Optimized model potential: exchange and correlation corrections and calculation of magnesium phonon spectrum

Expressions for the exchange and correlation corrections to the model potential form factor wq(k) and the normalized energy-wavenumber characteristic FN(q), which were derived in a recent paper by Shaw, are evaluated for eight simple metals. An expression for the second derivative of the Kohn-Sham density functional for the exchange and correlation energy is proposed and then is used in these calculations. The energy-wavenumber characteristic computed from the optimum model potential, corrected for exchange and correlation, is used to calculate the phonon spectrum of magnesium. The predicted spectrum is found to agree very well with the experimental data, and the exchange and correlation corrections are shown to be important in obtaining this agreement. The corrections to FN(q) and wq(k) which are tabulated for eight metals can be used to determine the importance of exchange and correlation in the prediction of other metallic properties.