UPPER AND LOWER BONDS FOR MOLECULAR-ENERGIES

We have revisited the molecular Hamiltonian to emphasize its nuclear charge dependence. We have studied the variations in PSI due to changes in these charges, and we have related them variationally to isoelectronic isoprotonic molecular systems in the nuclear charge space, through simplicial complexes. We built a general way of comparing B-O energies for these kind of molecules, and we are able to generate an order between them. Up to the case of Z = 3, we have shown that the energy of the united atom of nuclear charge z = N and that corresponding to a cluster of N hydrogen atoms play the role of upper and lower bounds for the energy of any molecular system between them.