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HF expectation value

  1. Jan 5, 2016 #1
    I am not sure why a factor of (½) appears in front of the summation over orbitals, i, j to N, of the Coulomb and exchange integrals in the HF energy expectation value.
  2. jcsd
  3. Jan 5, 2016 #2


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    A constant factor appearing in an equation in a specialized field of physics, uncommon to the majority of physicists, is susceptible to the definition of the one who derives the said equation. I have seen several authors write their own version of Hartree-Fock energy which differ in the prefactors. It's a lot more helpful if you write the particular form which you are confused with.
  4. Jan 5, 2016 #3
    Thank you, but the thing is if the summation runs from i<j instead of i,j, something that is claimed to be equivalent in general I think, then the factor is omitted, and I am not sure how this is so.
  5. Jan 5, 2016 #4

    A. Neumaier

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    You may perhaps claim this, but it is not equivalent in general.

    Instead of getting each pair of distinct indices once you get it twice and hence need a factor 1/2. You also need to ensure that equal indices don't make a contribution.
  6. Jan 5, 2016 #5
    Thank you. I refer to "Basic Principles and Techniques of Molecular Quantum Mechanics" by Ralph E. Christoffersen, p. 445 + 483 footnotes, when I write: "something that is claimed to be equivalent in general I think".
  7. Jan 5, 2016 #6


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    If the factor of 1/2 appears, that means the index of summation must be written like ##\sum_i \sum_j## with the condition ##i\neq j## being imposed as Neumaier said. You need to check how the indices in the summation are written when 1/2 is appearing.
  8. Jan 5, 2016 #7
    Thank you
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