Difference Map
What a partial model is missing. Subtract the calculated amplitudes from the measured ones, keep the model’s phases, and transform: what stands up is the density the model does not account for. Here the missing atom is one you delete on purpose, so the answer is known before the map is drawn.
- You supply
- One of the named structures and which of its sites to leave out. The amplitudes come from the complete structure and the phases from what is left of it, which is the only difference between this and a real refinement.
- Reading it
- A difference map needs most of the scattering already in the model. Over every omission this page offers, deleting a site worth less than 40 % of the cell’s scattering was found at the strongest peak every time; above that it succeeds about half as often, and the page names which case you are in. Every failure still shows the atom when given the true phases, so what fails is the model rather than the map.
Input
What is missing from the model you already have
The Fourier page states the phase problem, and the three pages after it are ways out of it: the Patterson function, direct methods and charge flipping. All three stop in the same place — a partial structure, some atoms found and some not — and every real determination goes on from there the same way.
Compute the structure factors of the model you have. Subtract their amplitudes from the measured ones, keep the model’s phases, and transform. What stands up in the result is what the model does not account for. Repeat until nothing does.
Here the missing atom is one you delete on purpose, so the answer is known from the start: choose a structure, choose a site to leave out, and see whether the difference map puts its strongest peak where that site was.
This runs on the projection down c, using only the hk0 reflections, so the map is a plane and the transform is two-dimensional. Atoms at the same x and y but different z fall on one another, which is why a structure can have more atoms than the map has sites. In one dimension the same algorithm fails on everything but the simplest structures, because a 1-D projection is not sparse and sparseness is the whole assumption the flip enforces.
Where this comes from
- Some properties of the (Fo − Fc)-synthesis
W. Cochran, Acta Cryst. 1951, 4, 408–411 · doi:10.1107/S0365110X51001355
Why the difference synthesis is the right map to look at rather than the observed one: the errors in the model largely cancel, so a peak in it is what the model is missing rather than what the model already says.