Preconditioned iterative minimization for linear-scaling electronic structure calculations

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

Abstract:

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