Phonon spectrum of metallic lithium from first-principles bandstructure

It is shown that enormous numerical difficulties occur for a simple metal like lithium when realistic wavefunctions are used in Pick's formulation (1970) of lattice dynamics based on the Fourier transform of the ionic potential. A new formalism is suggested in which the ionic potential is separated in a term which is essentially nonzero near the nuclei and a weakly varying part. In contrast to Pick, only the latter is described by a Fourier expansion. The contributions of the higher bands can be summed exactly yielding a term which contains only the density of the conduction electrons. As a consequence, it is sufficient to know the inverse microscopic dielectric function epsilon -1(q+K, q+K') for about a hundred different reciprocal lattice vectors K and K' respectively. As a by-product it is found that the local field corrections of the microscopic dielectric function epsilon (q+K, q+K') are of decisive importance for the electron-phonon interaction in lithium. The numerical results for lithium are in satisfactory agreement with experiment.

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