Is science sometimes in danger of getting tunnel vision? Recently published ebook author, Ian Miller, looks at other possible theories arising from data that we think we understand. Can looking problems in a different light give scientists a different perspective?

My First Theoretical Paper: 1

I received my PhD, but I never heard from supervisor again. He wrote up a paper (published 1969) on the amine dissociation constants and rate constants, which also reported the synthesis and properties of some new compounds, but with no amines with mesomeric withdrawing ability, he ignored the issue of conjugation. As far as I am aware, he ignored the acidities in toluene, which was really his only contribution, and which gave a critical answer but one that conflicted with the emerging consensus. Make of that what you will.
 
In the meantime, I was determined to write up my theory, which had to show how certain effects could occur without cyclopropane having delocalized electrons. The two main observations to explain were the reduced dipole moment of cyclopropyl chloride, and the stabilization of adjacent positive charge. How to go about it? The first objective was to show qualitatively how these effects could be generated.
 
If I take an electron at a distance x from a proton and move it to y, where is the energy stored? In my interpretation of Maxwell's electromagnetic theory, it is stored in the electric field. Accordingly, the stabilization of positive charge adjacent to a cyclopropane ring compared with charge adjacent to a standard aliphatic hydrocarbon fragment can arise simply from the charged site receiving a stronger negative electric field. My qualitative argument to get such a field involved the strain forcing the charge in four of the orbitals around the distal atoms to move closer to the source of charge, while there was little effect from the two geminal orbitals, because their motion was more rotatory. (That may not have been the easiest way of looking at it.  If strain in the cyclopropane ring arises because of the greater electron repulsion through the orbitals being moved closer together, then adjacent positive charge would overturn that repulsion for four of the orbital lobes.)
 
The problem now was to put numbers to the cause, and this is where I had what I thought was an inspiration. Suppose you were beside a wall, and could measure electric fields, and such a field corresponding to Do was coming from the other side of the wall. Since cyclopropyl is electrically neutral overall and has no electric moment, Do = 0. Now, suppose you experience an increase in field. This can be explained two ways. The first is that charge q has been added, in which case the displacement field increases from Do to D1. In the second case, the original charge has moved, and there are now two fields: the original displacement field Do and a polarization field P, which are dimensionally equivalent. If charge is added to the original charge, at its point location div D1 = q. But for the case of the charge having moved, since we measure an electric field we can also write,  div P = q’, and the situation is numerically equivalent to having added a pseudocharge q’. Of course, since their fields are equivalent, q' = q. 
 
Why do that? Because if we wish to calculate how far the charge moved, we must solve the Schrodinger equation, which cannot be done, but if we think in terms of adding a pseudocharge, there is a mathematical simplification. If the cyclopropane ring bonds are represented by a torus, we have an analytical solution to the otherwise impossible differential equations. The work done assembling the pseudocharge on that torus is proportional to the strain energy. There remains one unknown: the minor radius of the torus, but before addressing that there was also the issue of determining the strain energy. More next post.
Posted by Ian Miller on Jan 12, 2013 1:17 AM Europe/London

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