Gradient corrections to the Hartree-Fock-Slater exchange and their influence on bond energy calculations

Summary

Density functional approximations based on a local representation of the exchange energy tend to over-estimate bond energies. We show that the tendency is due to the incorrect form of the Fermi hole correlation function adopted by these methods. This function is adequate at the maxima of the radial density in isolated atoms, at the corresponding maxima of atoms in molecules, and at the saddle points of the molecular density in the bonding regions. However, the Fermi hole correlation function yields too low exchange energy contributions in absolute terms from the tails of the core shells and the valence density. On bond formation electron density is transferred from the tails of the atomic core shells to the density maximum of the valence shell. At the same time, parts of the atomic valence tails are transformed into the bonding region with a saddle point. In both cases the contributions from the tail regions to the exchange energy are under-estimated in the local approximation, with the result that the calculated bond energies are too large. Similar considerations can be used to explain why local exchange density functional methods under-estimate ionization potentials.

The addition of non-local gradient correction terms to the local exchange functionals greatly improves calculated bond energies and ionization potentials by rectifying the qualitatively incorrect behaviour of the local Fermi hole correlation function in the tails of the core shells and the valence density. A detailed graphic analysis is provided of the contributions from non-local corrections to the calculated bond energies.