Density-functional electronic structure calculations are performed on the molecules Cr-2(hpp)(4), Mo-2(hpp)(4), and W-2(hpp)(4), where the bridging ligand, hpp, is the anion of 1,3,4,6,7,8-hexahydro-2H-pyrimido[1,2-a]-pyrimadine. The calculated electronic densities are used to determine the Fukui functions. These molecules are unique not only in their ability as electron donors but also because orbital relaxation plays a decisive role in their reactivity. Unlike other examples in the literature, the reactivity of these compounds cannot be expressed solely in terms of the highest occupied and lowest unoccupied Kohn-Sham orbitals but only using the Fukui function, which includes the effects of orbital relaxation.