Kevin Cowtan wrote:
This is absolutely correct - in the analysis you present, the
non-anomalous scattering drops with resolution, but the anomalous part
does not. And since counting noise varies with intensity, we should
actually be better off at high resolution, since there is less
non-anomalous scattering to contribute to the noise! (This is somewhat
masked by the background, however).
So why don't we see this in practice?
The reason is that you've missed out one important term: the atomic
displacement parameters (B-factors), which describe a combination of
thermal motion and positional disorder between unit cells. This motion
and disorder applies equally to the core and outer electrons, and so
causes a drop-off in both the anomalous and non-anomalous scattering,
over and above that caused by the atomic scattering factors.
I agree with everything but would like to add the following: if we
assume an overall atomic displacement parameter, the drop-off in both
the anomalous and non-anomalous scattering is the same. Therefore, the
ratio of anomalous differences over mean intensity (which is what comes
closest to R_{ano} - in whichever way this is defined) is essentially
unaffected by atomic displacements and should still go up at high
resolution, irrespective of the values of the atomic displacement
parameter !
Things are more complicated if individual isotropic atomic displacements
are considered, because the anomalously scattering atoms (e.g. the Se
atoms) may have significantly larger or smaller displacement parameters
than the average.
All this is discussed in section 4.4. of Flack & Shmueli (2007) Acta
Cryst. A63, 257--265.
Marc
But your reasoning was sound as far as it went, and it is a point which
many people haven't recognised!
Kevin
Raja Dey wrote:
Dear James,
I don't understand why measuring anomalous differences has nothing to do
with resolution.
Heavy atoms
scatter anomalously because the inner shell electrons
of the heavy atom cannot be considered to be free anymore
as was assumed for normal Thomson scattering. As a result
the atomic scattering factor of the heavy atom becomes
complex and this compex contribution to the structure
factor leads to non-equality of Friedel pairs in non-centro
symmetric systems(excluding centric zone). This feature is taken
advantage in
phase determination. Since the inner shell electrons
being relatively more strongly bound in heavy atoms
contribute to anomalous scattering and its effect
is more discernable for high angle reflections . Here
the anomalous component of the scattering do not
decrease much because of the effectively small atomic
radii (only inner shell being effective). FOR HIGH
ANGLE REFLECTIONS ANOMALOUS DATA
BECOMES IMPORTANT.
Raja
--
Marc SCHILTZ http://lcr.epfl.ch
