**Arash A. Mostofi, Peter D. Haynes,
Chris-Kriton Skylaris and Mike C. Payne**

**Theory of Condensed Matter, Cavendish
Laboratory, Madingley Road, Cambridge CB3 0HE, UK**

Linear-scaling electronic structure methods are essential for
calculations on large systems. Some of these approaches use a
*systematic* basis set, the completeness of which may be tuned
with an adjustable parameter similar to the energy cut-off
of plane wave techniques. The search for the electronic ground state
in such methods suffers from an ill-conditioning which is related to
the kinetic contribution to the total energy and which results in
unacceptably slow convergence. We present a general preconditioning
scheme to overcome this ill-conditioning and implement it within our
own first-principles linear-scaling density functional theory
method. The scheme may be
applied in either real space or reciprocal space with equal
success. The rate of convergence is improved by an order of magnitude
and is found to be almost independent of the size of the basis.

PACS numbers: 71.15.-m, 31.15.-p

Keywords: Preconditioning; Systematic basis; Linear scaling; Electronic structure

- Introduction
- Formulation of the problem
- Principles of kinetic energy ill-conditioning
- General formalism for kinetic energy preconditioning
- The case of an orthogonal basis
- Preconditioning and periodic sinc functions
- Results
- Conclusions
- Acknowledgments
- The psinc basis
- Bibliography
- About this document ...

Arash Mostofi 2003-10-27