3. The solved structure is not the expected compound, but this unexpected twist is beside the point:

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Example 13. A pseudo-merohedral twin. By Ilia A. Guzei. Reviewed by Bruce C. Noll. November 6, 2018.

The two orientations of the monoclinic unit cell are related by a 180 rotation about a certain direction. In this particular case the unit cell parameters are a = 12.665(8) Å α = 90 b = 12.

1 Example 13. A pseudo-merohedral twin. By Ilia A. Guzei. Reviewed by Bruce C. Noll. November 6, This example illustrates a typical situation an apparently orthorhombic unit cell that is in fact a pseudomerohedrally twinned monoclinic unit cell with the β angle very close to 90. The two orientations of the monoclinic unit cell are related by a 180 rotation about a certain direction. In this particular case the unit cell parameters are a = (8) Å α = 90 b = (9) Å β = 90.00(2) c = (15) Å γ = 90 and the relationship between the twin domains is a 180 rotation about the [001] vector in real space (c axis). This example explains how to identify signs of twinning (ST) and determine the twin law. XPREP is proprietary software, whereas PLATON and OLEX2 are free. The structure corresponds to the product of this reaction: 1. Run XPREP as usual with Example13.p4p and Example13.raw files (the raw file has the same format as the hkl file, but is not overwritten by XPREP). The space group determination will fail because no acceptable orthorhombic space group can be assigned: 1

2. Return to the main menu, then a. Select option T [Change tolerances] b. Select option T [THRESHOLD in degrees for terminating cell search] and enter zero as the new threshold. c. Exit to the main menu d.

Now the space group can be determined as P2 1/c with CFOM = 4.15. 3. The solved structure is not the expected compound, but this unexpected twist is beside the point: 4.

2 2. Return to the main menu, then a. Select option T [Change tolerances] b. Select option T [THRESHOLD in degrees for terminating cell search] and enter zero as the new threshold. c. Exit to the main menu d. Select option H [Search for HIGHER metric symmetry]. Among the many options shown below, option B with the lowest R(sym) = should be chosen. e. Now the space group can be determined as P2 1/c with CFOM = The solved structure is not the expected compound, but this unexpected twist is beside the point: 4. Most atoms can be found and assigned, but the isotropic refinement will not be satisfactory, given the apparent quality of the data: 5. At this point it is necessary to check for signs of twinning (ST). Herein ST s are considered briefly. [A thoroughly analyzed practical example of a pseudo-merohedral twin is presented by Guzei, I. A.; Herbst-Irmer, R.; Munyaneza, A.; Darkwa, J. in Detailed example of the identification and crystallographic analysis of a pseudo-merohedrally twinned crystal. Acta Crystallogr., Sect. B: Struct. Sci. 2012, 68 (2), This paper is available for download from 2

3 Typical warning signs of pseudo-merohedral twinning (ST) include: a. (ST1) The metric symmetry is higher than the Laue symmetry; b. (ST2) The RR ssyyyy = FF oo 2 <FF oo 2 > FF oo 2 value for the higher-symmetry Laue group is only slightly higher than that for the lower-symmetry Laue group; c. (ST3) The mean value for E 2-1 is much lower than the expected mean value of for a non-centrosymmetric space group; d. (ST4) Indicated systematic absences are inconsistent with those for any known space group; e. (ST5) K = <F o 2 > is systematically high for reflections with low intensity; <F 2 c > f. (ST6) For all the "most disagreeable" reflections, generally F o F c. In Example13 we have already seen ST1, ST2, and ST4 when we ran XPREP. During the refinement, the LST output file ought to be examined for ST5 and ST6. For ST5 look at this table in the second half of the LST file: The K values are close to unity, thus ST5 is not clearly manifested. The very next table in the LST file clearly shows the presence of ST6 (F o F c): 3

Due to the presence of several STs it is necessary to try and identify the twin law. 6. Add the following cards in the INS file LIST 4 ACTA then refine the structure.

corresponding to a 180 rotation about the c axis: 8. The INS file should be modified accordingly. Insert TWIN -1 0 0 0-1 0 0 0 1 BASF 0.

4 Due to the presence of several STs it is necessary to try and identify the twin law. 6. Add the following cards in the INS file LIST 4 ACTA then refine the structure. 7. Launch PLATON from within OLEX2 with the leftmost button at top right: and choose TwinRotMatt at the bottom of the Symmetry panel PLATON will identify the twin law corresponding to a 180 rotation about the c axis: 8. The INS file should be modified accordingly. Insert TWIN BASF 0.46 in the INS file and run a refinement. There should be a dramatic improvement in the quality of the refinement: atomic positions will show no ambiguity and the R factor will drop like a rock: 4

5 9. Complete the refinement as usual. One THF group should be modeled as disordered over two positions. Add appropriate restraints. Comment: This dataset was integrated and scaled consistently with a centrosymmetric monoclinic space group after the twin law was determined. 5

Examples of (Pseudo-) Merohedral Twins

Twinning Göttingen, Februar 15th, 212 Examples of (Pseudo-) Merohedral Twins rherbst@shelx.uni-ac.gwdg.de http://shelx.uni-ac.gwdg.de/~rherbst/twin.html Space Group Determination Crystal system H and Lattice