Parametrized Models of Aqueous Free Energies of Solvation Based on Pairwise Descreening
of Solute Atomic Charges from a Dielectric Medium
Gregory D. Hawkins, Christopher J. Cramer,* and Donald G. Truhlar*
Department of Chemistry and Supercomputer Institute, UniVersity of Minnesota,
Minneapolis, Minnesota 55455-0431
ReceiVed: June 11, 1996; In Final Form: August 21, 1996
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The pairwise descreening approximation provides a rapid computational algorithm for the evaluation of solute
shape effects on electrostatic contributions to solvation energies. In this article we show that solvation models
based on this algorithm are useful for predicting free energies of solvation across a wide range of solute
functionalities, and we present six new general parametrizations of aqueous free energies of solvation based
on this approach. The first new model is based on SM2-type atomic surface tensions, the AM1 model for
the solute, and Mulliken charges. The next two new models are based on SM5-type surface tensions, either
the AM1 or the PM3 model for the solute, and Mulliken charges. The final three models are based on
SM5-type atomic surface tensions and are parametrized using the AM1 or the PM3 model for the solute and
CM1 charges. The parametrizations are based on experimental data for a set of 219 neutral solute molecules
containing a wide range of organic functional groups and the atom types H, C, N, O, F, P, S, Cl, Br, and I
and on data for 42 ions containing the same elements. The average errors relative to experiment are slightly
better than previous methods, butsmore significantlysthe computational cost is reduced for large molecules,
and the methods are well suited to using analytic derivatives.
1. Introduction
In previous papers
1-10
we and our co-workers have introduced
a new approach to solvation modeling based on the following
elements.
(1) Electrostatics are modeled by the generalized Born
approximation
11-17
with atom-centered charges and dielectric
descreening by other parts of the solute calculated from a
conformationally sensitive solute-shape molecular model
1,18
based on overlapping atomic spheres. This electrostatic ap-
proach is called density descreening (DD) because it is based
on integrating an approximation to the free energy density
19
of
the polarized dielectric medium over the region not occupied
by the descreening solute. The original applications
1-4,18
of
DD used a rectangular quadrature rule for the radial integrations
about each atomic center. This approximation in calculating
the volume integral over the dielectric free energy density caused
a systematic error which was compensated by parametrization.
1-4
(As discussed extensively in previous papers, and as is always
true in semiempirical work, the parametrization also makes up
in part for any systematic physical deficiencies of the model,
e.g., for the approximation of the dielectric field in the free
energy density by the Coulomb field.) Later work carried out
this radial quadrature by a converged trapezoidal rule.
5-10
(2) The atomic charges used in the electrostatic calculations
are based on either class II
20
or class IV
21
charge models.
(3) First solvation shell effects (i.e., short-range effects)
attributable to deviations of the solvation free energies from
the predictions of a purely homogeneous continuum model of
the solvent are calculated from atomic solvent-accessible surface
areas
22,23
with micro-interfacial atomic surface tensions depend-
ing on the local nature of the solute.
24
The various functional
forms of the surface tensions are denoted by SMx, in particular
by the x in SMx, where x may be 1,
1,4
1a,
1,4
2,
2,4
3,
3,4
4,
6-9
or
5.
10
(The functional form of SM3 is the same as SM2.)
(4) Solute electronic and geometric relaxation in the presence
of the solvent are modeled by including the solute-solvent
interactions and the solute-induced changes in the solvent-
solvent interactions self-consistently in a solute Fock opera-
tor,
1,12-16,25,26
and geometries are optimized in solution. Several
general parametrizations of this kind of model have been
proposed,
1-10
differing in the model used for the solute internal
energy
27,28
and partial charges,
20,21
the quadrature method used
for dielectric descreening calculations,
1,4,5,18
and the functional
form used for the dependence of the surface tensions on the
local nature of the solute.
1,2,6,10
Table 1 summarizes previous
parametrizations. (The models for which the reference is
“present” are new in this paper and are explained below.)
In a recent letter,
29
we introduced a computationally appealing
modification of our previous approach in which the three-
dimensional quadratures
1,5,19
in the original dielectric descreen-
ing calculations are replaced by a sum of pair terms involving
scaled atoms, and we presented a preliminary set of parameters
for solutes containing C, H, O, and N in aqueous solution. This
electrostatic approach, which was inspired by the work of
Schaefer and Froemmel,
30
is called pairwise descreening (PD).
(The PD approach and the DD approach both utilize the
approximation that the electric field is replaced by the Coulomb
field in the free energy density.) The parameters required were
the same as in the previous SM2
2
and SM2.1
5
models plus C,
H, O, and N scale factors for the new step. This was called
solvation model 2.2 because it closely resembles SM2
2
and
SM2.1.
5
A major component of the widespread usefulness of modern
electronic structure theory is associated with the availability of
a variety of “levels” differing in cost and reliability. Thus,
various combinations of computational choices may be more
or less useful depending on the problem being studied. For
example, one has various levels of one-electron basis sets and
various degrees of the inclusion of electron correlation. The
various methods of treating solvation in our own previous work,
e.g., SM2
2
and SM4,
6
have not been developed in a level
framework. Rather, they reflect different choices in the
functional forms used for modeling first solvation shell effects
and different algorithms for calculating electrostatic descreening
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Abstract published in AdVance ACS Abstracts, November 15, 1996.
19824 J. Phys. Chem. 1996, 100, 19824-19839
S0022-3654(96)01710-8 CCC: $12.00 © 1996 American Chemical Society