When considering the fragmentation of a single bond, the attractive singlet and repulsive triplet potential energy curves of the prototype H-2 --> 2H dissociation often come to mind. For species in which homolytic bond cleavage is energetically favored, such comparisons are reasonable. For other species where heterolytic cleavage gives lower-energy products, the H-2 analogy is inappropriate. This paper offers a qualitative theoretical treatment of the singlet and triplet potential energy curves that arise when a single bond formed by an electron pair is cleaved either homolytically or heterolytically. This analysis is shown to provide insight into several problems involving transition metal systems: transition metal carbonyls, metal ion-ligand complexes, and transition metal dimers.