Analytical multiconfiguration treatment to one-center many-electron He-isoelectronic ions and Period-II elements with H-like bound-states

• Published in: Theoretical chemistry accounts Vol. 142; no. 10
• Main Authors: Kapil, Bharti, Sharma, Shivalika, Aggarwal, Priyanka, Hazra, Ram Kuntal
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2023; Springer Nature B.V
• Subjects: Atomic/Molecular Structure and Spectra; Chemistry; Chemistry and Materials Science; Configurations; Dipoles; Electron spin; Electronic structure; Electrons; Hartree approximation; Inorganic Chemistry; Integrals; Mathematical analysis; Organic Chemistry; Physical Chemistry; Polynomials; Quadrupoles; Self consistent fields; Theoretical and Computational Chemistry; Ground state energies; Hydrogenic bound states; Period-II elements; Analytical multiconfiguration treatment; isoelectronic ions; Coulomb Green function
• ISSN: 1432-881X; 1432-2234
• DOI: 10.1007/s00214-023-03011-x

Employing H -like spin-orbitals (SOs) in electronic structure theory is a long-awaited quantum problem as the analytical integral of Coulomb interaction is very difficult to solve for one-center many-electron (1 c - ne ) system. He -isoelectronic ions become a benchmark. Complexity grows fast for Period-II s - and p -block elements with increasing number of electrons. Moreover, Hartree-Fock Self-Consistent Field (SCF) and post Hartree-Fock SCF theories generally make use of closed-shell, restricted and unrestricted open-shell single configurations (SCs) but actual electronic bound states urge for multiconfigurations (MCs). After Born-Oppenheimer (BO) approximation, utilization of associated Laguerre polynomial/Whittaker- M function basis sets of H -like SOs for the Coulomb Green ′ s function among electrons furnishes analytical, terminable, simple and finitely summed integrals in terms of Lauricella functions. MCs complying with so-called ground, singly and multiply excited states incurring s - and p -SOs are constructed to capture monopole and dipole factors only. However, we believe that quadrupole and higher order poles can be achieved as a product of angular integrals using Wigner 3- j symbols and closed forms of radial integrals. We have observed good agreement among literature and exact ground state energies (GSEs) of He -isoelectronic ions and Period-II elements with both their so-called ground electronic configurations as well as MCs. For certain elements, we have found satisfactory results for ionization energies (IEs).