Subject: Re: CCL:Fwd: for Fermi and Coulomb holes

From: Christoph van Wüllen <[email-masked]>
Date: Thu, 21 Feb 2002 09:59:02 +0100

>Dear CCL'ers,
>
>Recently, I've been asked a question about the difference between the Coulomb
>hole and the Fermi hole. Could someone give me an answer?
>
In my opinion, the "fermi hole" comes along only by the pauli principle,
that is, it is there even if there is no electron-electron interaction.
The "coulomb hole" on the other hand vanishes if the electron interaction
is switched off.

Yours,

+---------------------------------+----------------------------------+
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From: Rodolphe Pollet <[email-masked]>
Date: Wed, 20 Feb 2002 20:51:43 +0100

>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
[email-masked]