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

Harrison's a priori theory is used to construct a first-principles nonlocal pseudopotential for magnesium, a metal with the hexagonal close-packed (hcp) structure and two atoms per unit cell. A response function for the exchange interaction among conduction electrons, which uses the Kohn-Sham approximation for the long-wavelength limit, is employed in the calculation of the energy-wave-number characteristic $F\left(q\right)\mathrm{}$. The phonon spectra were calculated for the [0001], [$01\overline{1}0$], and [$11\overline{2}0$] directions. The theoretical dispersion relations show excellent agreement, for all directions, when compared with data obtained from neutron diffraction experiments. Various other approximations for the inclusion of conduction-electron exchange and correlation are discussed, and the choice of a particular response function is shown to be not significant in these first-principles calculations for hcp metals. Comparison is made with other recent treatments of exchange and correlation effects in different formulations of pseudopotential theory for magnesium. The total binding energy and elastic shear constants are also calculated and show good agreement with experiment.