The MISSYM Family:
Software for the detection of
Missed or Pseudo Symmetry
A.L.Spek
Utrecht University
The Netherlands
OVERVIEW
• Correct space group assignment to a crystal
structure is not always trivial.
• As a result, many (uncorrected) errors can be
found in the literature and databases.
• Some errors are harmful others are of a more
esthetic nature.
• Bob Sparks was addressing this issue with the
program FINDSYM he has been working on.
• For this reason I choose this topic for my
presentation in this Bob Sparks Symposium.
Crystalline Material
• Type A: 3-D Translation Lattice
230 Space groups.
• Type B: non-3D Translation Lattice
Incommensurate, Misfit, Quasicrystal.
We will Focus here on Type A structures.
Preliminary Structure
Determination
• All 3D structures can be solved in principle
in space group P1 (Direct Methods etc.)
• Subsequent standard least-squares
refinement of the model requires
classification as either:
- non-centrosymmetric (P1) or
- (pseudo) centrosymmetric (P-1)
Centro or Non-centrosymmetric ?
• Correct assignment is not always trivial.
• Refinement of (close to) centrosymmetric
structures in P1 is mathematically unstable.
• Mis-assignment -> geometry artifacts.
• Dick Marsh: Borderline cases are best treated as
centro-symmetric (static/dynamic disorder)
• Inspect Fo/Fc of weak reflection data.
• In general: chiral molecules-> non-centro SpGr.
• Literature Example P1 <-> P-1.
Praseodymium complex
J.A.C.S. (2000),122,3413 – P1, Z = 2
P-1, Z=2
Praseodymium complex
J.A.C.S. (2000),122,3413 – P1, Z = 2
Lattice Symmetry
• 229 higher symmetry groups than P1
• 1979, Dick Marsh paper in Inorg. Chem.
‘Some Incorrect Space groups in
Inorganic Chemistry Volume 16’ (7!)
• Change of Laue Group and/or crystal
system (e.g. –1 to 2/m, i.e. triclinic to
monoclinic; 4/m to 4/mmm)
• Example Triclinic P-1 to Monoclinic C2/c
Orthorhombic Pbca to Cubic Pa-3
New Algorithm
• 1982: CREDUC, Y Le Page J.A.C.,15,255.
• Determination of the Metrical Symmetry of the
lattice from the number of compatible two-fold
axes.
E.g. 5  tetragonal, 9  cubic
• Two-axis = coinciding low-index (0,1,2) direct
and reciprocal lattice vectors within a tolerance.
• Actual symmetry can be lower, not higher than the
metrical symmetry.
• Extended version => Twin laws.
The MISSYM Algorithm
• Y. Le Page published in 1987 a follow-up to
CREDUC called MISSYM (J.A.C.,20,264).
• MISSYM Looks for support in the actual
structure (I.e. coordinate set) for the
proposed metrical symmetry elements.
• Liberal tolerances are used in general.
• Reflection data are needed for follow-up
analysis by least-squares refinement.
MISSYM Implementations
• Y. Le Page – MISSYM/NRCVAX
Leaves evaluation and implementation of
reported higher symmetry to the researcher.
• Hannemann et al. Part of ICSD Software
• Bob Sparks, FINDSYM (Bruker Nonius)
• A.L.Spek, ADDSYM (PLATON)
• ?? MSI – Insight II ???
PLATON/ADDSYM Extensions
• Suggests automatically a revised space group, unit
cell and origin transformation.
• Generation of new ‘.res’ file for SHELXL refinm.
• Allows for a number of non-fitting atoms.
• Handles sub-cells. (structure prediction)
• Accepts data in ‘.res’ and ‘.cif’ format.
• Runs on files with multiple entries (CSD/CIF).
• Display of revised (averaged) structure.
+
Comments
• Hydrogen atoms and Disordered atoms are
not included in the analysis.
• Pseudo-symmetry can be both problematic
and/or interesting (Inorganic Structures)
• Missing Atoms (Incomplete structures)
• Algorithm not suitable for macromolecules
ADDSYM run on CSD
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April 2002 release
Space group C2 (#5)
2190 entries
162 entries to be inspected for missed or pseudosymmetry
• About 90 entries pseudo-symmetric
• Transformations to: C2/m, C2/c, I222, C2221,
Aba2, Fddd, R32, R-3m, R-3c, P3121, I-4
• See also Acta Cryst. (2001), B57, 800-805.
Section out of complete suspect entry list
J.A.C.S. 2001
T
Pseudo Symmetry Example
Concluding Remarks
• Software to check for missed/pseudo
symmetry is now readily available
e.g. www.cryst.chem.uu.nl/platon/
• ADDSYM included in IUCR/CHECKCIF
• Proposed higher symmetry should either be
implemented or convincingly discussed as
pseudo-symmetry in a structure report.
• Thanks Bob & Yvonne !