Coulomb Sturmians in spheroidal coordinates and their application for diatomic molecular calculations

Coulomb Sturmians are obtained in prolate spheroidal coordinates by separation of variables in the Schr¨odinger equation and direct solution of the appropriate one-dimensional equations. Molecular orbitals are expressed as linear combinations of the introduced Coulomb Sturmians and some low-lying energy terms and corresponding wave functions are calculated for one-electron diatomic molecules. It is shown that similarity of the one- and two-centre orbitals in spheroidal coordinates, combined with completeness and good convergence properties of Coulomb Sturmians, substantially speeds up convergence and makes the calculated results closer to the exact ones. Application of the elaborated calculating scheme for diatomic many-electron molecules is discussed. Keywords: diatomic molecules; spheroidal coordinates; Coulomb Sturmian