Dear Bob

I agree entirely with Alan that the "football" style of ellipsoids
will be extremely valuable, especially if it can be realised in
short order. More ornamental ellipsoids at some stage in the future
will still be appreciated, and offer yet more added value.

If you want to test your efforts against independent calculations,
note that all the papers in Acta Cryst. Section E are now open
access and have CIFs available; nearly all will also
contain thermal ellipsoid plots for comparison. For example,
http://journals.iucr.org/e/issues/2008/05/00/bh2165/index.html
shows a structure with some nice ellipsoids oriented along ring
planes, and various heavier-atom ellipsoids at the end of a
variety of bonds. Unfortunately (for the purposes of testing
edge cases) Acta Cryst. rarely publishes papers nowadays with
highly distorted or non-positive-definite ellipsoids!

Cheers
Brian


On Tue, Apr 15, 2008 at 10:24:33PM +0200, Alan Hewat wrote:
> Bob, if you can render the Uij ellipsoids without drawing the axes for
> now, that would already be very interesting. Anisotropic thermal
> ellipsoids are useful because they indicate disorder of some kind, either
> static or dynamic (or else a problem with the refinement :-) Of particular
> interest is an indication of possible structural instability, and being
> able to see which way those footballs are pointing can be very
> instructive. BTW, with neutrons we can also obtain meaningful anisotropic
> data for hydrogen, so that should not be systematically set to the
> isotropic average - disordered hydrogen bonds are of interest in many
> types of structures. When you have it working, I'll copy it to ICSD where
> I have long had a 3D display of anisotropic temperature factors using VRML
> (without ellipsoid axes :-)
> Alan.
> 
> Bob Hanson said:
>> Alan and Brian,
>>
>> At least for starters, here's what I have done:
>>
>> 1) programmed the CIF reader to read Uij data from CIF and mmCIF files
>> 2) added an ISOSURFACE option to display Cartesian Uij' data:
>>
>>   isosurface ellipsoid {[U11'],[U22'],[U33'],[U12'],[U13'],[U23']}
>>
>> 3) read Jeffery, Methods in X-Ray Crystallography (1971) Appendix VI.
>>
>> My plan is to do the {a*,b*,c*} coordinate transformation of the Uij
>> data to cartesian Uij' today, so it appears as cartesian data ready for
>> the isosurface command. Then we can do something like this:
>>
>>   isosurface ellipsoid {not hydrogen} 50%
>>
>>
>> (Do we need to be storing both the original Uij data and the
>> cartesian-transformed parameters?) I don't fully understand how to get
>> the eigenvectors,
>>
>> The problem are twofold: (1) transforming the Uij coefficients and (2)
>> depicting the ellipsoids in appropriate ways. Now, here's the trick:
>> Turns out I can do the rendering without ever figuring out what the
>> actual axes are. The isosurface command accepts ANY function, and the
>> function describing an arbitrary ellipsoid,
>>
>>   a_1 x^2 + a_2 y^2 + a_3 z^2 + a_4 xy + a_5 xz + a_6 yz - c = 0
>>
>> is a perfectly fine surface. So that mechanism works now with just a few
>> added lines to Jmol -- much like displaying an atomic orbital.
>>
>> Ultimately we may have the question as to whether we want to use
>> isosurfaces to render these, but there are some nice advantages to doing
>> it this way, at least at first. My overall plan would be to create a new
>> "special" shape class, perhaps, "thermalEllipsoid":
>>
>>  select model=3.1
>>  thermalEllipsoids 50%
>>
>> or something like that? If that's the case, and we want to visualize
>> those axes, then I will have to figure out a completely different way to
>> render these. So the compromize may be that initially all we have are
>> the footballs, and later (this summer?) that may be upgraded.
>>
>> Bob

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