Analytical two-center one-electron overlap and exchange integrals for 1Σ states: Lah number guided Coulomb Green function of <bold>H</bold>-like <bold>s</bold>-orbitals.

Theoretical studies of two-center one-electron (2c-1e) small microcluster are associated with hurdles in Schr o &#168; dinger equation (SE) born out of divergence of Coulomb interactions and nuclear separation (R). The SE deals with morphologically altered H-like AOs, Slater type orbitals (STO), Gaussian type orbitals (GTO), B-spline, Sturmian function and etc in both VBT and MOT calculations. Few elegant computational and analytical methods are available for STO, GTO and other square integrable trial wavefunction under Born-Oppenheimer approximation. Even so, analytical treatment for H-like AOs has become very necessary. Utilizing Sheffer identity in associated Laguerre polynomial/Whittaker-MH-like AOs and adopting elliptic coordinates provide exact, analytical and simple 2c-1e Coulomb exchange interactions (Ks) and overlap integrals as functions of R with different scaling factors associated with electrons. The energetics of diatomic molecule is evident to be the function of R with extrema as Lah number moderated L n - 1 for nuclear coordinates. Analytical and simple 2c-1e Coulomb exchange interactions (Ks) and overlap integrals (Ss) as functions of R are presented utilizing Sheffer identity in associated Laguerre polynomial/ Whittaker-MH-like AOs and adopting elliptic coordinates mediated through Lah number. The energetics of the diatomic molecule is evident to be the function of R. [ABSTRACT FROM AUTHOR]