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?

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Archive for January, 2013
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.
Posted by Ian Miller on Jan 28, 2013 1:42 AM GMT
My next problem was that I needed a means of estimating strain energy for molecules. For cyclopropane, I could have used observed values from heats of combustion, but I wanted something for general strained molecules. It may be of some interest to see how I arrived at what I did. Assume a standard carbon-carbon single bond. Now, put the rest of the molecule in place, and consider the bent bond model of Coulson and Moffitt, Phil. Mag. 1949, 40, 1-35.) As the extra parts of the molecule are put in place, the electrons in the chosen bond move outwards, approximately to some fraction of where the orbitals would intersect if all bonds are sp3. Now, as a first guess, I put the strain energy as being proportional to the displacement from the C – C bond axis, which is proportional to sine theta/2, theta being the total deformation of the bond angle from the tetrahedral angle. (With two bonds required to make an angle, the total deformation is divided evenly between the two orbitals. The energy is force times distance, so I started by assuming a constant force as deformation progressed.) This was really more a first guess, but I was hoping the difference DELTA between observed and calculated would help me guess the manner in which the force varied. What surprised me was that this almost worked, and it worked even better if I divided by [square root (bond distance)]. Also, if I used the bond energy scheme of Cox and Pilcher (Thermochemistry of Organic and Organometallic Compounds.  Academic Press: London, 1970) it also correctly calculated the "strain energy" of ethylene and acetylene! Two membered strained rings, and fused two membered rings! Since DELTA was < 10 kJ/mol for every molecule for which I had data, and usually significantly better, I was then happy enough to use this as an empirical relationship for estimating the strain energy of a number of molecules for which no determination had been made. As an aside, this relationship gives a very large strain energy for tetrahedrane, greater than that of the strength of a carbon-carbon bond. Of course that does not mean that tetrahedrane cannot be made, because simply breaking a bond leaves the great majority of the strain still there.
 
There is clear evidence this had little effect on the scientific community. In 1984, Dewar (JACS 106, 669-82) produced an argument that, since bond bending was simple harmonic, the strain energy would be proportional to the square of theta/2, or maybe theta, which gave an enormous value of DELTA. However, molecular orbital theory showed that this energy was greatly reduced by something called sigma conjugation, and sigma conjugation exactly offset DELTA. Then, in 1985, Cremer and Cracka (JACS 107, 3800-3810, 3811-2819) announced that Dewar had the wrong force constant, and his enormous strain energy should be reduced by approximately 100 kJ/mol, leaving only a huge DELTA. But not to worry! Revised molecular orbital calculations showed that there was sigma conjugation that exactly offset this new DELTA. Two computations, using what purported to be the same methodology, got exact agreement with observation, despite the key term differing by 100 kJ/mol. How could that be? Of course, there was no mention of my work, which argued that the whole argument was spurious because there is a very big difference between the square of an angle and its sine. If I were correct, there is no huge discrepancy to explain, and no sigma conjugation.
 
Of course, when I wrote my paper, there was no thought of sigma conjugation. But the question I now have to ask myself is, should I have put this strain formula in a separate paper? On the plus side is the argument that a paper should really make only one point, and ideally the whole point of the paper can be summarized by a single statement. This makes it easier to find, particularly then when "finding" was done by reading journal contents pages, and later through Chemical Abstracts. On the negative side, and what swayed me at the time, was the thought that a complete argument should be in one place. There was also the worry that the strain relationship alone may not have been sufficient to get into a reasonable journal.  Whatever the validity of either argument, the fact of the matter is, I put the strain relationship into the middle of my first paper, and I doubt many people even know about it. 
Posted by Ian Miller on Jan 21, 2013 1:51 AM GMT
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 GMT