To investigate the relative importance of various small sources of
error in theoretical predictions of molecular properties, we report
spectroscopic constants for the ground electronic states of BH,
CH^{+}, and NH which are nearly converged to the adiabatic
*ab initio* limit. Computations are performed using full
configuration interaction (FCI) and coupled-cluster singles, doubles and
perturbative triples [CCSD(T)] methods with correlation consistent
basis sets of double to sextuple-zeta quality. The equilibrium
bond lengths, r_{e}, harmonic vibrational frequencies,
omega_{e}, anharmonicity constants, omega_{e}x_{e},
centrifugal distortion constants, D_{e}, and other quantities are
compared with experiment for each species. The systematic dependence of
spectroscopic constants on the one-particle basis is used to estimate
the complete basis set limit (CBS) values by using a two-point linear
extrapolation scheme. The importance of core correlation, scalar
relativistic corrections, higher-order electron correlation, and
basis set completeness are carefully investigated. Moreover,
deviations from the Born-Oppenheimer approximation are studied by
computing the diagonal Born-Oppenheimer correction (DBOC).
The remaining error is attributed primarily to nonadiabatic effects.
Our *ab initio* limit, adiabatic results for r_{e}
are within 0.0007 angstrom of
experiment when nonadiabatic effects are insignificant or have been removed.
Adiabatic predictions of omega_{e} are within 0.5 cm^{-1}
of experiment.