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?

A 1960s PhD – Crisis In The Final Straight?

When writing up, I had to explain why my results were contradicting the emerging paradigm. How would you enjoy that, when future employment depends on success? My first step was to define some terms, and I interpreted "conjugation" to mean a system where a common wave function extended over more than two atoms. In particular, if cyclopropyl (Cy) conjugated with unit A, there was at least one two-electron wave function in the system Cy-A. Now, suppose there was a unit B; if Cy conjugated, then there was at least one two-electron wave function in the system Cy-B.  Thus in hexatriene, there are wave functions extending over the entire system. Now, I reasoned that if Cy-A was a delocalized system, through the virial theorem and the fact that a solution consistent with the stationary state Schrodinger equation can have only one energy, the wave function extending over the system had a common potential. The same applied to Cy-B. Therefore, if Cy conjugates, within this definition if substitution changed the potential at B, there must be a change at A. I had shown there was no mesomeric change, therefore there was no linking wave function. Now, at the very least, I had to explain how cyclopropane stabilized adjacent positive charge, why did cyclopropane give significant bathochromic shifts to certain UV spectra, and why was the dipole moment of cyclopropyl chloride reduced compared with other alkyl chlorides? Fortunately, if the first was answered, so was the second. The reason is, from Maxwell’s electromagnetic theory, light can only be absorbed if there is a change of electric moment, and if cyclopropyl stabilizes adjacent positive charge, it will stabilize the excited state when positive charge is adjacent, and by doing so, it will also increase the extinction coefficient. (In this respect, I think Pauling’s canonical structures/VB approach make these effects so much easier to understand at a lower level than MO theory.)
 
It was then that I saw what I believed was the answer. Coulson and Moffatt had proposed bent bonds. If we consider the carbon atoms to have orbitals in the sp3 configuration that overlap, in a bond, the forces from the opposing nucleus pull the orbital closer to the C-C line, the movement being opposed by the remaining four ring electrons, and an equilibrium was reached whereby the charge density of each bond was moved some distance towards the centroid of the ring. This movement of electrons might be symmetrical in cyclopropane, but it was not with respect to a substituent. Four lobes on the two distal carbon atoms moved more or less directly towards the substituent, but the two lobes on the geminal carbon atom changed their angles, but did not significantly change the electron distance to the substituent.
 
There were two ways of viewing this, and I probably chose the harder of the two, although in the event it was the way with the greatest ability to explain a wider range of observations. Both depend on the obvious: the potential energy is stored in electric fields. (That is due to Maxwell.) The first is to note that the repulsion energy on the four distal lobes will be overridden by the positive charge on the substituent. If so, the stabilization energy of a carbenium ion should not exceed 2/3 the strain energy, together with a standard polarization energy of alkane bonds. The second way of looking at it is that the four distal lobes move towards the positive charge and stabilize it. In short, at least qualitatively, the stabilization, in excess of that given by standard alkyl groups, of adjacent positive charge by the cyclopropyl group is required by Maxwell’s electromagnetic theory, and there is no necessity for special quantum effects.
 
I proposed to explain the electric moment of cyclopropyl chloride this way. Assume the linear combination of atomic wave functions. (Quantum mechanics is a linear theory. Waves always combine in a linear fashion.)  The reason alkyl chlorides have a dipole moment (as I saw it then) is that on wave interference, each orbital tries to increase its electron density by a given proportion, but the electron density is much higher around the chlorine atom before wave interference, so electron density has to move towards the chlorine after it. The higher electron density in the cyclopropane ring, which I referred to as a monopole, partly offsets that. So I had my explanations. I could write up the conclusions.
 
However, I had a minor problem: I had nobody to beta test what I was writing, because supervisor had gone to North America. This was a serious problem because I had nobody to check whether I might be going wrong somewhere, and nobody to check whether what I was writing was readily comprehensible. I was effectively saying everyone else was wrong. What should have happened was that supervisor should have sat me down in front of a physicist and straightened out what I was thinking so I could put it in a more orthodox form. That did not happen.
Posted by Ian Miller on Dec 1, 2012 2:09 AM Europe/London

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