Dear Gerard
Your point concerning my admittedly somewhat cavalier usage of the
term 'setting' in the R23:r vs R23:h context is well taken, however I
would point out that a) I'm not the first to use this terminology
(e.g. the CCN article I referred to talks about "triple-cell
settings"), and b) ITC doesn't use the specific term 'lattice mode'
either, though it does use 'centring type' which I guess means the
same thing? It would clearly be nice to have a single term that
encapsulates both concepts, otherwise what are we to call, for
example, the symbol R32:r - does it define a setting or a centring
type?
In ITC the rhombohedral/hexagonal dichotomy is dealt with by assigning
a property called alternatively 'centring type' and 'description'; the
first is too specific for what we want, the second it seems to me
rather too bland and general. Either way it would appear that R32:r
is both a symbol for the setting in the context of obverse vs reverse
rhombohedral settings (conventionally the obverse is chosen so
presumably the symbol R32:r applies only to that setting, otherwise
it's ambiguous), and a symbol for the centring type in the context of
rhombohedral vs hexagonal cells! However 'description' does seem to
be the common denominator term: it is used in ITC to indicate both
settings and centring types - but as I said it does seem rather bland
('space group description' could mean almost anything!). As you
indicate, for practical purposes getting a consistent vocabulary would
seem to be of lesser importance than getting a consistent
nomenclature.
On the question of primitive vs centred monoclinic lattice types, I
would point out that in ITC unique axis 'a' settings are also not
considered to be candidates for the conventional cell, though 'b' and
'c' settings are. So self-evidently not all possible 'descriptions'
are considered to be conventional and the subset listed in ITC is
merely a matter of convention (a tautology if ever there was!).
Cheers
-- Ian
On 30 July 2012 17:55, Gerard Bricogne <g...@globalphasing.com> wrote:
> Dear Ian,
>
> I made a modest contribution to this discussion a long time ago, and I
> will only limit myself to one point.
>
> I think you may be confusing "setting" and "lattice mode". A change of
> setting is performed by an integer matrix with determinant 1 (a "unimodular"
> matrix) whereas a change of lattice mode involves two mutually inverse
> integer matrices with determinants (mutually inverse, of course) different
> from 1.
>
> The case of R32 and H32 seems to stick out like a sore thumb because we
> never use the primitive-lattice versions of the centered-lattice space
> groups in the monoclinic, orthorhombic and tetragonal classes - and yet they
> exist! The problem with them is that e.g. 2-fold axes are represented by
> non-diagonal matrices that are somehow thought to be an eyesore, so we
> sacrifice mathematical rigour (the theory of "arithmetic classes") to the
> comfort of having a 2-fold axis represented by the familiar diagonal matrix
> with one 1 and two -1 on it. The matrices that would reindex those primitive
> lattices to the usual centered ones would have determinants 2 or 4 in one
> direction, and 1/2 or 1/4 in the other. However, as we never see these
> representations of "centered" space groups in a primitive lattice basis, we
> are startled when we come to the trigonal class. Here, the 3-fold axis has
> two distinct representations by integer matrices: one in which the three
> axes undergo a circular permutation (so they have to be of equal lengths and
> separated by equal angles), and the other in which one axis (z) is
> invariant, and the 3-fold symmetry is represented by a 120-degree rotation
> in the (x,y) plane. These two representations cannot be mapped into each
> other by means of a unimodular matrix: if one reindexes one representation
> into the other, the determinant is 3 in one direction and 1/3 in the other.
> In this case, it is a matter of opinion which representation of a 3-fold
> axis has the greatest aesthetic merit, so the two possibilities are in use,
> unlike the poor non-diagonal 2-fold axis representations that no one wants
> to see.
>
> It is a matter of convention and vocabulary whether one calls these two
> modes of indexing the rhombohedral and hexagonal "lattice modes", or calls
> them "settings": one thing is certain, and that is that the mathematical
> phenomenon in question is of a different kind from the reindexing of P21212
> into P22121 with which you draw a parallel.
>
> At least this is what my distant memories of space-group theory seem to
> be telling me :-)) .
>
>
> With best wishes,
>
> Gerard.
>
> --
> On Mon, Jul 30, 2012 at 04:23:02PM +0100, Ian Tickle wrote:
>> 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 <ber...@upstate.edu> 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<hofkristall...@gmail.com> 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:CCP4BB@JISCMAIL.AC.UK] On Behalf Of
>> >>> Theresa Hsu
>> >>> Sent: Friday, July 27, 2012 12:54 PM
>> >>> To: CCP4BB@JISCMAIL.AC.UK
>> >>> 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.
>> >>
>> >>
>> >
>
> --
>
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