Explicit full configuration interaction (FCI) computations
in a double-zeta plus polarization (DZP) basis, involving
over 100 million Slater determinants, have been performed
to sample the potential energy curves of X ^{
1}Sigma_{g}^{+} C_{2} and X
^{1}Sigma^{+} CN^{+} for benchmark
purposes. Quartic force fields have been determined at the
optimized structures, and sets of anharmonic spectroscopic
constants [r_{e}, omega_{e}, B_{e},
D_{e}, alpha_{e}, and
omega_{e}x_{e}] 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 ^{1}Sigma_{g} C_{2} and
X ^{1}Sigma^{+} 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 mH, 0.001 Angstroms, and 4
cm^{-1} in the total energy, r_{e}, and
omega_{e}, 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.