I lost track. What's the date today?
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
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Robert M. Sweet E-Dress: [EMAIL PROTECTED]
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)
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