Calculation of Wavefunction Overlaps in First Principles Electronic Structure Codes

Abstract

In the work with this Master thesis, expressions for the wavefunction overlap factor between eigenfunctions are obtained. These expressions should be suitable for numeric integration over the Brillouin zone, and are derived in the Linearized Augmented plane-wave (+local orbitals) ((L)APW(+lo)) and Maximally localized Wannier functions (MLWFs) bases. The expression obtained for both bases is found to be suitable for numeric integration over the Brillouin zone. A routine computing the (L)APW(+lo) overlap has been implemented for normal scattering processes. Based on a Wien2k-simulation for GaAs, the bandstructure of GaAs is discussed. Furthermore, the implemented routine is used to plot the norm of near-band edge states. As expected, values very close to 1 are obtained. The distribution of the wavefunction between the two regions of the Augmented plane-wave method is also discussed for the near-band edge electron states.