The MISSYM Family:Software for the detection ofMissed 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.

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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

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.

Section out of suspect entry list

Section out of complete suspect entry list

TJ.A.C.S. 2001

Pseudo Symmetry Example

Concluding Remarks

• Software to check for missed/pseudo symmetry is now readily availablee.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 !