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									         Corrections and Twinning
   Absorption Correction
   Extinction Correction
   Determination of Absolute Configuration
   Twinning
                      Absorption
   Since the diffractometer has 4 circles and there
    are three dimensions there must be many ways
    to bring the crystal into the diffracting position—
    that is so it obeys Bragg's Law.
   If the crystal is not spherical than the orientation
    of the crystal will effect the intensity because of
    absorption.
   There are two beams to be considered
       The entering (incident) beam
       The scattered beam.
Numerical Correction
        What are the Symptoms of
              Absorption?
   Badly shaped atoms that all point in the same
    direction
   Lots of ghosts (electron density close to atoms
    that is not real).
   Non-positive definite atoms.
Effects of Absorption
          Spherical Correction

INPUT: absorption coefficient μ, crystal radius,
 data with θ angle

OUTPUT: transmission factors for each datum

ADVANTAGES: exact calculation

DISADVANTAGES: few spherical crystal
                                 samples
           Analytical Correction


INPUT: absorption coefficient μ, data
with direction cosines, description of the crystal by
bounding faces

OUTPUT: transmission factors for each datum

ADVANTAGES: exact calculation

DISADVANTAGES: crystal must have well
defined faces
     Semi-Empirical Corrections

INPUT: data with direction cosines or Eulerian
 angles, equivalent reflection intensities

OUTPUT: relative corrections

ADVANTAGES: no crystal description required

DISADVANTAGES: much cruder than previous
 methods; may correct for systematic errors
               All Hell Breaks Out
Before using DIFABS, it is suggested that you read the
following journal article:
Nigel Walker and David Stuart, "An Empirical Method
for Correcting Diffractometer Data for Absorption
Effects", Acta Cryst. (1983), A39, 158-166.
DIFABS has received a large amount of bad verbage
as a practical method ("DIFABS is EVIL!"). How much
of this is based in reality, paranoia, philosophy, etc is
still up for discussion(?). It is possible for DIFABS to be
used to soak up sloppy practises in diffractometer
setup and crystal alignment (non-full irradiation of the
crystal), etc, etc, etc.
A web page to refer to is "Should DIFABS be
Banned?":
http://www.unige.ch/crystal/stxnews/stx/discuss/dis-dif2

Within the limitations described in the original DIFABS
paper above, it does seem(?) to be a method worth
keeping in your crystallographic bag of tricks to get the
job done under some circumstances.




    http://www.ccp14.ac.uk/tutorial/wingx/absorp/difabs.htm
                 What is Difabs?
The idea is that the averaging of multiple independent
measurements of a reflection allow the true value of Fo to
be determined.

The idea of DIFABS is that Fc is an equivalent
determination of the true value of Fo. Fc must be
calculated for isotropic atoms with all atoms in the cell
refined.

Then do a calculation to determine the absorption surface.
                Is DIFABS valid?

The question--Is it correct to use the data calculated
from a model to adjust the data on which the model is
refined?


I have no idea as it is way outside my area of expertise.


 As DIFABS was published in ACTA CRYST. A the referees who
 reviewed it should have been able to determine this.
     How Does Difabs Compare
At an ACA meeting Ton Spek compared the
calculated absorption surfaces from a numeric,
a semi-empirical, and a difabs correction.

