We fitted the electronic densities of the atoms in the first three rows of the periodic table with a combination of three s-type Gaussian basis-functions. Using this basis, the first-order interaction energies can be calculated from the non-interacting electronic densities. More accurate interaction energies are obtained by expanding the densities in a series of their derivatives. The terms appearing can be interpreted as the exchange and correlation interaction correction terms. Using the Hohenberg-Kohn theorem we show that such a kind of functional exists. A rather high order expansion (6 or above) is necessary, though, to accurately model the interaction energies. We test our force field model on a wide variety of water dimer configurations and a few oxygen dimer configurations. Overall, our model accurately predicts the interaction energies between dimers of water that do not exceed 400 kJ/mol. This limit stems from the electronic densities being approximated from an ECP basis-set and is not intrinsic to our method. For interaction energies below 400 kJ/mol our model far outperforms other popular force fields in the literature concerning the repulsive "high temperature" part of the potential energy surfaces.