From the obtained configurations, it was possible to discuss the characteristics of the stable proton configurations. Firstly, in many cases, hydrogen atoms attach to the oxygen sites between the scandium ions, forming Sc-O-Sc species. This indicates that the position of hydrogen is more stable on the oxygen atom of Sc-O-Sc than on Sc-O-Zr or Zr-O-Zr. This stabilization of protons near the scandium ions was consistent with the results of previous ab initio calculations and nuclear magnetic resonance experiments. Subsequently, hydrogen bond pairs appear, as denoted by the red triangles in Figure . Figure compares the most stable configuration containing a pair of hydrogen bonds and a metastable configuration containing two independent hydrogen bonds when 𝑥 = 2. lengths of the hydrogen bonds were calculated to be 1.89 and 1.81 Å in the most stable case, which are longer than those calculated for the metastable case, i.e., 1.73 and 1.67 Å.