Analytic expressions for the large-dimension limit, when renormalized by introducing:a suitable effective nuclear charge zeta yield accurate D=3 nonrelativistic energies for ground states of many-electron atoms. Using Hartree-Fock data to estimate zeta, which typically differs from the actual charge Z by similar to 1% or less, we find this dimensional renormalization method (denoted DR-O) gives results substantially better than the HF input. Comparison of the 1/Z expansion for the large-D limit with that for D=3 atoms provides expressions for the leading error terms in the renormalized total energy and correlation energy. When configuration;mixing occurs in the Z-->infinity limit (as for Be and many other atoms), we find the renormalization procedure is markedly improved by including the zeroth-order mixing (denoted DR-1); this-contributes-a term linear in Z. Including the Z-independent term (DR-2) also improves the accuracy when zeroth-order mixing is absent (e.g., ground-state atoms with N=2, 3, and 7-11) but not otherwise. Correlation energies for atoms and cations with N=2-18 electrons and Z=2-28 are obtained with a mean error of 26% using just the large-D limit or HF input (DR-O); the mean error improves to only 5% when the leading 1/Z term is included (either DR-1 or DR-2). Results much better than the HF approximation are likewise obtained for the ionization potentials and electron affinities of neutral atoms.