Convergence properties and large-order behavior of the polarization expansion for the interaction energy of hydrogen atoms

High-order corrections in the polarization expansion for the interaction energy of two ground-state hydrogen atoms are computed for a wide range of interatomic distances R. At large R, the convergence radius ρ of the expansion is found to be only slightly greater than unity, e.g. ρ = 1.0000000031 at the van der Waals minimum for the triplet state. The branch points determining ρ are calculated and used in a convergence acceleration procedure, which shows that the polarization expansion is a sum of two series — one converging quickly to the Coulomb energy and the other also converging, although extremely slowly for large R, to the negative of the exchange energy. The total series converges to the energy of the ground state of the hydrogen molecule. A simple formula describing the large-order behavior of the polarization series at large R is derived and used to show that the exchange energy can be accurately calculated from the knowledge of three consecutive large-order polarization energies.