Comparison of Dielectric Screening Methods Used in Phonon-Frequency Calculation of Normal Metals

The various prevalent forms of the dielectric screening function relevant to a calculation of phonon frequencies of a normal metal are critically studied. Detailed calculations for sodium are carried out to investigate the variation of phonon frequencies with several dielectric screening functions. Each of these dielectric functions is used in conjunction with two forms of the electron-ion matrix element: (a) the single-OPW (orthogonalized-plane-wave) electron-ion matrix element of Vosko et al. and (b) Bardeen's electron-ion matrix element. When we use the single-OPW electron-ion matrix element, a systematic trend is manifest in the variation of $G\left(p\right)\mathrm{}$ functions and phonon frequencies with the use of different dielectric functions, while no such trends are revealed if we adopt Bardeen's form of the electron-ion matrix element. It is observed that the dielectric function of Singwi et al. combined with the single-OPW electron-ion matrix element yields the best agreement with experimental phonon frequencies.