The MISSYM Family: Software for the detection of Missed or Pseudo Symmetry

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The MISSYM FamilySoftware for the detection
ofMissed or Pseudo Symmetry

• A.L.Spek
• Utrecht University
• The Netherlands

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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.

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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.

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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)

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Centro or Non-centrosymmetric ?

• Correct assignment is not always trivial.
• Refinement of (close to) centrosymmetric
  structures in P1 is mathematically unstable.
• Mis-assignment -gt 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-gt non-centro SpGr.
• Literature Example P1 lt-gt P-1.

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Praseodymium complex
J.A.C.S. (2000),122,3413 P1, Z 2
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P-1, Z2
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Praseodymium complex
J.A.C.S. (2000),122,3413 P1, Z 2
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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

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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 gt Twin laws.

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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.

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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 ???

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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.

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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

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ADDSYM run on CSD

• April 2002 release
• Space group C2 (5)
• 2190 entries
• 162 entries to be inspected for missed or
  pseudo-symmetry
• 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.

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Section out of suspect entry list
Section out of complete suspect entry list
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T
J.A.C.S. 2001
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Pseudo Symmetry Example
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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 !