Essentials of Computational Chemistry

410 11 IMPLICIT MODELS FOR CONDENSED PHASES
opposed to surface area) of a finite shell surrounding each atom. This model, too, is primarily
designed for use with biomolecular simulations, although its performance for more general
small neutral solutes is perfectly acceptable.
11.4 Strengths and Weaknesses of Continuum Solvation Models
11.4.1 General Performance for Solvation Free Energies
For neutral solutes experimental free energies of solvation between the range of
+5 and −15 kcal mol −1 are typically amenable to measurement with an accuracy of
±0.1 kcal mol −1 . Carefully parameterized surface-tension-augmented continuum models
typically exhibit average errors over large data sets on the order of 0.5 kcal mol −1 .
Ionic solutes pose more difficulties experimentally, since measurement of a gas/solution
equilibrium is no longer a viable methodology. However, for singly charged species, solvation
free energies ranging from −40 to −110 kcal mol −1 can be obtained with accuracies of
±2–5 kcal mol −1 , depending on the experimental technique. Well parameterized continuum
models achieve mean absolute errors at the high end of the experimental error range, which
is perhaps the best that can be expected. Reliable data for more highly charged species are
extremely scarce, so no legitimate comparison can be made.
It is worth noting that the solvation free energy of the proton is a somewhat special case.
Determining the solvation free energy of the proton is equivalent to determining the absolute
potential of the normal hydrogen electrode (NHE), which is a tricky issue in electrochemistry
(Trasatti 1986). In 1986, the International Union of Pure and Applied Chemistry (IUPAC)
recommended an absolute value of 4.44 V for the NHE which corresponds to a 1 M gas phase
to 1 M solution standard-state aqueous proton solvation free energy of −261.7 kcalmol −1 .
In the 1990s, however, Tissandier et al. (1998) used ion-cluster measurements to establish
a value of −264.0 kcalmol −1 for the same standard-state process, which corresponds to
an NHE potential of 4.36 V (Lewis et al. 2004). Subsequent experimental and theoretical
work has been supportive of the greater accuracy of the newer value and its use can
be recommended. Note that most methods for determining ionic solvation free energies
experimentally rely on having a benchmark value for the proton solvation free energy, so
a change in the benchmark changes all ionic solvation free energies. Thus, care should
be employed in comparing tabulations of such values in the literature to ensure common
standard-state conventions and proton solvation free energies.
One of the reasons that it is hard to predict accurate solvation free energies for charged
species is that such predictions tend to be very sensitive to the size of the solute cavity,
leading to many proposals in the literature for how to go about choosing the ‘best’
electrostatic cavity. However, insofar as the electrostatic component of the solvation free
energy is not an observable, there is not much weight to these arguments. The essentially
equivalent performances of surface-tension augmented models like MST-ST and SMx for
full free energies of solvation, even though they use very different cavity radii in some cases
and therefore determine very different electrostatic free energies of solvation (Curutchet et al.
2003a), speak to the ability of the parameterization process to mask any lack of physicality
in the cavity definitions.