Asymptotics of the two-centre wave function in the spheroidal and spherical bases

Abstract

The first two terms of the asymptotics (for large internuclear distances R) of the spheroidal wave function of the two-Coulomb-center problem are calculated both in the internuclear region and in the vicinity of each of centers. In the spherical basis, the general formula is obtained for the expansion of a two-center wave function of the left center in two-center spheroidal wave functions. Using this formula, the asymptotics of the two-center wave function in a spherical basis is calculated, which in boundary cases is compared with the results of other authors. The combined use of the approach developed in this paper and the Holstein-Herring method made it possible for the first time to calculate the term proportional to R−2 of the asymptotic expansion of the quasimolecule energy in spherical quantum numbers.