  Accurate description of the excess charge in water cluster anions is
challenging for standard semi-local and (global) hybrid density functional
approximations (DFAs). Using the recent unitary invariant implementation of the
Perdew-Zunger self-interaction correction (SIC) method using Fermi-L\"owdin
orbitals, we assess the effect of self-interaction error on the vertical
detachment energies of water clusters anions with the local spin density
approximation (LSDA), Perdew-Burke-Ernzerhof (PBE) generalized gradient
approximation, and the strongly constrained and appropriately normed (SCAN)
meta-GGA functionals. Our results show that for the relative energies of
isomers with respect to reference CCSD(T) values, the uncorrected SCAN
functional has the smallest deviation of 21 meV, better than that for the MP2
method. The performance of SIC-SCAN is comparable to that of MP2 and is better
than SIC-LSDA and SIC-PBE, but it reverses the ordering of the two lowest
isomers for water hexamer anions. Removing self interaction error (SIE)
corrects the tendency of LSDA, PBE, and SCAN to over-bind the extra electron.
The vertical detachment energies (VDEs) of water cluster anions, obtained from
the total energy differences of corresponding anion and neutral clusters, are
significantly improved by removing self-interaction and are better than the
hybrid B3LYP functional, but fall short of MP2 accuracy. Removing SIE results
in substantial improvement in the position of the eigenvalue of the extra
electron. The negative of the highest occupied eigenvalue after SIC provides an
excellent approximation to the VDE, especially for SIC-PBE where the mean
absolute error with respect to CCSD(T) is only 17 meV, the best among all
approximations compared in this work.
