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 related?

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 obeyed approximately.