Analysis of atomic orbital basis sets from the projection of plane-wave results

The projection of the eigenfunctions obtained in standard plane-wave first-principles calculations is used for analysing atomic orbital basis sets. The `spillage' defining the error in such a projection allows the evaluation of the quality of an atomic orbital basis set for a given system and its systematic variational optimization. The spillage is shown to correlate with the mean square error in the energy bands obtained from the projected Hamiltonian matrix. The method is applied to the characterization of finite-range pseudo-atomic orbitals (Sankey O F and Niklewski D J 1989 Phys. Rev. B 40 3979) in comparison to infinite-range pseudo-atomic and Slater-type orbitals. The bases are evaluated and optimized for several zinc-blende semiconductors and for aluminium; the finite-range orbitals display high quality in spite of the limited range. A simple scheme is proposed to systematically enlarge the basis without increasing its range.