Based on one of the initial proton configurations, structural relaxation calculations were performed using VASP. To effectively obtain accurate stable configurations, multiple-step structure relaxation is often performed. Thus, for this study, three total energies were used as metrics to determine a stable configuration. The first is the total energy of the initial proton configuration without the relaxation calculation, which is expressed as 𝐸 ! and is known as the no-relaxation total energy. The second is the total energy with normal accuracy in the structural relaxation (𝐸 " ), and the third is the highly accurate total energy after structural relaxation (𝐸 # ). The detailed setup of the VASP calculations employed for multiple-step structural relaxation to obtain the total energy is summarized in Supplementary Note A.