The addition of a lithium salt forms an insoluble lithium aluminate salt film on an aluminum surface, effectively preventing aluminum corrosion. Other aluminate salts of alkali metals lack this behavior, being easily dissolved into water. In this study, the reason for the difference in behavior is investigated by applying molecular orbital calculation to clusters of ions and molecules. The difference in solubility among aluminate salts of alkali metals is attributed to the difference in binding energy between the anion cluster and the alkali metal ion cluster with the first layer of water molecules surrounding the alkali metal ion. Calculations show that this difference of binding energy arises from the difference in the sum of the cohesive energy, the variation of the coordinate bond energy between an alkali metal ion and water molecules surrounding it, and the interaction energy between those water molecules and an anion, in a salt molecule cluster. These three factors, in turn, derive from the difference in ion radius of the alkali metals. The binding energy in lithium aluminate is about 25 kJ/mol larger than that in sodium aluminate and about 45 kJ/mol larger than in potassium aluminate. The binding energy of antimonate salts of alkali metals is also calculated as a second example in which the value of the ion radii causes the insolubility, to verify the explanation. Then, the binding energy in the sodium antimonate is about 5 kJ/mol larger than in the lithium antimonate, and about 15 kJ/mol larger than that in the potassium antimonate. The ratio of the lithium ion radius to the aluminum ion radius is 1.4, nearly as much as that of the sodium ion radius to the antimony ion radius. This value of ion radii ratio made the binding energy largest of the aluminate or antimonate salts.