Abstract
The Fock transformation reduces the momentum-space Schrödinger equation for one-electron diatomics to a homogeneous Fredholm-type integral equation with a degenerate kernel. Two nonvariational linear combination of atomic orbitals (LCAO) solutions to this integral equation are rederived in a systematic manner and their mutual relation is clarified. The upper boundness of these nonvariational solutions is proved explicitly. Relative superiority of the two solutions is discussed theoretically based on their convergence rates. The momentum-space LCAO method is shown to reproduce the exact electronic energy for the hydrogen molecular ion at various internuclear distances.
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