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Methods, Problems and Solutions

Disorder, Single Crystal Structure Refinement and effects of Resolution

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Tue, 13 Mar 2001 15:18:02
Refinement and Resolution
Phillip Fanwick [fanwick@xray.chem.purdue.edu]
Purdue University
Newsgroups: sci.techniques.xtallography

I am working on a problem where chemistry requires that two carbon atoms
be refined as two independent sets of carbons which are about 0.45A
apart.  The data were collected to a resolution of 0.75A and the
splitting is suggested by Shelx from the highly anisotropic adp's and by
the chemistry (a totally unsaturated ring is currently nearly planar).
Is it valid to refine atoms below the resolution of the experiment?  If
so where do you draw the line?  I know the FAQ to Shelx suggest that
most suggestions for splitting atoms be ignored.

If one can reliably refine atomic distances below the resolution of the
experiment then what does the resolution signify?
Some authors suggest it is simply the resolution of the Fourier map.  If
this is its only meaning it would suggest one can
collect low resolution data and then refine the individual atoms based
on chemical knowledge using fixed geometry.  The exact meaning of
resolution is not discussed or well defined in most small molecule
crystallography texts.

Thanks for any help and clarification you can give me.

Phil Fanwick
fanwick@xray.chem.purdue.edu


Tue, 13 Mar 2001 19:20:41
Re: Refinement and Resolution
Dr. Artem Evdokimov [eudokima@mail.ncifcrf.gov]
NCI-FCRDC PSB-MCL Protein En
Newsgroups: sci.techniques.xtallography

Could you clarify a bit ? What kind of ring is it ? What are the
numerical values for the ADP's that look suspicious ?

In general, unless you're dealing with special cases, saturated
carbocycles are not planar (I assume you're working with the ring larger
than cyclopropane).

Cyclopentane derivatives are known to have conformational disorder in
crystals due to low pseudorotation barriers (CCD has at least a few
examples I think).

In general, though the experimental resolution does not extend to 0.45,
I would try and see what happens if you split the pesky carbons and
refine with disorder. If the statistics allows it, i.e. if this
manipulation does not introduce a significant drop in data/parameter
ratio, if the ADP's of the resulting disorder components are normal or
close to normal, and if the geometry of the resulting molecule(s) makes
more sense - then I'd stick to disordered carbons. Obviously, your
discussion of the structure would have a caveat that this part of the
molecule cannot be trusted if important conclusions have to be made on
the basis of the geometry of these carbons - but then, even if you do
not split them you would still have reservations about model accuracy in
this area.

If it is paramount to your work, can you obtain a higher resolution
dataset ? Or go to lower temperature (or perhaps check if rising the
temperature does not result in averaging of the disorder or elimination
of one of the components)...

Just a few thoughts.

Artem Evdokimov


--
|Dr. Artem Evdokimov   Protein Engineering |
| NCI-Frederick        Tel. (301)846-5401  |
|              FAX (301)846-7148           |
|        eudokima@mail.ncifcrf.gov         |
|      http://www.ncifcrf.gov/plague       |


Wed, 14 Mar 2001 01:27:40
Re: Refinement and Resolution
Larry M. Henling ]lmh@cco.caltech.edu] 
California Institute of Technology, 
Newsgroups: sci.techniques.xtallography

 Ah, the vagaries of trn

Phillip Fanwick   wrote:
>
>be refined as two independent sets of carbons which are about 0.45A
>The data were collected to a resolution of 0.75A and the splitting is

 Whether you can refine two carbon atoms (perhaps isotropically) 0.45A
apart depends primarily on two factors:
 1) how good your dataset is
 2) more importantly, whether the two atoms are 'discretely' disordered
   or continuously disordered.  In the first case, you should have no
   problem with a well-measured dataset and not a lot of really heavy
   atoms in the structure (we recently had a structure with disordered
   Cl/H2O columns where the Cl-O distance was 0.338(16)A; both the
   .5 Cl and .5 O refined nicely anisotropically and the two .5 H's
   refined acceptably (x,y,z,Uiso).  In the latter case, for example
   a floppy tetra-n-butyl ammonium ion where the alkyl groups are
   all over the place, splitting the atoms usually does no good
   whatsoever - it is not possible to model the range of atomic
   positions with a few sites and ellipsoids.

