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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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Up: Miscellaneous
Previous: Totally symmetric singlets for
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TURBOMOLE M