Projection of plane-wave calculations into atomic orbitals

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.