Up: Localised spherical-wave basis set
Previous: 7. Computational implementation
We have shown that it is possible to construct a set of basis
functions which are solutions of the free-electron Schrödinger
equation, subject to being localised in spherical regions. Basis
functions within the same region are mutually orthogonal, avoiding the
problem of the overlap matrix becoming singular when the size of the
basis set is increased. It is also possible to truncate the basis set
using the kinetic energy cut-off used to truncate the plane-wave
We have shown in detail how to obtain analytic results for the
overlap integral between any two basis functions, and presented these
in a form which can be implemented computationally.
The same results can be adapted to obtain matrix elements of the
kinetic energy operator, providing an efficient and accurate method of
computing the kinetic energy in real space and avoiding the use of
finite difference methods.
The projection of basis functions onto ionic core angular
momentum states can also be performed analytically so that non-local
pseudopotentials can be used.