This paper has three goals: (1) to provide a first step in understanding the atomic basis of the role of magnesium in facilitating the dissociation of the P-O bond in phosphorylated biochemical fuel molecules (such as ATP or GTP), (2) to compare second-order Møller-Plesset perturbation theory (MP2) results with those obtained at the more economical density functional theory (DFT) level for a future study of larger more realistic models of ATP/GTP, and (3) to examine the calculation of atomic total energies from atomic kinetic energies within a Kohn-Sham implemention of DFT, as compared to ab initio methods. A newly described method based on the quantum theory of atoms in molecules (QTAIM), which is termed the "atomic partitioning of the bond dissociation energy" (APBDE), is applied to a simple model of phosphorylated biological molecules (HPO42-). The APBDE approach is applied in the presence and in the absence of magnesium. It is found that the P-O(H) bond in the magnesium complex is shorter, exhibits a higher stretching frequency, and has a higher electron density at the bond critical point than in the magnesium-free hydrogen phosphate anion. Though these data would seem to suggest a stronger P-O(H) bond in the magnesium complex compared to the magnesium-free case, the homolytic breaking of the P-O(H) bond in the complex is found to be easier, i.e., has a lower BDE. This effect is the result of the balance of several atomic contributions to the BDE induced by the magnesium cation, which stabilizes the dissociation product more than it stabilizes the intact model molecule.