Spatially resolved proton momentum distributions in KDP from first-principles.

The ferroelectric to paraelectric (PE) phase transition of KHPO (KDP) is investigated as a stringent test of the first-principles, normal modes framework proposed for calculating anharmonic quantum nuclear motion. Accurate spatially resolved momentum distribution functions (MDFs) are directly calculated from the nuclear wavefunction, overcoming the limitations of path-integral molecular dynamics methods. They indicate coherent, correlated tunneling of protons across hydrogen bonds in the PE phase in agreement with neutron Compton scattering data and reproduces the key features of the experimental MDF. It further highlights the role of Slater's lateral configurations in the PE phase. The analysis in terms of normal modes demonstrates the importance of collective, correlated proton motion and underlines the value of the employed framework in interpreting experimental data. This also makes the framework very attractive for application to deuterated KDP to further elucidate the nature of the PE transition and to systems exhibiting strong quantum nuclear effects in general.