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

Employing H-like spin-orbitals (SOs) in electronic structure theory is a long-awaited quantum problemas the analytical integral of Coulomb interaction is very difficult to solve for one-center manyelectron(1c-ne) system. He-isoelectronic ions become a benchmark. Complexity grows fast forPeriod-II s- and p-block elements with increasing number of electrons. Moreover, Hartree-FockSelf-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 statesurge for multiconfigurations (MCs). After Born-Oppenheimer (BO) approximation, utilization ofassociated Laguerre polynomial/Whittaker-M function basis sets of H-like SOs for the CoulombGreen′s function among electrons furnishes analytical, terminable, simple and finitely summed integralsin terms of Lauricella functions. MCs complying with so-called ground, singly and multiplyexcited 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 angularintegrals using Wigner 3-j symbols and closed forms of radial integrals. We have observed goodagreement among literature and exact ground state energies (GSEs) of He-isoelectronic ions andPeriod-II elements with both their so-called ground electronic configurations as well as MCs. Forcertain elements, we have found satisfactory results for ionization energies (IEs).