Analysis in Global Symmetry

Each of the two molecules has a total of 40 valence electrons, lodged in 20 doubly-occupied MOs. The 8 (Tcc and 8 tch bonds that make up the r frame of COT have identical symmetry properties in cubane, so it is enough to consider the MOs comprising the four bonds that are interconverted during the isomerization. 

We place COT in the xy plane and allow it to relax to its stable tub conformation. Atoms 1, 2, 5 and 6 move to positive z and 3, 4, 7 and 8 to negative z, behind the plane of the diagram, but the four tt bonds can still be thought of essentially as being linear combinations of their Pz AOs. The four linear combinations of bond orbitals (LCBOs), labeled by their irreps in D2rf, are  

Cubane has cubic (Oj symmetry, but a slight elongation of the four a bonds emphasized in the digram, desymmetrizes the molecule to The four LCBOs are characterized as follows  

The electron-configurations of the two molecules correlate directly in D2rf, so the reaction must be characterized as allowed. 

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