Finite basis set corrections to total energy pseudopotential calculations

A means of correcting total energy pseudopotential calculations performed using a fixed cut-off energy for the plane waves in the basis set is presented. The use of a finite set of special k-points in such a calculation will introduce errors in the total energies which decrease only slowly with increasing cut-off energy. In particular, total energy differences are not accurate unless the cut-off energy used is sufficiently large that the total energies are themselves converged. This would not be the case if a truly constant cut-off energy could be used. Unfortunately this can only be achieved by using an infinite k-point set. The authors have derived a correction which will explicitly eliminate these errors to give total energies which can correspond to a strictly constant cut-off energy. In this way, total energy differences and hence many physical properties can be accurately calculated using cut-off energies significantly lower than otherwise possible, with substantial savings in computational time.