In this section we investigate whether the overlap population provides a measure of the modulus of the bond between two atoms. As the overlap population is a measure of the shared electronic density between two atoms, we would intuitively expect a correlation between these quantities. However, it is unclear whether the dependence would be on the magnitude of the overlap population or on its average value over the length of the bond.
For the purposes of this investigation, we will use a straightforward harmonic model of the interatomic bond. The values of the bond modulus, k, and overlap have been calculated for a variety of bulk crystals and simple molecules. These data will be used to investigate the applicability of a simple model for the relationship between k, the overlap population and the equilibrium bond length , of the form
where and are parameters to be determined.