The zero-point energy in the molecular hydrogen crystal

We propose a modified Einstein approximation to describe zero-point energy vibrations in a quantum crystal. Our aim was to develop a computationally cheap tool suitable for lattice structure optimisation. As in the classical Einstein model the representative atom vibrates in an effective potential due to the surrounding atoms of the crystal; the atoms however are not strictly placed at the positions corresponding to the crystal potential energy minima but their positions are described by the quantum mechanical density distributions. The effective potential computed that way is suitable for the application in solid para-hydrogen in contrast to the normal (unmodified) Einstein approximation. We compute the cohesive energy of the para-hydrogen crystal and perform lattice structure optimisation. The hexagonal closed packed is more stable than the fcc closed packed lattice and the lattice constants obtained are in very good agreement with the experimental values.