Development and Testing of the OPLS All-Atom Force Field
on Conformational Energetics and Properties of Organic
Liquids
William L. Jorgensen,* David S. Maxwell, and Julian Tirado-Rives
Contribution from the Department of Chemistry, Yale UniVersity,
New HaVen, Connecticut 06520-8107
ReceiVed June 27, 1996. ReVised Manuscript ReceiVed September 5, 1996
X
Abstract: The parametrization and testing of the OPLS all-atom force field for organic molecules and peptides are
described. Parameters for both torsional and nonbonded energetics have been derived, while the bond stretching
and angle bending parameters have been adopted mostly from the AMBER all-atom force field. The torsional
parameters were determined by fitting to rotational energy profiles obtained from ab initio molecular orbital calculations
at the RHF/6-31G*//RHF/6-31G* level for more than 50 organic molecules and ions. The quality of the fits was
high with average errors for conformational energies of less than 0.2 kcal/mol. The force-field results for molecular
structures are also demonstrated to closely match the ab initio predictions. The nonbonded parameters were developed
in conjunction with Monte Carlo statistical mechanics simulations by computing thermodynamic and structural
properties for 34 pure organic liquids including alkanes, alkenes, alcohols, ethers, acetals, thiols, sulfides, disulfides,
aldehydes, ketones, and amides. Average errors in comparison with experimental data are 2% for heats of vaporization
and densities. The Monte Carlo simulations included sampling all internal and intermolecular degrees of freedom.
It is found that such non-polar and monofunctional systems do not show significant condensed-phase effects on
internal energies in going from the gas phase to the pure liquids.
Introduction
Computer modeling of fluid systems is now commonplace
with applications ranging from elucidating the structures and
properties of pure liquids to predictions on protein stability and
ligand binding.
1
The principal computational methods are
molecular dynamics (MD) and Monte Carlo statistical mechanics
(MC) in a classical framework.
2
The outcome of the simulations
is primarily controlled by the expressions for the total energy,
which are collectively referred to as the force field. Most force
fields in widespread use for macromolecular systems have a
similar form including harmonic bond stretching and angle
bending, Fourier series for torsional energetics, and Coulomb
plus Lennard-Jones terms for intermolecular and intramolecular
nonbonded interactions.
3-6
Anharmonic and cross-terms may
be added.
7
The incorporation of instantaneous polarization
effects is also desirable and is being pursued, though it is not
yet widely adopted owing to increased computational demands
and a lack of fully developed polarizable force fields.
8,9
The
differences for the non-polarizable force fields are mainly in
choices on the numbers of interaction sites and the origin and
extent of testing of the parameters in the energy expressions.
Our efforts, as embodied in the development of the TIP3P and
TIP4P models for water
10
and the OPLS force field for organic
and biomolecular systems, have emphasized the importance of
conformational energetics, basic intermolecular energetics in the
gas phase, and the value of testing the force field on thermo-
dynamic properties of pure organic liquids, especially heats of
vaporization and densities,
11-15
and on free energies of hydra-
tion.
16
Correct representation of the latter properties gives
confidence in the description of nonbonded interactions includ-
ing hydrogen bonding and in the size of molecules. It should
be obvious that force fields intended for use in simulations of
fluid systems should be tested by making predictions on
X
Abstract published in AdVance ACS Abstracts, October 15, 1996.
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(7) See: Halgren, T. A. J. Comput. Chem. 1996, 17, 490 and references
therein.
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(b) Caldwell, J. W.; Kollman, P. A. J. Am. Chem. Soc. 1995, 117, 4177.
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Am. Chem. Soc. 1995, 117, 11809.
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Klein, M. L. J. Chem. Phys. 1983, 79, 926. Jorgensen, W. L.; Madura, J.
D. Mol. Phys. 1985, 56, 1381.
(11) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. J. Am. Chem. Soc.
1984, 106, 6638.
(12) (a) Jorgensen, W. L. J. Phys. Chem. 1986, 90, 1276. (b) Jorgensen,
W. L. J. Phys. Chem. 1986, 90, 6379. (c) Briggs, J. M.; Matsui, T.;
Jorgensen, W. L. J. Comput. Chem. 1990, 11, 958. (d) Briggs, J. M.;
Nguyen, T. B.; Jorgensen, W. L. J. Phys. Chem. 1991, 95, 3315.
