Absolute Structure

A brief description of the principles of our method

In a structure without classical heavy atoms, no single reflection or Bijvoet pair contains enough information to make the distinction between the two enantiomeric structures. We therefore must find a way to use the collective information in all Bijvoet pairs to make the decision.

To be able to "weigh" all contributions from each Bijvoet pair to the decision, our method calculates how likely each observation is for each of the two model structures: the "normal" one and the "inverted" one. As an example, if one Bijvoet difference is measured as 7+/-10, and the calculated difference for the normal model is 4 and the inverted model is -4, we can calculate how likely it is that the value of 7 is made for the two models. In this example it looks like the normal model is more likely than the inverted model (the value of 4 deviates only 0.3 times the standard uncertainty, -4 deviates 1.1 times the standard uncertainty in the observation, which is somewhat less likely).

To determine by how much one model is more likely than the other, our 2008 paper used a Gaussian distribution. Since then we have found that using a Students t distribution can give even more robust results in case the standard uncertainties in the observations have not been accurately determined, this is described in our 2010 paper.

Using this technique, we end up with probability ratios for the two models for each of the measured reflection pairs. And since all reflection pairs are independent, we can simply multiply all of these probability ratios together to get a final probability ratio based on all data.

We get to this result without arbitrary cutoffs and without leaving out data, without selecting suitable reflection pairs and without refining any additional parameters.

Even if individual Bijvoet pairs only give 1% more probability to one model over the other, compounding thousands of observations makes it possible to make an assignment of the absolute structure.

Older methods to determine absolute structure suffer from minor problems. They really are minor, but for difficult problems where the anomalous scattering differences are really small, they make a difference.

  • The Flack x parameter has the problem that it is determined from the intensities directly rather than the Bijvoet Differences. Even small errors in the structural model can therefore increase the variance of the Flack x parameter, thereby making it impossible to decide.
  • Other methods based on Bijvoet differences are based on arbitrary cutoffs; they do not work if all reflection pairs are included. The fact that adding more data can make the result less reliable shows that the collective information from all pairs is not correctly assembled by these methods.