Essentials of Computational Chemistry

11.2 ELECTROSTATIC INTERACTIONS WITH A CONTINUUM 401
of the authors’ last names) finds roughly equal usage, and some authors use PCM to refer
generically to any continuum SCRF scheme.
A number of variations on the PCM formalism have appeared since its first publication.
Some are purely technical in nature, designed to improve the computational performance of
the method, e.g., an integral equation formalism for solving the relevant SCRF equations
which facilitates computation of gradients and molecular response properties (IEF-PCM;
Cossi et al. 2002), an extension to permit application to infinite periodic systems in one and
two dimensions (Cossi 2004), and an extension to liquid/liquid and liquid/vapor interfaces
(Frediani et al. 2004). Others reflect differences in how the molecular cavity is defined.
For the most part, Tomasi and co-workers have maintained a strategy where the cavity is
constructed from overlapping atomic spheres having radii 20% larger than their tabulated
van der Waals radii, with a special distinction being made between ‘polar’ and ‘non-polar’
hydrogen atoms. As an alternative, Foresman et al. (1996) suggested defining the cavity
as that region of space surrounded by an arbitrary isodensity surface, i.e., a surface characterized
by a constant value of the electron density. That surface can either be located
from the gas-phase density, and held fixed (IPCM) or determined self-consistently, adding
yet another iterative level to the SCRF process (SCIPCM). Part of the motivation for these
latter two modifications was to decrease the number of cavity parameters from one per atom
to one total. However, insofar as the modeling of a molecular solvent by a continuum is
by nature a fictional construct, it is not obvious that such a decrease in parameters can be
regarded as a virtue. A further discussion of cavity definitions is deferred to Section 11.4.1,
and it suffices to note here that the IPCM and SCIPCM methods tend to be considerably
less stable in implementation than the original PCM process, and can be subject to
erratic behavior in charged systems, so their use cannot be recommended (Cossi et al.
1996).
A third possibility that has received extensive study in the SCRF regime is one that has
seen less use at the classical level, at least within the context of general cavities, and that
is representation of the reaction field by a multipole expansion. Rinaldi and Rivail (1973)
presented this methodology in what is arguably the first paper to have clearly defined the
SCRF procedure. While the original work focused on ideal cavities, this group later extended
the method to cavities of arbitrary shape. In formalism, Eq. (11.17) is used for any choice of
cavity shape, but the reaction field factors f must be evaluated numerically when the cavity
is not a sphere or ellipsoid (Dillet et al. 1993). Analytic derivatives for this approach have
been derived and implemented (Rinaldi et al. 2004).
Most of the models described above have also been implemented at correlated levels of
theory, including perturbation theory, CI, and coupled-cluster theory (of course, the DFT
SCRF process is correlated by construction of the functional). Unsurprisingly, if a molecule
is subject to large correlation effects, so too is the electrostatic component of its solvation
free energy.
Note that, insofar as all of the above models simply represent alternative mathematical
approaches to solving the Poisson equation, in the limit of converging them with respect
to grid density, tesserae density, multipole expansion, etc., they should all give identical