Essentials of Computational Chemistry

11.4 STRENGTHS AND WEAKNESSES OF CONTINUUM SOLVATION MODELS 415
Friesner (2002) have reported average errors of about 150 mV for various organometallic
species in different organic solutions. As already discussed for pKas, still better accuracy in
redox potentials can often be achieved through the use of isodesmic equations or functionalgroup-specific
correction schemes (see, for example, Winget et al. 2000).
11.4.1.3 Supermolecular solutes
Some final technical points merit attention. In SCRF models that use the full electronic
distribution as part of the representation of the density, a problem arises in that the wave
function has non-zero amplitude in the space outside the cavity. Thus, the construction of the
cavity truncates the charge distribution, so that, for instance, neutral molecules have a small
net positive charge inside the cavity. To return to integral charge values, the charge inside
the cavity must somehow be renormalized. There are many different approaches to rectifying
this problem; early methods tended to introduce considerable instability into the solvation
computation, although more modern approaches seem reasonably robust (see, for example,
Curutchet et al. 2004). Methods that do not suffer from the charge-penetration problem
include all those that represent the density as either a single- or multi-center multipole or
monopole expansion (this then includes GB methods). In addition, approaches have been
developed that specifically handle, as a separate physical component, the polarization energy
associated with penetration of charge into the solvent, and these models too seem to be well
balanced (Chipman 2002).
The charge-penetration problem is in some sense related to a specific drawback of current
continuum models, namely, that they have no mechanism to account for possible charge
transfer between the solute and the surrounding solvent. It is not yet clear to what extent
such solute/solvent charge transfer is important.
Of course, the simplest way to account for charge transfer would be to ‘materialize’ one or
more solvent molecules around the solute and to treat the resulting cluster as a supermolecule
embedded in the continuum. Pliego and Riveros (2002) and Fu et al. (2004) have recently
suggested that such an approach provides a more robust protocol for the computation of
accurate pKa values, for instance. However, while this model has conceptual merits, it
can introduce significant computational overhead. First, the supermolecule is obviously
bigger than the solute, and depending on the level of theory employed the difference in
computational time for a single SCRF calculation may be large. Second, clusters tend to
generate fairly complex PESs, with many minima, and any attempt to compute free energy
must sample over all of the minima in a statistically correct fashion. Since part of the
motivation for using a continuum model is to avoid the sampling issues associated with
explicit models, the representation of specific solvent molecules is usually not undertaken in
the absence of compelling need.
One case, however, where materialization of a specific solvent molecule out of the
continuum is indeed critical is when that solvent molecule loses its ‘solvent’ character.
For instance, a water molecule tightly bound as both a hydrogen-bond donor and acceptor
in a chain involving two solute functional groups clearly should be regarded as a unique
fragment in what is fundamentally a two-piece supermolecule. Unfortunately, it is not always