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<U|V> overlap integral of two many-electron determinant wave functions

  1. Sep 5, 2014 #1
    Hello,

    If we let U and V be two single determinant wave functions built up of spin orbitlas ui and vj respectively, will the overlap between them be as follows:

    <U|V> = Det{<ui|vi>}

    Thank you
     
  2. jcsd
  3. Sep 5, 2014 #2

    cgk

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    This is not the third thread you make with exactly the same question. Your question has been answered in the thread in the Quantum Physics forum.
     
  4. Oct 29, 2014 #3
    Dear cgk,

    According to your answer in another forum I can calculate the SAB by computing a singular value decomposition (SVD) of the occupied orbital overlap Socc. However, I would be very glad to know if the SAB can also be calculated by
    SAB=<U|V> = Det{<ui|vj>},

    Thank you for your support
     
  5. Oct 30, 2014 #4

    cgk

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    I think so, yes. This would even get the sign right. Note that for a square matrix (as you have here) the determinant is equal to the product of singular values multiplied by a phase factor (since if SAB = U diag(sig) V (i.e., a SVD, with U and V unitary), then det(SAB) = det(U diag(sig) V) = det(U) det(diag(sig)) det(V) = e^{i phi} det(diag(sig)) = e^{i phi} prod{sig_i}, since unitary matrices have determinants with absolute value 1).
     
  6. Oct 31, 2014 #5
     
  7. Jan 20, 2015 #6

    Dear cgk,

    Thank you very much for your kind answers. I was wondering whether you could help me again... I calculate the SAB of the two slater determinants. I have two sets of molecular orbitals, in both sets I have equivalent orbitals, just in different energy order and different electrons occupation. Since using SAB=<U|V> = Det{<ui|vj>} does not take into account the occupation or the order of the orbitals (changing the order will just change the sign of the determinant value), I get actually SAB=1... It seems not to calculate what I need...since SAB should reflect the probability of electron transfer between this two sets...
    p.s. for my calculation I take only the occupied orbitals (I have one singly and the other doubly occupied).

    Thank you
     
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