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Re: [ccp4bb] into the looking glass |
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CCP4bb navigationCCP4bb <-- 2008 <-- April 2008 <-- 01 April 2008Subject: Re: into the looking glass From: Robert Sweet sweet {- at -} BNL {- dot -} GOV Date: 2008-04-01 On Tue, 1 Apr 2008, James Holton wrote: > > Dear CCP4BB, > > I think it prudent at this point for me to announce what could be a very > old, but serious error in the fundamental mathematics of crystallography. To > be brief, I have uncovered evidence that the "hand" of the micro-world is > actually the opposite of what we have believed since Bijvoet's classic paper > in 1951. > > Those of you who know me know that I have been trying to lay down the > whole of x-ray diffraction into a single program. This is harder than it > sounds. We all know what anomalous scattering is, but a detailed description > of the math behind translating this "dynamical theory" effect all the way to > the intensity of a particular detector pixel is hard to find all in one > place. Most references in the literature about how anomalous scattering is > connected to absolute configuration point to the classic Nature paper: > Bijvoet et. al. (1951). Unfortunately, since this is a Nature paper, it is > too short to describe the math in detail. For the calculations, the reader > is referred to another paper by Bijvoet in the Proc. Roy. Acad. Amsterdam > v52, 313 (1949). Essentially, the only new information in Bijvoet et. al. > (1951) is the assertion that Emil Fischer "got it right" in his initial > (arbitrary) assignment of the "R" and "S" reference compounds for the > absolute configuration of molecules. > I decided to follow this paper trail. The PRAA document was hard to come > by and, to my disappointment, again referenced the "real" calculation to > another work. Eventually, however, all roads lead back to R. W. James > (1946). This is the definitive textbook on scattering theory (originally > edited by Sir Lawrence Bragg himself). It is extremely useful, and I highly > recommend that anyone who wants to really understand scattering should read > it. However, even this wonderful text does not go through the full > quantum-mechanical derivation of scattering, but rather rests on J. J. > Thompson's original classical treatment. There is nothing wrong with this > because the the exact value of the phase lag of the scattering event does not > effect anything as long as the phase lag from all the atoms is the same. The > only time it does become important is anomalous scattering. Even so, > changing the sign of the phase lag will have no effect on any of the > anomalous scattering equations as long as all the anomalous contributions > have the same sign. The only time the sign of the phase lag is important is > in the assignment of absolute configuration. Unfortunately, a full quantum > mechanical treatment of the scattering process DOES produce a phase lag with > the opposite sign of the classical treatment. This is not the only example > of this sort of thing cropping up. One you can find in any quantum text book > is the treatment of "tilting" a quantum-mechanical spin (such as an > electron). It was shown by Heisenberg that a "tilt" of 360 degrees actually > only turns an electron upside-down. You have to "tilt" it by 720 degrees to > restore the initial state, or get it "right-side-up" again. This is very > counterintuitive, but true, and unfortunately a similar treatment of > scattering results in a phase lag of +270 degrees to "restore" the electron > after the scattering event, not +90 degrees as was derived classically. To > be brief, there is a sign error. > > Perhaps the reason why noone caught this until now is not just that the > quantum calculations are a pain, but that it was very tempting to accept that > the large body of literature following Fischer's convention would not have to > be "corrected" by inverting the hand of every chiral center described up to > that time. Unfortunately, we now have an even larger body of literature > (including the PDB) that must now be "corrected". > > It is an under-appreciated fact in chemistry that anomalous scattering is > arguably the only direct evidence we have about the "hand" of the > micro-world. There are other lines of evidence, such as the morphology of > macroscopic crystals and some recent STEM-type microscope observations of > DNA. However, as someone with a lot of experience in motor control I don't > mind telling you how easy it is to make a sign error in the direction of an > axis. This is especially easy when the range of motion of the axis is too > small to see by eye. You end up just swapping wires and flipping bits in the > axis definitions until you "get it right". The "right" configuration (we > have all assumed) is the one asserted in Bijvoet et. al. (1951). Apparently, > the STEM observations fell prey to such a "mistake". But can you blame them? > Inverting the "hand of the world" is going to be very hard for a lot of > people to accept. Indeed, if anyone can find an error in my math, please > tell me! I would really like to be wrong about this. > > -James Holton > MAD Scientist > -- ========================================================================= Robert M. Sweet E-Dress: sweet@bnl.gov Group Leader, PXRR: Macromolecular ^ (that's L Crystallography Research Resource at NSLS not 1) http://px.nsls.bnl.gov/ Biology Dept Brookhaven Nat'l Lab. Phones: Upton, NY 11973 631 344 3401 (Office) U.S.A. 631 344 2741 (Facsimile) ========================================================================= CCP4bb navigationCCP4bb <-- 2008 <-- April 2008 <-- 01 April 2008 |
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