Frequently asked questions about the Bayesian statistics / Maximum likelihood method of determining absolute structure

Frequently Asked Questions

Since we have developed the maximum likelihood/ Bayesian statistics approach of determining absolute structure we have received many questions about the practicalities of the method. This list attempts to answer these questions.

If any question remains, or any of the answers given here is unclear, please contact one of the authors for help.

What is the Slope in PLATON? And the correlation coefficient?

The slope refers to the slope of a normal probability plot of Z-values for the Bijvoet pairs. This is calculated as a verification of the estimated standard uncertainties of the reflections. The slope should be around 1.0.

If the related correlation coefficient is smaller than 0.999, this may indicate a problem in the error model.

Since the maximum likelihood estimation of the absolute structure depends critically on the accuracy of the estimated standard uncertainties in the reflection intensities, it is critical that any deviations from 1.0 are researched before the values resulting from the calculation are used.

What do I do if the correlation coefficient in PLATON is smaller than 0.999?

Please check the PLATON listing file. It shows the normal probability plot in ASCII graphics. Most likely you will find that the plot has a (slight) inverted "S" shape. This means that the error distribution is deviation from the normal distribution; outliers are more likely. In such cases the probability estimates given for P2 and P3 are too extreme, and the estimated standard uncertainty in y is too small. We are working on improving the algorithm for such cases.

What does it mean if the Slope in PLATON is larger than 1.0?

If the slope is larger than 1.0, this indicates that the standard uncertainties in the reflection intensities may be underestimated. This should be checked.

What does it mean if the Slope in PLATON is smaller than 1.0?

We often observe that the slope is around 0.85-0.95. This can occur because the Bijvoet differences are determined more accurately than the two individual reflection intensities. Most probably, there are errors in the reflection intensity determination that affect both reflections of a pair in the same way (e.g. absorption).

Should I measure some sensitive reflections with extra care?

We have carefully avoided the need for this in our method. In fact, adding any data to the data set will always improve the result. It is a lot easier to add general redundancy to a data set than it is to go out and measure specific sensitve Friedel pairs using a CCD system. If you would go through the specific-pair effort, you would also get many other reflections measured on those frames, and adding those other reflections to the mix can only improve the result further.

How come the discrimination is so clear even though almost half of all Bijvoet differences are pointing the other way?

In every structure where determination of the absolute structure is difficult, for almost all Bijvoet pairs the difference is of the same order of magnitude as its standard uncertainty. In such a case one expects that almost half of all Bijvoet pairs is pointing in the wrong direction. Only by using the maximum likelihood approach the cumulative signal of all Bijvoet pairs can be picked up with full sensitivity.

How sensitive is the determination of the absolute structure to inaccuracies in the model?

It is fairly insensitive to changes in the structure that only affect the non-anomalous scatterers. In early attempts we have tried to determine the absolute structure of a model refined without hydrogen atoms, and results were still surprisingly discriminative. Errors in the model that concern the anomalously scattering atoms will disrupt the correct absolute structure determination (most likely you will get the result that both absolute structures are equally (un)likely).

How reliable is this method to estimate the ratio of the two components in a racemic mixture?

There is no experience with crystals that are inversion twins. If you have interesting samples, we would like to hear from you. There is one check you can do yourself even if you are not able to share your data with us: Before trusting an off-zero value of y you should examine the PLATON output very carefully. It is essential that the normal probability plot has a good correlation coefficient and a slope around 1.0 (see also related questions above).

Can I use this method in combination with SQUEEZE?

You will need to be extra careful when combining an absolute structure determination and SQUEEZE. The anomalous effect makes the scattering factors of atoms complex; they have a "real" and an "imaginary" component. The SQUEEZE procedure will only remove the real component of the solvent from the structure, the imaginary component will stay. Therefore, if the atoms with the strongest anomalous effect (the "heaviest") are in the squeezed solvent, you will not be able to determine the absolute structure reliably. If the anomalous effect of the squeezed solvent is negligible in compared to the anomalous effect in the main structure, the absolute structure determination can be combined with SQUEEZE without problems.