Lattice dynamics of aluminum: An investigation of exchange and correlation effects

Using Harrison's first-principles, nonlocal pseudopotential theory, an investigation was made to determine the influence of the electronic exchange and correlation interactions on the lattice dynamics and on the structural, cohesive, and electronic properties of aluminum. Different varieties of the local statistical $X\alpha$ exchange and correlation approximation are used to describe the core-core and conduction-band-core interactions. Exchange and correlation among the conduction electrons are taken into account by using different modified forms of the dielectric function. It is shown that a correct formulation of the conduction-band-core interaction is crucial for a correct description of atomic as well as electronic properties. The Lindgren approximation to this potential allows a nearly perfect reproduction of the experimental dispersion relations, but is shown to be inappropriate for the calculation of structural, cohesive, and electronic properties. The conventional ${\rho }_{\mathrm{core}}^{\frac{1}{3}}$ ansatz for this potential, while being only moderately successful in the phonon calculations, still yields the best over-all picture of the properties of metallic aluminum. The remaining discrepancies between theory and experiment are to be attributed to the too long range of the ${\rho }^{\frac{1}{3}}$ exchange and correlation potential. Conduction-electron exchange and correlation are of only minor importance in the calculation of static crystal properties. In the lattice-dynamical calculations, the exchange and correlation corrections to the Hartree dielectric function strongly reduce the phonon frequencies. Different forms proposed for this correction are analyzed. It is demonstrated that the long-wavelength limit of the correction function most effectively influences the phonon energies. The satisfaction of the compressibility sum rule is a necessary, but not sufficient condition for a correct description of the dispersion relations.