The convergence method.



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The convergence method.

The choice of starting point for the phase generation by direct methods is crucial since if one starts with a triplet phase invariant which, for example, leads immediately to a poorly indicated phase with a large error then these initial errors will tend to propagate through the phase determination process and in general lead to a poor or incorrect solution. The convergence method is a means by which a starting point for phase generation can be found which will, with more certainty, lead to well determined phases from multiple indications in the early stages of the phasing procedure. The strength of a phase relationship may be judged by the value of from Eq. gif. However since there is no phase information available at these early stages this cannot be used. Germain et al [36] showed that an expected value of , may be calculated without prior phase information by replacing the and terms of Eq. gif with their respective expectation values [24]. Thus it is possible to calculate for each of the triplet phase relationships found in step 2 above.

The convergence method is an iterative procedure by which the reflection with the minimum value of is temporarily removed from the list of reflections along with all phase relationships which indicate its phase. (N.B. structure semi-invariants are not removed from the reflection list). A new list of 's is calculated from the updated set of phase relationships and the procedure is repeated. In this way the procedure converges towards a set of reflections which will give strong indications for new phases in the early stages of phase generation with the weighted Tangent formula.



Gwyndaf Evans
Fri Oct 7 15:42:16 MET 1994