Dear Ian,
Well, "it" *IS* broke. If you are running some type of process, as you
implied in referring to LIMS, then there is a step in which you move from
the crystal system and point group to the actual space group. So, at that
point you identify P22121. The next clear step, automatically by software,
is to convert to P21212, and move on. That doesn't take an enormous amount
of code writing, and you have a clear trail on how you got there.
To be even more intrusive, what if you had cell parameters of 51.100,
51.101, and 51.102, and it's orthorhombic, P21212. For other co-crystals,
soaks, mutants, etc., you might have both experimental errors and real
differences in the unit cell, so you're telling me that you would process
according to the a < b < c rule in P222 to average and scale, and then it
might turn out to be P22121, P21221, or P21212 later on? When you wish to
compare coordinates, then you have re-assign one coordinate data to match
the other by using superposition, rather than taking on an earlier step of
just using the conventional space group of P21212?
Again, while I see use of the a < b < c rule when there isn't an
overriding reason to assign it otherwise, as in P222 or P212121, there
*is* a reason to stick to the convention of one standard setting. That's
the rationale on using P21/n sometimes vs. P21/c, or I2 vs C2, to avoid a
large beta angle, and adopt a non-standard setting.
Finally, if you think it's fine to use P22121, then can I assume that you
also allow the use of space group A2 and B2?
Bernie
Bernie
On Fri, April 1, 2011 8:46 am, Ian Tickle wrote:
> Dear Gerard,
>
> The theory's fine as long as the space group can be unambiguously
> determined from the diffraction pattern. However practice is
> frequently just like the ugly fact that destroys the beautiful theory,
> which means that a decision on the choice of unit cell may have to be
> made on the basis of incomplete or imperfect information (i.e.
> mis-identification of the systematic absences). The 'conservative'
> choice (particularly if it's not necessary to make a choice at that
> time!) is to choose the space group without screw axes (i.e. P222 for
> orthorhombic). Then if it turns out later that you were wrong it's
> easy to throw away the systematic absences and change the space group
> symbol. If you make any other choice and it turns out you were wrong
> you might find it hard sometime later to recover the reflections you
> threw away! This of course implies that the unit-cell choice
> automatically conforms to the IT convention; this convention is of
> course completely arbitrary but you have to make a choice and that one
> is as good as any.
>
> So at that point lets say this is the 1970s and you know it might be
> several years before your graduate student is able to collect the
> high-res data and do the model-building and refinement, so you publish
> the unit cell and tentative space group, and everyone starts making
> use of your data. Some years later the structure solution and
> refinement is completed and the space group can now be assigned
> unambiguously. The question is do you then revise your previous
> choice of unit cell risking the possibility of confusing everyone
> including yourself, just in order that the space-group setting
> complies with a completely arbitrary 'standard' (and the unit cell
> non-conventional), and requiring a re-index of your data (and
> permutation of the co-ordinate datasets). Or do you stick with the IT
> unit cell convention and leave it as it is? For me the choice is easy
> ('if it ain't broke then don't fix it!').
>
> Cheers
>
> -- Ian
>
> On Fri, Apr 1, 2011 at 1:40 PM, Gerard Bricogne <g...@globalphasing.com>
> wrote:
>> Dear Boaz,
>>
>> Â Â I think you are the one who is finally asking the essential
>> question.
>>
>> Â Â The classification we all know about, which goes back to the 19th
>> century, is not into 230 space groups, but 230 space-group *types*, i.e.
>> classes where every form of equivalencing (esp. by choice of setting)
>> has
>> been applied to the enumeration of the classes and the choice of a
>> unique
>> representative for each of them. This process of maximum reduction
>> leaves
>> very little room for the introducing "conventions" like a certain
>> ordering
>> of the lengths of cell parameters. This seems to me to be a major
>> mess-up in
>> the field - a sort of "second-hand mathematics by (IUCr) committee"
>> which
>> has remained so ill-understood as to generate all these confusions. The
>> work
>> on the derivation of the classes of 4-dimensional space groups explained
>> the
>> steps of this classification beautifully (arithmetic classes ->
>> extension by
>> non-primitive translations -> equivalencing under the action of the
>> normaliser), the last step being the choice of a privileged setting *in
>> termns of the group itself* in choosing the representative of each
>> class.
