Most empirical force fields use atom-centered point charges (PCs) to represent the electrostatic potential (ESP) around molecules. While such PC models are computationally efficient, they are unable to capture anisotropic electronic features, such as σ holes or lone pairs. These features are better described using atomic multipole (MTP) moments, which significantly improve the quality of the resulting ESP. However, the improvement comes at the expense of a considerably increased computational complexity and cost for calculating the interaction energies and forces. In the present work, a novel minimal distributed charge model (MDCM) based on off-centered point charges is presented and the quality of the resulting ESP is compared to the performance of MTPs and atom-centered PC models for several test molecules. All three models are fitted using the same algorithm based on differential evolution, which is available as a Fortran90 program from the authors upon request. We show that the MDCM is capable of approximating the reference ab initio ESP with an accuracy as good as, or better than, MTPs without the need for computationally expensive higher order multipoles. Further it is demonstrated that the MDCM is numerically stable in molecular dynamics simulations and is able to reproduce electrostatic interaction energies and thermodynamic quantities with the same accuracy as MTPs at reduced computational cost.

1.
J. W.
Ponder
and
D. A.
Case
,
Adv. Protein Chem.
66
,
27
85
(
2003
).
2.
B. R.
Brooks
,
C. L.
Brooks
,
A. D.
MacKerell
,
L.
Nilsson
,
R. J.
Petrella
,
B.
Roux
,
Y.
Won
,
G.
Archontis
,
C.
Bartels
,
S.
Boresch
 et al,
J. Comput. Chem.
30
,
1545
1614
(
2009
).
3.
D. A.
Case
,
T. E.
Cheatham
,
T.
Darden
,
H.
Gohlke
,
R.
Luo
,
K. M.
Merz
,
A.
Onufriev
,
C.
Simmerling
,
B.
Wang
, and
R. J.
Woods
,
J. Comput. Chem.
26
,
1668
1688
(
2005
).
4.
C.
Oostenbrink
,
A.
Villa
,
A. E.
Mark
, and
W. F.
Van Gunsteren
,
J. Comput. Chem.
25
,
1656
1676
(
2004
).
5.
G. A.
Kaminski
,
R. A.
Friesner
,
J.
Tirado-Rives
, and
W. L.
Jorgensen
,
J. Phys. Chem. B
105
,
6474
6487
(
2001
).
6.
A.
Stone
,
Chem. Phys. Lett.
83
,
233
239
(
1981
).
7.
A.
Stone
,
The Theory of Intermolecular Forces
, 2nd ed. (
Oxford University Press
,
Oxford
,
2013
).
8.
C.
Kramer
,
P.
Gedeck
, and
M.
Meuwly
,
J. Comput. Chem.
33
,
1673
1688
(
2012
).
9.
D. R.
Nutt
and
M.
Meuwly
,
Proc. Natl. Acad. Sci. U. S. A.
101
,
5998
6002
(
2004
).
10.
I. T.
Suydam
,
C. D.
Snow
,
V. S.
Pande
, and
S. G.
Boxer
,
Science
313
,
200
204
(
2006
).
11.
M. W.
Lee
,
J. K.
Carr
,
M.
Göllner
,
P.
Hamm
, and
M.
Meuwly
,
J. Chem. Phys.
139
,
054506
(
2013
).
12.
M. W.
Lee
and
M.
Meuwly
,
Phys. Chem. Chem. Phys.
15
,
20303
20312
(
2013
).
13.
M.
Soloviov
,
A. K.
Das
, and
M.
Meuwly
,
Angew. Chem., Int. Ed.
55
,
10126
10130
(
2016
).
14.
Y.
Shi
,
Z.
Xia
,
J.
Zhang
,
R.
Best
,
C.
Wu
,
J. W.
Ponder
, and
P.
Ren
,
J. Chem. Theory Comput.
9
,
4046
4063
(
2013
).
15.
A. C.
Simmonett
,
F. C.
Pickard
 IV
,
H. F.
Schaefer
 III
, and
B. R.
Brooks
,
J. Chem. Phys.
140
,
184101
(
2014
).
16.
T.
Bereau
,
C.
Kramer
, and
M.
Meuwly
,
J. Chem. Theory Comput.
9
,
5450
5459
(
2013
).
17.
S.
Liem
and
P.
Popelier
,
J. Chem. Phys.
119
,
4560
4566
(
2003
).
18.
X.
Zheng
,
C.
