Electronic band structure of a perfect crystal. I. A new method for extending the calculations to the whole Brillouin zone

The method of the "special points" of Chadi and Cohen is applied to the electron Bloch function of a perfect crystal. It is shown that this function, at any $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ point, can be well expressed using a limited number of Fourier transforms ("band-structure parameters"). These parameters can be deduced easily if the wave function is known at some limited set of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ points (as a result of previous calculations based on any standard method). The wave function at any $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ point in the Brillouin zone can then be calculated by interpolation. The procedure is simple and saves the long calculations involved in solving the Schr\"odinger equation directly. The Wannier function can also be easily calculated. Furthermore, many physical parameters related to the electronic band structure can be expressed as functions of the proposed band-structure parameters, thus facilitating physical interpretation.