James must be too fast - he better be to follow the 93,000 (or is it
more?) csh lines of code in Elves in the speed I recall he does.
So, most likely he lost less time writing it than us reading it: its
a cunning plot, he is wasting our time not his.
A.
On 1 Apr 2008, at 21:54, So Iwata wrote:
Great job. But don't you have any better things to do (tm) ? s.
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
