  The projection of the eigenfunctions obtained in standard plane-wave
first-principle electronic-structure calculations into atomic-orbital basis
sets is proposed as a formal and practical link between the methods based on
plane waves and the ones based on atomic orbitals. Given a candidate atomic
basis, ({\it i}) its quality is evaluated by its projection into the plane-wave
eigenfunctions, ({\it ii}) it is optimized by maximizing that projection, ({\it
iii}) the associated tight-binding Hamiltonian and energy bands are obtained,
and ({\it iv}) population analysis is performed in a natural way. The proposed
method replaces the traditional trial-and-error procedures of finding
appropriate atomic bases and the fitting of bands to obtain tight-binding
Hamiltonians. Test calculations of some zincblende semiconductors are
presented.
