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All - I was just having a discussion here concerning the precise definition of the terms 'Harker vector' & 'Harker section'. This discussion was prompted by this webpage: http://www.doe-mbi.ucla.edu/~sawaya/m230d/Patterson/patterson.html - specifically the 'Table of Patterson Difference Vectors' for space group P43212 (right at the end). The legend states "Table of all possible self-vectors in space group P43212. Colored blocks appear on Harker sections.". The implication of this is that some self-vectors do not appear on Harker sections and thus are not Harker vectors. This conclusion is backed up by this table at the same site: http://www.doe-mbi.ucla.edu/~sawaya/tutorials/Phasing/crystal.lib - scroll down a bit to the second section with the header: #CCP4I DATA PATTERSON # # Header lines are: # spgp_# spgp_name patterson_spgp_# patterson_spgp_name #_harker_sections # # Harker sections are listed on the subsequent lines # # Info generated using EJDs harker.f jiffy with this entry for P43212: 96 P43212 123 PG422 5 X = 0.5000 1/2 2Y+1/2 2Z+3/4 Y = 0.5000 2X+1/2 1/2 2Z+1/4 Z = 0.2500 X+Y+1/2 -X+Y+1/2 1/4 Z = 0.7500 X-Y+1/2 X+Y+1/2 3/4 Z = 0.5000 2X 2Y 1/2 There will always be N-1 self-vectors where N is the number of primitive general equivalent positions, so there are 7 in P43212, hence 2 of the self-vectors are missing from the above entry, and similarly for most of the high-symmetry space-group entries (trigonal, tetragonal, hexagonal, cubic). I would contend that _all_ self-vectors are also Harker vectors without exception (in fact surely the terms are totally synonymous?). The 2 Harker vectors missing from the above entry are: X-Y, X-Y, 2Z and X+Y, X+Y, 1/2+2Z, both of which lie on the U-V = 0 Harker section. Just because this isn't a section perpendicular to a principal axis, hence FFT is unable print it on one page (though you can of course do it via MAPROT) seems a totally inadequate reason for excluding it from the definition! The locus of the vector between 2 points related by any rotation/screw axis is necessarily a plane perpendicular to that axis, and the U-V=0 section is merely the plane perpendicular to the 2-fold in the Laue group 422 along (1,1,0). Then, further seeking to justify my view, I turned to International Tables, which I've always regarded as the ultimate authority on matters crystallographic. The only explicit tabulation of Harker sections I could find there is in Vol. B, Chap. 2.3 by Rossmann & Arnold, Table 2.3.2.3 on p. 240. Worryingly for my point of view, this concurs with the definition in the webpage, and also omits the 2-fold U-V=0 and similar sections in trigonal, tetragonal, hexagonal and cubic space groups, though it does include the (1,1,1) 3-fold section in cubic (it calls it a 'special Harker plane' though it's not clear what's special about it!). Bizarrely, in the same table, space groups with 3, 4 and 6-folds are defined with the unique axis parallel to the _b_ axis (I wonder which version of the space-group tables they were using?). Finally I recalled that FFT helpfully prints out the Harker sections whenever you do a Patterson, so using some data in space group P321 I get: Symmetry operators: 1: X, Y, Z: 2:-Y, X-Y, Z Harker Vector: 2 X+Y, -X+2Y, 0 Harker Section is: Z = 0.00 Harker vector Matrix: 1.00 1.00 0.00 0.00 -1.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Symmetry operators: 1: X, Y, Z: 3:-X+Y, -X, Z Harker Vector: 3 2X-Y, X+Y, 0 Harker Section is: Z = 0.00 Harker vector Matrix: 2.00 -1.00 0.00 0.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 That's it! Looking at the code, FFT specifically excludes the additional 3 Harker vectors that I think should be listed (on the 3 sections U+V=0, 2U-V=0 & U-2V=0), so am I alone in the belief that all self-vectors are Harker vectors, or do we accept the apparent alternative definition that only sections that can be printed on one page by the FFT program can be Harker sections (with the apparent special exception of U+V+W=0 in cubic)? It would be interesting to know how David Harker in his original paper viewed his eponymous section, unfortunately I don't have easy access to it. -- Ian ******************************************** Ian J. Tickle, DPhil. Director of X-ray Technology Astex Therapeutics Ltd 436 Cambridge Science Park Milton Road, Cambridge CB4 0QA, UK Tel: +44(0)1223 226214 Fax: +44(0)1223 226201 www.astex-therapeutics.com Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing [EMAIL PROTECTED] and destroy all copies of the message and any attached documents. 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