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