An efficient protocol is presented to compensate for the basis set superposition error (BSSE) in DFT molecular dynamics (MD) simulations using localized Gaussian basis sets. We propose a classical correction term that can be added a posteriori to account for BSSE. It is tested to what extension this term will improve radial distribution functions (RDFs). The proposed term is pairwise between certain atoms in different molecules and was calibrated by fitting reference BSSE data points computed with the counterpoise method. It is verified that the proposed exponential decaying functional form of the model is valid. This work focuses on hydrogen-bonded liquids, i.e., methanol, and more specific on the intermolecular hydrogen bond, but in principle the method is generally applicable on any type of interaction where BSSE is significant. We evaluated the relative importance of the Grimme-dispersion versus BSSE and found that they are of the same order of magnitude, but with an opposite sign. Upon introduction of the correction, the relevant RDFs, obtained from MD, have amplitudes equal to experiment.

1.
M. P.
Allen
and
D. J.
Tildesley
,
Computer Simulation of Liquids
, 1st ed. (
Oxford University Press
,
1991
), Chap. 2.
2.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
(
1964
).
3.
P.
Hohenberg
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
4.
O.
,
M.
Yáñez
, and
J.
Elguero
,
J. Chem. Phys.
107
,
3592
(
1997
).
5.
E.
Tsuchida
,
Y.
Kanada
, and
M.
Tsukada
,
Chem. Phys. Lett.
311
,
236
(
1999
).
7.
J. A. B.
da Silva
,
F. G. B.
Moreira
,
V. M. L.
dos Santos
, and
R. L.
Longo
,
Phys. Chem. Chem. Phys.
13
,
593
(
2011
).
8.
T.
Yamaguchi
,
K.
Hidaka
, and
A.
Soper
,
Mol. Phys.
96
,
1159
(
1999
).
9.
T.
Yamaguchi
,
K.
Hidaka
, and
A.
Soper
,
Mol. Phys.
97
,
603
(
1999
).
10.
T.
Yamaguchi
,
C. J.
Benmore
, and
A. K.
Soper
,
J. Chem. Phys.
112
,
8976
(
2000
).
11.
A. K.
Adya
,
L.
Bianchi
, and
C. J.
Wormald
,
J. Chem. Phys.
112
,
4231
(
2000
).
12.
J.-W.
Handgraaf
,
T. S.
van Erp
, and
E. J.
Meijer
,
Chem. Phys. Lett.
367
,
617
(
2003
).
13.
J.-W.
Handgraaf
,
E. J.
Meijer
, and
M.-P.
Gaigeot
,
J. Chem. Phys.
121
,
10111
(
2004
).
14.
M.
Pagliai
,
G.
Cardini
,
R.
Righini
, and
V.
Schettino
,
J. Chem. Phys.
119
,
6655
(
2003
).
15.
M. J.
McGrath
,
I.-F.
Kuo
, and
J. I.
Siepmann
,
Phys. Chem. Chem. Phys.
13
,
19943
(
2011
).
16.
M. E.
Martín
,
M. L.
Sánchez
,
F. J.
del Valle
, and
M. A.
Aguilar
,
J. Chem. Phys.
116
,
1613
(
2002
).
17.
M. L.
Sánchez
,
M. E.
Martín
,
M. A.
Aguilar
, and
F. J.
del Valle
,
J. Comput. Chem.
21
,
705
(
2000
).
18.
M.
Haughney
,
M.
Ferrario
, and
I. R.
McDonald
,
J. Phys. Chem.
91
,
4934
(
1987
).
19.
L.
Bianchi
,
O. N.
Kalugin
,
A. K.
Adya
, and
C. J.
Wormald
,
Mol. Simulat.
25
,
321
(
2000
).
20.
J. L.
Thomas
,
D. J.
Tobiass
, and
A. D.
MacKerell
,
J. Phys. Chem. B
111
,
12941
(
2007
).
21.
L.
Zoranić
,
F.
Sokolić
, and
A.
Perera
,
J. Chem. Phys.
127
,
024502
(
2007
).
22.
T.
Kosztolányi
,
I.
Bakó
, and
G.
Pálinkás
,
J. Chem. Phys.
118
,
4546
(
2003
).
23.
T.
