We present a reformulation of the plane-wave pseudopotential
method for insulators.
This new approach allows us to perform density-functional
calculations by solving directly for `Non-orthogonal Generalised Wannier
Functions' rather than extended Bloch states. We outline the
theory on which our method is based and present test calculations
on a variety of systems. Comparison of our results with
a standard plane-wave code shows that they are
equivalent. Apart from the usual advantages of the plane-wave
approach such as the applicability to any lattice symmetry
and the high accuracy, our
method also benefits from the localisation properties of our
functions in real-space. The localisation of all
our functions greatly facilitates the future extension
of our method to linear-scaling schemes or calculations of the
electric polarisation of crystalline insulators.
PACS: 71.15.-m, 71.15.Ap, 31.15.-p, 31.15.Ew
