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The MISSYM Family: Software for the detection of Missed 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 -> 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.

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Praseodymium complex J.A.C.S. (2000),122,3413 – P1, Z = 2

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P-1, Z=2

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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 => 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,

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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. 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 !

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