May 2013: Simon Parsons, Howard Flack and Trixie Wagner have published a paper (Acta Cryst. B69, 249-259) that refines a number of structures on Bijvoet differences and on similarly purposed quotients. This procedure can take care of the suspected correlations between the absolute structure and other structural parameters. One of their conclusions is that no difference can be seen: post-refinement determination of absolute structure using Gaussian error distributions in PLATON or CRYSTALS is equally good as their full-matrix refinements.
March 2011: A screencast was made to show how to use PLATON to determine the absolute structure using our method.
March 2011: We have found a mistake in a formula in our 2009 paper on using the t-distribution in probability plots. See: Erratum
February 2011: Our method is now implemented and automatically run in OLEX2
Since J.M. Bijvoet discovered that X-ray crystallography could be used to
determine the absolute structure of molecules, this technique has been refined
Our quest for absolute structures of C/H/N/O crystals
This site concentrates on the discussion about a method described by
Rob Hooft, Leo Straver and Anthony Spek that has been published
in the Journal of Applied Crystallography in February 2008: J. Appl. Cryst. (2008). 41, 96-103 (pdf).
This method gives a more reliable calculation of the absolute structure than
other existing methods. Imagine: you can finally determine the absolute
structure for a structure containing no atoms heavier than oxygen. Without resorting to exceptional data collection techniques.
It is easy with CuKa, but in good cases it can be done even using a MoKa data set.
You do not only get a qualitative assignment of the absolute structure, but also
a quantitative estimate of the reliability of that assignment. The paper uses a
combination of maximum likelihood estimation and Bayesian statistics
A value y, comparable to the value of the Flack x parameter,
with its standard deviation. This does not assume any prior knowledge about
A pair of values P2(right) and P2(wrong) expressing the likelihood that
the given absolute structure is right or wrong, assuming the prior knowledge
that the compound is enantiopure.
A triplet of values P3(right), P3(twin) and P3(wrong) expressing the likelihood
that the given absolute structure is right, that the crystal is a 50%/50% inversion twin,
or that the absolute structure should be inverted. This assumes the prior knowledge
that the crystal can not be an inversion twin with another ratio.