Since this discussion doesn't want to end. I should point out
(a) The IUCr has, in its wisdom, decided to use the */Hall space group
symbols/* to settle the matter. See International Tables for
Crystallography, Vol. B (2001), Chapter 1.4, Appendix 1.4.2//and /Acta
Cryst./ (1981). A*37*, 517-525. These are obligatory input for CheckCIF
as part of small molecule verification. 'P 21 21 21' becomes 'P 2ac
2ab' and 'P 21 2 21' becomes equally logically 'P 2ac 2ac'. Fortunately
for the users, SHELXL-2014 derives the Hall symbols from the symmetry
operators.
(b) Isn't it time to introduce the 'R 3' or 'H 3' or 'R 3 :H' issue again?
(c) As pointed out already, small molecule crystallographers never have
this problem because the coordinates of the general position are used to
define the space group symmetry unambiguously, in conventional settings
or otherwise. Ian's argument that there could be too much to type in for
cubic space groups is irrelevant, because the list is always generated
by a program (e.g. XPREP or its clones).
George
On 10/03/2014 05:13 PM, Ian Tickle wrote:
Hi Kay
On 2 October 2014 15:04, Kay Diederichs
<[email protected]
<mailto:[email protected]>> wrote:
Once again, citing from ITC Vol A Table 9.3.2 (p. 747 in my 1995
edition) , these "conventions refer to the cell obtained by the
transformations from Table 9.3.1. They have been chosen for
convenience in this table". To me, this indicates that a<b<c
_could_ be obtained _if_ one were to transform. But the question
is: why would one want to transform? I don't see "sticking to the
original indexing" as a convincing convenience.
I'm sorry, unfortunately my edition of ITC-A (5th Ed., 2002) is later
than yours (4th Ed.) and I have been unable to get hold of a copy of
the edition that you refer to. In my edition the table equivalent to
your 9.3.2 seems to be 9.3.4.1 on p.758 and there doesn't seem to be a
table equivalent to your 9.3.1 (the only other table in that section
is 9.3.5.1 but that doesn't seem to be relevant). Also I am unable to
match up the text that you quote with what I see in my edition: it
seems to be completely different. So it's very difficult to comment.
According to the Foreword "The present 5th Edition is much more
extensively revised than any of its predecessors ..." so I can only
assume that the text that you quote was considered unclear and was
removed. But I agree that if one is concerned with a specific
structure without reference to any other structure, why would one want
to transform anything? It makes no sense. The conventional setting
is selected according to table 9.3.4.1, end of story.
My copy of ITC Vol A says (p 41) about Table 3.2: "the 'standard'
space group symbols ... are printed in bold face". The Table has
"P 21 21 2" (18) and "P 2 2 21" (17) in bold face. There is no
ambiguity here.
Again I'm sorry but I don't see that text in my edition (p.41 is just
a list of references for Chap. 2) and I can't find the corresponding
section in my Edition. However I do agree that the standard symbol
for each space group is printed in bold face in the top-left corner of
each double-spread page dealing with that space group (also in smaller
type in the top-right corner). Perfectly true observation I agree but
how is it relevant? The 230 standard symbols are the names of the 230
equivalence classes defined on the complete set of possible alternate
settings for the equivalence relations consisting of the possible
rotations and/or translations relating those alternate settings.
Since they only serve as labels one could equally well have chosen the
ordinals 1 through 230 (which are actually given equal prominence to
the names).
The important point is that the standard symbol is only the _name_ of
the equivalence class and that this is not sufficient for dealing with
crystal structures and calculating structure factors etc.: one must
specify which element of that class, i.e. from the subset of possible
unique _settings_ that are members of that class, to use. For example
in the 5th Ed. the 10 possible settings for standard symbol C2 are
shown, with the full H-M symbols C121, A121, I121, A112, B112 etc. So
e.g. A121 is one of the allowed conventional settings in the
equivalence class C2. Notice that the standard symbol C2 is _not_ a
full H-M symbol: it doesn't need to be, since it's only a name and it
doesn't need to carry any information. Its only requirement is that
it's unique among the 230 equivalence classes. Similarly the page for
standard symbol P2221 shows the possible settings (at least in my Ed.)
P2221, P2212 and P2122. In this case the standard symbol happens to
be the same as one of the full H-M symbols of the alternate settings
but that's not a requirement, any unique name would have done equally
well. Also in the setting P2221 there obviously remains an ambiguity
concerning the assignment of the a and b axes. How is that resolved?
You will probably say a<b but ITC doesn't specify that as a condition
anywhere, it just says "a<b<c", not "a<b<c unless it's P2221 or P21212
when it's a<b" (the first condition doesn't require exceptions).
Have you considered the fact that not all possible alternate settings
are listed for all space groups? For example no trigonal, tetragonal
or hexagonal settings have a or b unique (you can find many other
examples in the monoclinic & orthorhombic systems, e.g. there are no B
settings in orthorhombic). Why is that? What's so special about the
settings that are listed that doesn't apply to all the ones not
listed? You can be sure it's by very careful design since printing
space was at a premium when the tables were first published (I spent
my first post doc. at the Laboratorium voor Struktuurchemie at the
Rijksuniversiteit Groningen at the same time Dirk Fokkema was there:
he wrote the software for the computer-driven typesetting of the main
Vol. A table of space groups for his Ph.D. thesis; we had a number of
discussions about space groups and I can assure you that the table was
very carefully designed!). The answer is that the settings listed are
strictly those that satisfy the requirements of the rules on
conventional cells in table 9.3.4.1, no more, no less. The
appropriate setting is selected from the members of the equivalence
class of the space group in question according to those rules.
Switching the default in POINTLESS from "SETTING CELL-BASED" to
"SETTING SYMMETRY-BASED" would make me happy, but more
importantly, would avoid a lot of problems.
Maybe the answer is to fix the problem with pointless that you
highlighted originally, i.e. it's apparently reporting the wrong space
group in the log file! Actually extracting stuff from log files is a
very bad idea: log files are not guaranteed to remain the same across
different versions of the program! I learnt that the hard way!
Doesn't pointless output an XML file, or you could just read the MTZ
file header. That's what I do, it's much safer.
Cheers
-- Ian
--
Prof. George M. Sheldrick FRS
Dept. Structural Chemistry,
University of Goettingen,
Tammannstr. 4,
D37077 Goettingen, Germany
Tel. +49-551-39-33021 or -33068
Fax. +49-551-39-22582
