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 (2) Bond Bending Strain.

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 Europe/London

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