Nuclear momentum distribution in solid and liquid HF from ab initio calculation

A calculation of nuclear momentum distribution of liquid and solid hydrogen fluoride was performed. In both systems, density functional theory generalized gradient approximation functional of Perdew, Burke, and Ernzerhof was used for the calculation: for liquid hydrogen fluoride, using an atom centered basis set for an isolated molecule with optimized geometry, and for solid hydrogen fluoride using plane-wave basis sets on optimized orthorhombic crystal cell. For liquid hydrogen fluoride, a semiclassical approach was adopted with the vibrational contribution to momentum distribution obtained from the density functional theory calculation and translational and rotational contributions calculated classically. Nuclear momentum distribution in the solid hydrogen fluoride was calculated entirely quantum mechanically using phonon dispersion and vibrational density of states calculated in the framework of plane-wave density functional theory. Theoretical results were contrasted with recently obtained results of Compton (deep inelastic) neutron scattering on liquid and solid hydrogen fluoride. In case of liquid hydrogen fluoride, almost a perfect agreement between theory and experiment was achieved within the harmonic Born-Oppenheimer approximation. For the solid system under investigation, the harmonic approximation leads to small (4%) overestimation of the square root of the second moment indicating that neutron Compton scattering technique is sensitive to proton delocalization due to hydrogen bonding in solid hydrogen fluoride.