Electron-impact study of the SO radical using theR-matrix method

Abstract

The SO radical with an even number of electrons belongs to an open-shell system due to its ${\ensuremath{\pi}}^{2}$ ground-state electronic configuration. This configuration gives rise to three low-lying states $X {}^{3}{\ensuremath{\Sigma}}^{\ensuremath{-}}$, $a {}^{1}\ensuremath{\Delta}$, and $b {}^{1}{\ensuremath{\Sigma}}^{+}$. The inclusion of these target states in a trial wave function of the entire scattering have important implications in the resonances that may be detected in this open-shell molecule. The $R$-matrix method is a well-established ab initio formalism which is employed to calculate elastic differential and integral cross sections, momentum-transfer cross sections, and inelastic cross sections. The Hartree-Fock ground-state configuration of SO is $1{\ensuremath{\sigma}}^{2}2{\ensuremath{\sigma}}^{2}3{\ensuremath{\sigma}}^{2}4{\ensuremath{\sigma}}^{2}1{\ensuremath{\pi}}^{4}5{\ensuremath{\sigma}}^{2}6{\ensuremath{\sigma}}^{2}7{\ensuremath{\sigma}}^{2}2{\ensuremath{\pi}}^{4}3{\ensuremath{\pi}}^{2}$. We have included 28 target states in the trial wave function of the scattering system. In our configuration-interaction (CI) model, we freeze $12$ electrons in orbitals $1\ensuremath{\sigma}$, $2\ensuremath{\sigma}$, $3\ensuremath{\sigma}$, $4\ensuremath{\sigma}$, and $1\ensuremath{\pi}$, the remaining 12 electrons are free to move among the eight orbitals $4\ensuremath{\sigma}$, $5\ensuremath{\sigma}$, $6\ensuremath{\sigma}$, $7\ensuremath{\sigma}$, $8\ensuremath{\sigma}$, $9\ensuremath{\sigma}$, $2\ensuremath{\pi}$, and $3\ensuremath{\pi}$. We have carried our scattering calculations in static-exchange, one-state with CI wave function, and 28-state models. We have detected a stable anionic bound state ${}^{2}{B}_{1}$ of SO at various bond lengths of SO molecule. The vertical electron affinity value is 0.970 eV, which is comparable to the experimental value of 1.125 eV. We also detected two core-excited shape resonances, both of ${}^{2}\ensuremath{\Pi}$ symmetry and with ${}^{1}\ensuremath{\Delta}$ and ${}^{1}{\ensuremath{\Sigma}}^{+}$ as the parent states.