The bond energies of eight chemically bound diatomics are computed using several basis sets with and without bond functions (BF). The bond energies obtained using the aug-cc-pVnZ+BF basis sets (with a correction for basis set superposition error, BSSE) tend to be slightly smaller that the results obtained using the aug-cc-pV(n+1)Z basis sets, but slightly larger than the BSSE corrected aug-cc-pV(n+1)Z results. The aug-cc-pVDZ+BF and aug-cc-pVTZ+BF basis sets yield reasonable estimates of bond energies, but, in most cases, these results cannot be considered highly accurate. Extrapolation of the results obtained with basis sets including bond functions appears to be inferior to the results obtained by extrapolation using atom-centered basis sets. Therefore bond functions do not appear to offer a path for obtaining highly accurate results for chemically bound systems at a lower computational cost than atom centered basis sets.