Dependence of Induction and Dispersion Energies at Finite Internuclear Distances

The usual calculations of induction and dispersion energies lead to divergent series in negative powers of the distance $R$ which have been interpreted as asymptotic expansions. The system composed of a normal hydrogen and a proton at a finite separation is treated by an extended variation method, leading to Euler equations for the perturbed wave functions. Solutions in terms of known functions are used to calculate the two principal terms of the second-order energy for a number of values of $R$. The method is found to lead to convergent results for all values of $R$, and to be compatible with the virial theorem. Extension to more complex cases and to dispersion is qualitative. A variation calculation, using traditional and other plausible trial functions with the correct potential, is compared.