  We studied the effect of self-interaction error (SIE) on the static dipole
polarizabilities of water clusters modelled with three increasingly
sophisticated, non-empirical density functional approximations (DFAs), viz. the
local spin density approximation (LDA), the Perdew-Burke-Ernzherof (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-L\"owdin
orbital SIC (FLO-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 0.58
Bohr$^3$ with respect to coupled cluster singles and doubles (CCSD) values.
Removing SIE using PZ-SIC correctly reduces the DFA polarizabilities, but
over-corrects, resulting in underestimated polarizabilities in SIC-LDA, -PBE,
and -SCAN. Finally, we applied a recently proposed local-scaling 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 error of 0.08
Bohr$^3$ for LSIC-LDA and 0.06 Bohr$^3$ for LSIC-PBE with most recent CCSD
polarizabilities. Likewise, the ionization energy estimates as an absolute of
highest occupied energy eigenvalue predicted by LSIC are also in excellent
agreement with CCSD(T) ionization energies with MAE of 0.4 eV for LSIC-LDA and
0.04 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 reported GW results.
