A dynamical model of the chemical bond: kinetic energy resonances between atomic electrons

While the theory of chemical bonding has advanced rapidly as more and more details of the quantum mechanical problem have been taken into account, surprisingly little effort has gone into the developement of intuitive models to interpret the results obtained by more sophisticated means. This article introduces an approach to chemical bonding, which should give a better connection between basic quantum mechanics and the covalent pair bond, focussing on the fact that, while the size of atoms and therefore the bond length are determined by an equilibrium between Coulomb attraction and the quantum incompressibility of the electrons, the energy of the bond is largely given by the electron kinetic energy term. This is well established in solid state physics, where the tight binding parameters for a large class of materials can be derived from the free electron dispersion relation. However, a similar argument can be made for small molecules if the electron density of the molecule is roughly similar to the atomic densities. It is shown that such an approach yields not only the energy of the bond but also a bonding potential as a function of bond length, which allows an estimate of vibrational frequencies for the molecule.