Essentials of Computational Chemistry

11.3 CONTINUUM MODELS FOR NON-ELECTROSTATIC INTERACTIONS 409
The surface tensions themselves in the GB/SA and MST-ST models were developed by
taking collections of experimental data for the free energy of solvation in a specific solvent,
removing the electrostatic component as calculated by the GB or MST model, and fitting
the surface tensions to best reproduce the residual free energy given the known SASA of the
solute atoms. Such a multilinear regression procedure requires a reasonably sized collection
of data to be statistically robust, and limitations in data have thus restricted these models to
water, carbon tetrachloride, chloroform, and octanol as solvents.
In order to be more generally applicable, the SMx models of Cramer and Truhlar address
the issue of data scarcity by making the atomic surface tensions a function of quantifiable
solvent properties, i.e.,
σk =
j
Ɣjη Ɣj
k
(11.23)
where j runs over the property list, Ɣ is the value of a particular property in convenient units,
and the quantities η Ɣj
k become the parameters needing to be fit by multilinear regression.
Although this introduces multiple parameters per atom type k, it permits regression over a
single data set containing solvation free energies into any solvent, so long as its required
solvent properties are known. In the SM5 versions of the models, the macroscopic solvent
properties include surface tension, index of refraction, hydrogen bonding acidity and basicity,
and percent composition of aromatic carbon atoms and electronegative halogen atoms, and
the parameterization set involves more than 2500 data in 91 different solvents (Li et al.
1999).
A separate flexibility built into the SMx models compared to most other QM continuum
models augmented with surface tensions is that no assignment of atom type need be made.
Instead, the SMx surface tensions are functions of local geometry, so that, for instance, a
carbon-bound hydrogen atom is distinguished from an oxygen-bound hydrogen atom and
assigned a different surface tension to reflect its different character. The surface tension
functions are smooth and differentiable, which facilitates their use in modeling situations
where an atom may change from one type to another along a reaction coordinate, for instance.
Surface-tension augmented continuum models permit the computation of full free energies
of solvation and may thus be used to construct solvated potential energy surfaces in the spirit
of Figure 11.1. Insofar as the solvation free energy itself and any equilibrium or kinetic
quantities computed for the solvated PES are physical observables, the accuracy of the
solvation models may be assessed by comparison to experimental data. We consider several
such comparisons in the next section in addition to addressing certain important technical
details. Prior to doing so, however, it must be mentioned that the use of atomic surface
tensions has been carried to the extreme of assuming that they can account for the entire
solvation free energy, i.e., the electrostatics are completely implicit and the parameters in
Eq. (11.23) are fit to the full solvation free energy (recent examples include Hawkins et al.
1998, Wang et al. 2001, and Hou et al. 2002). Such models are typically designed for use
with biopolymers, where there is a need for extreme efficiency and the range of atom types
is rather limited. An approach that is similar in its conceptual simplicity, albeit not entirely
devoid of electrostatics, is the solvation free energy density (SFED) approach of No et al.
(1999) where the full free energy of solvation is computed from the accessible volume (as