Dear George

I notice that the Oxford CRYSTALS program, which is what I used when I
did small-molecule crystallography and which is still quite popular
among the small-molecule people (maybe not as much as Shel-X!), uses
the CIF convention:

OCC= This parameter defines the site occupancy EXCLUDING special
position effects (i.e. is the 'chemical occupancy'). The default is
1.0.  Special position effects are computed by CRYSTALS and multiplied
onto this parameter.

(from http://www.xtl.ox.ac.uk/crystalsmanual-atomic.html )

Also the mmCIF specification on this is the same CIF one (hardly
surprising I guess since it's derived from it):

_atom_site.occupancy  The fraction of the atom type present at this site.
The sum of the occupancies of all the atom types at this site may not
significantly exceed 1.0 unless it is a dummy site.

(from http://mmcif.pdb.org/dictionaries/mmcif_std.dic/Items/_atom_site.occupancy.html
)

which doesn't say so specifically, but it's implied since if the
multiplicity is included then the maximum value of the sum is the
multiplicity, not 1.0.

So there's a real possibility of user - and programmer - confusion
here!  I must say that until I looked at the 4INS file I had assumed
that the PDB occupancy was what it claimed to be, i.e. the real
'chemical' occupancy not the multiplicity-fudged one.

Cheers

-- Ian

On Wed, Dec 15, 2010 at 1:53 PM, George M. Sheldrick
<[log in to unmask]> wrote:
>
> Dear Ian,
>
> Yes. Once an atom has been identified as on a special position because it
> is within a specied tolerance, SHELXL applies the appropriate contraints
> to both the coordinates and the Uij so there is no danger of the atom
> wandering off the special position. Usually, when an atom it very close to
> a special position but not actually on it, it is part of a disordered
> solvent molecule and will be prevented from misbehaving by distance and
> Uij restraints imposed by the user; in such a case the user usually also
> switches off the special position check for that disordered molecule
> (SPEC -1) to avoid atoms being idealized onto the special position by the
> program. For solvent molecules disordered on special positions it is
> also necessary to ignore symmetry equivalent atoms when generating
> idealized hydrogen atoms etc. (PART -N in SHELXL). This is all routine
> practice in small molecule crystallography. I agree that the use of
> orthogonal rather than crystal coordinates can obscur the situation,
> e.g. for an atom on a threefold axis.
>
> Best wishes, George
>
> Prof. George M. Sheldrick FRS
> Dept. Structural Chemistry,
> University of Goettingen,
> Tammannstr. 4,
> D37077 Goettingen, Germany
> Tel. +49-551-39-3021 or -3068
> Fax. +49-551-39-22582
>
>
> On Wed, 15 Dec 2010, Ian Tickle wrote:
>
>> Dear George
>>
>> I would say that an atom has fractional occupancy (but unit
>> multiplicity) unless it's exactly on the special position (though I
>> can foresee problems with rounding of decimal places for an atom say
>> at x=1/3), so that effectively once the atom is fixed exactly on the
>> s.p. the symmetry copies coalesce into a single atom with unit
>> occupancy (but fractional multiplicity).  This is at least one
>> advantage of having co-ordinates stored as fractional - it would
>> probably be more tricky with orthogonalised co-ordinates.  Presumably
>> once an input atom has satisfied the condition of being 'sufficiently
>> close' to a s.p. to be considered as 'on' the s.p. then the
>> constraints fix the co-ordinates exactly on the special position and
>> henceforth it's forcibly prevented from moving off it?  In any case if
>> an atom is very close to its symmetry copy you are going to have
>> matrix conditioning problems for the co-ordinates perpendicular to the
>> axis of symmetry (or mirror plane), so then you have no choice but to
>> disallow co-ordinate shifts of the atom which would take it off the
>> special position?
>>
>> Cheers
>>
>> -- Ian
>>
>> On Wed, Dec 15, 2010 at 11:42 AM, George M. Sheldrick
>> <[log in to unmask]> wrote:
>> >
>> > Dear Ian,
>> >
>> > Of course I could convert the occupancy on reading the atom in and convert
>> > it back agains on reading it out. This is not quite so trivial as it
>> > sounds because I need to set a threshold as to how close the atom has
>> > to be to a special position to be treated as special, and take care
>> > that rounding errors have the same effect on input and output and that
>> > the coordinates have not moved in or out of the special zone in the
>> > meantime.
>> >
>> > As it stands in SHELX, an atom that is near to a twofold will have an
>> > occupancy of 0.5 whether it is disordered close to a special position
>> > or whether it is really special, so this is never a problem.
>> >
>> > SHELXL is mainly used for small molecules that frequently have atoms on
>> > speical positions, and disordered solvent molecules approximately on
>> > sppecial positions are also very common (for example in centrosymmetric
>> > space groups toluene usually lies on the center of symmetry). Occupancies
>> > are often tied to free variables which would also complicate any changes
>> > to the code. And in any case, SHELX has been upwards compatible for the
>> > last 35 years and I wish it to remain that way.
>> >
>> > Best wishes, George
