Accounting for Polarization Cost When Using Fixed Charge Force Fields. I. Method for Computing Energy

Although it is not currently standard practice, the cost to change the electronic polarization from one appropriate for the gas phase to that implied by the charge model should be considered when deriving force fields based on fits to certain types of experimental data and for using force fields to compute observables that involve changes in molecular polarization. We present mathematical expressions and a method to estimate this polarization cost implied by a fixed charge model force field, where the fixed 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. These expressions illuminate the relationship between polarization costs associated with fixed charge models, self-polarization energies of polarizable models, and quantum chemical based approaches that use continuum representations of the solvent, such as the self-consistent reaction field and polarizable continuum models. The technique takes account of the tensorial nature of the polarizabilities and includes quadrupole as well as dipole polarization. The consistency of this approach to one that estimates polarization cost using an implicit solvent quantum chemistry method (PCM) is demonstrated.