Anisotropy of the proton kinetic energy in ice Ih

The partial vibrational density of states (pVDOS) of ice Ih, as simulated by first principle modeling based on density functional theory (DFT), is utilized for computing the Cartesian components of the proton and oxygen quantum kinetic energies, Ke(H) and Ke(O) respectively, along and perpendicular to the hydrogen bonds. The DFT method was found to yield better agreement with deep inelastic neutron scattering (DINS) measurements than the semi empirical (SE) calculations. The advantage of using the DFT method is to enable us to resolve the external and internal phonon bands of the Cartesian projections of the pVDOS, and hence those of the lattice and vibrational components of Ke(H). We show that a pVDOS analysis is a valuable tool in testing scattering results of complex systems and suggest its potential to explore competing quantum effects, e.g. on Ke(H) across phase transitions in water.