(13) Jorgensen, W. L.; Swenson, C. J. J. Am. Chem. Soc. 1985, 107,
569, 1489.
(14) Jorgensen, W. L.; Severance, D. L. J. Am. Chem. Soc. 1990, 112,
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113, 2810.
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1995, 3, 123.
11225J. Am. Chem. Soc. 1996, 118, 11225-11236
S0002-7863(96)02176-2 CCC: $12.00 © 1996 American Chemical Society

experimentally well-determined properties of fluids. Compari-
sons of computed and experimental results for solids can also
be productive,
6,15
though experimental energetic data on solids
is limited and the convergence of simulations of solids can be
challenging.
The original OPLS (optimized potentials for liquid simula-
tions) potential functions used a partially united-atom (UA)
model; sites for nonbonded interactions are placed on all non-
hydrogen atoms and on hydrogens attached to heteroatoms or
carbons in aromatic rings.
11-15
Thus, the only hydrogens that
are implicit are attached to aliphatic carbons. The computation
time for fluid simulations is roughly proportional to the total
number of interaction sites squared. Thus, the OPLS-UA model
is computationally attractive, since, for example, the number
of interaction sites for a molecule such as a propanol is 5 instead
of 12 in an all-atom (AA) representation. The focus in
development of the OPLS-UA model was on the nonbonded
parameters, which historically had been the most problematic,
and the new approach was to perform large numbers of Monte
Carlo simulations of pure organic liquids for their refinement.
For organic systems, the only internal degrees of freedom that
were varied were torsions. The torsional energy terms were
developed in an ad hoc manner by fitting to experimental or
computational results for conformational energy profiles, which
were considered to be the most reliable at the time.
11-14
The
results were gratifying with average errors of ca. 2% for densities
and heats of vaporization
10-14
and 1.0 kcal/mol for free energies
of hydration.
16
For peptides and proteins, the OPLS nonbonded
parameters were merged with the description of bond stretching,
angle bending, and torsional energetics from the AMBER
united-atom force field
3a
to yield the OPLS/AMBER force
field.
15
It has seen widespread use after the original testing on
conformational energetics for dipeptides and on the structures
and unit-cell dimensions for crystals of cyclic peptides.
15
Nevertheless, the added sites in all-atom models allow more
flexibility for charge distributions and torsional energetics. This
has been pursued and results have been reported for hydrocar-
bons with an OPLS-AA model; improved accord was obtained
with experiment in several areas, particularly for the free
energies of hydration of alkanes for which the average error
was reduced from 0.9 to 0.3 kcal/mol.
17
As described here,
this work has been extended to cover many common organic
functional groups and all organic components needed for a
protein force field. Besides parametrization of the nonbonded
interactions, torsional potential functions have been obtained
in a uniform manner by fitting to conformational energy profiles
from ab initio RHF/6-31G*//RHF/6-31G* calculations for over
50 organic molecules and ions.
18
The torsional energetics at
this level are in good agreement with experimental data and
show little improvement with inclusion of MP2 correlation
corrections.
18
The simultaneous parametrization of the non-
bonded and torsional energy terms is desirable since they are
coupled in the description of intramolecular energetics. The
bond stretching and angle bending terms are more standardized
and have largely been adopted from the AMBER AA force
field.
3b
Continuing with the OPLS philosophy, the parametriza-
tion of the AA force field has included MC simulations for 34
organic liquids: ethane, propane, butane, isobutane, cyclohex-
ane, propene, trans-2-butene, methanol, ethanol, propanol,
2-propanol, 2-methyl-2-propanol (t-BuOH), phenol, methaneth-
iol, ethanethiol, propanethiol, dimethyl sulfide, ethyl methyl
sulfide, dimethyl disulfide, acetamide, N-methylacetamide (NMA),
N-methylpropanamide (NMP), N,N-dimethylacetamide (DMA),
dimethyl ether (DME), ethyl methyl ether (EME), diethyl ether
(DEE), tetrahydrofuran (THF), dimethoxymethane (DMM), 1,3-
dioxolane, acetic acid, acetaldehyde, propanal, acetone, and
butanone. Presentation of the force field and the results on
conformational energetics and liquid properties are the focus
of this paper.
