Pseudopotential band calculations along a high-symmetry axis. Part 1: Central potential and the (111) direction

A method for band structure calculations along a high-symmetry axis is introduced in this report. It entails a cylindrical coordinate multipole expansion of the wave function and an exact reduction of the three-dimensional Schroedinger equation into a set of one-dimensional wave equations for the multipoles. Group theoretic considerations and energy arguments imply good convergence, regardless of the unit-cell extension along the high-symmetry direction. Band calculations of a test case, PbSe along the 111 direction, demonstrate the good convergence. This method is expected to be particularly useful for structures highly anisotropic along a high-symmetry axis, e.g., superlattices.