[New data item]: _cell.formula_units_Z_prime

[vaitkus]

Definition

Z' (Z prime) specifies the number of molecules in an asymmetric unit. It is defined as the number of formula units in the unit cell divided by the number of independent general positions.

Related resources:
[1] https://zprime.co.uk/introduction
[2] https://pubs.rsc.org/en/content/articlehtml/2025/ce/d4ce01186d

Restricted values

Value is not drawn from a predefined list

Example

5 (Example 1), 1.5 (Example 2), 0.5 (Example 3)

Explanation of example

Example 1

Crystal structure contains five molecules in the asymmetric unit. One such crystal structure of tetraphenylphosphonium octahydrotriborate is described in M. A. Beckett, P. N. Horton, M. B. Hursthouse, C. Pszolla, Acta Crystallogr., Sect. E: Struct. Rep. Online, 2010, 66, o833. https://doi.org/10.1107/S1600536810008263

Example 2

Crystal structure contains one and a half of a molecule in the asymmetric unit. One such crystal structure of 9-(Methoxymethyl)anthracene is described in Liu, J., Wei, G.-H., Ping, G.-J. & Ma, J.-F. (2007). 9-(Methoxy­meth­yl)anthracene. Acta Cryst. E63, o4442. https://doi.org/10.1107/S1600536807052324

Example 3

Crystal structure contains half of a molecule in the asymmetric unit. One such crystal structure of (E)-1,1,4,4-Tetraphenylbut-2-yne-1,4-diol is described in Sundar, J. K., Kumar, K. M., Vijayakumar, V., Suresh, J., Natarajan, S. & Lakshman, P. L. N. (2010). Acta Cryst. E66, o679. https://doi.org/10.1107/S160053681000629X

Looping

top level

Data name

_cell.formula_units_Z_prime, _cell.formula_units_Z-prime, _cell.formula_units_Z'

Type

Real

Data structure

None (a single value of type given in Type above)

Comments

1. Several crystallographic database such as the COD and the CSD already provide such calculated values as part of their interface therefore being able to record them using regular CIF means would be quite useful.
2. Now sure how easily this can be done, but the algorithm for deriving Z' values could be encoded as dREL code in the dictionary, thus providing additional insights into this concept.
3. The OPTIMADE API (https://github.com/Materials-Consortia/OPTIMADE) developers are currently experimenting with introducing the CIF namespace (https://github.com/Materials-Consortia/namespace-cif) which would inherit some data names/definitions from the CIF dictionaries. Z' prime was mentioned as one of the crystal structure properties that crystallographic databases would like to expose and it would much more preferred to use the official IUCr definition for this item.

[vaitkus]

@jamesrhester @nautolycus I ran a quick search, but did not find any mentions of such item in the official IUCr discussion channels. If I missed any previous discussions, I would be grateful if you could link me to them.

The definition and examples are quite a rough draft, but I think they sufficiently convey the general idea.

[nautolycus]

There was a proposal long ago (2002) from the CCDC and the discussion seemed to end with Howard Flack's contribution within https://www.iucr.org/__data/iucr/lists/coredmg/msg00196.html (see below). I'm meeting James on Thursday so we can discuss how best to pursue this. I suspect Carol Brock would be a good expert to get involved.

> >data_cell_formula_units_Z_prime
> >    _name                      '_cell_formula_units_Z_prime'
> >    _category                    cell
> >    _type                        numb
> >    _enumeration_range           1:
> >    _definition
> >;              The number of the formula units as specified
> >               by _chemical_formula_structural, _chemical_formula_moiety or
> >               _chemical_formula_sum in the asymmetric unit of the
> >               unit cell given in the CELL category and the 
> >               space group defined in the SYMMETRY or SPACE GROUP category.
> >               This item is used to indicate the number of chemically
> >               equivalent molecules in the asymmetric unit.
> >;

COMMENT: Requested by CCDC

STATUS: Preliminary approval 2002-10-14

HDF. *********

There are two HUGE problems with this definition. I recommend you send
it back to the CCDC for more careful consideration.
(1) There is not in fact a single Z' which describes what they are
trying to express. Take the example of the compound AB composed of two
molecules A and B in the ratio 1:1 as represented by the chemical
formula AB. The structure is in space group P2. Molecules A have point
symmetry 2 and sit on a 2-fold axis in the crystal structure. There are
two independent A molecules in the asymmetric unit. Molecules B have
symmetry 1 and sit in a general position. There is one independent
molecule B in the asymmetric unit. What is the value of your Z'?
(2) And, surprise surprise coming from HDF, there are problems of
chirality with this Z'.
_chemical_formula_structural
_chemical_formula_moiety
_chemical_formula_sum and
chemically equivalent molecules
do not necessarily refer to the same thing. Some may group opposite
enantiomers together and other may separate them. Opposite enantiomers
are not (in my view) "chemically equivalent molecules". In J. Appl.
Cryst. 33, 1143-1148, F&B (2000) wrote in section 3.10 on Molecular
symmetry "For this purpose, the most promising nomenclature suggested so
far is that of Chernikova et al (1991), but this would need to be
extended for the current purposes." CCDC has made a big step in the
right direction with their 'CSD symmetry' but this does not capture
chirality information. No one has tried to work out the way that
Chernikova's nomenclature could be usefully extended for encoding
molecular symmetry and chirality information. This is what is really
required and it needs to be provided by authors at publication time. A
single vague Z' is of limited practical value.
Back to the drawing board. (When the daffodils come into bloom next
spring, it would be a good time to have a small punting party working on
this problem!)

