Ambiguity in atom_site.disorder_group value -1

[Robert Hanson]

On Tue, Oct 18, 2022 at 11:42 AM Bollinger, John C via coreDMG <
coredmg at iucr.org> wrote:

> Hi Bob,
>
>
>
> My thinking is that the crystallographer might recognize "a" special
> symmetry element, but the application of symmetry creates n copies, not
> two, in a space group with n symmetry operations. Right?
>
>
>
> Thus, fundamentally, there is no such concept of a "specific" symmetry
> element. All n copies symmetry related, but all are not "complementary".
>
>
>
> There seems to be some mismatching terminology going on here. When I say
> “a symmetry element”, I mean a mirror plane, axis of rotational symmetry,
> *etc*. -- that is, an element of the relevant space group -- as realized
> in the particular structure.  I was under the impression that this usage
> was pretty conventional.  Surely you’ve listened to many talks and read
> many articles that discuss how a crystal structure contains a mirror plane
> here, or an inversion center there, or a rotation axis wherever?  I know I
> have.
>

Certainly my understanding. We are talking about the same thing. I was
reading "symmetry element" as you describe. My point was that there are
also inversion centers, glide planes, and translations all at work in this
example. Let's see what reads below...



>
>
> In this sense, there are many symmetry elements in any crystal structure,
> and usually several distinct ones in or passing through each unit cell.
> The International Tables present diagrams showing their types and
> locations.  So yes, in this sense there absolutely is a concept of a
> specific symmetry element.  But you seem to be using the term differently.
>
>
>

Don't think so.


> This group can be considered to be disordered about any of these symmetry
> elements.
>
>
>
> Yes and no.  As a matter of terminology, when I say a group is disordered
> about a symmetry element, I am employing the typical reduction of the
> overall structure to a crystallographically unique unit, and looking at the
> symmetry elements that relate the chosen unit to a symmetry equivalent that
> overlaps that particular unit in space.  I think that this, too, is a
> relatively common usage in chemical and crystallographic jargon.  When I
> allow for the possibility of a group being disordered about multiple
> symmetry elements, I am talking about cases where the disorder occurs at a
> site where multiple symmetry elements intersect.  At such a site, multiple
> elements may generate images of the same unique unit that all overlap the
> original unit.
>

Sure. Q: Why did you choose the C2 axis rather than the Ci point, for
example? Same disordering there, I think. Maybe the C2 is "more obvious"?


>
>
> It is also true that when there is disorder, one can (always) find
> symmetry elements, sometimes of different kinds, that generate overlaps
> with a chosen unique unit from distinct symmetry copies of that unit.  But
> that’s not what I’m talking about, and I don’t think it’s very interesting
> because it follows as a necessary consequence of translational symmetry.
>
>
>
> *In addition to not being occupied simultaneously with sites belonging to
> different groups, the sites of such a group also are not occupied
> simultaneously with symmetry equivalents of sites belonging to the same
> group.  That is, the group's symmetry equivalents are among its disorder
> complements.  *
>
>
>
> I don't understand this statement. Why would it be true that sites related
> by symmetry are "not being occupied simultaneously"?
>
>
>
> It took me embarrassingly long to work out what the problem was here.
> Which is a great demonstration of why data dictionaries are valuable, and
> why collaborative development of them is important.  The point that is not
> adequately conveyed by my previous suggesting wording is that the bit about
> symmetry equivalents not being simultaneously occupied should be understood
> locally, not globally.
>

Locally meaning "involving a specific symmetry element of the
crystallographer's choice"?



> Perhaps this refinement would be more acceptable:
>
>
>
> ====
>
> [...] Sites belonging to the same group are simultaneously occupied, but
> those belonging to different groups are not.
>
>
>
> (paragraph break)
>
>
>
> A minus prefix (e.g. '-1') is used to indicate that the group is
> disordered about one or more symmetry elements. In addition to not being
> occupied simultaneously with sites belonging to different groups, the atom
> sites of such a group are not occupied simultaneously with local symmetry
> equivalents of sites belonging to the same group.  That is, some of the
> group's symmetry equivalents are among its disorder complements.
>

Begs the question of what is "local". Should I know what that means?

John, would you agree that "symmetry equivalents" are based on symmetry
operations? Maybe that's the problem -- You are identifying and building
your description around symmetry *elements*, which are not the subject of a
CIF file, rather than symmetry *operations*, which are all I have to go on
in general when working with a CIF file.

Yes, I can decode a symmetry operation and see that it refers to a C2 axis.
Yes, I can construct a C2 axis that relates pairs of clearly overlapping
disordered group complements (terminology?). But in this case, the "local"
C2 axis I think you are referring to is not one of the given CIF symmetry
operations. That would actually be quite challenging to define just from
the information in a CIF file, I think.

$ draw symop @2 @13
*2 -x+1/2,y,-z+1 C2 axis*

[image: image.png]
whereas the stated operation is:

* '-x+1/2, y, -z'*

Minor detail there, but *technically* this is a different "C2 axis". It
relates our asymmetric unit to a different copy. Maybe I should call this a
"global" C2 axis? Not sure.






> ====
>
>
>
> As far as I’m concerned, the three sentences in the latter paragraph are
> different ways of saying the same thing.
>
>
>

OK, let's unpack that:

1)

> A minus prefix (e.g. '-1') is used to indicate that the group is
> disordered about one or more symmetry elements.
>

I am totally OK with this. I would prefer sticking to concepts involving
symmetry operations, but I get it now.

 2)

> In addition to not being occupied simultaneously with sites belonging to
> different groups, the atom sites of such a group are not occupied
> simultaneously with local symmetry equivalents of sites belonging to the
> same group.
>

Maybe. I just have never heard of "local symmetry equivalents" -- that is
completely new to me. But if that is what people say, OK.

 3)

> That is, some of the group's symmetry equivalents are among its disorder
> complements.
>

Not sure this one is needed.


I guess I would just say that if this were the description, and it makes
sense to crystallographers, and that is our audience, perhaps that is an
improvement. I can't say, because I am not a crystallographer. If I had
read that, I would probably have had to ask Brian the same question,
because I wouldn't know what a "local symmetry element" is. ;)

BTW, the "software rendering" addition I was suggesting was from the SHELX
manual, which Brian quoted to me:

And from http://xrayweb.chem.ou.edu/notes/manuals/shelxl_user_guide.pdf:

"...the generation of equivalents (e.g. in a toluene molecule on
an inversion center) may be prevented by assigning a negative PART
number."

I understand the reason for not getting into rendering in the CIF
description. Still, someone working on Mercury apparently had the same
problem understanding this "-n" designation. Thus, maybe there is some
argument for at least mentioning bonding. Or not.

I think the addition of "local" does technically correct the issue I had
with John's suggested change.

Bob
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