Formulating the problem for a simple system of two atoms with electronic densities expressed as a single Gaussian function leads to exact expressions. Previous studies have shown that expanding electronic densities with primitive Hermite Gaussian functions can accurately describe Coulomb and exchange-repulsion energies between interacting molecules . For our model, we provide a general formula to include terms up to a K th order approximation for the exchange and correlation correction by means of consecutive applications of the Laplace operator, thus leading to a formula that does not make use of inverse power laws terms but instead linear combinations of expressions that are functionals of the non-interacting electron densities, that in our numerical preliminary tests are more accurate than several commonly used force field models for high energy interactions when using ab initio calculated results as reference. In the Methods sections we describe how the electronic density of each molecule is modeled from data acquired from quantum mechanical calculations, and how we use them to calibrate our exchange and correlation potential. In the results section we compare results for different molecules with established force field models. Finally, we present our conclusions.