Importance of Self-Interaction Correction in Hydrogen-Bonded Water Clusters and Water-Ion Clusters

Abstract

Density functional theory is the most commonly used computational tool to study properties of solids and molecules. Self-interaction error, that arises due to improper cancellation of the self-Hartree and the self exchange correlation energy, has long been identified as a major limitation of practical density functional approximations. We develop and test the performance of different self-interaction corrected functionals in accurately predicting a wide range of properties. This work focuses on use of the Fermi-L\"{o}wdin orbital self-interaction correction (FLOSIC) method to study neutral water complexes and interaction of ions with water clusters. The strongly constrained and appropriately normed (SCAN) density functional approximation (DFA) has been found to give the correct energy ordering of low-lying isomers of water hexamers, resolves the density anomaly between water and ice, and improves the relative lattice energy of ice polymorphs and the infrared spectra of liquid water. However, SCAN is not without its drawbacks. The binding energies of water clusters and lattice energies of ice phases are overestimated by SCAN. We find that by explicitly removing the self-interaction error, the hydrogen-bond binding energy of water clusters can be significantly improved. In particular, self-interaction correction to the SCAN functional (FLOSIC-SCAN) improves binding energies without altering the correct energetic ordering of the low-lying water hexamers. So, orbital-by-orbital removal of self-interaction error applied on top of a proper DFA can lead to an improved description of water complexes. To gain further insight into the performance of different functionals on the relative stability of water clusters, we decompose the total interaction energy into many-body components. We see that the major portion of error in SCAN comes from the two-body interaction, and the FLOSIC-SCAN improves two-body interactions over SCAN and predicts higher-order many-body interactions with about the same accuracy as SCAN. The SCAN functional gives good account of monomer deformation energy (one-body energy), PBE estimated it too low and self-interaction corrected methods FLOSIC-PBE and FLOSIC-SCAN estimated too high monomer deformation energies. Improvement in the total interaction energy by FLOSIC-PBE and FLOSIC-SCAN is happening because of error cancellation by one-body interaction energy.

Aqueous solutions of ions are of particular interest due to their profound applications in environmental chemistry, solvation mechanics, the desalination process, etc. This motivated us to study ion-water systems, which include hydronium ion-water clusters, hydroxyl ion-water clusters, halide ion-water clusters, and alkali ion-water clusters. The erroneous delocalization of the extra-electron in anions obtained with DFAs is basis-set dependent. DFAs like LSDA, PBE, or SCAN can bind only a fraction of the excess electron in the complete basis set limit, implying that a moderate-sized localized basis would be a good choice for them. But, accurate description of hydrogen bonds often requires a large basis with some extra diffuse functions. So, in negatively charged hydrogen-bonded systems like deprotonated water clusters, the suitable choice of basis-set is both difficult and ambiguous. We explore this issue systematically in this work. Further, we have found that the better performance by application of FLOSIC is seen in all systems that are connected at least with one hydrogen bond and the error in the binding energy decreases with increase in the size of an ion or equivalently decreases with the length of the hydrogen bond. Moreover, within the same ion-water system, error in the binding energy decreases with increase in the size of the cluster. Non-hydrogen-bonded water-alkali clusters are not affected by the self-interaction errors.