An explicit expression for the pair short-range effective interaction potential of "atoms" is derived based on the model of "pure" matter. This model represents the equilibrium Coulomb system of interacting electrons and nuclei of the same type, using the adiabatic approximation for nuclei, the self-consistent Hartree-Fock approximation for the electronic subsystem, the "one-center" approximation to describe localized electronic states, and the perturbation theory with respect to the fluctuating field. It is shown that the found potential is completely defined by the inhomogeneous density and inhomogeneous density matrix of electronic states in the isolated "atom".
Bobrov, V. B., Trigger, S. A., Heijst, van, G. J. F., & Sokolov, M. (2013). Effective pair potential for atoms in the Coulomb model of substance. EPL, 101(3), 35002-1/6. . https://doi.org/10.1209/0295-5075/101/35002