Dear Robert=2C 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=2C th= at is a perturbation Hamiltonian which applied the effect from the exchange= ?
THanks

Sergio

From: own= er-chemistry*|*ccl.net
To: sergio.manzetti*|*gmx.com
Subject: CCL: Exchan= ge correlation
Date: Thu=2C 12 Jun 2014 21:31:49 -0400

=0A= =0A= =0A= =0A= =0A= No. =3B The exchange refers to the energy penalty for=0A= anti-symmetrization of the wavefunction. =3B It is a permutation=0A= operator (K) applied to the Coulomb operator (J). =3B It is not eno= ugh=0A= to have Coulombic repulsion=3B QM dictates that no two fermions have=0A= the same quantum state. =3B If you want to work with fermions=2C yo= u have=0A= to represent a penalty toward having the same quantum state.
=0A=
=0A= Correlation is an extended euphemism to mean "everything you do not=0A= get from the restrictions placed on the wavefunction in restricted=0A= Hartree-Fock theory." =3B The term more precisely derives from the = fact=0A= that the joint probability distribution function of the one-particle=0A= reduced density matrix shows that the there is no statistical=0A= correlation between two orbitals and their density...hence the term=0A= "correlation."
=0A=
=0A=

On 06/12/2014 07:05 PM=2C William=0A= McDonald pchem=3D-=3Ducsc.edu wrote:
=0A=

=0A=

=0A=
But isn't that a consequence of the mean-field=0A= approximation and not an intrinsic property of the electron?
= =0A=

=0A=
=0A=
On Thu=2C Jun 12=2C 2014 at 2:48 PM= =2C Susi=0A= Lehtola susi.lehtola=3Dalumni.helsinki.fi <=3Bowner-chemistry]*[ccl.net<= /a>>=3B=0A= wrote:
=0A=

=0A= Sent to CCL by: Susi Lehtola [susi.lehtola##alumni.helsinki.fi]
=0A= On Thu=2C 12 Jun 2014 11:50:09 -0700
=0A= "William McDonald pchem]|[ucsc.edu"=0A= <=3Bowner-chemistry ~~ ccl.net>=3B=0A= wrote:
=0A= >=3B On Thu=2C Jun 12=2C 2014 at 3:27 AM=2C Sergio Manzetti= =0A= sergio.manzetti::
=0A= >=3B outlook= .com <=3Bowner-chemistry=2C=2Cccl.net>=3B wrote:
=0A= >=3B >=3B Dear all=2C when is it suitable to start consider= ing=0A= =3BExchange correlation
=0A= >=3B >=3B between Electrons=2C (e.g pass Oxygen=2C Mg=2C=0A= Phosporous or further up in the
=0A= >=3B >=3B system)?
=0A= >=3B
=0A= >=3B In a system with more than one electron of the same=0A= spin.
=0A= >=3B
=0A=
=0A= That is: in a system with more than zero electrons of the=0A= same spin.
=0A=
=0A= [Exchange is important even for a single electron=2C because=0A= it cancels
=0A= out (or tries to) the self-Coulomb interaction.]
=0A=
=0A= For correlation=2C you need at least two=2C but even with a=0A= single
=0A= electrons many correlation functionals yield non-zero=0A= correlation
=0A= energies...
=0A= --
=0A= ---------------------------------------------------------------
=0A= Mr. Susi Lehtola=2C PhD =3B =3B =3B =3B &nb= sp=3B =3B Research Associate
=0A= susi.lehtola ~~ alumni.helsinki.fi=0A= =3B Department of Applied Physics
=0A= = http://www.helsinki.fi/~jzlehtol=0A= =3BAalto University
=0A= =3B =3B =3B =3B =3B =3B =3B = =3B =3B =3B =3B =3B =3B =3B =3B &nb= sp=3B =3B Finland
=0A= ---------------------------------------------------------------
=0A= Susi Lehtola=2C FT =3B =3B =3B =3B =3B= =3B =3B =3B =3BTutkijatohtori
=0A= susi.lehtola ~~ alumni.helsinki.fi=0A= =3B Fysiikan laitos
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=0A=
=0A= --
=0A= William J. McDonald
=0A= Postdoctoral Scholar
=0A= Department of Chemistry and Biochemistry
=0A= University of California=2C Santa Cruz
=0A=
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=0A=