>> >
>> > Prof. George M. Sheldrick FRS
>> > Dept. Structural Chemistry,
>> > University of Goettingen,
>> > Tammannstr. 4,
>> > D37077 Goettingen, Germany
>> > Tel. +49-551-39-3021 or -3068
>> > Fax. +49-551-39-22582
>> >
>> >
>> > On Wed, 15 Dec 2010, Ian Tickle wrote:
>> >
>> >> Dear George
>> >>
>> >> Is applying the multiplicity factor to the occupancy internally in the
>> >> program such a issue anyway?  It need only be done once per atom on
>> >> input (i.e. you multiply each input occupancy by the multiplicity to
>> >> get the combined multiplicity*occupancy value that you would have
>> >> reading in directly in the current version), and then once per atom
>> >> again on output, reversing the process.  There shouldn't be any need
>> >> to change anything in the inner atom/reflection loop where obviously
>> >> it would indeed have slowed things down.
>> >>
>> >> I can see though that the backwards-compatibility issue is more
>> >> serious.  However I suspect it will affect only a small proportion of
>> >> cases (though I accept that the fact that it may affect any at all may
>> >> be sufficient grounds for you to reject it!).  If the input value
>> >> exceeds the multiplicity we can say that it's definitely an occupancy
>> >> (otherwise clearly the occupancy would be > 1).  If it's less there's
>> >> an ambiguity for sure; however then it's more likely to be the
>> >> multiplicity*occupancy (so the occupancy is nearer to 1), on the
>> >> grounds that small occupancies are less likely to be observed, because
>> >> the effect on diffraction will be less significant.  I accept that
>> >> second-guessing the user's intentions in this way is not ideal!  I
>> >> wonder how often fractional occupancies are observed at special
>> >> positions anyway?
>> >>
>> >> Regards
>> >>
>> >> -- Ian
>> >>
>> >> On Fri, Dec 10, 2010 at 11:28 PM, George M. Sheldrick
>> >> <[log in to unmask]> wrote:
>> >> > SHELXL also expects that the occupancy of a fully occupied atom on a
>> >> > threefold axis should be set at 1/3, and will generate this automatically
>> >> > if necessary. It will also generate automatically the necessary
>> >> > constraints for the x, y and z parameters (and for the Uij if the atom is
>> >> > anisotropic). It is essential that this is done correctly if a full-matrix
>> >> > refinement is being performed (e.g. to get esd estimates), otherwise
>> >> > the refinement can explode. The user may change or switch off the
>> >> > tolerance for detecting whether an atom is on a special position
>> >> > (with the SPEC instruction). Setting the occupancy to a fraction avoided
>> >> > a complicated IF construction inside a loop and 35 years ago computers
>> >> > were so slow! I can't change it now because I have to preserve upwards
>> >> > compatibility. Unfortunately the CIF committee decided to use the other
>> >> > definition (i.e. the Zn on the threefold axis has an occupancy of 1.0)
>> >> > and this has caused considerable confusion in the small molecule world
>> >> > ever since; atoms are frequently encountered on special positions in
>> >> > inorganic and mineral structures.
>> >> >
>> >> > George
>> >> >
>> >> > Prof. George M. Sheldrick FRS
>> >> > Dept. Structural Chemistry,
>> >> > University of Goettingen,
>> >> > Tammannstr. 4,
>> >> > D37077 Goettingen, Germany
>> >> > Tel. +49-551-39-3021 or -3068
>> >> > Fax. +49-551-39-22582
>> >> >
>> >> >
>> >> > On Fri, 10 Dec 2010, Ed Pozharski wrote:
>> >> >
>> >> >> On Fri, 2010-12-10 at 21:53 +0000, Ian Tickle wrote:
>> >> >> > Hmmm - but shouldn't the occupancy of the Zn be 1.00 if it's on the
>> >> >> > special position
>> >> >>
>> >> >> Shouldn't 1/3 be better for programming purposes?  If you set occupancy
>> >> >> to 1.0, then you should specify that symmetry operators do not apply for
>> >> >> these atoms, making Fc calculation a bit more cumbersome.
>> >> >>
>> >> >> If definition of the "asu content" is "you get full content of the unit
>> >> >> cell after applying symmetry operators", then occupancy *must* be 1/3,
>> >> >> right?
>> >> >>
>> >> >> The first zinc and the water are on special position, but because they
>> >> >> are not excluded from positional refinement (perhaps they should be),
>> >> >> they will drift a bit.  CNS has distance cutoff for treating atoms as
>> >> >> special positions, if it jumps over the limit during, say, simulated
>> >> >> annealing, it  will cause problems.  Perhaps PROLSQ did something
>> >> >> similar.  It is a good question if it's better to fix these in place or
>> >> >> let them wobble a bit to account for some potential disorder.  While I
>> >> >> see the formal argument that it should be nailed to three-fold axes, it
>> >> >> is also true that this is a mathematical compromise to simplify modeling
>> >> >> that does not reflect physical reality (i.e. you don't have three
>> >> >> partially occupied zinc ions, it's just one).  In any event, given that
>> >> >> this is a 1.5A structure, (-0.002 0.004) is statistically speaking the
>> >> >> same as (0 0).
>> >> >>
>> >> >> Cheers,
>> >> >>
>> >> >> Ed.
>> >> >>
>> >> >> --
>> >> >> "I'd jump in myself, if I weren't so good at whistling."
>> >> >>                                Julian, King of Lemurs
>> >> >>
>> >> >>
>> >> >
>> >>
>> >>
>>
>>