Truncated Taylor-series representations of /ital r//sub 12//sup /minus/1/yield a variety of resummation alternatives to the corresponding Legendreexpansion defining a basis-set--dependent Hamiltonian which allows afaster harmonic convergence of orbital methods. In this way, configurationinteraction calculations of He, Li, and Ne ground-state energies converge towithin a major fraction of the correlation energy with considerably lesseffort.