>> The extra "convention" a<b<c leads to choosing that representative in a
>> way
>> that depends on the metric properties of the sample instead of once and
>> for
>> all (how about that for a brilliant step backward!). Software providers
>> then
>> have to de-standardise the set of 230 space group *types* (where each
>> representative is uniquely defined once you give the space group
>> (*type*)
>> number) to accommodate all alternative choices of settings that might be
>> randomly thrown at them by the metric properties of e.g. everyone's
>> orthorhombic crystals. Mathematically, what one then needs to return to
>> is
>> the step before taking out the action of the normaliser, but this
>> picture
>> gets drowned in clerical disputes about low-level software issues.
>>
>> Â Â My own take on this (when I was writing symmetry-reduction
>> routines for
>> my NCS-averaging programs, along with space-group specific FFT routines
>> in
>> the dark ages) was: once you have a complete mathematical classification
>> that is engraved in stone (i.e. in the old International Tables and in
>> crystallographic software as we knew it), then stick to it and re-index
>> back
>> and forth to/from the unique representative listed under the IT number,
>> as
>> needed - don't try and extend group-theoretic Tables to re-introduce
>> incidental metrical properties that had been so neatly factored out from
>> the
>> final symmetry picture. Otherwise you get a dog's dinner.
>>
>>
>> Â Â So much for my 0.02 Euro.
>>
>>
>> Â Â With best wishes,
>>
>> Â Â Â Â Â Gerard.
>>
>> --
>> On Fri, Apr 01, 2011 at 11:30:12AM +0000, Boaz Shaanan wrote:
>>> Excuse my naive (perhaps ignorant) question: when was the
>>> Â a<b<c rule/convention/standard/whatever introduced? None of the
>>> textbooks I came across mentions it as far as I could see (not that
>>> this is reason for or against this rule of course).
>>>
>>> Â Â Â Thanks,
>>>
>>> Â Â Â Â Â Â Â Â Â Â Â Â Â Â Boaz
>>>
>>>
>>> Boaz Shaanan, Ph.D.
>>> Dept. of Life Sciences
>>> Ben-Gurion University of the Negev
>>> Beer-Sheva 84105
>>> Israel
>>> Phone: 972-8-647-2220 ; Fax: 646-1710
>>> Skype: boaz.shaananâ
>>
>> --
>>
>> Â Â ===============================================================
>> Â Â * Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
>> Â Â Â Â Â Â Â Â Â *
>>   * Gerard Bricogne          Â
>> g...@globalphasing.com  *
>> Â Â * Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
>> Â Â Â Â Â Â Â Â Â *
>> Â Â * Global Phasing Ltd. Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
>> Â Â Â Â Â *
>>   * Sheraton House, Castle Park     Tel: +44-(0)1223-353033
>> *
>> Â Â * Cambridge CB3 0AX, UK Â Â Â Â Â Â Â Fax:
>> +44-(0)1223-366889 *
>> Â Â * Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
>> Â Â Â Â Â Â Â Â Â *
>> Â Â ===============================================================
>>
>
--
Bernard D. Santarsiero
Research Professor
Center for Pharmaceutical Biotechnology and the
Department of Medicinal Chemistry and Pharmacognosy
Center for Structural Biology
Center for Clinical and Translational Science
University of Illinois at Chicago
MC870 3070MBRB 900 South Ashland Avenue
Chicago, IL 60607-7173 USA
(312) 413-0339 (office)
(312) 413-9303 (FAX)
http://www.uic.edu/labs/bds
