One-electron diatomics in momentum space. I. Implication of first iterated solutions for the ground state

For one-electron diatomic systems, an iterative solution of the momentum-space Schroedinger equation is examined using the Fock transformation which enables us to expand the kernel of the integral equation by the four-dimensional spherical harmonics. Starting from the united atom (UA) and simple LCAO approximations, first iterated solutions are derived and their properties are analyzed. The corresponding approximate energy eigenvalues are also obtained as a function of the internuclear distance R. The result from the LCAO starting function is found to be reliable semiquantitatively: in the range of 0< or =R< or =20, the maximum errors of the ground-state electronic energy are 4.7% and 1.7%, respectively, for the H+2 and HeH2+ systems, when compared with the exact values