Essentials of Computational Chemistry

416 11 IMPLICIT MODELS FOR CONDENSED PHASES
clear when such situations will arise, and modeling must simply be carried out with great
care to ensure that the possibility is not overlooked.
11.4.2 Partitioning
The free energy of solvation may be regarded as the quantity describing the partitioning of
a solute between the gas phase and a particular solvent. However, one is often interested in
the free energy associated with the partitioning of a solute between two different condensed
phases. Continuum solvent models may still conveniently be used to predict such partitioning
behavior, based on the procedure outlined in Figure 11.11. The validity of the thermodynamic
cycle is secure as drawn; however, under certain experimental conditions, the cycle is not
representative of the experiment and the performance of the model may thus be degraded.
For instance, the two solvents may be immiscible in a bulk sense, so the experiment may
be carried out simply by dissolving a solute into a container holding both solvents, shaking
the system until equilibrium is reached, and then measuring the solute concentration in the
two phases. However, in spite of the phases being immiscible in bulk, the small percentages
of each solvent that dissolve into the other may significantly affect the bulk’s ability to
solvate the solute in question. The continuum model, on the other hand, necessarily assumes
a homogeneous ‘pure’ medium.
One major motivation for studying partitioning behavior has been a desire to understand
the fashion in which drug molecules pass through largely non-polar (lipid) biomembranes
that separate largely aqueous biocompartments. Historically, the octanol/water partition
coefficient has been useful in this regard, as have some others. Such partition coefficients
are usually not expressed as free energies of transfer, but as the logarithm of the associated
equilibrium constant P . From a modeling perspective, using the formalism embodied in
Figure 11.11, one computes
log PA/B =− Go SA − Go SB
2.303RT
(11.30)
where A and B are the solvents of interest and the two terms in the numerator are the free
energies of transfer from the gas phase into solvent A and solvent B, respectively.
The similar accuracies of different well-parameterized continuum models implies that they
will also perform similarly for the computation of partition coefficients, and that has proven
to be the case in most studies to date (see, for example, Bordner, Cavasotto, and Abagyan
2002 and Curutchet et al. 2003b). In Table 11.4 the previously presented SMx results for the
chloroform/water partitioning of the methylated canonical nucleic acid bases are compared to
results from the MST-ST/HF/6-31G* method, and also to purely electrostatic results obtained
using a multipole expansion SCRF method. As the latter does not include any accounting for
non-electrostatic effects, its performance is significantly degraded compared to the other two.
11.4.3 Non-isotropic Media
All of the continua discussed thus far have been isotropic in nature. An interesting question
arises as to the ability of the continuum approximation to model non-isotropic media. In