 The resolution of the dataset pertains to whether features
in the Fourier map are separated or not.  However, structural
results are not based on the Fourier map, but instead on a
weighted least-squares fit of the model to the observed data.
With proper weights, it is often possible to refine H atoms
which do not even appear in the Fourier.  The least squares
procedure also produces estimated errors in parameters and
correlations between parameters.  These are the numbers used
to calculate, eg, bond length sigmas, which are much less
(~ thousandths of an A) than the 'resolution' of the data.
[The least squares refinement should use weights based as
much as possible on uncertainties in the measurements, and
not chosen simply to minimize the Goodness of Fit.
 Use a theta cutoff in a refinement to show that high angle
data gives you better results. The low angle data reflect
mostly how many electrons are present and the high angle
data the ADP's on heavy atoms.

 larry


Wed, 14 Mar 2001 16:07:32    
Re: Refinement and Resolution
Daniel Schlieper [aeg17@campfire.rrz.uni-koeln.de]
Newsgroups: sci.techniques.xtallography


Dear Phil,

"resolution" in x-ray crystallography the length of the spacing d
between the lattice planes to get a deviation angle theta of the Bragg
reflection. From the famous Bragg's Law:

             d = lambda/(2 sin theta)

with lambda the wavelength. The minimal d corresponds to the maximal
theta and is named "resolution".

This has nothing to do with "resolution" as used in light microscopy,
stating the minimal distance of two distinguishable points. In fact,
in x-ray crystallography, atoms can be distinguished even if they are
much closer together than the crystallographic resolution.

In protein crystallography, most structures are solved with a x-ray
"resolution" d(min) = 2.0--2.5 Angstrom. The root mean square
deviation of the atoms ( = "resolution" in light microscopy) in these
structures are approx. 0.3 Angstrom. Do you see the difference?
And yes, in the protein crystallography, we indeed collect "low"
resolution data and then refine the individual atoms based on chemical
knowledge.

Best regards, Daniel

--
Daniel Schlieper                      Institut fuer Biochemie
                                      Zuelpicher Strasse 47
Daniel.Schlieper@Uni-Koeln.De         Universitaet zu Koeln
Tel.: +49 221 470-6443, Fax: -5092    50674 Koeln, Germany


Mon, 19 Mar 2001 08:45:42
Re: Refinement and Resolution
Rob Hooft rob@hooft.net
Newsgroups: sci.techniques.xtallography

>>>>> "DS" == Daniel Schlieper  writes:

 DS> Phillip Fanwick  writes:

 >>  I am working on a problem where chemistry requires that two
 >> carbon atoms be refined as two independent sets of carbons which
 >> are about 0.45A apart.  The data were collected to a resolution of
 >> 0.75A and the splitting is suggested by Shelx from the highly
 >> anisotropic adp's and by the chemistry (a totally unsaturated ring
 >> is currently nearly planar). Is it valid to refine atoms below the
 >> resolution of the experiment?  If so where do you draw the line?
 >> I know the FAQ to Shelx suggest that most suggestions for
 >> splitting atoms be ignored.

 DS> Dear Phil, "resolution" in x-ray crystallography the length of
 DS> the spacing d between the lattice planes to get a deviation angle
 DS> theta of the Bragg reflection. From the famous Bragg's Law:

 DS>              d = lambda/(2 sin theta)
 DS> with lambda the wavelength. The minimal d corresponds to the
 DS> maximal theta and is named "resolution".

 DS> This has nothing to do with "resolution" as used in light
 DS> microscopy, stating the minimal distance of two distinguishable
 DS> points. In fact, in x-ray crystallography, atoms can be
 DS> distinguished even if they are much closer together than the
 DS> crystallographic resolution.

These two values do have something to do with each other. In fact, if
you collect data up to 0.8A resolution as is common in small molecule
crystallography, you can separate two peaks in the Fourier map only if
they are 0.8A or more apart; this is equivalent to the optical
microscopy resolution.

The difference occurs because in crystallography we have a model of
spherical atoms (note: even "anisotropically" refined B factors only
make a very small difference here, the resulting electron cloud is
still almost spherical). Once a spherical atom of the right type is
placed in a density peak, it can be seen quite clearly whether that
spherical blob of density can properly explain the form of the
electron density in the Fourier map. And one can even make a model
where two disorder positions for the atom nicely explain the form of
the density--- even if those two positions are closer together than
the resolution limit.

This principle makes Fo-Fc difference Fourier synthesis and structure
refinement using least squares possible. It also explains bond
distances that are accurate sometimes upto 0.0001 A at 0.7A resolution.

Regards,

Rob Hooft
--
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=====   R&D, Nonius BV, Delft  http://www.nonius.nl/             =====
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