Prolate-spheroidal orbitals for homonuclear and heteronuclear diatomic molecules. III. Shielding effects for the many-electron problem

The determination of shielded diatomic orbitals (SDO's) which are eigenfunctions in prolate-spheroidal coordinates, of the two-center problem with an effective (cylindrically symmetric) parametric potential, is extended to many-electron systems. The simultaneous iterative resolution of the separated equations is significantly improved by the consideration of a simple electrostatic model and of the connection with a Mathieu equation. Calculations are carried out for three- and four-electron diatomic systems, i.e., HeH, Li${\mathrm{H}}^{+}$, ${\mathrm{He}}_2^{+}$, LiH, and ${\mathrm{He}}_2$ in their ground states. From our results, the SDO's appear to be comparable to the self-consistent field orbitals. They should be also a good basis set for "diabatic" molecular states. Possibility of an extension, without supplementary difficulties, of the effective potential is investigated.