An accurate determination of the electron correlation energy is an essential prerequisite for describing the structure, stability, and function in a wide variety of systems. Therefore, the development of efficient approaches for the calculation of the correlation energy (and hence the dispersion energy as well) is essential and such methods can be coupled with many density-functional approximations, local methods for the electron correlation energy, and even interatomic force fields. In this work, we build upon the previously developed many-body dispersion (MBD) framework, which is intimately linked to the random-phase approximation for the correlation energy. We separate the correlation energy into short-range contributions that are modeled by semi-local functionals and long-range contributions that are calculated by mapping the complex all-electron problem onto a set of atomic response functions coupled in the dipole approximation. We propose an effective range-separation of the coupling between the atomic response functions that extends the already broad applicability of the MBD method to non-metallic materials with highly anisotropic responses, such as layered nanostructures. Application to a variety of high-quality benchmark datasets illustrates the accuracy and applicability of the improved MBD approach, which offers the prospect of first-principles modeling of large structurally complex systems with an accurate description of the long-range correlation energy.

1.
K.
Burke
,
J. Chem. Phys.
136
,
150901
(
2012
).
2.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
(
1964
).
3.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
4.
A. J.
Cohen
,
P.
Mori-Sánchez
, and
W.
Yang
,
Science
321
,
792
(
2008
).
5.
J.
Klimeš
and
A.
Michaelides
,
J. Chem. Phys.
137
,
120901
(
2012
).
6.
M.
Dion
,
H.
Rydberg
,
E.
Schröder
,
D. C.
Langreth
, and
B. I.
Lundqvist
,
Phys. Rev. Lett.
92
,
246401
(
2004
).
7.
A. D.
Becke
and
E. R.
Johnson
,
J. Chem. Phys.
127
,
154108
(
2007
).
8.
K. E.
Riley
,
M.
Pitoňák
,
P.
Jurěcka
, and
P.
Hobza
,
Chem. Rev.
110
,
5023
(
2010
).
9.
S.
Grimme
,
J.
Antony
,
S.
Ehrlich
, and
H.
Krieg
,
J. Chem. Phys.
132
,
154104
(
2010
).
10.
A.
Tkatchenko
and
M.
Scheffler
,
Phys. Rev. Lett.
102
,
073005
(
2009
).
11.
R.
Sabatini
,
T.
Gorni
, and
S.
de Gironcoli
,
Phys. Rev. B
87
,
041108
(R) (
2013
).
12.
A.
Ambrosetti
,
D.
Alfè
,
R. A.
DiStasio
 Jr.
, and
A.
Tkachenko
, “
Hard numbers for large molecules: Towards exact energetics for supramolecular systems
,”
J. Phys. Chem. Lett.
(to be published).
13.
A.
Otero-de-la-Roza
and
E. R.
Johnson
,
J. Chem. Phys.
137
,
054103
(
2012
).
14.
N.
Marom
,
R. A.
DiStasio
 Jr.
,
V.
Atalla
,
S.
Levchenko
,
A. M.
Reilly
,
J. R.
Chelikowsky
,
L.
Leiserowitz
, and
A.
Tkatchenko
,
Angew. Chem., Int. Ed.
52
,
6629
(
2013
).
15.
A. M.
Reilly
and
A.
Tkatchenko
,
J. Phys. Chem. Lett.
4
,
1028
(
2013
).
16.
T.
Björkman
,
A.
Gulans
,
A.
Krasheninnikov
, and
R. M.
Nieminen
,
Phys. Rev. Lett.
108
,
235502
(
2012
).
17.
T.
Risthaus
and
S.
Grimme
,
J. Chem. Theory Comput.
9
,
1580
(
2013
).
18.
R. A.
DiStasio
 Jr.
,
O. A.
von Lilienfeld
, and
A.
Tkatchenko
,
Proc. Natl. Acad. U.S.A.
109
,
14791
(
2012
).
19.
A.
Tkatchenko
,
R. A.
DiStasio
 Jr.
,
R.
Car
, and
M.
Scheffler
,
Phys. Rev. Lett.
108
,
236402
(
2012
).
20.
X.
Ren
,
P.
Rinke
,
V.
Blum
,
J.
Wieferink
,
A.
Tkatchenko
,
A.
Sanfilippo
,
K.
Reuter
, and
M.
Scheffler
,
New J. Phys.
14
,
053020
(
2012
).
21.
H.
Eshuis
,
J. E.
Bates
, and
F.
Furche
,
Theor. Chem. Acc.
131
,
1084
(
2012
).
22.
J. F.
Dobson
and
T.
Gould
,
J. Phys.: Condens. Matter
24
,
073201
(
2012
).
23.
D.
Lu
,
H.-V.
Nguyen
, and
G.
Galli
,
J. Chem. Phys.
133
,
154110
(
2010
).
24.
B. M.
Axilrod
and
E.
Teller
,
J. Chem. Phys.
11
,
299
(
1943
).
25.
A.
Otero-de-la-Roza
and
E. R.
Johnson
,
J. Chem. Phys.
138
,
054103
(
2013
).
26.
P. L.
Silvestrelli
,
J. Chem. Phys.
139
,
054106
(
2013
).
27.
A.
Tkatchenko
,
A.
Ambrosetti
, and
R. A.
DiStasio
 Jr.
,
J. Chem. Phys.
138
,
074106
(
2013
).
28.
A.
Tkatchenko
,
D.
Alfè
, and
K. S.
Kim
,
J. Chem. Theory Comput.
8
,
4317
(
2012
).
29.
Y.
