Self-interaction error overbinds water clusters but cancels in structural energy differences

Self-interaction error has long been identified as one of the limitations of practical density functional approximations. This error originates in the inability of approximate density functionals to exactly cancel self-Coulomb and self-exchange\textendashcorrelation for all one-electron densities. Self-interaction error can be subtracted from an approximate functional on an orbital-by-orbital basis, improving the description of stretched bonds. In this work, we show that, by explicitly removing self-interaction error, the hydrogen bond binding energies of water are also significantly improved. In particular, the self-interaction correction to SCAN improves binding energies and the many-body analysis without altering the correct energy ordering for small water clusters.We gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi\textendashL\"owdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew\textendashBurke\textendashErnzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a density-driven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction\textendashcorrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/H2O from about 42 meV/H2O for SCAN. By decomposing the total binding energy into many-body components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN and self-interaction\textendashcorrected SCAN. These results indicate that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes.