The Projector Basis Method For Electronic Band Structure Calculations

Over the last several decades, two methods have emerged as the standard tools for the calculation of electronic band structures. These methods, the Car-Parinello plane wave method and the linear augmented plane wave method (LAPW), each have strengths and weaknesses in different regimes of physical problems. The Car-Parinello algorithm is ideal for calculations with soft pseudopotentials and large numbers of atoms. The LAPW method, on the other hand, easily handles all-electron and hard-core pseudopotential calculations with a small number of atoms. The projector basis method, presented here, is a hybrid mixed basis method which allows the calculation of moderately large ({dollar}\sim{dollar}200) numbers of atoms represented by hard pseudopotentials. This method will then be used to calculate two members of a relatively new mass of materials, called electrides, in which the anion has been replaced with a localized electron.