Bijvoet-Pair Analysis Bijvoet-Pair AnalysisRequired data are a .cif and a .fcf (including Friedel related reflections) for the non-centrosymmetric structure. The structure factors that are used in the analysis are by default calculated from the parameter data in a regular CIF. Alternatively, calculated structure factors can be taken from the FCF by setting the appropriate switch.
Note In case that the Fcalc values are choosen to be taken from the .fcf, that file should NOT be based on a BASF/TWIN refinement. Flack parameter contributions to F(calc) are incorperated in the .fcf only with a TWIN/BASF refinement ! That is not the case with the default Flack parameter determination.
Warning: The currently accepted standard procedure for the determination of the absolute structure by X-ray diffraction techniques is based on the determination of the Flack parameter with its associated standard uncertainty as part of the least-squares refinement procedure. The alternative procedure that is implemented in PLATON (based on a theory developed by Rob Hooft) addresses in particular those marginal cases of relatively weak resonant power of enantiopure compounds where the results of the Flack analysis are inconclusive (the results of both procedures are consistent in cases of sufficient resonant power). Unfortunately, attempts to publish the underlying theory have failed to this date. Users of this analysis should therefor make their own judgement (perhaps based on experience with their own examples). The only thing we can offer is that we know of no well-documented example where the analysis failed. We are of-course interested in any well-documented counter example.
Example: [Flack x = -0.010(4), abs[F1(calc)**2 - F2(calc)**2] > 4 Sigma]
Calculated Bijvoet differences (Horizontal) are plotted against observed Bijvoet differences (Vertical). Vertical bars indicate one sigma spread.
Only differences above the preset sigma difference (Selected) are displayed out of the total number of Bijvoet pairs.
Plot entries are expected to be located in the upper right (or inversion related lower left) quadrant for the correct absolute structure. Deviating entries (i.e. located in the other two quadrants) are in red.
Reflection indices are displayed for the the largest Bijvoet differences.
Full details can be found in the listing file.
Sigma = sqrt(sigma**2(F1(obs)**2) + sigma**(F2(obs)**2)), where F1 and F2 represent the Friedel (Bijvoet) related reflections.
511 out of the 7738 Friedel related reflection meet the 4*sigma criterium, all except one are found to confirm the selected absolute structure. (note: the figure above is based on the less strickt 0.25*sigma criterium)
The Average Ratio parameter is expected to have a value close to 1.0 for a strongly determined absolute structure and is defined as:
Sum(weight((Fo1**2-Fo2**2)/(Fc1**2-Fc2**2))) / Sum(weight)
with: weight = abs(Fc1**2-Fc2**2) / sigma
Note: The strongest Bijvoet differences are shown with reflection indices.
An alternative analysis of the absolute structure is provided under the heading Bayesian Statistics.
Three types of analysis are done:
The value of FLEQ (SU) is to be compaired with the value of FLACK(SU).
P2(true) gives the probability (scale 0 to 1) that the current absolute structure is the correct one, assuming that the compound is enantiopure.
The Friedel Coverage is defined as the ratio of the number of Friedel pairs in the data set and the maximum possible number * 100%.
Note that the MoKa diffraction data used here are for the Nonius Ammonium bi tartrate test crystal of known absolute configuration. The Friedel pair coverage is 99.8 %.
Concluding remark: It is advised to base the analysis on data with close to 100% Friedel coverage and a fully refined structure. Having said that, it turns out that, in our experience, an analysis in the early isotropic refinement stage already predicts the correct absolute structure.
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