  Ab initio electronic structure calculations of two-dimensional layered
structures are typically performed using codes that were developed for
three-dimensional structures, which are periodic in all three directions. The
introduction of a periodicity in the third direction (perpendicular to the
layer) is completely artificial and may lead in some cases to spurious results
and to difficulties in treating the action of external fields. In this paper we
develop a new approach, which is "native" to quasi-2D materials, making use of
basis function that are periodic in the plane, but atomic-like in the
perpendicular direction. We show how some of the basic tools of ab initio
electronic structure theory -- density functional theory, GW approximation and
Bethe-Salpeter equation -- are implemented in the new basis. We argue that the
new approach will be preferable to the conventional one in treating the
peculiarities of layered materials, including the long range of the unscreened
Coulomb interaction in insulators, and the effects of strain, corrugations, and
external fields.
