Woodward and Hoffmann state in their seminal paper [1], that a ground-state pericyclic reaction is thermally allowed when $p+q=\textrm{odd}$, with $p=(4n)_{antara}$ and $q = (4m+2)_{supra}$. When I look at a cheletropic carbene addition to an ethene (see Figure, from [2]), this rule gets a bit shady for me.
Cheletropic Carbene insertion

Essentially, there are two ways to look at it:
1) The HOMO is the two-electron sp2 orbital on the carbene and the LUMO the the $\pi^*$ LUMO on the olefin.
2) The HOMO is the $\pi$ orbital on the olefin and the LUMO the pz orbital on the carbene.

Case 1) results in a $p=1$ from the sp2 and $q=1$ from the $\pi^*$, so $p+q=\textrm{even}$. The same can be verified for case 2). How can this be, since these kinds of insertion are usually thermally allowed? Even when I would add together both situations, I'd get an even number. Does the Woodward-Hoffmann system work here or am I missing something?

[1] http://onlinelibrary.wiley.com/doi/10.1002/anie.196907811/abstract
[2] http://chemistry.caltech.edu/courses/ch242/H1.pdf

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    $\begingroup$ Carbene additions are a little finicky under Woodward-Hoffmann rules - if you have library access, I would refer you to Ian Fleming's Pericyclic Reactions, pp 47-48. He also has lots to say in his other text Molecular Orbitals and Organic Chemical Reactions - there is a huge section on W-H rules and the part on carbenes begins at p281 of the Reference Edition. $\endgroup$ Jul 26, 2016 at 8:22
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    $\begingroup$ Molecular Orbitals and Organic Chemical Reactions is indeed an excellent suggestion. This [scripps.edu/baran/images/grpmtgpdf/Martinez_13.pdf] PDF from a Baran group meeting might also be useful, it discusses the same kind of cheloptropic additions you're interested in $\endgroup$
    – NotEvans.
    Jul 26, 2016 at 19:27


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