Ishiyama
,
V. V.
Sokolov
, and
A.
Morita
,
J. Chem. Phys.
134
,
024509
(
2011
).
24.
H.
Yu
,
D. P.
Geerke
,
H.
Liu
, and
W. F. V.
Gunsteren
,
J. Comput. Chem.
27
,
1494
(
2006
).
25.
S.
Patel
and
C. L.
Brooks
,
J. Chem. Phys.
122
,
024508
(
2005
).
26.
H.
Nakano
,
T.
Yamamoto
, and
S.
Kato
,
J. Chem. Phys.
132
,
044106
(
2010
).
27.
J.
Schmidt
,
J.
VandeVondele
,
I.-F. W.
Kuo
,
D.
Sebastiani
,
J. I.
Siepmann
,
J.
Hutter
, and
C. J.
Mundy
,
J. Phys. Chem. B
113
,
11959
(
2009
).
28.
I.-C.
Lin
,
A. P.
Seitsonen
,
M. D.
Coutinho-Neto
,
I.
Tavernelli
, and
U.
Rothlisberger
,
J. Phys. Chem. B
113
,
1127
(
2009
).
29.
J. C.
Grossman
,
E.
Schwegler
,
E. W.
Draeger
,
F.
Gygi
, and
G.
Galli
,
J. Chem. Phys.
120
,
300
(
2004
).
30.
T.
Ishiyama
and
A.
Morita
,
J. Chem. Phys.
131
,
244714
(
2009
).
31.
J.
VandeVondele
,
F.
Mohamed
,
M.
Krack
,
J.
Hutter
,
M.
Sprik
, and
M.
Parrinello
,
J. Chem. Phys.
122
,
014515
(
2005
).
32.
M.
Sprik
,
J.
Hutter
, and
M.
Parrinello
,
J. Chem. Phys.
105
,
1142
(
1996
).
33.
A. D.
Boese
,
N. L.
Doltsinis
,
N. C.
Handy
, and
M.
Sprik
,
J. Chem. Phys.
112
,
1670
(
2000
).
34.
G. S.
Fanourgakis
,
G. K.
Schenter
, and
S. S.
Xantheas
,
J. Chem. Phys.
125
,
141102
(
2006
).
35.
B.
Guillot
and
Y.
Guissani
,
J. Chem. Phys.
108
,
10162
(
1998
).
36.
M. E.
Tuckerman
,
D. M.
Marx
,
M. L.
Klein
, and
M.
Parrinello
,
Science
275
,
817
(
1997
).
37.
E.
Schwegler
,
J. C.
Grossman
,
F.
Gygi
, and
G.
Galli
,
J. Chem. Phys.
121
,
5400
(
2004
).
38.
C.
Swalina
,
Q.
Wang
,
A.
Chakraborty
, and
S.
Hammes-Schiffer
,
J. Phys. Chem. A
111
,
2206
(
2007
).
39.
E. G.
Noya
,
C.
Vega
,
L. M.
Sesé
, and
R.
Ramirez
,
J. Chem. Phys.
131
,
124518
(
2009
).
40.
E.
Balog
,
A. L.
Hughes
, and
G. J.
Martyna
,
J. Chem. Phys.
112
,
870
(
2000
).
41.
J. A.
Morrone
and
R.
Car
,
Phys. Rev. Lett.
101
,
017801
(
2008
).
42.
G. S.
Fanourgakis
and
S. S.
Xantheas
,
J. Chem. Phys.
128
,
074506
(
2008
).
43.
H. A.
Stern
and
B. J.
Berne
,
J. Chem. Phys.
115
,
7622
(
2001
).
44.
R.
Car
and
M.
Parrinello
,
Phys. Rev. Lett.
55
,
24712474
(
1985
).
45.
S.
Grimme
,
J. Comput. Chem.
25
,
1463
(
2004
).
46.
S.
Grimme
,
J. Comput. Chem.
27
,
1787
(
2006
).
47.
S.
Grimme
,
J.
Antony
,
S.
Ehrlich
, and
H.
Krieg
,
J. Chem. Phys.
132
,
154104
(
2010
).
48.
I.-C.
Lin
,
M. D.
Coutinho-Neto
,
C.
Felsenheimer
,
O. A.
von Lilienfeld
,
I.
