From owner-chemistry@ccl.net Sun May 31 15:56:01 2015 From: "JC Womack jw5533 ~ my.bristol.ac.uk" To: CCL Subject: CCL: Measuring Instantaneous Correlation of Individual Orbitals Message-Id: <-51413-150531155427-29789-MFJMLIE0JeZ4Gww3QtcZSg-#-server.ccl.net> X-Original-From: JC Womack Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset=utf-8 Date: Sun, 31 May 2015 20:54:15 +0100 MIME-Version: 1.0 Sent to CCL by: JC Womack [jw5533]=[my.bristol.ac.uk] These are interesting thoughts! You asked for some literature references. I would suggest looking at this excellent review: Hättig, C., Klopper, W., Köhn, A. & Tew, D. P. Explicitly Correlated Electrons in Molecules. Chem. Rev. 112, 4–74 (2012). http://pubs.acs.org/doi/abs/10.1021/cr200168z The review is about explicitly correlated electronic structure methods, but the introduction gives some useful insights into the nature of electron correlation. On 31/05/15 16:16, Billy McCann thebillywayne-,-gmail.com wrote: > > Sent to CCL by: Billy McCann [thebillywayne{=}gmail.com] > Greetings All. > > This is a subject I've been considering for a while, but it seems I > haven't a) found a way to express the problem to myself so that it > becomes more clear to me and b) come across literature that deals with > my line of questioning. > > If anyone can offer insight into this, it would be very much > appreciated. As a background, I have some training in chemical > physics, but am far from expert. So please bear with me if I expose my > ignorance. :) I'd like to frame the discussion within the wavefunction > interpretation of QM and canonical Hatree-Fock atomic orbitals and > LCAO-MO level of theory. > > I'd like to, for now, leave aside density functional theory because I > don't have much experience or insight into the nature of the > exchange-correlation operators; I can't seem to get a systematic > understanding of that particular operator in its various formulations. > And it's this correlation energy which I'm curious about. That the > operator contains both exchange, correlation, plus a correction to the > kinetic energies of the Kohn-Sham orbitals confounds me even more when > trying to understand it, not even mentioning double-hybrid DFA's. I > know that brilliant scientists have worked on various density > functional approximations, and I do not at all want to belittle their > work. DFA is a great tools for physicists and chemists. > > Now, on to my questions. > > Regarding instantaneous, dynamical electron correlation, I understand > that there are many ab initio methods which begin at the Hatree-Fock > approximation, starting with a Slater determinant expanded to various > numbers of basis functions, and then account for dynamical electron > correlation in different ways, typically, from what I can understand, > by the admixture of electronic states wherein n number of electrons > have been promoted to higher energy orbitals. If I understand > correctly, all methods begin from the HF approximation and correct for > dynamical correlation by making a linear combination of Slater > determinants by different methods. (Perhaps the electron propagator > method and the use of Dyson orbitals represents an alternative > approach that doesn't combine Slater determinants, but I'm unsure. > I've read Ortiz's review and let's just say it's a little out of my > depth. ;)) > > All of these methods measure the correlation energy of the entire > system in question, i.e. the atom or molecule in question. > > But what I'm wondering about is the correlation energy of a *single* > atomic or molecular orbital. Is it that comparing the HF orbital > energy to, say, a corresponding orbital resulting from a CCSD(T) > calculation would yield such an energy? I've pondered this question, > but I've read others who say that this isn't entirely the case because > HF does indeed account for some small degree of electron correlation, > but only in an averaged way. (I think I remember reading this in > Cramer's text.) Perhaps MC-SCF may provide such an answer, by > measuring the coefficients of each determinant? > > So my question is two-fold: > > 1. How can the dynamical electron correlation energy of a single > atomic or molecular orbital be measured? Can it even be done? > > 2. Is it possible to make a generalized statement such as, "Core > electrons experience a greater degree of correlation because they are > surrounded by more electrons," or "Valence electrons experience a > greater degree of electron correlation because they are bound more > loosely to the system, allowing their wavefunctions to fluctuate more > freely,"? > > I'd appreciate any insight that anyone has or any references to the > literature or textbooks. > > Also, if someone would like to reframe this question in terms of > non-canonicalized HF orbitals or from a NAO/NBO viewpoint, that would > be great as well. > > I hope I haven't embarrassed myself. > > Thanks for your attention, > Billy Wayne > > -- > Billy Wayne McCann, Ph.D. > http://bwayne.sdf.org > irc://irc.freenode.net:bwayne > > "There is nothing new under the sun." ~ Solomon> > -- James C. Womack PhD research student Centre for Computational Chemistry School of Chemistry University of Bristol BRISTOL BS8 1TS Email: jw5533-x-my.bristol.ac.uk Web: http://jcwomack.uk