From owner-chemistry-: at :-ccl.net Fri Jun 13 16:28:00 2014 From: "William McDonald pchem]=[ucsc.edu" To: CCL Subject: CCL: Exchange correlation Message-Id: <-50212-140613125632-21230-qux4cyQyhyfP3wfFx46IzA() server.ccl.net> X-Original-From: William McDonald Content-Type: multipart/alternative; boundary=001a11c30e22252a4004fbba8e7a Date: Fri, 13 Jun 2014 09:56:14 -0700 MIME-Version: 1.0 Sent to CCL by: William McDonald [pchem]^[ucsc.edu] --001a11c30e22252a4004fbba8e7a Content-Type: text/plain; charset=UTF-8 Sorry, my previous post was totally unclear. I understand what exchange and correlation refer to. I meant to ask "isn't the self-interaction error a consequence of the mean-field approximation?" As to Dr. Lehtola's comment that "Exchange is important even for a single electron, because it cancels out (or tries to) the self-Coulomb interaction." This seems odd, because why are two-electron (Coulomb repulsion) integrals being evaluated in a one-electron system? It seems to me that for any one-electron system, one simply evaluates the electronic kinetic energy and electron-nucleus attraction; there should not be a self-Coulomb interaction. On Thu, Jun 12, 2014 at 6:31 PM, Robert Molt Jr r.molt.chemical.physics.-x-. gmail.com wrote: > 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 pchem=-=ucsc.edu 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 susi.lehtola= > alumni.helsinki.fi wrote: > >> >> Sent to CCL by: Susi Lehtola [susi.lehtola##alumni.helsinki.fi] >> On Thu, 12 Jun 2014 11:50:09 -0700 >> "William McDonald pchem]|[ucsc.edu" wrote: >> > On Thu, Jun 12, 2014 at 3:27 AM, Sergio Manzetti sergio.manzetti:: >> > outlook.com 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 >> energies... >> -- >> --------------------------------------------------------------- >> Mr. Susi Lehtola, PhD Research Associate >> susi.lehtola ~~ alumni.helsinki.fi Department of Applied Physics >> http://www.helsinki.fi/~jzlehtol Aalto University >> Finland >> --------------------------------------------------------------- >> Susi Lehtola, FT Tutkijatohtori >> susi.lehtola ~~ alumni.helsinki.fi Fysiikan laitos >> http://www.helsinki.fi/~jzlehtol Aalto-yliopisto >> --------------------------------------------------------------- >> >> >> >> E-mail to subscribers: CHEMISTRY]*[ccl.net or use:>> >> E-mail to administrators: CHEMISTRY-REQUEST]*[ccl.net or use>> >> >> > > > -- > William J. McDonald > Postdoctoral Scholar > Department of Chemistry and Biochemistry > University of California, Santa Cruz > > > -- William J. McDonald Postdoctoral Scholar Department of Chemistry and Biochemistry University of California, Santa Cruz --001a11c30e22252a4004fbba8e7a Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
Sorry, my previous post was totally unclear. I understand = what exchange and correlation refer to. I meant to ask "isn't the = self-interaction error a consequence of the mean-field approximation?"=
As to Dr. Lehtola's comment that "Exchange is important even for a single electron, because it cancels= =C2=A0out (or tries to) the sel= f-Coulomb interaction." This seems odd, because why are two-electron (= Coulomb repulsion) integrals being evaluated in a one-electron system? It s= eems to me that for any one-electron system, one simply evaluates the elect= ronic kinetic energy and electron-nucleus attraction; there should not be a= self-Coulomb interaction.


On Thu,= Jun 12, 2014 at 6:31 PM, Robert Molt Jr r.molt.chemical.physics.-x-.gmail.com <owner-chemistry-x-ccl.net>= wrote:
=20 =20 =20
No.=C2=A0 The exchange refers to the energy penalty for anti-symmetrization of the wavefunction.=C2=A0 It is a permutation operator (K) applied to the Coulomb operator (J).=C2=A0 It is not enoug= h to have Coulombic repulsion; QM dictates that no two fermions have the same quantum state.=C2=A0 If you want to work with fermions, you ha= ve to represent a penalty toward having the same quantum state.

Correlation is an extended euphemism to mean "everything you do no= t get from the restrictions placed on the wavefunction in restricted Hartree-Fock theory."=C2=A0 The term more precisely derives from t= he 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 pchem=3D-=3Duc= sc.edu 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 susi.lehtola=3Dalumni.helsinki.fi <owner-chemistry]*[ccl.net> wrote:

Sent to CCL by: Susi Lehtola [susi.lehtola##alumni.helsinki.fi]
On Thu, 12 Jun 2014 11:50:09 -0700
"William McDonald pchem]|[ucsc.edu" <owner-chemistry ~~ ccl.net> wrote:
> On Thu, Jun 12, 2014 at 3:27 AM, Sergio Manzetti sergio.manzetti::
> outlook.c= om <owner-chemistry,,cc= l.net> wrote:
> > Dear all, when is it suitable to start considering =C2=A0Exchange 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
energies...
--
---------------------------------------------------------------
Mr. Susi Lehtola, PhD =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0= Research Associate
susi.lehtola ~~ alumni.helsinki.fi =C2=A0 Department of Applied Physics
http://www.helsinki.fi/~jzlehtol =C2=A0Aalto University
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 = =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 Finland
---------------------------------------------------------------
Susi Lehtola, FT =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2= =A0 =C2=A0 =C2=A0Tutkijatohtori
susi.lehtola ~~ alumni.helsinki.fi =C2=A0 Fysiikan laitos
http://www.helsinki.fi/~jzlehtol =C2=A0Aalto-yliopisto
---------------------------------------------------------------



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




--
William J. M= cDonald
Postdoctoral Scholar
Department of Chemistry and Biochemistry=
University of California, Santa Cruz
--001a11c30e22252a4004fbba8e7a--