Talk:Hartree–Fock method

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)

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)

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 

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.

This article was the subject of a Wiki Education Foundation-supported course assignment, between 26 August 2025 and 17 December 2025. Further details are available on the course page. Student editor(s): Waltsa6 (article contribs). Peer reviewers: Campbellromero.

— Assignment last updated by Campbellromero (talk) 13:50, 27 November 2025 (UTC)