Local self-interaction correction method with a simple scaling factor

A recently proposed local self-interaction correction (LSIC) method [Zope \textit{et al.} J. Chem. Phys., 2019,{\bf 151}, 214108] when applied to the simplest local density approximation provides significant improvement over standard Perdew-Zunger SIC (PZSIC) for both equilibrium properties such as total or atomization energies as well as properties involving stretched bond such as barrier heights. The method uses an iso-orbital indicator to identify the single-electron regions. To demonstrate the LSIC method, Zope \textit{et al.} used the ratio $z_\sigma$ of von Weizs\"acker $\tau_\sigma^W$ and total kinetic energy densities $\tau_\sigma$, ($z_\sigma = \tau_\sigma^W/\tau_\sigma$) as a scaling factor to scale the self-interaction correction. The present work further explores the LSIC method using a simpler scaling factor as a ratio of orbital and spin densities in place of the ratio of kinetic energy densities. We compute a wide array of both, equilibrium and non-equilibrium properties using the LSIC and orbital scaling methods using this simple scaling factor and compare them with previously reported results. Our study shows that the present results with simple scaling factor are comparable to those obtained by LSIC($z_\sigma$) for most properties but have slightly larger errors. We furthermore study the binding energies of small water clusters using both the scaling factors. Our results show that LSIC with $z_{\sigma}$ has limitation in predicting the binding energies of weakly bonded system due to the inability of $z_{\sigma}$ to distinguish weakly bonded region from slowly varying density region. LSIC when used with density ratio as a scaling factor, on the other hand, provides good description of water cluster binding energies, thus highlighting the appropriate choice of iso-orbital indicator.