Re: [ccp4bb]: projection map ?

[Bart Hazes <bhazes@ualberta.ca>]

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A response from a reader of the bulletin board made me realize that my answer
to the earlier question on making projection maps might not have made sense to
a reasonable number of CCP4BB subscribers. So here is a bit more background.

Here is the original question and my reply

>> I want to get the projection (fourier) map for h0l and
>> h-hl reflections separately. Is there a program that can perform this?
>> thanks in advance.

> Just select that subset of reflections and calculate the map. It will still be
> a 3D map of course, just look at the section you are interested in. I assume
> that CCP4 programs that plot 2D contours of maps can plot diagonal planes for
> your hhl case.

Here is the remark of Ricardo Aparicio and some extra explanation to hopefully
clarify things.

> 1) an electron density map is a real space entity, so it is not possible
> to project it onto a plane or direction in reciprocal space.

Yes it is a real space entity but as it turns out, the HK0 reflections, for
example, define the projection density along the C axis. Just consider the
math:

F(hkl) = Sum_j ( f_j exp(2*pi*i (hx+ky+lz)))

for l=0 this becomes

F(hk0) = Sum_j ( f_j exp(2*pi*i (hx+ky)))

So for hk0 reflections it doesn't matter what the z coordinate of an atom is.
For any z, electons with the same x and y will scatter in phase as if all
density along the z axis was located in one point. In real space this
corresponds to a projection along the z-axis.

The result should be the same. If MAPMAN can do this it may be easier.

> I asked myself these questions and your answers differ from mine.
> I would calculte the map using all HKLs and then use MAPMAN (DVD) to
> project it on the corresponding directions in real space.

If MAPMAN can do this than it may actually be easier and it also could handle
projections along arbitrary axes. Either way, the result should be the same.

Keep asking yourself question. That is what science is all about. For a more
detailed explanation I think you can find one the Jan Drenth's crystallography
book. It explains a lot of structure factor properties so if someone in your
lab has a copy you may want to have a look at it.

Bart

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