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Appendix F
All derivatives needed for assignment iteration are determined
analytically. The frequency derivatives are calculated from the usual
energy-level derivative expression:
∂ε m
∂
∂H
=
mH m = m
m
∂ pj ∂ pj
∂ pj
Calculation of intensity derivatives is more complicated and has not
been described before for this particular case. The basic expression is:
∂ I mn
∂
=
mI− n
∂ pj ∂ pj
2
 ∂m
∂n
I− n + mI−
= 2 m I − n 
∂ pj
 ∂ pj




The wave-function derivatives needed in this equation are given by
perturbation theory as:
∂H
l
∂ pj
∂m
=∑
∂ pj
l≠m ε m − ε l
This expression causes difficulties in cases of near-degeneracy. Since
assignment problems occur in such cases anyway, the perturbation
summand is replaced by:
2
ε m − εl )  ∂ H
(
ε m − εl 
2 −

l
2
2
ε thresh
ε thresh

 ∂ pj


for
ε m − ε l < ε thresh
This modified term goes smoothly to zero if l and m become
degenerate.
F.6. Full-lineshape iteration
Direct least-squares fitting of observed and calculated lineshapes,
though possible in theory, does not yield very satisfactory results in
practice because of the negligible overlap between corresponding
peaks in observed and calculated lineshapes. To overcome this
problem, Binsch13 devised a generalization of the least-squares
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Technical issues