Throughout my career in chemistry, one of the more interesting debates has been the nature of the cationic exo-2-norbornyl system, and recently (Angew. Chem. Int. Ed. 2014, 53, 5888) a paper was published that included, after a discussion of the original debate, the quote: "To our surprise, the structure of C7 H11+ obtained under our conditions is not that of 2NB+, but instead corresponds to a much more stable rearranged ion." Why was this surprising?
First, this is irrelevant to the original debate on the question, why is the rate of solvolysis of the exo-2-norbornyl X systems, where X is a leaving group, proceed much faster than that of the endo system? The isolated 2-norbornyl cation should be the same for each, and is hence irrelevant. The reason for the differences in solvolysis is not the structure of the isolated ion, but rather the activation energy required to reach the transition state, in which the ion is not fully developed. If the ion fully develops as a free ion, then both starting materials will lead to one ion with one energy and structure.
Another quote: "Although 2NB+ is well-known in the condensed phase, it is not generally recognized that it is not the C7 H11+ global energy minimum. Computational studies have explored some C7 H11+ isomers, but there has been no comprehensive study of the potential energy surface, and no studies of this system at higher levels of theory.[20, 28, 29]". The paper then went on to show from measuring the infrared spectrum of their cations generated in the MS that the ion was the 1,3-cyclopentenyl carbenium ion. This was apparently a surprise to them.
First, the fact that the 1,3-cyclopentenyl ion was at an energy minimum for this system has been known since the 1960s, and the fact that certain cyclohexenyl carbenium ions would contract to a cyclopentenyl system with the methyl generated at an adventitious position was also known in the 1960s. Then, in 1973 I published a paper explaining why such carbenium ion rearrangements take place, and giving a procedure for calculating the energies of the various species. As to why the rearrangement of the norbornyl to the cyclopentenyl system occurs, we might note that the norbornyl system is in effect a five-membered ring with a two-carbon bridge at the 1,3-positions. (Count from C1, and make what is usually C7 now C2.) The system is also highly strained, and forming the cyclopentenyl system relieves that strain. Lose the bridging bond, and the two "methyl" substituents are already in position following the required hydride shifts, which are known to be fast in this system.
To summarize, the fact that the system forms the 1,3-dimethylcyclopentenium cation should not be a surprise. More interesting is the reason this system is in an energy well, not so much for the norbornyl system, where the strain energy makes it somewhat obvious, but rather for the corresponding cyclohexenyl system. The calculations I made do not need "the highest level of quantum computing". What I assumed was that before the ion was formed, the bonds were standard. Now, when the ion is formed, the action in each bond must remain constant, because action is quantized. What does happen to such a standard framework comes from the application of Maxwell's electromagnetic theory. Very specifically, the enhanced electric field polarizes all electric distributions in the space around it If we assign a volume and a relative permittivity to each specific type of bond (in this case C – C and C – H ), then the stabilization depends on the bond's location with respect to the formal charge, which, for a cation, is a carbon atom. An important point was that the assumed permittivities and volumes were consistent with effects noted from electromagnetic radiation. Perhaps not quite as "glamorous" or "sophisticated" as "the highest level of quantum computing", but equally Maxwell's electromagnetic theory is not exactly fringe science either.