On the mean kinetic energy of the proton in strong hydrogen bonded systems

The mean atomic kinetic energies of the proton, Ke(H), and of the deuteron, Ke(D), were calculated in moderate and strongly hydrogen bonded (HB) systems, such as the ferro-electric crystals of the KDP type (XH2PO4, X = K, Cs, Rb, Tl), the DKDP (XD2PO4, X = K, Cs, Rb) type, and the X3H(SO4)2 superprotonic conductors (X = K, Rb). All calculations utilized the simulated partial phonon density of states, deduced from density functional theory based first-principle calculations and from empirical lattice dynamics simulations in which the Coulomb, short range, covalent, and van der Waals interactions were accounted for. The presently calculated Ke(H) values for the two systems were found to be in excellent agreement with published values obtained by deep inelastic neutron scattering measurements carried out using the VESUVIO instrument of the Rutherford Laboratory, UK. The Ke(H) values of the M3H(SO4)2 compounds, in which the hydrogen bonds are centro-symmetric, are much lower than those of the KDP type crystals, in direct consistency with the oxygen-oxygen distance ROO, being a measure of the HB strength.