Interatomic Repulsive Potentials at Very Small and Intermediate Separations

Using a minimal and a maximal principle, respectively, two approximate expressions for the interaction potential between atoms are given such that their mean, $\overline{U}\mathrm{}\left(R\right)\mathrm{}$, differs from the exact value, $U_0$, in the Thomas-Fermi-Dirac (TFD) approximation, by not more than 4% for the case of two-center system; and by not more than 14%, in the Thomas-Fermi (TF) approximation, for the case of a three-center system. The respective limits of applicability of these potentials are discussed, and some of their applications are pointed out.