Is it right to think that the Hartree procedure is called the SCF theory, as the notion of self-consistent field comes from approximating multi-electron wavefunction as multiple one-electron wavefunctions. Since we don't know the final charge density, we must iterate until it is self-consistent?

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    $\begingroup$ These are two different questions, and really should be divided. (It's site policy to only ask one question at a time, in a given Question.) Please re-ask your second paragraph in a new question. Check out the help center for more information on site policies. Thanks for asking here -- welcome to the site! $\endgroup$
    – hBy2Py
    Mar 16 '18 at 0:07
  • $\begingroup$ HF and SCF are used interchangeably quite often (whether you agree with it or not). $\endgroup$ Mar 16 '18 at 0:08
  • $\begingroup$ To those who think this question is too broad: it has a concrete answer which is given below and it is definitely not too broad. It is a fundamental part of the theory that is not discussed in modern literature. $\endgroup$ Mar 16 '18 at 16:49
  • $\begingroup$ As an extension of HF and SCF being used interchangeably, I often see (and use myself) SCF to cover both HF and DFT, as the Kohn-Sham equations are solved using an SCF procedure that is identical to the one used for HF. $\endgroup$ Mar 16 '18 at 16:51


The Hartree-Fock method encompasses a set of assumptions used to formulate and solve a series of equations embodying a mean-field, time-independent Schrödinger equation.

The self-consistent field method is a computational technique used in myriad applications where the equations to be solved are implicit—that is, where it is impossible to isolate an analytically solvable expression for a variable and its derivatives. To the best of my knowledge, any solution method involving a "guess-and-check" approach can be considered a 'self-consistent solution method'.

The Hartree-Fock method is an example of a use-case for a self-consistent field procedure, but they are not synonymous.

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    $\begingroup$ Excellent answer. I would note that the author's confusion likely stems from old literature using the phrase 'SCF' when describing HF, as back then it was the first widely used SCF method. Nowadays, as you've pointed out, there are numerous SCF methods that are not HF. $\endgroup$
    – jezzo
    Mar 17 '20 at 21:21

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