Multichannel quantum-defect theory provides an attractive framework for compact, a priori calculations of the binding energies or scattering resonances of highly excited, multielectron atoms. However, in addition to obtaining a good representation of interchannel interactions, it is difficult in practice to find a sufficiently accurate, selfconsistent, simple, one-electron potential for describing the average motion of a Rydberg electron in the multielectron core. Moreover, when there is a nonspherical core there is a significant non-Coulomb tail even at fairly large distances from the origin, and due to exchange and correlations, such a potential will be nonlocal. We describe a self-consistent, local-density approximation to calculate a single-particle potential with proper self-interaction corrections, which represents quite accurately the motion of the outer electron in the presence of a spherically averaged core. This is derived from the well-known solid-state calculational technique based on the Hedin-Lundqvist approximation. The channel interactions and nonspherical contributions to intrachannel potentials are then calculated by explicitly considering the motion of two electrons outside the outermost closed-shell configuration of the atom. This procedure permits greatly increased accuracy in the prediction of excited-state energies of the entire spectral series. Explicit numerical results for quantum-defect parameters are presented for many Rydberg series in several alkali-metal and alkaline-earth atoms. © 1981 The American Physical Society.