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Currently, I'm studying (again from zero and more in detail) Hartree Fock (HF) method, specifically the Restricted Hartree Fock (RHF).
I'm following two books:
"Introduction to Computational Chemistry" (Frank Jensen 2nd edition)
"Computational Chemistry, Introduction to the Theory and Applications of Molecular Quantum Mechanics" (Errol G. Lewars 2nd edition)

Both books describe the method starting from the Slater determinant of N (N = n° of electrons) Molecular Orbitals (MOs), in this way all the MOs are occupied. Then they generalize to the case where we have M > N MOs, so some will be empty.
But this last point is not well explained, I would like to understand this passage in detail, so I ask for an explanation or some references (books or articles ...).

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  • $\begingroup$ I have read the former book, and I don't think Jensen assumed that "all the MOs are occupied" in any part of his derivation. This is likely a misunderstanding. If you are sure he did assume this, could you please quote the part that says this? $\endgroup$
    – wzkchem5
    May 6, 2023 at 16:02
  • $\begingroup$ @wzkchem5 Until page 92 the Slater determinant is supposed to be constructed by N MOs, and the HF equations are in fact N. Until page 92 there is no summation over occupied MOs but only summation over all electrons. On page 94 he substitutes the MOs with a linear combination of basis set functions, then he says "Multiplying from the left by a specific basis function and integrating yields the Roothaan–Hall equations" assuming now that there are M (M = n° of basis functions) MOs, and in fact, the summation over occupied orbitals appear in page 95 for the first time. $\endgroup$
    – Al1010
    May 6, 2023 at 16:24
  • $\begingroup$ You should look at Szabo-Ostlund. Even though a lot of the book is outdated (it is from the early 1980s), it is unbeatable in its clarity. It also discusses such issues as linear dependence in the basis set, which many books still omit or get wrong... $\endgroup$ May 9, 2023 at 15:20
  • $\begingroup$ @SusiLehtola Ok thank you, I will try it and let you know. $\endgroup$
    – Al1010
    May 9, 2023 at 17:59
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    $\begingroup$ I believe Nike means that it would be potentially useful to other users if you self-answered your question in the answer box, rather than in the comments. $\endgroup$
    – Tyberius
    Dec 15, 2023 at 4:43

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