Talk:Hartree–Fock method

Could someone acquanted in the field give a list of the original and also some of the convenient references in scientific literature on this subject? This can be found in the density functional theory page, for example, and such references make wikipedia really a good starting point for actual research. -- Mipmip 04:06, 15 November 2006 (UTC)

Fundamental physics concept

I had several discussions with colleagues on just what constitutes a fundamental physics concept. What we decided was that a fundamental physics concept was one that any physicist would need to be familiar with before embarking on a specialized experimental or theoretical track. By "familiar" we meant being able to solve problems at the end of the chapter on that topic. I am not sure, by this criterion, that "Fundamental physics concepts" should have been removed as a category, but maybe I am wrong. What is the opinion out there?Complexica 18:23, 16 March 2007 (UTC)

There is a discussion at Wikipedia talk:WikiProject Physics#Is not Category:Fundamental physics concepts being over used? which looks as if it is concluding exactly that. The Category is over used. Specifically on Hartree-Fock, I think the criteria you suggest, would lead it to be removed from this article. Hartree-Fock of course is, these days, used much more by chemists than physicists, but a physicist going down the track of theory of atoms would start with quantum mechanics. That would be the fundamental concept. Hartree-Fock is just an applied tool, he/she would learn as they went down the track. It is not a fundamental concept. It is just an important approximate method --Bduke 22:01, 16 March 2007 (UTC)

Misnomer

There is no such thing as the "Hartree-Fock algorithm." Hartree-Fock is a set of assumptions made in order to solve the electronic Schrodinger equation. The problem is solved by the self consistent field algorithm. This page would be fine, if that were pointed out. I may get to it soon, but somebody else feel free to beat me to it. —Preceding unsigned comment added by Jal173 (talk • contribs) 20:43, 7 August 2008

There is some mention of this at the beginning, but the in general due to this problem the article has a very amateur and inexact tone.--Jal173 (talk) 20:51, 7 August 2008 (UTC)

Can you be more precise about where the tone is inexact and the article amateur? What some people see as inexact and amateur, is seen by others as making the material accessible to non-experts. I would use the term "the self consistent field algorithm" to refer to the original numerical approach by Hartree. The most common method now is solving the Roothaan-Hall equations in terms of a basis set expansion. It comes to the same result of course if the basis set is complete enough. However, it is this approach that should be described in most detail. If one wants to be exact, Hartree-Fock is a set of assumptions made in order to solve the electronic Schrodinger equation within the Born-Oppenheimer approximation (at least for molecules and solids) and it does not solve it but gives an approximate solution which is often very poor indeed. --Bduke (talk) 22:31, 7 August 2008 (UTC).

The fact that HFSCF(via basis set expansion) and HF are talked about as if they are the same thing is the problem. You make this very distinction in your comment. This is what needs to be addressed. --Jal173 (talk) 03:40, 11 August 2008 (UTC)

I think the problem is that the terms used in the science are not clear. For example, you use SCF for the basis set expansion approach but I think it predates the Roothaan-Hall equations. I think it was used to describe Hartree's calculations either before the Fock modifications or after. However now it is used to describe the iterative cycles used to solve the Roothaan-Hall equations. There really is no clear set of terms that differeniate between the original method used for atoms and the use of the Roothaan-Hall equations. Where the former has been used in a few cases to study molecules it has been called the numerical Hartree-Fock method to distinguish it from the basis set expansion method. The later is generally just called Hartree-Fock in current molecular ab initio codes where the terms RHF, UHF and ROHF are used as key words in the data, and also in the literature to describe the single determinant reference function for post-Hartree-Fock methods when of course a basis set expansion is being used. So while I think the article can be improved to be clearer in parts I do not think the terms "inexact" and "amateur" are appropriate. Could you bring some suggested rewrites to the talk page here for discussion?

I think more important is to add something saying just how bad Hartree-Fock actually is for many molecules.--Bduke (talk) 07:16, 11 August 2008 (UTC)

Actual results and correlation with experimental data

Anything? no results, failed method? V8rik (talk) 21:30, 2 August 2009 (UTC)

Article title

I've always seen this written as "Hartree–Fock method" - just "Hartree–Fock" on its own looks strange. Is this actually the normal style in other fields, or should we move the article to "Hartree–Fock method"? Djr32 (talk) 18:59, 3 October 2009 (UTC)

I support moving it to Hartree–Fock method. Dicklyon (talk) 19:03, 3 October 2009 (UTC)

Done. Djr32 (talk) 18:18, 13 October 2009 (UTC)

Coulomb Operator

Where is the 2 in front of the Coulomb Operator coming from? I thought about it a lot and many sources miss the 2. Is this a mistake? — Preceding unsigned comment added by 92.229.145.226 (talk) 20:36, 19 April 2012 (UTC)

One source which does include the 2 is I.N.Levine, Quantum Chemistry (4th ed 1991) p.403. He explains that the factor 2 occurs because there are two electrons in each spatial orbital. So j is summed over spatial orbitals, as implied by the n/2 over the summation sign. Sources which omit the 2 are summing over spin-orbitals, of which there are twice as many in a closed-shell state. So we can retain the factor 2, but we should specify that this form is for a closed-shell state. And for consistency we should replace the phrase "the Coulomb operator, defining the electron-electron repulsion energy due to the orbital of the jth electron" by "the Coulomb operator, defining the electron-electron repulsion energy due to the jth doubly occupied orbital". Dirac66 (talk) 21:11, 19 April 2012 (UTC)

Additional citations

In part brief history, Fock´s and Slater contribution, some citations may be missing. "FOCK, V. Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems. Zeitschrift für Physik, 1930, 61.1-2: 126-148." and "SLATER, John C. Note on Hartree's method. Physical Review, 1930, 35.2: 210." — Preceding unsigned comment added by 95.105.235.30 (talk) 16:55, 18 May 2013 (UTC)

How bad are the approximations, is there a rough quantitative guide?