They all had very similar features and produce
similar results.
     How Do We Handle Absorption
   After integrating the data, frame scaling is
    performed.
       For DENZO the program SCALEPACK is used
       For EVAL the programs SADABS or TWINABS
   Frame scaling makes sure that any loss of
    intensity from frame to frame is corrected for.
   This automatically corrects for absorption
   Can save data with direction cosines for use in
    other correction programs.
                     Extinction
   For very intense reflections in high quality
    crystals it is possible that the diffracted beam
    can be further scattered by other unit cells.
   This is called extinction and results in the very
    intense reflections being weaker than expected.
   It can be corrected for in SHELX by adding an
    EXTI card or using the refine gui to insert one.
   The SHELX output will indicate when an
    extinction correction is required.
   Note this should be done after OUTLIER.
Numerical Correction
               Absolute Configuration
   It is possible to determine the absolute
    configuration of a molecule using
    crystallographic data.
   There are two cases that must be considered
       The space group is polar and the molecule is
        enantiomorphic.
            There can be no mirrors, glide planes, inversion, or
             improper rotation axes.
            Such space groups contain no letters or bars in the
             symbols after the centering type.
             Absolute Configuration
       The unit cell is accentric and enantiomorphic but
        the individual contents are not.
       Polar space groups—P21, P212121, P61
       Accentric non-polar space groups – Pna21, I41/a
   For both cases the absolute configuration of the
    unit cell must be determined even if the
    contents are racemic!
   Absolute structure determination involves
    anomalous scattering.
    Source of Anomalous Scattering
   The normal scattering of the x-ray beam is all in
    phase – 180° off of the incident beam.
   It is possible to have absorption, followed by
    emission. These photons will have a different
    phase from the normally scattered beam
    depending on the lifetime of the virtual state.
   These are the anomalous photons.
   Since there is an equal probability for emission
    in any direction, the intensity is NOT a function
    of θ.
      Representation of Anomalous
               Photons
   One way to represent a wave is by using an
    imaginary number.
   The real part represents the intensity in the
    phase unsifted wave.
   The imaginary part represents the phase shift.
   Anomalous scattering is given as f' and f” where
    f' is the real part and f” is the imaginary part.
    Crystal Symmetry and Anomalous
               Scattering.
   Centric Space Groups.
       In this case the imaginary part of the anomalous
        scattering must cancel out and become zero.
       This is because by symmetry + and – must be
        identical
       Friedel's law (Ihkl = I-h-k-l) is fully obeyed
   Accentric crystals
       The imaginary part will either add or subtract to the
        regular scattering.
       When the absolute configuration is correct the sign
        will be correct otherwise it will be reversed.
              Some Comments
   To observe anomalous scattering there must be
    some absorption.
   In general first row elements do NOT absorb
    enough of a Mo beam to provide data. Use
    copper.
   Because the anomalous scattering does not fall
    off with theta but the normal scattering does,
    the high angle reflections will have the biggest
    changes when anomalous scattering is
    included.
         How to Determine Absolute
                 Structure
   Johannes Martin Bijvoet at the University of
    Utrecht was the first to realize this could be
    done.
   His method
       Collect all data including Friedel Pairs
       Solve and fully refine the structure.
       Change the enantiomer and re-refine
       Look for data where the Friedel pairs differ greatly
        in one of the two refinements
       The refinement with the lower differences is the
        correct one.
                The Bijvoet Method
   Problems with it
       Requires twice as much data
       Requires a good deal of manual work
       Provides no quantitative measure of the
        correctness
       Fairly slow
            R-factor Comparison
   Refine both enantiomers.
   Look at the r-factors.
   Use the Hamilton t-test to determine if any
    difference is statistically meaningful and to what
    degree.
   Rarely done anymore.
                  Refinement Methods
   The idea is to add a parameter to determine
    the correctness of the configuration.
       Rogers suggested using a multiplier to the sign of
        the imaginary part of the scattering factor.
            If refined to +1 then correct, -1 incorrect.
            This parameter does not converge well in least squares
             calculations so does not work well
       Howard Flack suggested that both enantiomers be
        refined together.
            The one given would be given a multiplier of (1-x) while
             the other one would be x
                  Flack Parameter
   Thus if the Flack Parameter (x) refines to zero
    than the enantiomer is correct, while 1 is
    incorrect.
   The Flack Parameter can take on values
    outside of 0 to 1. These are generally
    meaningless and suggest the anomalous
    scattering is too weak to provide the answer.
   The s.u. in the Flack Parameter is important.
       0.2(1) suggests correct.
       0.2 (6) suggests nothing.
                   Flack Parameter
   Advantages
       Do not need Friedel pairs to calculate.
       Provides a quantitative indicator of the absolute
        configuration.
   Disadvantages
       The Flack Parameter tends to correlate with other
        parameters when there is not much Friedel pair
        data.
       It is not Chemist friendly
            The Hooft Approach
   Rob Hooft and Ton Spek worked on a new
    approach which was recently published.
   They assumed that most of the Friedel data
    would be collected which is true for modern
    area detectors.
   Their method is in PLATON as Bijvoet
    calculation.
                                Good Output
              Absolute Structure Analysis


    Flack Parameter                     0.050 +/- 0.060

    Hooft Parameter                     0.024 +/- 0.037

    Friedel Coverage                         99.6%

    Assuming No Racemic Twinning is Present
    Probability Absolute Structure is Correct 1.000

    Probabilities Allowing for Racemic Twinning
    Probability Absolute Structure is Correct   1.000
    Probability Absolute Structure is Incorrect 0.0E+00
    Probability Crystal is a Racemic Twin       0.2E-35


Hooft,R.W.W.,Straver,L.H.,and Spek, A.L.(2008). J. Appl. Cryst.,41,96-103.
                    Undetermined Output
              Absolute Structure Analysis


    Flack Parameter                     0.400 +/- 1.200

    Hooft Parameter                     0.417 +/- 0.634

    Friedel Coverage                         98.6%

    Assuming No Racemic Twinning is Present
    Probability Absolute Structure is Correct 0.551

    Probabilities Allowing for Racemic Twinning
    Probability Absolute Structure is Correct    0.329
    Probability Absolute Structure is Incorrect 0.267
    Probability Crystal is a Racemic Twin       0.404
    The absoloute structure could be better determined by
    collecting another data set using copper radiation!


Hooft,R.W.W.,Straver,L.H.,and Spek, A.L.(2008). J. Appl. Cryst.,41,96-103.
                              Borderline
          Absolute Structure Analysis


Flack Parameter                     0.210 +/- 0.180

Hooft Parameter                     0.216 +/- 0.070

Friedel Coverage                         94.6

Assuming No Racemic Twinning is Present
Probability Absolute Structure is Correct n/a

Probabilities Allowing for Racemic Twinning
Probability Absolute Structure is Correct   0.970
Probability Absolute Structure is Incorrect 0.8E-25
Probability Crystal is a Racemic Twin       0.030
                     Hooft Method
   Advantages
       Very Quantitative
       Chemist Friendly
       Lower errors on the Hooft y Parameter than the
        Flack Parameter
   Disadvantages
       Requires Friedel pair data
       Is very sensitive to how data is collected.


								
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