Full configuration interaction (CI) calculations on the group-IIIA–group-VA diatomic molecules BN, BP, AlN, and AlP have been performed with the cc-pVTZ correlation-consistent basis set and compared to CCSD(T) calculations with the same basis set. The CCSD(T) calculations are good to better than 1kcal∕mol in comparison with the full CI results if the T1 diagnostic is small and to within about 2kcal∕mol if the T1 diagnostic is large. Inspection of the T2 amplitudes shows that the simple T1 diagnostic is providing useful insight into the quality of the starting wave function. The ground state of BN, BP, and AlN is predicted to be the Π3 and, for AlP, the ground state is predicted to be Σ−3. For all molecules except BP, there is an excited state within 1.1kcal∕mol of the ground state. The ordering of the state energies can be explained in terms of simple orbital and bonding models. The results provide little evidence for placing the π orbital below the σ orbital for the ground state of these heteronuclear diatomic molecules.