Accuracy of fragmentation in ab initio calculations of hydrated sodium cation

We discuss the accuracy of fragmentation in fragment molecular orbital (FMO) calculations for the hydrated sodium ion. Two-body expansion shows a considerable error in total energy even if water molecules in the second hydration shell are included in the same fragment as the sodium ion. Inclusion of the three-body term significantly improves both the total energy and the charge distributions. We also illustrate the dependence of the net charge of sodium ion on solvent size and the interfacial property of water molecules. The present study will thus provide fundamental information about hydrated ion to facilitate further theoretical and experimental studies.