Convergence of multipole expanded intermolecular interaction energies for Gaussian-type-function and Slater-type-function basis sets

It is shown that the multipole expansion of each order of the polarization series converges for large enough intermolecular distances when finite basi s sets of Gaussian or Slater-type functions are used to approximate molecul ar response properties. Convergence of the multipole expansion for each ord er of the polarization series does not imply convergence of the polarizatio n series itself. A corresponding convergence condition is extracted from th e general perturbation theory in a finite-dimensional space and is applied to the H + H+ problem.