Partitioning and Additivity of the Chemical Bond

One of the oldest and most useful concepts in chemistry is that of the chemical bond. While the current understanding of a chemical bond has become relatively sophisticated, the original representation of a single bond between two atoms by a line and a double bond by two lines, dates from Odling (1860) and Kekule (1861). Although the theory of the chemical bond has enjoyed considerable development since that time and particularly in the last thirty years, the value of the concept in the hands of the experimentalist does not appear to have diminished. The development of quantum chemistry with its emphasis on electron densities, atomic and molecular orbitals, and orbital and Hartree-Fock energies, while facilitating both the interpretation of experimental data and the prediction of the results of experiments has at the same time presented the chemist with a significant challenge. How does one incorporate the concept of the chemical bond into quantum chemistry? While in quantum chemistry, the interactions between electrons, between nuclei and each other must be introduced explicitly, the idea of a chemical bond is not introduced in either the formulation of the appropriate fundamental quantum mechanical relationships nor their solution. Indeed, the evidence to this date would suggest that it is not possible to introduce the concept of a bond into the formulations of the requisite quantum theory at the level of the Hamiltonian operator.