Theory

Eon TK is used to model the electrostatics of molecules via charge density and via Poisson-Boltzmann (PB) potential. Some key conceptual points for both of these approaches are discussed below.

Electrostatic Charge Gaussians

The charge density of a molecule is modeled via the sum of distributed Gaussians centered at the atom centers and with prefactors proportional to partial charges:

\[\rho_{\text{charge}} = \sum_{i=1}^{N_{\text{A}} }\frac{C_i}{\left(\sqrt{2\pi}\sigma\right)^3} \, e^{-\left[(x-x_i)^2+(y-y_i)^2+(z-z_i)^2\right]^2/{2\sigma^2}}\]

where C_i , x_i , y_i , and z_i are the charge coordinates of atom i and sigma is the charge density Gaussian width. With this charge density, the charge density similarity and the shape and charge density similarity combo can be computed, leveraging the Gaussian technology at the heart of Shape TK.

Electrostatic PB Potential

The potential similarity measurement uses Zap TK and the field-based Tanimoto, which depends on partial charges on the molecule as well as on the dielectric properties of the medium. For the electrostatics PB overlay, the molecules are aligned with shape and charge similarity first. A certain number of the best hits (typically five) are kept, which are further rescored with shape and PB potential similarity to find the best hit. This is a fast approach compared to rigid optimization of the PB potential similarity. This approach has been explored in the literature ([Muchmore-2006]; [Naylor-2009]; [Boström-2013]).