Wu
,
J. W.
Ponder
, and
G. R.
Marshall
,
J. Am. Chem. Soc.
134
,
15970
15978
(
2012
).
19.
N.
Plattner
and
M.
Meuwly
,
Biophys. J.
94
,
2505
2515
(
2008
).
20.
J.-P.
Piquemal
,
G. A.
Cisneros
,
P.
Reinhardt
,
N.
Gresh
, and
T. A.
Darden
,
J. Chem. Phys.
124
,
104101
(
2006
).
21.
M.
Devereux
,
S.
Raghunathan
,
D. G.
Fedorov
, and
M.
Meuwly
,
J. Chem. Theory Comput.
10
,
4229
4241
(
2014
).
22.
A.
Sawaryn
and
W. A.
Sokalski
,
Comput. Phys. Commun.
52
,
397
408
(
1989
).
23.
Q.
Gao
,
S.
Yokojima
,
D. G.
Fedorov
,
K.
Kitaura
,
M.
Sakurai
, and
S.
Nakamura
,
Chem. Phys. Lett.
593
,
165
173
(
2014
).
24.
R.
Anandakrishnan
,
C.
Baker
,
S.
Izadi
, and
A. V.
Onufriev
,
PLoS One
8
,
e67715
(
2013
).
25.
N.
Gresh
,
P.
Claverie
, and
A.
Pullman
,
Int. J. Quantum Chem.
16
,
243
253
(
1979
).
26.
S.
Jakobsen
and
F.
Jensen
,
J. Chem. Theory Comput.
12
,
1824
1832
(
2016
).
27.
R. F. W.
Bader
,
Atoms in Molecules—A Quantum Theory
(
Oxford University Press
,
Oxford
,
1990
).
28.
A. J.
Stone
,
J. Chem. Theory Comput.
1
,
1128
1132
(
2005
).
29.
L.
Joubert
and
P.
Popelier
,
Mol. Phys.
100
,
3357
3365
(
2002
).
30.
W. L.
Jorgensen
,
J.
Chandrasekhar
,
J. D.
Madura
,
R. W.
Impey
, and
M. L.
Klein
,
J. Chem. Phys.
79
,
926
935
(
1983
).
31.
E.
Harder
,
W.
Damm
,
J.
Maple
,
C.
Wu
,
M.
Reboul
,
J. Y.
Xiang
,
L.
Wang
,
D.
Lupyan
,
M. K.
Dahlgren
, and
J. L.
Knight
,
J. Chem. Theory Comput.
12
,
281
296
(
2015
).
32.
M. V.
Ivanov
,
M. R.
Talipov
, and
Q. K.
Timerghazin
,
J. Chem. Phys.
143
,
134102
(
2015
).
33.
D. W.
Marquardt
,
SIAM J. Appl. Math.
11
,
431
441
(
1963
).
34.
L. M.
Rios
and
N. V.
Sahinidis
,
J. Global Optim.
56
,
1247
1293
(
2013
).
35.
R.
Storn
and
K.
Price
,
J. Global Optim.
11
,
341
359
(
1997
).
36.
S.
Das
and
P. N.
Suganthan
,
IEEE Trans. Evol. Comput.
15
,
4
31
(
2011
).
37.
G. S.
Tschumper
,
M. L.
Leininger
,
B. C.
Hoffman
,
E. F.
Valeev
,
H. F.
Schaefer
 III
, and
M.
Quack
,
J. Chem. Phys.
116
,
690
701
(
2002
).
38.
K.
El Hage
,
T.
Bereau
,
S.
Jakobsen
, and
M.
Meuwly
,
J. Chem. Theory Comput.
12
,
3008
3019
(
2016
).
39.
E.
Mezura-Montes
,
J.
Velázquez-Reyes
, and
C. C.
Coello
, “
Modified differential evolution for constrained optimization
,” in
2006 IEEE International Conference on Evolutionary Computation
(
IEEE
,
2006
), pp.
25
32
.
40.
A.
Bondi
,
J. Phys. Chem.
68
,
441
451
(
1964
).
41.
P. L. A.
Popelier
,
F. M.
Aicken
, and
S. E.
O’Brien
,
Chem. Modell.: Appl. Theory
1
,
143
198
(
2000
).
42.
T. C.
Lillestolen
and
R. J.
Wheatley
,
Chem. Commun.
2008
,
5909
5911
.
43.
A. J.
Misquitta
,
A. J.
Stone
, and
F.
Fazeli
,
J. Chem. Theory Comput.
10
,
5405
5418
(
2014
).
