These results indicate that the metastable state has a lower energy (i.e., it is more stable) if the length of the hydrogen bonds is considered. In contrast, lattice deformation was found to increase the total energy, and in the most stable state, the lattice deformation was reduced by the formation of a pair of hydrogen bonds. This property of forming a hydrogen bond pair in a stable proton configuration was observed even when the number of scandium ions was increased (see Figure ).