Degenerate symmetry‐adapted perturbation theory. Convergence properties of perturbation expansions for excited states of H 2 + ion

The degenerate Rayleigh-Schrodinger (RS), Murrell–Shaw–Musher–Amos (MSMA), and Eisenschitz–London—Hirschfelder–van der Avoird (EL–HAV) perturbation theories are formulated and applied through high order to the interaction of a hydrogen atom with a proton for the excited 2sσg, 3pσu, 3dσg, and 4fσu states of the system. In contrast to the 1sσg and 2pσu states all the formalisms fail to provide a convergent series for any of the above states. However, numerical evidence is given that for sufficiently large internuclear separations the RS series is able to reproduce the Coulomb energy with an accuracy better than an arbitrary fraction of the exchange energy. Similarly the exchange energy can be reproduced by the sum of a few exchange corrections of the MSMA method. It has also been shown that both the MSMA and EL–HAV series can be continued analytically beyond the convergence radius by means of Pade approximants.