First principles study of isotope effect in hydrogen-bonded K3H(SO4):: II — Zero-point oscillation effect

First principles calculation is performed to find the difference between K3H(SO4)2 (KHS) and K3D(SO4)2 (DKHS) by taking account of the zero-point oscillation effects of the proton and the deuteron. First, we calculate the potential surface for the proton in the crystal. The ground-state energies and the wavefunctions of the proton and the deuteron in that potential are calculated. Then, the stable positions of the proton and the deuteron are calculated taking account of zero-point energy, and the electric charge distributions are calculated taking account of the spread wavefunctions of the proton and the deuteron. As a result, we find that the anharmonicity of the proton potential surface makes the position of the hydrogen closer to the center of the hydrogen bond than that of the deuterium. We also find that the zero-point oscillation effect diminishes the dipole moments, and that the shrinkage of the dipole moment in the hydrogen system is larger than that of the deuteron. These two effects play significant roles in the mechanism of the isotope effect in KHS.