Tavernelli
, and
U.
Rothlisberger
,
Phys. Rev. B
75
,
205131
(
2007
).
49.
A.
Tkatchenko
and
M.
Scheffler
,
Phys. Rev. Lett.
102
,
073005
(
2009
).
50.
M.
Mantina
,
A. C.
Chamberlin
,
R.
Valero
,
C. J.
Cramer
, and
D. G.
Truhlar
,
J. Phys. Chem. A
113
,
5806
(
2009
).
51.
S.
Simon
,
M.
Duran
, and
J. J.
Dannenberg
,
J. Chem. Phys.
105
,
11024
(
1996
).
52.
K. N.
Kirschner
,
J. B.
Sorensen
, and
J. P.
Bowen
,
J. Chem. Educ.
84
,
1225
(
2007
).
53.
S.
Simon
,
J.
Bertran
, and
M.
Sodupe
,
J. Phys. Chem. A
105
,
4359
(
2001
).
54.
S.
Scheiner
,
Molecular Interactions. From van der Waals to Strongly Bound Complexes
, 1st ed. (
Wiley
,
1997
).
55.
D.
Hadži
,
Theoretical Treatments of Hydrogen Bonding
, 1st ed. (
Wiley
,
1997
).
56.
F. B.
van Duijneveldt
,
J. G. C. M.
van Duijneveldt-van de Rijdt
, and
J. H.
van Lenthe
,
Chem. Rev.
94
,
1873
(
1994
).
57.
A.
Bende
and
S.
Suhai
,
Int. J. Quantum Chem.
103
,
841
(
2005
).
58.
T.
van Mourik
,
J. Phys. Chem. A
112
,
11017
(
2008
).
59.
D.
Tzeli
,
I. D.
Petsalakis
, and
G.
Theodorakopoulos
,
J. Phys. Chem. A
111
,
8892
(
2007
).
60.
A. E.
Shields
and
T.
van Mourik
,
J. Phys. Chem. A
111
,
13272
(
2007
).
61.
L. F.
Holroyd
and
T.
van Mourik
,
Chem. Phys. Lett.
442
,
42
(
2007
).
62.
P.
Hobza
and
Z.
Havlas
,
Theor. Chem. Acc.
99
,
372
(
1998
).
63.
R.
Crespo-Otero
,
L. A.
Montero
,
W.-D.
Stohrer
, and
J. M. D.
la Vega
,
J. Chem. Phys.
123
,
134107
(
2005
).
64.
D.
Tzeli
and
A. A.
Tsekouras
,
Chem. Phys. Lett.
496
,
42
(
2010
).
65.
H.
Kruse
and
S.
Grimme
,
J. Chem. Phys.
136
,
154101
(
2012
).
66.
CP2K, 2011, see http://cp2k.berlios.de.
67.
J.
VandeVondele
,
M.
Krack
,
F.
Mohamed
,
M.
Parrinello
,
T.
Chassaing
, and
J.
Hutter
,
Comput. Phys. Commun.
167
,
103
(
2005
).
68.
A. D.
Becke
,
Phys. Rev. A
38
,
3098
(
1988
).
69.
C.
Lee
,
W.
Yang
, and
R. G.
Parr
,
Phys. Rev. B
37
,
785
(
1988
).
70.
G.
Lippert
,
J.
Hutter
,
P.
Ballone
, and
M.
Parrinello
,
J. Phys. Chem.
100
,
6231
(
1996
).
71.
S.
Goedecker
,
M.
Teter
, and
J.
Hutter
,
Phys. Rev. B
54
,
1703
(
1996
).
72.
C.
Harwigsen
,
S.
Goedecker
, and
J.
Hutter
,
Phys. Rev. B
58
,
3641
(
1998
).
73.
E. J.
Meijer
and
T. S.
van Erp
,
Chem. Phys. Lett.
333
,
290
(
2001
).
74.
P.
Hobza
,
J.
Šponer
, and
T.
Reschel
,
J. Comput. Chem.
16
,
1315
(
1995
).
75.
S.
Kristyán
and
P.
Pulay
,
Chem. Phys. Lett.
229
,
175
(
1994
).
76.
S.
Grimme
,
J.
Antony
,
T.
Schwabe
, and
C.
