Hi Jon, A lot of what you'll need is in the back of the International Tables Vol. A in Chapter 15 which goes under the snappy title of "Euclidean and affine normalisers of space groups and their use in crystallography". From memory, earlier incarnations of Vol. A do not have this chapter.
Bill -----Original Message----- From: Jon Wright [mailto:[EMAIL PROTECTED] Sent: 31 March 2004 21:14 To: [EMAIL PROTECTED] > > > >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 >
