Accounting for Polarization Cost When Using Fixed Charge Force Fields. II. Method and Application for Computing Effect of Polarization Cost on Free Energy of Hydration

Polarization cost is the energy needed to distort the wave function of a molecule from one appropriate to the gas phase to one appropriate for sonic condensed phase. Although it is not currently standard practice, polarization cost should be considered when deriving improved fixed charge force fields based on fits to certain types of experimental data and when using such force fields to compute observables that involve changes in molecular polarization. Building on earlier work, we present mathematical expressions and a method to estimate the effect of polarization cost on free energy and enthalpy implied by a charge model meant to represent a solvated state. The charge model can be any combination of point charges, higher-order multipoles, or even distributed charge densities, as long as they do not change in response to environment. The method is illustrated by computing the effect of polarization cost on free energies of hydration for the neutral amino acid side chain analogues as predicted using two popular fixed charge force fields and one based on electron densities computed using quantum chemistry techniques that employ an implicit model to represent aqueous solvent. From comparison of the computed and experimental hydration free energies, we find that two commonly used force fields are too underpolarized in their description of the solute water interaction. On the other hand, a charge model based on the charge density from a hybrid density functional calculation that used an implicit model for aqueous solvent performs well for hydration free energies of these molecules after the correction for dipole polarization is applied. As such, an improved description of the density (e.g., B3LYP, MP2) in conjunction with an implicit solvent (e.g., PCM) or explicit solvent (e.g., QM/MM) approach may offer promise as a starting point for the development of improved fixed charge models for force fields.