Mück-Lichtenfeld
,
Org. Biomol. Chem.
5
,
741
(
2007
).
77.
S.
Nosé
,
J. Chem. Phys.
81
,
511
(
1984
).
78.
I.
Mayer
and
P. R.
Surján
,
Int. J. Quantum Chem.
36
,
225
(
1989
).
79.
I.
Mayer
and
Á.
Vibók
,
Int. J. Quantum Chem.
40
,
139
(
1991
).
80.
J.
Noga
and
Á.
Vibók
,
Chem. Phys. Lett.
180
,
114
(
1991
).
81.
P.
Valiron
,
Á.
Vibók
, and
I.
Mayer
,
J. Comput. Chem.
14
,
401
(
1993
).
82.
Á.
Vibók
and
I.
Mayer
,
Int. J. Quantum Chem.
43
,
801
(
1992
).
83.
S. F.
Boys
and
F.
Bernardi
,
Mol. Phys.
19
,
553
(
1970
).
84.
D.
Feller
,
J. Chem. Phys.
98
,
7059
(
1993
).
85.
B.
Paizs
,
P.
Salvador
,
A. G.
Császár
,
M.
Duran
, and
S.
Suhai
,
J. Comput. Chem.
22
,
196
(
2001
).
86.
I.
Alkorta
,
C.
Trujillo
,
J.
Elguero
, and
M.
Solimannejad
,
Comput. Theor. Chem.
967
,
147
(
2011
).
87.
T.
Helgaker
,
W.
Klopper
,
H.
Koch
, and
J.
Noga
,
J. Chem. Phys.
106
,
9639
(
1997
).
88.
S. K.
Min
,
E. C.
Lee
,
H. M.
Lee
,
D. Y.
Kim
,
D.
Kim
, and
K. S.
Kim
,
J. Comput. Chem.
29
,
1208
(
2008
).
89.
T.
Verstraelen
,
M.
Van Houteghem
,
V.
Van Speybroeck
, and
M.
Waroquier
,
J. Chem. Inf. Mod.
48
,
2414
(
2008
).
90.
See http://molmod.ugent.be/software for more information on MD-TRACKS, a trajectory analysis toolkit for MD and Monte Carlo simulations, and other software for preparing and post-processing data from molecular simulations.
91.
L.
Vanduyfhuys
,
T.
Verstraelen
,
M.
Vandichel
,
M.
Waroquier
, and
V.
Van Speybroeck
, “
Ab initio parametrized force field for the flexible metal-organic framework MIL-53(Al)
,”
J. Chem. Theory Comput.
(in press).
92.
K.
Levenberg
,
Quart. Appl. Math.
2
,
164
(
1944
).
93.
D.
Marquardt
,
SIAM J. Appl. Math.
11
,
431
(
1963
).
94.
E.
Artacho
,
E.
Anglada
,
O.
Diéguez
,
J. D.
Gale
,
A.
García
,
J.
Junquera
,
R. M.
Martin
,
P.
Ordejón
,
J. M.
Pruneda
,
D.
Sánchez-Portal
, and
J. M.
Soler
,
J. Phys.: Condens. Matter
20
,
064208
(
2008
).
95.
J. M.
Soler
,
E.
Artacho
,
J. D.
Gale
,
A.
García
,
J.
Junquera
,
P.
Ordejón
, and
D.
Sánchez-Portal
,
J. Phys.: Condens. Matter
14
,
2745
(
2002
).
96.
E.
Anglada
and
J. M.
Soler
,
Phys. Rev. B
73
,
115122
(
2006
).
97.
See supplementary material at http://dx.doi.org/10.1063/1.4749929 for O–O RDF in Fig. S2; dispersion contributions to the interaction potentials for oxygen-hydrogen pair in Fig. S3; and an extended potential energy scan ranging from 0.6 Å to 7.5 Å in Fig. S4.
99.
A. K.
Soper
,
J. Phys. Condens. Matter
9
,
2717
(
1997
).
100.
101.
D. T.
Bowron
,
J. L.
Finney
, and
A. K.
Soper
,
J. Phys. Chem. B
102
,
3551
(
1998
).
102.
A. K.
Soper
,
Phys. Rev. B
72
,
104204
(
2005
).
103.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
104.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
78
,
1396
(
1997
).

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