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5. Localised basis-set

One elegant and popular choice of basis in traditional calculations has been the plane-wave basis. However, because of the extended nature of these basis functions they cannot be used in linear-scaling calculations, and a different choice has to be made, in which the basis functions are localised in real-space. Gaussians [144] are a popular choice since many quantities can be calculated analytically [145], an advantage shared by the basis-set proposed here. Other choices include truncated atomic orbitals [146], $B$-splines or ``blip'' functions [147], wavelets [148] and real-space grids [149].

In this chapter we consider a localised spherical-wave basis set suitable for linear-scaling total-energy pseudopotential calculations. The basis-set is conveniently truncated using a single parameter, the kinetic energy cut-off 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. Two methods for analytically performing the projection of the basis states onto angular momentum states required for the use of non-local pseudopotentials are also presented. This work has been published in [150].


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Next: 5.1 Introduction Up: thesis Previous: 4.6 Non-orthogonal orbitals   Contents
Peter Haynes