Semi-empirical APW calculation of the band structure of silicon

We propose a modification to the usual augmented-plane-wave muffin-tin approximation approach which fits exactly the measured value of the band gap of Si. The method involves one adjustable parameter which is introduced by a uniform shift of the s-like logarithmic derivatives. The results are in good agreement with those of the empirical pseudopotential method not only for the gap but also for an energy range of approximately 3eV from the top of the valence band.