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

• Published in: Journal of chemical sciences (Bangalore, India) Vol. 135; no. 2
• Main Authors: Kapil, Bharti, Hazra, Ram Kuntal
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 30.05.2023
• Subjects: Chemical Reactivity and Biological Systems; Chemistry; Chemistry and Materials Science; Chemistry/Food Science; Interplay of Structure and Dynamics in Reaction Pathways; Regular Article
• ISSN: 0973-7103
• DOI: 10.1007/s12039-023-02153-6

Theoretical studies of two-center one-electron (2 c -1 e ) small microcluster are associated with hurdles in Schr o ¨ 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- M H -like AOs and adopting elliptic coordinates provide exact, analytical and simple 2c-1 e Coulomb exchange interactions ( K s) 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. Graphical abstract Analytical and simple 2 c -1 e Coulomb exchange interactions ( Ks ) and overlap integrals ( Ss ) as functions of R are presented utilizing Sheffer identity in associated Laguerre polynomial/ Whittaker- M H -like AOs and adopting elliptic coordinates mediated through Lah number. The energetics of the diatomic molecule is evident to be the function of R.