Here is my question: I have recently been reading "A Chemist's Guide to Density Functional Theory". On page 26 of the book the authors discuss the Fermi hole in terms of pair density and state that "Usually the exchange hole is largest around the probe electron." Can anyone tell me why this is so? Why is it not largest at the reference electron, like the Coulomb hole?
The Fermi hole is the exchange-hole and it is delocalized over the nuclei. Its shape resembles a localized orbital that would describe the bond, when the reference electron is in the corresponding bonding region. The simplest example is the H2 molecule, where the Fermi hole equals minus the HOMO density and is thus completely independent of the reference electron. Moreover, the Coulomb hole in molecules is not really centered around the reference electron but actually strongly depends on the position of the nucleus nearest to that electron. You can find more on this subject by searching for Buijse & Baerends articles. You will also soon find an article by me, A. Savin and F. Colonna in IJQC, where we show correlation holes along a nonlinear adiabatic connection path.
--- R. Pollet pollet at.at pandora.saclay.cea.fr