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Average of high-spin states: n electrons in MO with
degenerate nir.

a = $\displaystyle {\frac{{n_{ir}\bigl(4k(k+l-1)+l(l-1)\bigr)}}{{(n_{ir}-1)n^2}}}$    
b = $\displaystyle {\frac{{2 n_{ir}\bigl(2k(k+l-1)+l(l-1)\bigr)}}{{(n_{ir}-1)n^2}}}$    

where: k = max(0, n - nir) , l = n - 2k = 2S    (spin)

This covers most of the cases given above. A CSF results only if n = {1,(nir - 1), nir, (nir + 1), (2nir -1)} since there is a single high-spin CSF in these cases.

The last equations for a and b can be rewritten in many ways, the probably most concise form is

a = $\displaystyle {\frac{{n(n-2)+2S}}{{(n-2f)n}}}$    
b = $\displaystyle {\frac{{n(n-2)+(2S)^2}}{{(n-2f)n}}}$ .    

This applies to shells with one electron, one hole, the high-spin couplings of half-filled shells and those with one electron more ore less. For d2, d3, d7, and d8 it represents the (weighted) average of high-spin cases: 3F + 3P for d2,d8, 4F + 4P for d3, d7.


next up previous contents index
Next: Two-component Hartree-Fock and DFT Up: Miscellaneous Previous: Totally symmetric singlets for   Contents   Index
TURBOMOLE 15888