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How Numerous are the Reliable Triplets and Quartets?

In the following table numbers of relations are given together with their percentage of correct indications for triplets, quartets and negative quartets above variable thresholds of respectively the triplet product E3 and a quartet product E*4 (Schenk, 1973). The numbers are given for an aza-steroid with N = 40, in space group $P\overline{1}$.

 


    Triplets Positive quartets Negative quartets
   

E3 no. relations % correct relations E4 no. % no. %

6.0 21 100 6.0 185 100    
4.0 143 100 4.0 1213 100    
3.0 353 100 3.0 3295 100 1 100
2.5 583 99.8 2.5 5813 99.8 2 100
2.0 980 99.7 2.0 10,006 99.5 17 100
1.5 1823 99.2 1.5 13,114 98.8 38 100
1.0 3395 96.9          

As can be seen many relations are available to solve this small N = 40 structure. As a rule the number of useful triplets and quartets diminishes as N increases; this effect is quite noticeable for quartets.

One comment regarding the use of negative quartets. If phase relationships such as the triplet relation

\begin{displaymath}
\phi_H + \phi_K + \phi_{-H-K} \approx 0.\end{displaymath}

are used exclusively and there is no translational symmetry, the trivial solution with all phases $\phi_H$ = 0 is the most consistent one. To find phases equal to $\pi$ (e.g. in space group $P\overline{1}$) it is necessary to use relations of the type

\begin{displaymath}
\phi_H + \phi_K + \cdots \approx \pi.\end{displaymath}

Thus relations such as negative quartets (34), although few in number, play an important role in these structure determinations.


next up previous
Next: Direct Methods in Action Up: An Introduction to Direct Methods. The Previous: The Negative Quartet Relation

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