Andersson
,
D. C.
Langreth
, and
B. I.
Lundqvist
,
Phys. Rev. Lett.
76
,
102
(
1996
).
30.
H.-V.
Nguyen
and
S.
de Gironcoli
,
Phys. Rev. B
79
,
205114
(
2009
).
31.
X.
Ren
,
A.
Tkatchenko
,
P.
Rinke
, and
M.
Scheffler
,
Phys. Rev. Lett.
106
,
153003
(
2011
).
32.
J.
Paier
,
B. G.
Janesko
,
T. M.
Henderson
,
G. E.
Scuseria
,
A.
Grüneis
, and
G.
Kresse
,
J. Chem. Phys.
132
,
094103
(
2010
).
33.
J.
Toulouse
,
F.
Colonna
, and
A.
Savin
,
Phys. Rev. A
70
,
062505
(
2004
).
34.
J.
Toulouse
,
W.
Zhu
,
J. G.
Ángyán
, and
A.
Savin
,
Phys. Rev. A
82
,
032502
(
2010
).
35.
S. L.
Adler
,
Phys. Rev.
126
,
413
(
1962
).
36.
N.
Wiser
,
Phys. Rev.
129
,
62
(
1963
).
37.
A. P.
Jones
,
J.
Crain
,
V. P.
Sokhan
,
T. W.
Whitfield
, and
G. J.
Martyna
,
Phys. Rev. B
87
,
144103
(
2013
).
38.
P. L.
Silvestrelli
,
Phys. Rev. Lett.
100
,
053002
(
2008
).
39.
O. A.
Vydrov
and
T.
Van Voorhis
,
J. Chem. Phys.
133
,
244103
(
2010
).
40.
X.
Chu
and
A.
Dalgarno
,
J. Chem. Phys.
121
,
4083
(
2004
).
41.
Q.
Wu
and
W.
Yang
,
J. Chem. Phys.
116
,
515
(
2002
).
42.
S.
Grimme
,
J. Comput. Chem.
27
,
1787
(
2006
).
43.
V. V.
Gobre
and
A.
Tkatchenko
,
Nat. Commun.
4
,
2341
(
2013
).
44.
T.
Bučko
,
S.
Lebègue
,
J.
Hafner
, and
J. G.
Ángyán
,
Phys. Rev. B
87
,
064110
(
2013
).
45.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
46.
C.
Adamo
and
V.
Barone
,
J. Chem. Phys.
110
,
6158
(
1999
).
47.
P.
Jurěcka
,
J.
Šponer
,
J.
Černý
, and
P.
Hobza
,
Phys. Chem. Chem. Phys.
8
,
1985
(
2006
).
48.
J.
Řezáč
,
K. E.
Riley
, and
P.
Hobza
,
J. Chem. Theory Comput.
7
,
2427
(
2011
).
49.
S.
Grimme
,
Chem. Eur. J.
18
,
9955
(
2012
).
50.
A. M.
Reilly
and
A.
Tkatchenko
,
J. Chem. Phys.
139
,
024705
(
2013
).
51.
V.
Blum
,
R.
Gehrke
,
F.
Hanke
,
P.
Havu
,
V.
Havu
,
X.
Ren
,
K.
Reuter
, and
M.
Scheffler
,
Comput. Phys. Commun.
180
,
2175
(
2009
).
52.
A.
Tkatchenko
and
O. A.
von Lilienfeld
,
Phys. Rev. B
78
,
045116
(
2008
).
53.
O. A.
Vydrov
and
T.
Van Voorhis
,
Phys. Rev. A
81
,
062708
(
2010
).
54.
D.
Bermejo
,
S.
Montero
,
M.
Cardona
, and
A.
Muramatsu
,
Solid State Commun.
42
,
153
(
1982
).
55.
G.-X.
Zhang
,
A.
Tkatchenko
,
J.
Paier
,
H.
Appel
, and
M.
Scheffler
,
Phys. Rev. Lett.
107
,
245501
(
2011
).
56.
B.
Schatschneider
,
J.-J.
Liang
,
A. M.
Reilly
,
N.
Marom
,
G.-X.
Zhang
, and
A.
Tkatchenko
,
Phys. Rev. B
87
,
060104
(R) (
2013
).
57.
L.
Goerigk
,
H.
Kruse
, and
S.
Grimme
,
ChemPhysChem
12
,
3421
(
2011
).
58.
K.
Lee
,
E. D.
Murray
,
L.
Kong
,
B. I.
Lundqvist
, and
D. C.
Langreth
,
Phys. Rev. B
82
,
081101
(R) (
2010
).
59.
J.
Heyd
,
G. E.
Scuseria
, and
M.
Ernzerhof
,
J. Chem. Phys.
118
,
8207
(
2003
).
60.
A.
Otero-de-la-Roza
and
E. R.
Johnson
,
J. Chem. Phys.
136
,
174109
(
2012
).
61.
D. D. L.
Chung
,
J. Mater. Sci.
37
,
1475
(
2002
).
62.
R.
Zacharia
,
H.
Ulbricht
, and
T.
Hertel
,
Phys. Rev. B
69
,
155406
(
2004
).
63.
S.
Lebègue
,
J.
Harl
,
T.
Gould
,
J. G.
Ángyán
,
G.
Kresse
, and
J. F.
Dobson
,
Phys. Rev. Lett.
105
,
196401
(
2010
).
64.
P.
Agrawal
,
A.
Tkatchenko
, and
L.
Kronik
,
J. Chem. Theory Comput.
9
,
3473
(
2013
).
65.
W. L.
Bade
,
J. Chem. Phys.
27
,
1280
(
1957
).
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