Study of self-interaction errors in density functional predictions of dipole polarizabilities and ionization energies of water clusters using Perdew-Zunger and locally scaled self-interaction corrected methods.

We studied the effect of self-interaction error (SIE) on the static dipole polarizabilities of water clusters modeled with three increasingly sophisticated, non-empirical density functional approximations (DFAs), viz., the local spin density approximation (LDA), the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA), and the strongly constrained and appropriately normed (SCAN) meta-GGA, using the Perdew-Zunger self-interaction-correction (PZ-SIC) energy functional in the Fermi-Löwdin orbital SIC framework. Our results show that while all three DFAs overestimate the cluster polarizabilities, the description systematically improves from LDA to PBE to SCAN. The self-correlation free SCAN predicts polarizabilities quite accurately with a mean absolute error (MAE) of 0.53 bohr with respect to coupled cluster singles and doubles (CCSD) values. Removing SIE using PZ-SIC correctly reduces the DFA polarizabilities, but overcorrects, resulting in underestimated polarizabilities in SIC-LDA, SIC-PBE, and SIC-SCAN. Finally, we applied a recently proposed locally scaled SIC (LSIC) method using a quasi self-consistent scheme and using the kinetic energy density ratio as an iso-orbital indicator. The results show that the LSIC polarizabilities are in excellent agreement with mean absolute errors of 0.08 bohr for LSIC-LDA and 0.06 bohr for LSIC-PBE with most recent CCSD polarizabilities. Likewise, the ionization energy estimates as absolute of highest occupied energy eigenvalue predicted by LSIC are also in excellent agreement with CCSD(T) ionization energies with MAEs of 0.4 eV for LSIC-LDA and 0.06 eV for LSIC-PBE. The LSIC-LDA predictions of ionization energies are comparable to the reported GW ionization energies, while the LSIC-PBE ionization energies are more accurate than the reported GW results.