Smooth energy-band interpolation with gradient utilization

Shankland's smooth interpolation procedure based on roughness minimization is extended to include energy-band derivatives. Real symmetrized Fourier functions are used, with the method obtained being numerically stable and utilizing more available information for a given set of $\overrightarrow{\mathrm{k}}$ points at which energy bands are calculated. The fact that regular mesh is not required allows the inclusion of extra points on symmetry lines and planes to improve the interpolant. Because of roughness minimization, unphysical oscillations are suppressed. The drawback of the method is that cusps must be dealt with separately. The energy bands of graphite and boron nitride are interpolated to demonstrate the usefulness and convergence properties of the method.