Localised spherical-wave basis set for O(N) total-energy pseudopotential calculations

We consider a localised spherical-wave basis set suitable for O(N) total-energy pseudopotential calculations. The basis set is conveniently truncated using a single parameter, the kinetic energy cutoff used with the plane-wave basis. We present analytic results for the overlap integrals between any two basis functions centred on different sites, as well as for the kinetic energy matrix-elements which can therefore be evaluated accurately in real-space. A method for analytically performing the projection of the basis states onto angular-momentum states required for the use of nonlocal pseudopotentials is also presented.