Let's say I want to use Hartree Fock to calculate some parameter of a simple system which has been measured to high accuracy, like the electron affinity of a particular atom. How well does the Hartree Fock method compare to reality? Nanite (talk) 11:16, 28 January 2014 (UTC)

This is really not the place to discuss this, as the talk page is for discussing the article. You need to get a a good book that covers computational quantum chemistry. However, as a quick summary, if you want high accuracy you do not use Hartree-Fock, and electron affinities are particularly difficult to calculate to high accuracy. --Bduke (Discussion) 19:51, 28 January 2014 (UTC)

Five approximations theme is inaccurate

The "five approximations" approach of this article is inaccurate.

1. The fourth and fifth approximation are the same

2. The third approximation (finite basis set) is not inherent to the Hartree-Fock method. You can very well solve the Hartree-Fock differential equations numerically without selecting a basis set. The choice of numerical method for solving the problem is orthogonal to the choice of Hartree-Fock.

3. The first and second, Born-Oppenheimer and non-relativistic, I agree are approximations commonly used alongside Hartree-Fock, but I wouldn't go so far as to consider them fundamental to Hartree-Fock.

I'm not making an edit to the article, because this set of five approximations is threaded throughout the article, and it would be nice to have some degree of consensus prior to making any change. And I don't know where this idea of these five approximations comes from. If it's how chemists (for instance) commonly think of Hartree-Fock, then we could add a citation and an explanation, perhaps. (I'm a physicist, for context.)

As I've seen it used and discussed (and consistent with the concept of the "Hartree Fock limit" as currently discussed in the article), the essence of Hartree-Fock is to assume a single Slater determinant form for a many-body wavefunction. Applying the variational method to this gives the Hartree Fock result for the ground state.

Droundy (talk) 20:31, 30 May 2017 (UTC)

What Droundy writes is correct in all points. Specifically: 1. What the article treats as two approximations (single Slater determinant and mean field approximation) amount to the same thing. BTW, the 'single Slater derminant' is true only for closed shell electronic states; in the case of open shells (ie non-zero spin) we need, in the general case, more than one determinant (as done in ROHF theory). It's also called 'mean field approximation'.

2. Numerical Hartree-Fock calculations are routine for atoms and are possible for diatomics... the use of basis function was famously introduced by Roothaan and, independently, by Hall in (about) 1951, it is important in practice in molecule but it's not an intrinsic feature of the Hartree-Fock method.

3. Again, Born-Oppenheimer and relativistic approximations are very common but are rather separate from the Hartree-Fock approximation. Non-adiabatic Hartree-Fock-type calculations have been done (by a Japanese group if I remember right) and relativistic Hartree-Fock (Dirac-Fock) calculations are the norm.

I agree that the article should be changed.

L0rents (talk) 11:44, 30 March 2018 (UTC)

ROHF is essentially a single determinant. For a singlet with 2n + 1 electrons there are n doubly occupied orbitals and 1 singly occupied orbital. A triplet with 2n electrons has 2 doubly occupied orbitals with the same spin and n-1 singly occupied orbitals with the same spin. Technically there are 3 determinants with different spin terms but you only need to calculate one of them. UHF is also a single determinant but with different orbitals for each spin. --Bduke (Discussion) 20:00, 30 March 2018 (UTC)

Sorry but I think you typed that too quickly, and that what you meant was:

ROHF is essentially a single determinant. For a DOUBLET with 2n + 1 electrons there are n doubly occupied orbitals and 1 singly occupied orbital. A triplet with 2n electrons has 2 SINGLY occupied orbitals with the same spin and n-1 DOUBLY occupied orbitals with the same spin. Technically etc. Dirac66 (talk) 02:36, 31 March 2018 (UTC)

Indeed. Apologies and many thanks. --Bduke (Discussion) 01:21, 1 April 2018 (UTC)

Restructuring requirements

Chemistry vs physics

I saw later that this article is probably "mostly" under chemistry umbrella and not under physics as actually I initially thought, in regards to the discussion above, a lot of confusions of what topic shall be in / how etc. comes actually from this, i.e. that in chemistry hartree fock is merely a computational thing where from a physics standpoint is a foundational thing (e.g in regards to anti-symmetric states). Also I started editing Hartree equation where there is some historical perspective of the different variants of these hartree vs Hartree fock, and Slater Determinant where there are implications to 2nd quantization (also relevant here). Now that work shall be ended before attacking a new one, but it is relevant to jot down some requirements for this article. In general there is an overall need to clarify split between physics and Chemistry in this article (e.g. Foundation vs computational etc. / 5 hypothesis vs different computational methods etc. ) Maybe it may help adding/splitting content into some sections like "Hartree fock as a set of computational methods" "Hartree fock and slater determinants" etc.

New physics related sections Requirements

I come from physics and would like to see some more content related to:

• Add "advanced" section on Feynmann diagrams and Hartree fock

 (E.g. Mattuck pg. 89-92)

• Add some explanations why hartree fock is a fixed point iteration vs multi-point iteration

• Add "advanced" section on Grassmannian and Hartree fock

 e.g. see both refs to Hartree here [1]

This may go under this article in an advanced section/box or in a spin-off article for the physics part, but you can argue that also the Feynman diagrams parts are relevant to a modern discussion on perturbative quantum chemistry algorithms.