Lattice Dynamics of Beryllium from a First-Principles Nonlocal Pseudopotential Approach

The lattice dynamics of beryllium, a metal with hexagonal close-packed structure and two atoms per unit cell, is investigated within the framework of Harrison's first-principles pseudopotential theory, using (i) the Slater approximation for the conduction-band-core exchange, and (ii) a modified dielectric-screening function employing the Kohn-Sham approximation for exchange among the conduction electrons. The energy-wave-number characteristic $F(q)$ is constructed from the Hartree-Fock-Slater (HFS) wave function for Be⁺⁺; this is used to calculate the phonon dispersion relations in the [0001], [011̄0], and [112̄0] directions. Good agreement is obtained with neutron diffraction experiments. The three independent elastic shear constants are also calculated from $F(q)$; good agreement with experiment is obtained for C and C^', but only fair results obtain for c₄₄.