From the material in the two previous posts, I now had the concepts necessary to address the issue of cyclopropane interactions with substituents. I now had to select something to apply them. What I chose was the problem of why the dipole moment of cyclopropyl chloride was about 0.4 D less than an alkyl chloride. This was important for two reasons. The first was that the generally accepted viewpoint was that this was evidence for back-conjugation, indeed it was the only evidence for it. The second was that following classical electrostatic theory, increasing the charge density on the cyclopropane ring should repel electrons, and if my concept was correct, at first sight the dipole moment should increase. On the other hand, there was a serious reason why that classical thinking must be wrong: the dipole moments of methyl acetylene and propene, where the former was approximately twice the latter. How could that be? Conjugation did not seem to be correct here.
 
My answer invoked quantum theory, albeit a version a little at odds with the standard version. I proposed that the wave function can be factorized. (According to the State Vector formalism, it cannot!) The key is that the stationary state is determined by quantized action, which requires that the frequencies in the bond zone cannot lead to destructive interference with components outside the overlap zone, and recall, p orbitals have two lobes, only one of which overlaps. If so, when the electron density increases in the cyclopropane ring, the electron density in bonds to substituents must correspondingly increase close to the cyclopropyl carbon atom. The "back donation" was not from lone pairs, but was simply movement of charge distribution in the bond from the substituent. Interestingly, nuclear quadrapole coupling parameters indicate that there is a small but axially symmetric movement of charge towards the cyclopropane ring. Such was the power of the current paradigm, this was interpreted as indicating conjugation equally from both p orbitals. That, of course, violates all other theory of delocalization of wave functions. (Incidentally, in all reviews, textbooks, etc, this difficulty is avoided by omitting all reference to these nuclear quadrapole parameter data. We cannot have observation getting in the road of a good theory!) Anyway, as far as I was concerned, I had worked out an answer to the key problem of the dipole moment of cyclopropyl chloride.
 
The problem now was to put numbers to it. Returning to my argument that the increase in charge density due to strain is mathematically equivalent (at least in terms of the equations I intended to use) as adding a pseudocharge to the original framework, I could use cyclopropyl chloride to fix the value of that pseudocharge, (via a value for the minor radius of a torus on which the pseudocharge was placed) then apply that to a number of "strained" systems. The change in dipole moment should be equal (so I thought) to the change of dipole moment generated by adding the pseudocharge to the neutral ring. I got almost exact agreement for methyl acetylene (0.75 D) and propene (0.36 D) and close agreement for methyl cyclobutane (calc. 0.07 D, measured 0.05 D) although I overestimated the dipole moment of methyl cyclopropane. Nevertheless, I felt I had achieved something. I had explained why the lower dipole moment of cyclopropyl chloride did not necessarily indicate conjugation, which should have been self-evident from the dipole moment of methyl cyclopropane, and I had an estimate for the source of this polarization field.
 
More interesting, in my opinion, this requirement that action be quantized (a general requirement for quantum theory) and the requirement that all parts of the wave have a common frequency is one of the best ways of considering electronegativity. There is what I feel is a very important point here: in classical physics, increasing electron density in part of a molecule would tend to repel additional electrons. Because of the quantization conditions that fix the wavelengths of stationary waves, it attracts them, which is why fluorine is so electronegative. Thus in my interpretation, electronegativity is determined by the electron density about the atom, and in the bond, the dipole moment gives a measurement of the electronegativity. As you can see, that is not exactly a standard interpretation! You, the reader, understandably, will not be convinced, nor should you be. All I ask is, bear with me. In future posts you will see that this goes somewhat further than you might at first think.