**P.D. Haynes - M.C. Payne**

**Theory of Condensed Matter, Cavendish Laboratory, Madingley
Road, Cambridge, CB3 0HE, U.K.**

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
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. A method
for analytically performing the projection of the basis states onto
angular-momentum states required for the use of non-local
pseudopotentials is also presented.

PACS numbers: 71.10.+x, 71.20.Ad

PACS numbers: 71.10.+x, 71.20.Ad

- 1. Introduction
- 2. Origin of the basis functions
- 3. Fourier transform of the basis functions
- 4. Overlap matrix elements
- 5. Kinetic energy matrix elements
- 6. Non-local pseudopotential
- 7. Computational implementation
- 8. Conclusions
- Appendix
- Acknowledgements
- Bibliography

Peter Haynes