Have to learn crystallography again.............. and now along with quantum mechanics!
worried.... Anthony > 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 >
