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Average of highspin states:
n electrons in MO with
degenerate n_{ir}.
a 
= 

b 
= 

where:
k = max(0, n  n_{ir}) ,
l = n  2k = 2S (spin)
This covers most of the cases given above. A CSF results only if
n = {1,(n_{ir}  1), n_{ir},
(n_{ir} + 1),
(2n_{ir} 1)} since there
is a single highspin CSF in these cases.
The last equations for a and b can be rewritten in many ways, the probably most concise form is
a 
= 

b 
= . 

This applies to shells with one electron, one hole, the highspin couplings of halffilled shells and those with one electron more ore less. For d^{2}, d^{3}, d^{7}, and d^{8} it represents the (weighted) average of highspin cases: ^{3}F + ^{3}P for d^{2},d^{8}, ^{4}F + ^{4}P for d^{3}, d^{7}.
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TURBOMOLE 15888