The screened nuclear potential and the lattice dynamics of solid nitrogen

Abstract

The pseudo-atom approximation has been introduced into the quantum-mechanical formulation of the second-order variation of the effective nuclear potential. The electronic charge density function of a molecule has been represented as a superposition of functions, centred on the nuclei. The latter fully characterize the effective electron distribution of pseudo-atoms. The linear response of the total electronic charge density to nuclear displacements has also been represented as contributions from pseudo-atoms. A simple expression for the force constant tensors depending on an explicit form of the pseudo-atom charge density function has been derived. The lattice dynamics of molecular crystals have been formulated employing the standard procedure within the rigid molecule approximation. This approach, which can be treated as a semi-microscopic formulation of lattice dynamics, is illustrated by numerical calculations of phonon frequencies for the α and γ phases of solid nitrogen. Assuming a gaussian electronic charge distribution for nitrogen pseudo-atoms, the screened nuclear potential has been developed. The lattice dynamics calculations for both phases of nitrogen give results in a good agreement with experimental phonon frequencies.