Explicit full configuration interaction (FCI) computations in a double-ζ plus polarization (DZP) basis, involving as many as 105 million Slater determinants, have been performed to sample the potential energy curves of X 1Σg+ C2 and X 1Σ+ CN+ for benchmark purposes. Quartic force fields have been determined at the optimized structures, and sets of anharmonic spectroscopic constants [re, ωe, Be, D̄e, αe, and ωexe] have been ascertained. Analogous results obtained from high-level but inexact correlation treatments establish a CISDTQ<CCSDT<CISDTQPH≈FCI series of increasing accuracy for the notorious X 1Σg+ C2 and X 1Σ+ CN+ multireference systems. The data also reveal that recent schemes for CI+PT extrapolations to the FCI limit are quite accurate, to within 0.4 mEh, 0.001 Å, and 4 cm−1 in the total energy, re, and ωe, respectively. Whether such schemes approximate FCI curves with sufficient smoothness to reproduce the anharmonic data obtained here is elevated as a challenge for future work. © 1998 American Institute of Physics.