenko
,
M.
Scheffler
, and
L.
Kronik
,
J. Chem. Theory Comput.
6
,
81
(
2010
).
50.
H. B. G.
Casimir
and
D.
Polder
,
Phys. Rev.
73
,
360
(
1948
).
51.
R. A.
DiStasio
, Jr.
,
O. A.
von Lilienfeld
, and
T.
Tkatchenko
,
Proc. Natl. Acad. Sci. U. S. A.
109
,
14791
(
2012
).
52.
T.
Gould
and
T.
Bučko
,
J. Chem. Theory Comput.
12
,
3603
(
2016
).
53.

Note that in the original manuscript the square bracket was misplaced. The expression used here is correct.

54.
G.
Kresse
and
J.
Hafner
,
Phys. Rev. B
48
,
13115
(
1993
).
55.
G.
Kresse
and
J.
Furthmüller
,
Phys. Rev. B
54
,
11169
(
1996
).
56.
J.
Klimeš
,
D. R.
Bowler
, and
A.
Michaelides
,
Phys. Rev. B
83
,
195131
(
2011
).
57.
G.
Román-Pérez
and
J. M.
Soler
,
Phys. Rev. Lett.
103
,
096102
(
2009
).
58.
T.
Björkman
,
J. Chem. Phys
141
,
074708
(
2014
).
59.
T.
Bucko
,
S.
Lebègue
,
J.
Hafner
, and
J. G.
Ángyán
,
Phys. Rev. B
87
,
064110
(
2013
).
60.
T.
Bučko
,
S.
Lebègue
,
T.
Gould
, and
J. G.
Ángyán
,
J. Phys.: Condens. Matter
28
,
045201
(
2016
).
61.
P. E.
Blöchl
,
Phys. Rev. B
50
,
17953
(
1994
).
62.
G.
Kresse
and
J.
Joubert
,
Phys. Rev. B
59
,
1758
(
1999
).
63.
F.
Gygi
,
IBM J. Res. Dev.
52
,
137
144
(
2008
).
64.
P.
Jurečka
,
J.
Cerný
,
P.
Hobza
, and
D. R.
Salahub
,
J. Comput. Chem.
28
,
555
(
2007
).
65.
S.
Lebègue
,
J.
Harl
,
T.
Gould
,
J. G.
Ángyán
,
G.
Kresse
, and
J. F.
Dobson
,
Phys. Rev. Lett.
105
,
196401
(
2010
).
66.
T.
Björkman
,
A.
Gulans
,
A. V.
Krasheninnikov
, and
R. M.
Nieminen
,
Phys. Rev. Lett.
108
,
235502
(
2012
).
67.
S. A.
Tawfik
,
T.
Gould
,
C.
Stamp
, and
M. J.
Ford
, preprint arXiv:1712.08327 (
2017
).
68.
S.
Grimme
,
A.
Hansen
,
J. G.
Brandenburg
, and
C.
Bannwarth
,
Chem. Rev.
116
,
5105
(
2016
).
69.
E. M.
Lifshitz
,
J. Exp. Theor. Phys. USSR
29
,
94
(
1954
).
70.
T.
Bučko
,
J.
Hafner
,
S.
Lebègue
, and
J. G.
Ángyán
,
J. Phys. Chem. A
114
,
11814
(
2010
).
71.
J. F.
Dobson
and
T.
Gould
,
J. Phys.: Condens. Matter
24
,
073201
(
2012
).
72.
J. F.
Dobson
,
T.
Gould
, and
G.
Vignale
,
Phys. Rev. X
4
,
021040
(
2014
).
73.
N.
Marom
,
A.
Tkatchenko
,
M.
Rossi
,
V. V.
Gobre
,
O.
Hod
,
M.
Scheffler
, and
L.
Kronik
,
J. Chem. Theory Comput.
7
,
3944
(
2011
).
74.
M.
Fuchs
and
X.
Gonze
,
Phys. Rev. B
65
,
235109
(
2002
).
You do not currently have access to this content.