This posting concerning positional precision prompted me to recall a
CCP4 meeting (not a recent one) where a well-known crystallographer
(who shall remain nameless - present company excepted BTW - AFAIK the
crystallographer in question has never posted to this BB) claimed that
an atom with a B factor of 100 Ang^2 is undetectable in a map because
it has a positional uncertainty of > 1 Ang, as given by its RMS
vibration amplitude (sqrt(100/8pi^2) to be precise). This is nonsense
of course: I have a structure where some atoms have B factors of 120
Ang^2 and their density is indisputable. While it's certainly true
that atoms with high B factors tend to have large uncertainties, the
calculation is not as simple as that, and other factors (such as the
resolution and the atomic number) are involved.
As an analogy consider the Foucault's Pendulum in the Panthéon in
Paris. This particular pendulum has a maximum displacement of about 2
metres, so an RMS amplitude ~ 1.4 metres. However I would guess that
its mean position (i.e. at the centre of a swing directly under the
point of suspension) is known to within a few mm. Positional
uncertainty is of course the uncertainty in the _average_ position of
an atom which is not directly related to its RMS amplitude of motion.
-- Ian
On Thu, Dec 23, 2010 at 9:20 AM, Nicholas keep
<[log in to unmask]> wrote:
> We clearly have confidence in distance measurements in crystal structures of
> an order of magnitude better than the resolution ie 0.1-0.3 Angstroms, but
> can anyone point me to a more exact theory of distance accuracy compared to
> optical resolution, preferably one that would apply to microscopy as well.
> Have a Happy Christmas and see many of you at CCP4
> Nick
>
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