k-point sampling and the k.p method in pseudopotential total energy calculations

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Abstract
A fast method is presented for the calculation of total energies within the density functional formalism for systems that require a large number of k-points. Approximate solutions at a large number of k-points are obtained from exact self-consistent solutions at a smaller number of k-points using an extension of the k.p method. The method is demonstrated by a calculation of the total energy of FCC aluminium at a series of lattice parameters. An analysis is presented that partitions the errors in the calculations into those inherent in any finite sampling procedure and those that are specific to the k.p method. The extra error due to the k.p method is shown to be around 10% of energy differences for these calculations but a simple modification to the calculations requiring no more computational time reduces this error to 2%. For these simple calculations the time saved by using the k.p method is fairly small but for larger calculations the method is several orders of magnitude quicker. Errors from either source are shown to be far less important in the electronic potentials than in the eigenvalue sums. It is concluded that in any total energy calculation fewer k-points are required to describe the potential than to calculate the eigenvalue sum. This could be exploited to gain an order of magnitude saving in computational time in any calculation.