Pairwise Polarization

The Problem:

The use of macroscopic equations at the molecular scale has led to incongruities in methodology. Force field models generally assume a vacuum dielectric permittivity of one, ε_r=1. However, when the model is later used, the permittivity is generally set to 2 to 4 as indicated for protein simulations. This introduces inconsistency into the methodology. In particular, force fields reproduce binding affinity. The use of larger permittivity in applications produces calculated electrostatic affinities (drug-protein interaction energies) that are a fraction of the experimental result.

Electrostatic equations use a classical raisin-in-plum-pudding model of point charges in continuous dielectric material. However this model does not accommodate the atomistic nature of the dielectric at the molecular scale. In particular it does not consider the near vacuum between atoms, or the near vacuum field about a charged atom, or the distance over which the wavefunction responds to the charge, or the rapid change in potential between nearby atoms when there is sufficient separation to permit a third atom to intervene. Most analyses also do not consider the attraction between a charge and the charge it induces. These aspects are handled properly in a microscopic calculation with polarizable atoms, however polarizable methods require significant computational resources and this level of calculation is not accessible for many applications.