Self-consistent electrostatic embedding for liquid phase polarization

While it is well known that molecules can be strongly polarized when transferred from the gas phase to a polar liquid, quantifying polarization effects explicitly using either experiment or theory has remained elusive. In this paper, we present a new QM/MM method involving a self-consistent calculation of the liquid state dipole moments, that is able to yield realistic, accurate estimates of the multipole moments of molecules in the liquid state. As a proof-of-concept, we apply our Self-Consistent Electrostatic Embedding (SCEE) method to the widely studied system of pure water. The method gives molecular dipole moments that are significantly enhanced with respect to the isolated gas-phase molecule and that are consistent with the best current experimental estimate of this property. While previous QM/MM calculations on the same system systematically underestimate the liquid dipole moment, those predictions become consistent with our own when several shortcomings are accounted for in an approximate way. Furthermore, sampling liquid configurations using several (but not all) fixed-charge force fields yields results that are consistent with sampling from a classical polarizable model. We then extract several contributions to the polarization energy (i.e. the change in energy when transferring a molecule from the gas to the liquid phase) and show that the distortion correction is cancelled out by the purely electronic contribution to the polarization energy. This insight is very important from the point of view of force-field development, since it allows us to unequivocally quantify the two missing energy terms in classical non-polarizable models. This provides a way to systematically improve predictions of phase-change energies (e.g. enthalpy of vaporization, hydration free energies) from such force-fields by correcting for the missing polarization effects.