9. Direct Methods
In this section we look at the triplet phase relationship, which is
widely used in small molecule direct methods.
The map shows markers representing two atoms. Two structure factors,
(1,1) (phase = 100 degrees) and (-2,1) (phase = -30
degrees) have been set. These are consistent with the position of
these atoms. Select each of these two structure factors in turn and
examine how they lead to the features in the map.
Is it possible to deduce what reflections will improve the map?
Ideally the atomic peaks should be more compact, and the troughs in
between them should be less negative. One way of achieving both of
these objectives would be to add a reflection whose Bragg planes link
the two atoms, reinforcing both the atoms and reducing the troughs.
Select the (-1,2) reflection. Find a phase where it reinforces
the current density peaks. Set the magnitude to 6, equal to the other
reflections, and add it to the map. Is the map improved?
Are there any obvious relationships between these structure factors?
Try summing the Miller indices of the three reflections. What do you
find? Try summing the phases of the three reflections. Are the phases
Reset the map. Since each reflection has a Friedel opposite, we could
have chosen a different pair of reflections to start with. This time,
start with the (1,1) and (2,-1) reflections. Which
reflection should you pick to make a similar triplet with these two
reflections? Select the phase of this reflection to reinforce the
atomic peaks. Does the same relationship between the phases apply?
Go back to Structure Factors (1). Examine some triplets of
reflections. You should find that the strongest triplets obey this
phase relationship. For weaker triplets the relationship is only
approximate. In Structure Factors (2) the relationship is only ever