The optimal conversion of a continuous inter-particle potential to a discrete equivalent is considered here. Existing and novel algorithms are evaluated to determine the best technique for creating accurate discrete forms using the minimum number of discontinuities. This allows the event-driven molecular dynamics technique to be efficiently applied to the wide range of continuous force models available in the literature, and facilitates a direct comparison of event-driven and time-driven molecular dynamics. The performance of the proposed conversion techniques are evaluated through application to the Lennard-Jones model. A surprising linear dependence of the computational cost on the number of discontinuities is found, allowing accuracy to be traded for speed in a controlled manner. Excellent agreement is found for static and dynamic properties using a relatively low number of discontinuities. For the Lennard-Jones potential, the optimized discrete form outperforms the original continuous form at gas densities but is significantly slower at higher densities.

1.
B. J.
Alder
and
T. E.
Wainwright
,
J. Chem. Phys.
27
,
1208
(
1957
).
2.
T.
Pöschel
and
T.
Schwager
,
Computational Granular Dynamics
(
Springer
,
New York
,
2005
).
3.
R. A.
Gingold
and
J. J.
Monaghan
,
Mon. Not. R. Astron. Soc.
181
,
375
(
1977
).
4.
R.
van Zon
and
J.
Schofield
,
J. Chem. Phys.
128
,
154119
(
2008
).
5.
J. M.
Haile
,
Molecular Dynamics Simulation – Elementary Methods
(
Wiley-Interscience
,
New York
,
1997
).
6.
G.
Chapela
,
L. E.
Scriven
, and
H. T.
Davis
,
J. Chem. Phys.
91
,
4307
(
1989
).
7.
L.
Verlet
,
Phys. Rev.
159
,
98
(
1967
).
8.
J.
Ponder
and
D.
Case
,
Adv. Prot. Chem.
66
,
27
(
2003
).
9.
A.
MacKerel
 Jr.
,
C.
Brooks
 III
,
L.
Nilsson
,
B.
Roux
,
Y.
Won
, and
M.
Karplus
, in
The Encyclopedia of Computational Chemistry
, edited by
P.
von R. Schleyer
(
John Wiley and Sons
,
Chichester
,
1998
), Vol.
1
, pp.
271
277
.
10.
J. A.
Barker
and
D.
Henderson
,
J. Chem. Phys.
47
,
2856
(
1967
).
11.
S.
Chapman
and
T. G.
Cowling
,
The Mathematical Theory of Non-uniform Gases
, 3rd ed. (
Cambridge Mathematical Library
,
1991
).
12.
D.
Van der Spoel
,
E.
Lindahl
,
B.
Hess
,
G.
Groenhof
,
A. E.
Mark
, and
H. J. C.
Berendsen
,
J. Comput. Chem.
26
,
1701
(
2005
).
13.
H.-J.
Limbach
,
A.
Arnold
,
B. A.
Mann
, and
C.
Holm
,
Comput. Phys. Commun.
174
,
704
(
2006
).
14.
J.
Cui
and
J. J. R.
Elliott
,
J. Chem. Phys.
116
,
8625
(
2002
).
15.
A. D.
Sans
and
J. R.
Elliott
,
Fluid Phase Equilib.
263
,
182
(
2008
).
16.
A.
Vahid
,
A. D.
Sans
, and
J. R.
Elliott
,
Ind. Eng. Chem. Res.
47
,
7955
(
2008
).
17.
F. S.
Baskaya
,
N. H.
Gray
,
Z. N.
Gerek
, and
J. R.
Elliott
,
Fluid Phase Equilib.
236
,
42
(
2005
).
18.
A. M.
Hassan
,
D. T.
Vu
,
D. A.
Bernard-Brunel
,
J. R.
Elliott
,
D. J.
Miller
, and
C. T.
Lira
,
Ind. Eng. Chem. Res.
51
,
3209
(
2012
).
19.
E. M.
Curtis
and
C. K.
Hall
,
J. Phys. Chem. B
117
,
5019
(
2013
).
20.
H. D.
Nguyen
and
C. K.
Hall
,
Biophys. J.
87
,
4122
(
2004
).
21.
O.
Unlu
,
N. H.
Gray
,
Z. N.
Gerek
, and
J. R.
Elliott
,
Ind. Eng. Chem. Res.
43
,
1788
(
2004
).
22.
M. C.
dos Ramos
,
H.
Docherty
,
F. J.
Blas
, and
A.
Galindo
,
Fluid Phase Equilib.
276
,
116
(
2009
).
23.
M. N.
Bannerman
,
R.
Sargant
, and
L.
Lue
,
J. Comput. Chem.
32
,
3329
(
2011
).
24.
G. A.
Chapela
,
F.
del Rio
,
A. L.
Denavides
, and
J.
Alejandre
,
J. Chem. Phys.
133
,
234107
(
2010
).
25.
G. A.
Chapela
,
F.
del Rio
, and
J.
Alejandre
,
J. Chem. Phys.
138
,
054507
(
2013
).
26.
S.
Ucyigitler
,
M. C.
Camurdan
, and
J. R.
Elliott
,
Ind. Eng. Chem. Res.
51
,
6219
(
2012
).
27.
J.
Torres-Arenas
,
L. A.
Cervantes
,
A. L.
Benavides
,
G. A.
Chapela
, and
F.
del Rio
,
J. Chem. Phys.
132
,
034501
(
2010
).
28.
P.
Müller
and
T.
Pöschel
,
Phys. Rev. E
87
,
033301
(
2013
).
29.
J. A.
Barker
and
D.
Henderson
,
J. Chem. Phys.
47
,
4714
(
1967
).
30.
B.
Smit
,
J. Chem. Phys.
96
,
8639
(
1992
).
31.
N. B.
Wilding
,
Phys. Rev. E
52
,
602
(
1995
).
32.
G.
Orkoulas
and
A. Z.
Panagiotopoulos
,
J. Chem. Phys.
110
,
1581
(
1999
).
33.
N. B.
Wilding
,
Am. J. Phys.
69
,
1147
(
2001
).
34.
M. N.
Bannerman
and
L.
Lue
,
J. Chem. Phys.
133
,
124506
(
2010
).
35.
K.
Meier
, “
Computer simulation and interpretation of the transport coefficients of the Lennard-Jones model fluid
,” Ph.D. thesis,
Department of Mechanical Engineering, University of the Federal Armed forces
, Hamburg,
2002
.
36.
K.
Meier
,
A.
Laesecke
, and
S.
Kabelac
,
J. Chem. Phys.
121
,
3671
(
2004
).
37.
K.
Meier
,
A.
Laesecke
, and
S.
Kabelac
,
J. Chem. Phys.
121
,
9526
(
2004
).
38.
M.
Bugel
and
G.
Galliero
,
Chem. Phys.
352
,
249
(
2008
).
39.
P.
Valentini
and
T. E.
Schwartzentruber
,
J. Comput. Phys.
228
,
8766
(
2009
).
40.
S.
Miller
and
S.
Luding
,
J. Comput. Phys.
193
,
306
(
2004
).
41.
N. V.
Dokholyan
,
Curr. Opin. Struct. Biol.
16
,
79
(
2006
).
42.
F.
Ding
,
S. V.
Buldyrev
, and
N. V.
Dokholyan
,
Biophys. J.
88
,
147
(
2005
).
43.
F.
Ding
,
R. K.
Jha
, and
N. V.
Dokholyan
,
Structure
13
,
1047
(
2005
).
44.
M.
Cheon
,
I.
Chang
, and
C. K.
Hall
,
Biophys. J.
101
,
2493
(
2011
).
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