Intracules, conjectures and the correlation problem

One of the most urgent and important issues in quantum chemistry is the electron correlation problem. We have been working for several years to develop a paradigm in which the correlated motion of electrons can be understood through their two-electron probability densities, or intracules. During 2006 and 2007, we published five papers on this topic, introducing the Omega intracule Ω(u,v,ω), a function that gives the probability of finding two electrons whose interelectronic position and momentum vectors have magnitudes u and v, respectively, and which subtend an angle ω. Through systematic computational studies, we have shown that the correlation energies of atoms can be predicted very accurately but that molecules with small HOMO-LUMO gaps are more difficult to treat. We are determining the reasons for this so that we can then improve our models appropriately.