Use of Solution-Phase Vibrational Frequencies in Continuum Models for the Free Energy of Solvation

Ribeiro, R. F.; Marenich, A. V.; Cramer, C. J.; Truhlar, D. G.

* J. Phys. Chem. B*
in press
(doi:10.1021/jp205508z).

We find that vibrational contributions to a solute's free energy are in
general insensitive to whether the solute vibrational frequencies are
computed in the gas phase or in solution. In most cases the difference is
smaller than the intrinsic error in solvation free energies associated with
the continuum approximation to solvation modeling, although care must be
taken to avoid spurious results associated with limitations in the
quantum-mechanical harmonic-oscillator approximation for very low-frequency
molecular vibrations. We compute solute vibrational partition functions in
aqueous- and carbon-tetrachloride-solution and compare them to gas-phase
molecular partition functions computed with the same level of theory and
the same quasiharmonic approximation for the diverse and extensive set of
molecules and ions included in the training set of the SMD continuum
solvation model, and we find mean unsigned differences in vibrational
contributions to the solute free energy of only about 0.2 kcal/mol. Based
on these results and a review of the theory, we conclude, in contrast to
previous work (Ho, J.; Klamt, H.; Coote, M. L. *J. Phys. Chem. A*
**2010**, *114*, 13442), that using partition functions computed
for molecules optimized in solution is a correct and useful approach for
averaging over solute degrees of freedom when computing free energies of
solutes in solution, and is moreover recommended for cases where liquid and
gas-phase solute structures differ appreciably or when stationary points
present in liquid solution do not exist in the gas phase, for which we
provide some examples. When gas-phase and solution-phase geometries and
frequencies are similar, the use of gas-phase geometries and frequencies is
a useful approximation.