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.

Peter Haynes