Difference Map
https://xraytools.com/difference
What a partial model is missing. The page runs the standard step — subtract, keep the phases, transform — on a structure whose absent atom you removed yourself, so the answer is known before the map is drawn.
- Before this
- This is the difference between what was measured and what a partial model calculates, so it assumes there is a model. The ordinary synthesis comes first.
- 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.
Worked examples: zirconia without O1 — a small omission, found · zirconia without Zr — the heavy atom, lost · cristobalite without O — what the projection cannot show
Earlier on the path: Charge Flipping On From intensities to a structure, step 6 of 6
Notation here: F, |F| — what each one means here
See also: Fourier Synthesis and the Phase Problem · Charge Flipping · Displacement Parameters and NPD Atoms · Refinement Statistics and R Factors
What each input changes
- Omitted atom
- Which atom is left out of the calculated model. What appears in the map is what the model is missing — so this is the control that shows the map working on an answer you already know.
Teaching with this page
- Objective
- After this page a learner can read a difference map, and say what a peak in one does and does not establish.
- Start from
- this worked example
- Ask first
- A difference map shows a maximum close to a heavy atom. Is that an atom the model is missing?
- Watch for
- “Yes — the map shows what the model does not account for”
Check yourself: A difference map shows a maximum close to a heavy atom. Is that an atom the model is missing?
Not established — the model’s own errors appear there too Yes — the map shows what the model does not account for
It does show what the model does not account for, and that includes the model being slightly wrong: a position out by a little, a displacement parameter too small, or the truncation ripple that surrounds a heavy scatterer all leave residual density. Height, distance and chemistry decide together, and beside a heavy atom is where each of the three is worth checking before anything is added.
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 — |Fo| − |Fc| — 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. What the projection costs here is resolution rather than the method: a difference map asks what a model fails to account for, so it needs a partial structure rather than a sparse one and works in any number of dimensions. The price is that two sites projecting onto one another cannot be separated, so a peak that stands up may belong to either of them.
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.