end of HDF ********

[vaitkus]

I was wondering if there are any updates on how to best proceed with this?

[nautolycus]

When James and I met, we agreed that this proposal should be explored with the coreDMG group and possible other interested parties (I mentioned Carol Brock; Gervais Chapuis and Massimo Nespolo are potential other participants). I have worked up possible dictionary definitions for Z' based on the original proposal, and also a Z_prime_details which might be appropriate given the caveats raised by Howard Flack and others. My concern is that the referenced documentation, though currently useful for following the arguments, consists of web pages rather than durable (e.g. published literature) sources.

We might want to discuss the proposal further here before sending it to coreDMG et al.

save_cell.formula_units_z_prime

    _definition.id                '_cell.formula_units_Z_prime'
    _definition.update            2025-10-21
    _description.text
;
    Z' specifies the number of molecules in the asymmetric unit.
    It is defined as the number of formula units in the unit cell
    (_cell.formula_units_Z) divided by the multiplicity of the
    general position of the corresponding space group. Z' can be
    a fraction or a positive integer.

    Note that correct assignment of Z' may be difficult for some
    complex structures (Flack, 2002; Steed et al., 2014). For such
    cases a justification of the assigned value should be given in
    _cell.formula_units_Z_prime_details.

    Ref: Flack, H. D. (2002).
         https://www.iucr.org/__data/iucr/lists/coredmg/msg00196.html
         Steed, J. et al. (2014). https://zprime.co.uk/limitations
;
    _name.category_id             cell
    _name.object_id               formula_units_Z_prime
    _type.purpose                 Number
    _type.source                  Assigned
    _type.container               Single
    _type.contents                Real
    _enumeration.range            0:
    _units.code                   none

    loop_
      _description_example.case
      _description_example.detail
         5
;
         Crystal structure contains five molecules in the asymmetric unit.
         One such crystal structure (tetraphenylphosphonium octahydrotriborate)
         is described  by Beckett, M. A. et al. (2010). Acta Cryst. E66, o833.
;
         1.5
;
         Crystal structure contains one and a half instances of a molecule
         in the asymmetric unit. One such crystal structure
         [9-(methoxymethyl)anthracene] is described by Liu, J. et al.
         (2007). Acta Cryst. E63, o4442.
;
         0.5
;
         Crystal structure contains half of a molecule in the asymmetric unit.
         One such crystal structure [(E)-1,1,4,4-tetraphenylbut-2-yne-1,4-diol]
         is described by Sundar, J. K. et al. (2010). Acta Cryst. E66, o679.
;

save_

save_cell.formula_units_z_prime_details

    _definition.id                '_cell.formula_units_Z_prime_details'
    _definition.update            2025-10-21
    _description.text
;
    An account of the assigned value of Z', the number of molecules in
    the asymmetric unit, where there is difficulty in deciding the
    appropriate value for reasons of symmetry, chirality, disorder etc.
    (Flack, 2002; Steed et al., 2014).

    Ref: Flack, H. D. (2002).
         https://www.iucr.org/__data/iucr/lists/coredmg/msg00196.html
         Steed, J. et al. (2014). https://zprime.co.uk/limitations
;
    _name.category_id             cell
    _name.object_id               formula_units_Z_prime_details
    _type.purpose                 Describe
    _type.source                  Recorded
    _type.container               Single
    _type.contents                Text
    _description_example.case
;
         Z' has been assigned the value 1 as the catenane is considered
         a single complex of two interlocked molecules that cannot be
         chemically separated, in preference to a crystallographic
         interpretation that considers it as two interlinked independent
         molecules that would suggest setting Z' = 2.
;
    _description_example.detail
;
         Based on a discussion in https://zprime.co.uk/limitations of a
         structure (QINJIG) reported by Watanabe, N. et al. (1999).
         Chem. Lett. 28, 915-916.
;

save_

[jamesrhester]

I think the above definition is sufficiently well worked out for it to form the basis of consultation with the coreDMG. @nautolycus : if you agree, could you create a PR and further discussion will then take place on the coreDMG and under that PR?

[vaitkus]

@nautolycus very nice work, thank you! I agree with @jamesrhester that the proposed definitions are ready for the coreDMG group.