Computational Methods
Force Field. The nonbonded interactions are represented by the
Coulomb plus Lennard-Jones terms in eq 1, where E
ab
is the interaction
energy between molecules a and b.
Standard combining rules are used such that σ
ij
) (σ
ii
σ
jj
)
1/2
and ²
ij
)
(²
ii
²
jj
)
1/2
. The same expression is used for intramolecular nonbonded
interactions between all pairs of atoms (i < j) separated by three or
more bonds. Furthermore, f
ij
) 1.0 except for intramolecular 1,4-
interactions for which f
ij
) 0.5, as discussed below. The parameters
were adopted as much as possible from the OPLS-UA force field. Initial
charges for CH
n
groups were obtained from the UA charge and
assignment of charges of +0.06 e to the hydrogens as for alkanes.
17
Testing for the properties of pure liquids showed that this scheme was
often inadequate and some adjustments to the charges and, more rarely,
to the Lennard-Jones parameters were required. Thus, the charges for
the OPLS force fields are empirical and have been obtained largely
from fitting to reproduce properties of organic liquids. The charges
for functional groups are taken to be transferable between molecules
and the use of neutral subunits makes the derivation of charges for
large molecules straightforward. This represents a major difference
with the AMBER94 force field
3c
for which charges are obtained on a
case-by-case basis from fitting to electrostatic potential surfaces from
ab initio 6-31G* calculations.
Nonbonded interactions are also evaluated for intramolecular atom
pairs separated by three or more bonds. As in prior work, it was found
to be necessary to scale the 1,4-nonbonded interactions to permit use
of the same parameters for inter- and intramolecular interactions.
Scaling factors f
ij
)
1
/
2
for both the Coulombic and Lennard-Jones
interactions emerged as the final choice, which is the same as in some
AMBER force fields.
3a,b
The OPLS/AMBER force field uses scaling
factors of
1
/
2
and
1
/
8
, respectively.
15
Some advantages of
1
/
8
and
1
/
8
were initially found here, but turned out to be problematic for molecules
that can form internal hydrogen bonds including dipeptides. All
nonbonded parameters for the OPLS-AA force field are reported in
the Supporting Information, Tables 1-5. The previous AA nonbonded
parameters reported for water and nucleoside bases can be used in
conjunction with the new parameters.
10,14
The energetics for bond stretching and angle bending are represented
by eqs 2 and 3.
Almost all constants in this case were taken from the AMBER all-
atom force field.
3b
The principal exceptions were the parameters for
alkanes that are summarized in the Supporting Information, Table 6.
The listed values from a recent CHARMM force field
4
were adopted
because they led to significant improvements for both structures and
energetics. The values of 109.5° for the θ
eq
of C-C-C, C-C-H,
and H-C-H in the AMBER force fields were most problematic.
3b,c
Energy minimizations for ethane, propane, and butane with these
parameters led to widening of the bond angles in the same order as
obtained from the ab initio calculations (C-C-C > C-C-H > H-C-
H). However, comparatively higher angle bending energies were
obtained, which required some compensation in the torsional parameters.
(17) Kaminski, G.; Duffy, E. M.; Matsui, T.; Jorgensen, W. L. J. Phys.
Chem. 1994, 98, 13077.
(18) Maxwell, D. S.; Tirado-Rives, J.; Jorgensen, W. L. J. Comput. Chem.
1995, 16, 984.
E
ab
)
∑
i
on a
∑
j
on b
[q
i
q
j
e
2
/r
ij
+ 4²
ij
(σ
ij
12
/r
ij
12
- σ
ij
6
/r
ij
6
)]f
ij
(1)
E
bond
)
∑
bonds
K
r
(r - r
eq
)
2
(2)
E
angle
)
∑
angles
K
θ
(θ - θ
eq
)
2
(3)
11226 J. Am. Chem. Soc., Vol. 118, No. 45, 1996 Jorgensen et al.