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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: So Iwata so_iwata {- at -} MAC {- dot -} COM Date: 2008-04-01 On 1 Apr 2008, at 18:59, 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 CCP4bb navigationCCP4bb <-- 2008 <-- April 2008 <-- 01 April 2008 |
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