From owner-chemistry@ccl.net Thu Jun 26 13:59:00 2014 From: "N. Sukumar nagams=rpi.edu" To: CCL Subject: CCL: Exchange correlation Message-Id: <-50287-140626103821-17620-JpMPgdbZ2G8habh+z+wiIQ++server.ccl.net> X-Original-From: "N. Sukumar" Content-Disposition: inline Content-Transfer-Encoding: binary Content-Type: text/plain Date: Thu, 26 Jun 2014 10:39:12 -0400 MIME-Version: 1.0 Sent to CCL by: "N. Sukumar" [nagams _ rpi.edu] "isn't the self-interaction error a consequence of the mean-field approximation?" Of course, but so is correlation! N. Sukumar Professor of Chemistry Shiv Nadar University, India ---------------------------- "Pursue something so important that even if you fail, the world is better off with you having tried." -- Tim O'Reilly http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470769009.html ==============Original message text=============== On Fri, 13 Jun 2014 12:56:14 EDT "William McDonald pchem]=[ucsc.edu" wrote: 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.,+,. 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 ===========End of original message text=========== From owner-chemistry@ccl.net Thu Jun 26 17:15:00 2014 From: "Susi Lehtola susi.lehtola.,.alumni.helsinki.fi" To: CCL Subject: CCL: Exchange correlation Message-Id: <-50288-140626171145-15588-XnKohn8YlVvx9BI8GNcv6g,server.ccl.net> X-Original-From: Susi Lehtola Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII Date: Fri, 27 Jun 2014 00:11:30 +0300 MIME-Version: 1.0 Sent to CCL by: Susi Lehtola [susi.lehtola===alumni.helsinki.fi] On Thu, 26 Jun 2014 10:39:12 -0400 "N. Sukumar nagams=rpi.edu" wrote: > Sent to CCL by: "N. Sukumar" [nagams _ rpi.edu] > "isn't the self-interaction error a consequence of the mean-field > approximation?" > > Of course, but so is correlation! No and yes. The lack of correlation is consequence of the mean-field approximation (Hartree--Fock), but Hartree--Fock is free of self-interaction. In contrast, density-functional theory accounts for all exchange and correlation effects; all within a single determinant. This is because the real physical information is *not* in the Kohn-Sham orbitals, but rather the ground state electron density that they span, which has a one-to-one mapping to the exact N-electron wave function, and the potential for the system. However, we don't know the exact exchange-correlation functional (which in effect describes the mapping from the N-electron wave function to the density), we only have a variety of approximations to it. This is the density functional zoo. Most functionals don't satisfy the properties that we know the exact functional satisfies, perhaps first and foremost that with the exact functional J [n_{i \sigma}] + K [n_{i \sigma}] = 0 (1) where J[n] and K[n] denote the Coulomb energy and K the exchange energy and n_{i \sigma} is any single-electron density. In reality J+K != 0, which often leads to spurious charge delocalization, as well as too small band gaps in DFT. -- --------------------------------------------------------------- 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 --------------------------------------------------------------- From owner-chemistry@ccl.net Thu Jun 26 21:10:00 2014 From: "Dr. Robert Molt Jr. r.molt.chemical.physics(!)gmail.com" To: CCL Subject: CCL: Exchange correlation Message-Id: <-50289-140626145735-20358-ht0dyurEnJR2VyPJHQunJw]*[server.ccl.net> X-Original-From: "Dr. Robert Molt Jr." Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=ISO-8859-1; format=flowed Date: Thu, 26 Jun 2014 14:57:22 -0400 MIME-Version: 1.0 Sent to CCL by: "Dr. Robert Molt Jr." [r.molt.chemical.physics(a)gmail.com] It is wrong to say that self interaction is a consequence of the mean field approximation. Hartree-Fock is a mean-field methodology and does not have self interaction. Self interaction is a result of having an ad-hoc, not rigorously formulated exchange-correlation functional. In HF theory, particles do not interact with themselves ( coulomb (J) and exchange (K) are such that J-K=0 when the indices sum over the same particle). The K operator does not exist in KS-DFT formalism, and hence there is self interaction error in 99% of KS-DFT functionals. Dr. Robert Molt Jr. r.molt.chemical.physics,,gmail.com On 06/26/2014 10:39 AM, N. Sukumar nagams=rpi.edu wrote: > Sent to CCL by: "N. Sukumar" [nagams _ rpi.edu] > "isn't the self-interaction error a consequence of the mean-field > approximation?" > > Of course, but so is correlation! > > N. Sukumar > Professor of Chemistry > Shiv Nadar University, India > ---------------------------- > "Pursue something so important that even if you fail, the world is better > off with you having tried." -- Tim O'Reilly > http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470769009.html > ==============Original message text=============== > On Fri, 13 Jun 2014 12:56:14 EDT "William McDonald pchem]=[ucsc.edu" wrote: > > 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.,+,. > 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 >> >> >> >