CCL: Exchange correlation

Dear Robert, I am not familiar with the method for applying an exchange correlation. But is this applied by using perturbation on the Hamiltonian of the multi/electron system, that is a perturbation Hamiltonian which applied the effect from the exchange?


From: owner-chemistry*|*
To: sergio.manzetti*|*
Subject: CCL: Exchange correlation
Date: Thu, 12 Jun 2014 21:31:49 -0400

No.  The exchange refers to the energy penalty for anti-symmetrization of the wavefunction.  It is a permutation operator (K) applied to the Coulomb operator (J).  It is not enough to have Coulombic repulsion; QM dictates that no two fermions have the same quantum state.  If you want to work with fermions, you have to represent a penalty toward having the same quantum state.

Correlation is an extended euphemism to mean "everything you do not get from the restrictions placed on the wavefunction in restricted Hartree-Fock theory."  The term more precisely derives from the fact that the joint probability distribution function of the one-particle reduced density matrix shows that the there is no statistical correlation between two orbitals and their density...hence the term "correlation."

On 06/12/2014 07:05 PM, William McDonald wrote:
But isn't that a consequence of the mean-field approximation and not an intrinsic property of the electron?

On Thu, Jun 12, 2014 at 2:48 PM, Susi Lehtola <owner-chemistry]*[> wrote:

Sent to CCL by: Susi Lehtola []
On Thu, 12 Jun 2014 11:50:09 -0700
"William McDonald pchem]|[" <owner-chemistry ~~> wrote:
> On Thu, Jun 12, 2014 at 3:27 AM, Sergio Manzetti sergio.manzetti::
> <owner-chemistry,,> wrote:
> > Dear all, when is it suitable to start considering  Exchange correlation
> > between Electrons, (e.g pass Oxygen, Mg, Phosporous or further up in the
> > system)?
> In a system with more than one electron of the same spin.

That is: in a system with more than zero electrons of the same spin.

[Exchange is important even for a single electron, because it cancels
out (or tries to) the self-Coulomb interaction.]

For correlation, you need at least two, but even with a single
electrons many correlation functionals yield non-zero correlation
Mr. Susi Lehtola, PhD             Research Associate
susi.lehtola ~~   Department of Applied Physics  Aalto University
Susi Lehtola, FT                  Tutkijatohtori
susi.lehtola ~~   Fysiikan laitos  Aalto-yliopisto


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William J. McDonald
Postdoctoral Scholar
Department of Chemistry and Biochemistry
University of California, Santa Cruz