Extended hyperline

Let us summarize briefly at this stage. We have seen that the point of degeneracy forms an extended hyperline which we have illnstrated in detail for a four electrons in four Is orbitals model. The geometries that lie on the hyperline are predictable for the 4 orbital 4 electron case using the VB bond energy (Eq. 9.1) and the London formula (Eq. 9.2). This concept can be nsed to provide nseful qualitative information in other problems. Thns we were able to rationalize the conical intersection geometry for a [2+2] photochemical cycloaddition and the di-Jt-methane rearrangement. 

We now proceed to look at three examples from recent work in some depth. In the first example, we wish to illustrate that a knowledge of the VB structure or of the states involved in photophysics and photochemistry rationalize the potential surface topology in an intuitively appealing way. We then proceed to look at an example where the extended hyperline concept has interesting mechanistic implications. Finally, we shall look at an example of how conical intersections can control electron transfer problems. 

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