The k.p method in pseudopotential total energy calculations: error reduction and absolute energies

The scope and potential of the k.p total energy method is investigated. The method provides for the generation of rapid but approximate solution of the Kohn-Sham equations at many k-points from the exact solution at a few k-points. The method is applied to three diverse aluminium structures and the errors are partitioned into those which are due to the k.p method and those which are general to any finite sampling method. Both of the errors that are associated with any finite sampling technique are shown to be significant even for dense sampling of k-space. One of the k.p errors is shown to be insignificant. The other k.p error is significant. However, a method is introduced which allows the magnitude of the error to be reduced to the level of insignificance. The resulting k.p total energy method is shown to be immune from any additional errors beyond those associated with any finite sampling method. Thus it is a quick and accurate method for the calculation of absolute total energies.