The concepts underlying the definition of bond energies in terms of potentials at the nuclei are outlined. The theory is rooted, first, in a definition of the energy, E,, of "atom" i in the molecule in terms of the potential energy, V ( i , mol), of nucleus Z, in the field of all the electrons and nuclei of the molecule: E, = K:"'V(I, mol). The K Y ' parameter, which is not required to be a constant in the derivation of the energy expression describing the contribution of an i j bond, turns out to be virtually constant for each atomic species-a situation which is exploited in numerical applications. Second, the Hellmann-Feynman theorem is applied in the calculation of the derivative, dAE$/aZ,, of the atomization energy, AEZ, using (i) the exact quantum-chemical definition of AEZ and (ii) the view that AEZ is the sum of bond energy contributions, E,,, plus a small interaction between nonbonded atoms. The individual bond energies derived in this manner necessarily depend on local charges at the bond-forming atoms. Numerical applications illustrate how this new bond-energy formula provides a simple link between typical saturated, olefinic, acetylenic, and aromatic hydrocarbons.