# When does the Hartree-Fock approximation fail?

• iibewegung
In summary, the conversation discusses the Hartree-Fock approximation and when it may fail. The original question was about the type of wave functions that would be used in the case of the approximation failing, and the conversation also touches on when the mean field approximation may fail. The conversation concludes with a question about the general term for when the mean field approximation fails.
iibewegung

## Homework Statement

Hi, I've read from Wikipedia that in the Hartree-Fock approximation, "Each energy eigenfunction is assumed to be describable by a single Slater determinant".

My question is... if the approximation fails and the system has to be described by linear combinations of more than one type of Slater determinants, what type of wave functions would they be determinants of? (besides the one-electron wave functions)

Last edited:
You can't have Hartee Fock if the potential the particles move is is not the mean field. To answer the question "when does the Hartree-Fock approximation fail? "

actually... i decided to change the question to the one you see now (edited) on the first msg, a few minutes after writing it the first time...

i was able to change the body of the msg but not the title of the thread.
can this new question be answered here as well?

.. or is it a better idea to start a new thread with the right title?

just to ask - when would a mean field approximation fail?

Well I come from nuclear physics point of view, and the MFA fails when one takes into account the hard repulsive core of the Nuclear force at short distances.

But what it is called in general, I have no clue :)

## 1. What is the Hartree-Fock approximation?

The Hartree-Fock approximation is a mathematical model used in quantum mechanics to describe the behavior of a many-body system, such as a collection of atoms or molecules. It is based on the assumption that each electron in the system moves independently in an average field created by all the other electrons.

## 2. When does the Hartree-Fock approximation fail?

The Hartree-Fock approximation fails when the system being studied has strong electron correlation, which means that the behavior of one electron is highly dependent on the behavior of the others. This occurs in systems with many interacting electrons, such as those found in strongly correlated materials or in chemical reactions involving multiple bonds.

## 3. How does the failure of the Hartree-Fock approximation affect the accuracy of calculations?

When the Hartree-Fock approximation fails, the calculated energies and properties of the system may deviate significantly from the true values. This can result in errors in predicting experimental outcomes or understanding the behavior of a system.

## 4. Are there any methods that can improve upon the Hartree-Fock approximation?

Yes, there are many methods that have been developed to improve upon the Hartree-Fock approximation and account for electron correlation. These include post-Hartree-Fock methods, such as Møller-Plesset perturbation theory and coupled cluster theory, as well as density functional theory.

## 5. Are there any specific examples where the Hartree-Fock approximation fails?

Yes, the Hartree-Fock approximation is known to fail in systems with large numbers of electrons, such as transition metal complexes, where strong electron correlation is present. It also fails in systems with delocalized electrons, such as conjugated molecules, due to the inability to accurately describe the electron density distribution.

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