As outlined in a previous post, my PhD  results meant that I had to find a way to account for the strange properties of the cyclopropane ring without invoking conjugation. What I came up with was to account for them through a polarization field that was generated through the work done moving orbitals towards the centre of the strained ring. Thanks to the dimensional equivalence of a polarization field and a displacement field, and thanks to Maxwell’s electromagnetic theory, I could represent the movement of charge (the real cause of  the polarization field) in terms of the addition of a pseudocharge to orbitals that had not moved (equivalent to a change of displacement field). I could do that similarly with increased charge density, and the reason for doing this was that it permitted a known solution to the partial differential equations, with only one constant required to be set. I used the electric moment of cyclopropyl chloride to set that constant, and hence the pseudocharge. Now, the question was, would the same pseudocharge properly account for the stabilization of adjacent positive charge?

The cyclopropylcarbinyl cation was known to be stabilized compared with corresponding alkyl cations through studies of solvolysis of tosylates, etc, but these studies were of lesser value because there was the problem of solvation energies. There was also an issue that the cyclopropylcarbinyl cation is also unstable and promptly rearranges. (This is the famous bicyclobutonium "non-classical" carbenium ion.) Substitution can stabilize it, but that adds complications. Then, luck! Well, sort of. The stability of the cyclopropylcarbinyl cation was published in a PhD thesis, and reported in some books on mass spectrometry, but for some reason it never seemed to have made its way into a paper. Someone else was having trouble getting supervisors to publish! 

However, I had a reported value for the gas phase cation and I could use my pseudocharge to calculate the energy of the interaction of such a polarization field with the cationic centre. Obviously, this would be a fairly crude calculation, and there would be a number of minor effects overlooked, but I needed to know whether I was even in the right ball park. To my surprise, the agreement with observation was very good.

Of course, there was an easier way of doing this calculation. If the strain energy arose through charge in orbitals moving closer together and thus raising repulsive energies, and if four of the six moved closer to the substituent, then the cationic charge would neutralize the repulsive energy on these, hence the maximum energy of interaction with adjacent charge would be 2/3 the strain energy, plus any additional standard stabilizations that would occur in any carbenium ion. However, as far as I was concerned, the triumph was that the same value of my pseudocharge gave correct values for a completely different type of observation for which there was no obvious relationship other than the proposed theory. Being young and inexperienced in the ways of the world, I  thought I was making headway.