Metal oxide molecules are of particular interest from both a scientific and technological perspective in view of their elementary nature and role in such processes as high-temperature vaporization. A fundamental and important property is the bond energy between the metal center and the oxygen in neutral and ionic monoxide molecules, BDE[MO] and BDE[MO+]. For the 4f-block lanthanide (Ln) and 5f-block actinide (An) inner transition metals, it has been demonstrated that many chemical properties can be rationalized from the electronic structures and energetics of the isolated metal atom or ion. In the present work, a relationship is developed to reliably predict known BDE[LnO], BDE[LnO(+)], BDE[AnO], and BDE[AnO(+)] energies from spectroscopically determined electronic properties; this relationship is employed to estimate unknown bond energies. A notable implication of the results is that effective bonding between the metal center and the oxygen atom in these species requires two unpaired valence d electrons.