44.
M. J.
Frisch
 et al, gaussian 09, Revision A.02,
Gaussian, Inc.
,
Wallingford, CT
,
2009
.
45.
A.
Stone
, GDMA: A Program for Performing Distributed Multipole Analysis of Wave Functions Calculated Using the Gaussian Program System, version 1.0,
1999
.
46.
B.
Lee
and
F. M.
Richards
,
J. Mol. Biol.
55
,
379
IN4
(
1971
).
47.
M.
Devereux
,
N.
Gresh
,
J.-P.
Piquemal
, and
M.
Meuwly
,
J. Comput. Chem.
35
,
1577
1591
(
2014
).
48.
N.
Gresh
,
G. A.
Cisneros
,
T. A.
Darden
, and
J.-P.
Piquemal
,
J. Chem. Theory Comput.
3
,
1960
1980
(
2007
).
49.
P.
Auffinger
,
F. A.
Hays
,
E.
Westhof
, and
P. S.
Ho
,
Proc. Natl. Acad. Sci. U. S. A.
101
,
16789
16794
(
2004
).
50.
P.
Politzer
,
J. S.
Murray
, and
M. C.
Concha
,
J. Mol. Model.
14
,
659
665
(
2008
).
51.
W. L.
Jorgensen
and
P.
Schyman
,
J. Chem. Theory Comput.
8
,
3895
3901
(
2012
).
52.
F.
Hédin
,
K.
El Hage
, and
M.
Meuwly
,
J. Chem. Inf. Model.
56
,
1479
1489
(
2016
).
53.
J.-P.
Ryckaert
,
G.
Ciccotti
, and
H. J.
Berendsen
,
J. Comput. Phys.
23
,
327
341
(
1977
).
54.
A. J.
Stone
,
J. Phys. Chem. A
115
,
7017
7027
(
2011
).
55.
Q.
Wang
,
J.
Rackers
,
C.
He
,
R.
Qi
,
C.
Narth
,
L.
Lagardere
,
N.
Gresh
,
J.
Ponder
,
J.-P.
Piquemal
, and
P.
Ren
,
J. Chem. Theory Comput.
11
,
2609
2618
(
2015
).
56.
J.
Benesty
,
J.
Chen
,
Y.
Huang
, and
I.
Cohen
,
Noise Reduction in Speech Processing
(
Springer
,
2009
), pp.
1
4
.
57.
P.
Troster
,
K.
Lorenzen
, and
P.
Tavan
,
J. Phys. Chem. B
118
,
1589
1602
(
2014
).
58.
P. G.
Kusalik
and
I. M.
Svishchev
,
Science
265
,
1219
1221
(
1994
).
59.
M. W.
Mahoney
and
W. L.
Jorgensen
,
J. Chem. Phys.
112
,
8910
8922
(
2000
).
60.
D. L.
Mobley
, “
Experimental and calculated small molecule hydration free energies
,” http://escholarship.org/uc/item/6sd403pz (accessed 1 June 2016).
61.
D. L.
Mobley
and
J. P.
Guthrie
,
J. Comput.- Aided Mol. Des.
28
,
711
720
(
2014
).
62.
D. R.
Nutt
and
M.
Meuwly
,
Biophys. J.
85
,
3612
3623
(
2003
).
63.
P.
Mondal
and
M.
Meuwly
,
Phys. Chem. Chem. Phys.
19
,
16131
16143
(
2017
).
64.
T.
Nagy
,
J. Y.
Reyes
, and
M.
Meuwly
,
J. Chem. Theory Comput.
10
,
1366
1375
(
2014
).
65.
H. J.
Berendsen
,
D.
van der Spoel
, and
R.
van Drunen
,
Comput. Phys. Commun.
91
,
43
56
(
1995
).
66.
J. C.
Phillips
,
R.
Braun
,
W.
Wang
,
J.
Gumbart
,
E.
Tajkhorshid
,
E.
Villa
,
C.
Chipot
,
R. D.
Skeel
,
L.
Kale
, and
K.
Schulten
,
J. Comput. Chem.
26
,
1781
1802
(
2005
).
67.
B.
Hess
,
H.
Bekker
,
H. J.
Berendsen
, and
J. G.
Fraaije
,
J. Comput. Chem.
18
,
1463
1472
(
1997
).
68.
C.
Sagui
,
L. G.
Pedersen
, and
T. A.
Darden
,
J. Chem. Phys.
120
,
73
87
(
2004
).

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