A connection between domain-averaged Fermi hole orbitals and electron number distribution functions in real space

We show in this article how for single-determinant wave functions the one-electron functions derived from the diagonalization of the Fermi hole, averaged over an arbitrary domain Omega of real space, and expressed in terms of the occupied canonical orbitals, describe coarse-grained statistically independent electrons. With these domain-averaged Fermi hole (DAFH) orbitals, the full electron number distribution function (EDF) is given by a simple product of one-electron events. This useful property follows from the simultaneous orthogonality of the DAFH orbitals in Omega, Omega' = R-3-Omega, and R-3. We also show how the interfragment (shared electron) delocalization index, delta(Omega,Omega') transforms into a sum of one-electron DAFH contributions. Description of chemical bonding in terms of DAFH orbitals provides a vivid picture relating bonding and delocalization in real space. DAFH and EDF analyses are performed on several test systems to illustrate the close relationship between both concepts. Finally, these analyses clearly prove how DAFH orbitals well localized in Omega or Omega' can be simply ignored in computing the EDFs and/or delta(Omega,Omega') and thus do not contribute to the chemical bonding between the two fragments. (C) 2009 American Institute of Physics. [doi:10.1063/1.3239467]