We study the importance of self-interaction errors in density functional approximations for various water-ion clusters. We have employed the Fermi-Lowdin orbital self-interaction correction (FLOSIC) method in conjunction with LSDA, PBE, and SCAN to describe binding energies of hydrogen-bonded water-ion clusters, textit{i.e.}, water-hydronium, water-hydroxide, water-halide, as well as non-hydrogen-bonded water-alkali clusters. In the hydrogen-bonded water-ion clusters, the building blocks are linked by hydrogen atoms, although the links are much stronger and longer-ranged than the normal hydrogen bonds between water molecules, because the monopole on the ion interacts with both permanent and induced dipoles on the water molecules. We find that self-interaction errors overbind the hydrogen-bonded water-ion clusters and that FLOSIC reduces the error and brings the binding energies into closer agreement with higher-level calculations. The non-hydrogen-bonded water-alkali clusters are not significantly affected by self-interaction errors. Self-interaction corrected PBE predicts the lowest mean unsigned error in binding energies ($leq$ 50 meV/ce{H2O}) for hydrogen-bonded water-ion clusters. Self-interaction errors are also largely dependent on the cluster size, and FLOSIC does not accurately capture the subtle variation in all clusters, indicating the need for further refinement.
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