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

Local self-interaction correction method with a simple scaling factor