Total-energy calculations on a real space grid with localised functions and a plane-wave basis

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

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

Abstract:

We present a novel real space formalism for ab initio electronic structure calculations. We use localised non-orthogonal functions that are expressed in terms of a basis set that is equivalent to a plane-wave basis. As a result, advantages of the plane-wave approach also apply to our method: its applicability to any lattice symmetry, and systematic basis set improvement via the kinetic energy cut-off parameter. The localisation of our functions enables the use of fast Fourier transforms over small regions of the simulation cell to calculate the total energy with efficiency and accuracy. With just one further variational approximation, namely the truncation of the density matrix, the calculation may be performed with a cost that scales linearly with system size for insulating systems.

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

Keywords: Electronic structure; Density functional theory; Linear-scaling; FFT; Systematic basis set