United Atom Treatment of the Behavior of Potential Energy Surfaces of Polyatomic Molecules at Small Internuclear Distances

It is shown that the potential energy function of any state of a polyatomic molecule can be expanded for small internuclear distances in the form $$\mathrm{V=}{\displaystyle \sum }{\displaystyle \sum _{\mathrm{\alpha >\beta }}}{Z}_{\alpha }{Z}_{\beta }{\mathrm{/R}}_{\mathrm{\alpha \beta }}{\mathrm{+W}}_u+{\displaystyle \sum _{\alpha }}{\mathrm{(E}}_{\text{2α}}{\mathrm{·R}}_{\alpha }^2{\mathrm{+E}}_{\text{3α}}{\mathrm{·R}}_{\alpha }^3\mathrm{+···),}$$ where W_u is the energy of the particular state u of the united atom (UA) to which the molecular state in question connects, and R_α is the distance of the αth nucleus from the UA. Explicit expressions for the coefficients E_2α, E_3α are given in terms of the electronic charge density of the UA. The derived energy expansion is applied to the molecules CH₄, NH₃, H₂O, and HF which all correspond to the united atom Ne.