According to MO theory there can be no exceptions to the WH rules, nevertheless there are exceptions. On the other hand, in my opinion Pauling's valence bond theory that invokes canonical structures predicts
where exceptions would occur, and why. In my example of the pentadienyl carbenium ion the concept of canonical structures puts positive charge evenly on C1, C3 and C5. If we substitute the ends with alkyl groups, which stabilize carbenium ions, then positive charge is preferentially located at C1 and C5. An empty orbital represents positive charge localized on a given atom and according to molecular orbital theory, the effect of an empty orbital should be the same as that of an occupied one. As far as I can make out, this concept originated with Mullikan (Phys Rev 41: 49-71, 1932), but essentially as an assertion.
Why do the WH rules work? The usual argument is that a +signed function must overlap with another +signed function, and from that observation, the rotational characteristics of the WH rules follow. (Actually, the same rules follow if a bond forms only when plus interferes with minus, but the diagrams are more messy. This is actually the rule for forming antisymmetric wave functions, which at least in some formalisms is a requirement for the Exclusion Principle, but since the same outcome always arises, this issue is irrelevant here.) This gets to the point where we have to ask, what does the sign mean?
In general theory of wave interference it refers to the phase of the wave. When amplitudes have the same sign, they reinforce. The important point is there must be a phase relationship between the ends. Now, the phase of the wave is proportional to the action, and it changes because the action (the time integral of the Lagrange function) evolves in time. However, no matter how long zero is integrated with respect to time, you still get zero, and the Lagrange function of an entity with zero mass and zero charge, which is what an empty orbital has, is zero. The solution to the Schrodinger equation when E, V and m each equal zero is zero everywhere in all time. Zero can be added any number of times, but it makes no difference.
If so, the canonical structure with positive charge on an end carbon atom gives zero directional effect. Therefore, the strength of the preference (because there is always
some of the canonical structure with the required phase relationship) is reduced whenever there is a carbenium ion involved in the transition state, and the carbenium site is substituted. The orientation of the substituent is significant too because the bigger the steric clash on the complying path, the easier it is for the canonical structure that permits non-compliance to become more significant because it forces rotation to start before significant orbital interactions.
Now, I believe this alternative interpretation is important for two reasons. The first is, it gives a specific reason why there should be exceptions to the Woodward Hoffmann rules, and it predicts where they will be found. Thus if nothing else, it will guide further experimental work. The alternative theory is either right or wrong, and there is one obvious way to find out. The second reason is more important: I believe that if this alternative interpretation is found to be correct, it forces chemists to revisit the concept canonical structures, which I believe gives far more fertile ground for understanding chemistry than the current MO theory, at least for the average bench chemist. Further, I suspect there are no aspects of organic chemistry (and probably not of other chemistry, except I am not familiar enough with that to be sure) that does not comply with the concept of canonical structures, if these are properly used. So, there is a further challenge: find some aspect of chemistry where canonical structures, properly used, fail.
