Without wishing to re-ignite previous discussions on this topic (perhaps <FLAME> ... </FLAME> tags would be in order!), I would point out that this and similar confusion with other space groups has arisen largely from a failure of some programmers (and users!) to fully comprehend the important difference between a 'standard symbol' and a 'setting symbol' for a space group, no doubt because in many cases these are superficially identical, or a least very similar. This point is also made in the Computational Crystallography Newsletter article on H3 and H32 that I referenced earlier.
The Hermann-Mauguin symbol (aka 'standard symbol') is unique to a space group and crucially is designed to be independent of the setting (orientation and/or origin). It is used to identify a space group without reference to the setting, and therefore its main use is to provide page headings and index entries in ITC. There exist exactly 230 H-M standard symbols for the 230 unique 3D space groups. The H-M standard symbol is the same for all settings of a particular space group and therefore cannot be used to define the setting: for that you obviously need additional information. The standard symbol is thus of little or no relevance to practical crystallography: for that you must use a setting symbol. However for the majority of space groups only one setting is accepted as 'conventional' so in those cases the standard and setting symbols are identical; it's only where there are multiple settings that problems arise. A simple analogy might be to say that an object is called 'building' and that is also its standard symbol. It describes the object without reference to its orientation or position and so is not relevant to the practical problem of defining the view of the building: for that you need extra symbols. For example you might need to specify one of the setting symbols 'building (front elevation)', 'building (side elevation)' or 'building (plan)'. So R32 is a H-M standard symbol which corresponds to the 2 alternate setting symbols R32:r and R32:h as described in the article. Plainly you can't use the H-M symbol R32 to uniquely specify the setting since it is the standard symbol for both the R32:r and R32:h settings. The latter are _not_ H-M symbols: they are ITC extensions of the H-M symbol. For other space groups further confusion has arisen because ITC often uses the exact same character string for both the standard symbol and one of the corresponding alternate setting symbols. An obvious example is P21212: this is the H-M standard symbol for SG #18 but is also one of the 3 ITC setting symbols for P21212, the other two being P22121 and P21221. Perhaps the intention would have been clearer if the ITC setting symbols had all been made different from the standard symbol, as they are in the R32 case. For example P21212a, P21212b and P21212c would have been equally valid choices for the ITC setting symbols but do not express a 'preferred' setting (since there isn't one). Similarly the standard symbol for SG #5 (unique axis b) is C2, and the alternate setting symbols are A2, C2 and I2, but they could equally well have been (for example) C2a, C2c and C2i, which doesn't express a preference for any one of the alternate settings. Either way, according to the ITC rules, the choice of 'conventional' setting for a space group (i.e. the recommended default choice when there are no other grounds such as isomorphism with a previously determined structure) is made by reference to the unit cell. For R32 the conventional cell happens to be the hexagonal one (a = b != c, alpha = beta = 90, gamma = 120) with symbol R32:h; for all orthorhombic SGs the convention is a < b < c and the setting symbol derives from that. Cheers -- Ian On 28 July 2012 22:22, Edward A. Berry <[email protected]> wrote: > Are all the software packages consistent in their (mis)use of these > symbols? Recently I scaled data (scalepack) as R3, imported to ccp4 as H3, > and had to make a link in $ODAT/symm from R32 to H32 (which it turned out to > be). > > > > Ian Tickle wrote: >> >> If we're all agreed that ITC(A) is taken as the authority on all >> matters of space group symbology (and I for one certainly agree that >> it should be), then SG symbol H32 (SG #145: >> http://img.chem.ucl.ac.uk/sgp/medium/145bz1.htm) has nothing to do >> with R32 (SG #155: http://img.chem.ucl.ac.uk/sgp/medium/155az1.htm)! >> According to the Hermann-Mauguin system of nomenclature H32 (more >> correctly written as H3_2 where the '_' indicates a subscripted screw >> axis) would be the hexagonal-centred (H) lattice setting of P32 (P3_2 >> in H-M). H32 as an alternate setting symbol for R32 is a very recent >> PDB invention which conflicts with the well-established H-M convention >> used throughout ITC. The ITC symbols for the rhombohedral& hexagonal >> >> axis settings of SG R32 are R32:r and R32:h respectively, i.e. obvious >> extensions of the H-M symbols without introducing any conflict with >> the existing convention, as the PDB symbol does. The confusion has >> arisen from the failure to distinguish the lattice type (the first >> letter of the symbol) from the symbol for the basis system of the >> setting (the final letter after the ':'). >> >> See http://cci.lbl.gov/~rwgk/my_papers/CCN_2011_01_H3_H32.pdf for an >> excellent explanation of all this and of the confusion that arises >> when programmers ignore established conventions and 're-invent the >> wheel' (e.g. SCALEPACK apparently swaps the meaning of the PDB symbols >> R32& H32 and uses R32 for PDB H32 and vice-versa!). >> >> >> Cheers >> >> -- Ian >> >> On 27 July 2012 21:09, Bernhard Rupp<[email protected]> wrote: >>> >>> H32 indicates the hexagonal obverse setting (as you list) for a R >>> centered trigonal cell, which is 3x larger than the primitive R32 cell >>> indexed a=b=c, al=be=ga<> 90. Standard imho is the H32 setting, for which I >>> will probably get flamed. >>> The relation between H and R cells is depicted here: >>> >>> http://www.ruppweb.org/Garland/gallery/Ch5/pages/Biomolecular_Crystallography_Fig_5-29.htm >>> >>> This has been discussed and is explained in the ccp4 tutorials and doc >>> afaik, where you can find more detailed info. >>> >>> For proper format in a journal, I would suggest to adhere to the format >>> given in the ITC (International tables for Crystallography), I.e. Bravais >>> Italic, subscripted screw symbols. Note that this is not the format you put >>> it into most programs - their docs help. >>> >>> You can also try my old space croup decoding program to see general >>> positions, operators, matrices and other useful stuff. >>> >>> http://www.ruppweb.org/new_comp/spacegroup_decoder.htm >>> >>> HTH, BR >>> >>> -----Original Message----- >>> From: CCP4 bulletin board [mailto:[email protected]] On Behalf Of >>> Theresa Hsu >>> Sent: Friday, July 27, 2012 12:54 PM >>> To: [email protected] >>> Subject: [ccp4bb] Space group R32 and H32 >>> >>> Dear all >>> >>> I have a confusion on the space group R32 and H32. For a cell parameter >>> of a = b not equal to c, alpha=beta, not equal to gamma, is it considered as >>> R32 or H32? >>> >>> I tried searching the mail list archives but it does not help a beginner >>> crystallographer like me. >>> >>> I also have another basic question. What is the correct way for writing >>> space groups? Is the Bravais lattice in italic and is there space after >>> that? Or it does not matter because both are used in literature? >>> >>> Thank you. >> >> >
