Proton dynamics in ice VII at high pressures

Abstract

We calculated the proton kinetic energies Ke(H) of ice under high pressures up to 63 GPa by assuming the harmonic approximation. The input measured optical frequencies of vibration, libration, and translation of ice VII versus pressure as well as the H2O geometry and the distances R(OH) necessary for calculating Ke(H) (at 298 K) were taken from the literature. The resulting Ke(H) values were found to decrease gradually with increasing pressure, approaching the region where the H-atom is symmetrically hydrogen bonded between two oxygens in the OH-O system. Interestingly, the Ke(H) results were found to be consistent with those of other materials such as Rb3H(PO4)2 and KH2PO4 having similar R(OH) and R(OO) distances in the OH-O system. Similar calculations were also carried out for D2O.

Temperature dependence of the zero point kinetic energy in ice and water above room temperature

“…The empirical decoupled harmonic models of Refs. [39,29,24], can instead be regarded as ''ex post'' quasiharmonic descriptions, since deviations from harmonicity are implicitly assumed in the phase/state -dependent principal frequencies and/or density of states from spectroscopic measurements.…”

“…The other method consists in using empirical models assuming that hE K ðTÞi is obtained from a set of decoupled quantum harmonic oscillators whose frequency is derived from optical data and/or measured vibrational density of states [39,29,24]. Typically, translational degrees of freedom are assumed classical, while a quantum harmonic description is used for librational, bending and stretching vibrations [39,29,24]: where S a are the kinetic energy fractions shared by the proton in translation, libration, bending, stretching, respectively, and hx a are the corresponding energies derived from complementary spectroscopic data, for each phase/thermodynamic state investigated. It is immediately apparent that the use of phase/temperature dependent energies, hx a , reflects the deviations from purely harmonic description, which however is inherent in Eq.…”

“…Recent computational methods make use of advanced methodologies for the inclusion of nuclear quantum effects, such as Path Integral Car-Parrinello Molecular Dynamics (PICPMD) [32], or Path Integral Molecular Dynamics employing empirical potential models for water [43], or coupled with Generalized Lanvegin equations [3]. The other method consists in using empirical models assuming that hE K ðTÞi is obtained from a set of decoupled quantum harmonic oscillators whose frequency is derived from optical data and/or measured vibrational density of states [39,29,24]. Typically, translational degrees of freedom are assumed classical, while a quantum harmonic description is used for librational, bending and stretching vibrations [39,29,24]: where S a are the kinetic energy fractions shared by the proton in translation, libration, bending, stretching, respectively, and hx a are the corresponding energies derived from complementary spectroscopic data, for each phase/thermodynamic state investigated.…”

“…In the whole temperature range in the solid, hE K ðTÞi is approximately five times larger than the classical values, highlighting the role played by nuclear quantum effects on the protons in ice. Thermal excitation acts as a relatively small perturbation to the quantum kinetic energy of the proton [43,39].…”

“…They obtained good agreement with DINS data at 5 K [37] but not at 269 K [38], assuming free rotation of the entire molecule. More recently, Finkelstein and Moreh [39] reported new calculations on ice at ambient (and high) pressure, which account for a revised evaluation of the librational component from the literature, obtaining a $ 10 meV increase in the calculated kinetic energy. This is not surprising, given the importance of the coupling and modulation of the stretching by librational motions, with various degrees of anharmonicity [40].…”