I am amazed by the flow of miss information that flows on this list whenever an
apparent problem with a space group comes up.
I asked a related question on sci.techniques.xtallography a few weeks ago, but have yet to hear anything, misinformation or otherwise. If anyone here can give me some pointers, I'd be very grateful. I just want to find all the allowed equivalent origin choices for comparing structures, and I'm wondering if there is a way to choose a specific one (for example in terms of the phases of certain reflections?).
Thanks,
Jon
Forwarded from sci.techniques.xtallography, with my apologies if you have seen it before.
I was looking at models coming back from a molecular replacement program being run using various datasets and then trying to decide if the models are "good" or "bad", and therefore if the data were "good" or "bad". In a specific example with space group P212121, frequently the resulting model was found displaced by <1/2,0,0> from the ideal position (and invariably moved still further away by one of 21 axes). [All programs are using x,y,z; 1/2-x,-y,1/2+z; -x,1/2+y,1/2-z; 1/2+x,1/2-y,-z for P212121.]
From looking at the space group diagrams in Int Tables, this seems to be a perfectly good origin shift, as the symmetry operators are arranged around [1/2,0,0] in the same way as [0,0,0]. So I wrote a little script which applies all the origin shifts and symmetry operators to a test model and tells me which origin shift and symmetry operator gives the closest fit a target model. All well and good for P212121, but now I was thinking that one day I might want to do this for another space group...
The first attempt to generalise was to apply the space group symmetry to the point [0,0,0], which gives me three face centers, but misses the body center and points <1/2,0,0>. Then it occurred to look at the Patterson symmetry (apparently Pmmm here) and from that I could probably have gotten a list of possible origin shifts, with a concern about sometimes flipping enantiomers. Now I'm scared that one day I'll meet a trigonal thing which has hexagonal Patterson symmetry and could come back rotated by 60 degrees, but still be the same structure!
So the question is: "How can the full list coordinate transformations be generated which leave a structure invarient?"
For P212121 it seems that "add [0.5,0,0]" is allowed, but I didn't see how I should figure that out from the info in Int tables, or algorithmically.
There's a followup: "How should the transformation be chosen in order to end up at a unique and reproducible representation of the structure?"
Would something like platon just do all this? At least one pair of structures in the PDB database seem to represent different choices about this origin shifting, but they represent the same packing and structure... realising that was not as straightforward as it would have been had both structures been recorded in a standardised way.
Thanks in advance,
Jon
