DOES THE POLARIZATION APPROXIMATION CONVERGE FOR LARGE-R TO A PRIMITIVE OR A SYMMETRY-ADAPTED WAVE-FUNCTION

Asymptotic expressions for the branch points that most likely determine the radii of convergence for the polarization approximation of the ground states of H-2(+) and H-2 are derived. In both cases the radius of convergence is greater than 1 for all R. The radius of convergence for H-2(+) differs from unity by a term asymptotically proportional to R3e-2R, for H-2 by a term of the order R6e-4R. In view of these results, for large R the convergence of the polarization approximation to the exact ground states is so slow that this expansion behaves as if it were converging to a primitive wavefunction (and to the average of the energies of the g and u states). The Hirschfelder-Silbey expansion is free from this defect.