Phase transition and structures of the twinned low-temperature phases of (Et4N)[ReS4]

The crystal structures of three phases of [(C2H5)4N][ReS4] were determined by single-crystal X-ray diffraction analysis at different temperatures.


Synthesis and crystallization
Et 4 NReS 4 was synthesized according to the literature method of Goodman & Rauchfuss (2002). Slow evaporation of an acetonitrile solution of Et 4 NReS 4 in air afforded crystals suitable for X-ray diffraction analysis.

Refinement
Crystal data, data collection and structure refinement details are summarized in Table 1. The phase designations Ia-Ic are analogous to that used for Et 4 NFeCl 4 (Lutz et al., 2014).
2.2.1. a-phase. The crystal structure of the -phase (denoted Ia) at 297 K was refined in the space group P6 3 mc (Table 1) starting from the structure of Et 4 NFeCl 4 at 290 K (Lutz et al., 2014). The ReS 4 À anion is completely ordered. The whole tetraethylammonium cation is disordered about special position b with 3m symmetry. A whole cation with an occupancy of 1/6 was modelled. Similarity distance restraints were applied for the ethyl groups. All the atoms of the cation were refined isotropically because of this severe disorder, whereas the atoms of the ordered anion were refined anisotropically (Fig. 1a). H atoms were attached to geometrically optimized positions and refined with the riding model. Twinning by inversion was considered. The fractional contribution of the minor domain refined to 0.14 (4). The C-H distances were fixed at 0.96 (CH 3 ) or 0.97 Å (CH 2 ). The U iso (H) values were constrained to 1.5U eq (C) for methyl H atoms and 1.2U eq (C) otherwise.
2.2.2. c-phase. Upon slow cooling (ca 5 K min À1 ) to 285 K, crystals of the -phase (i.e. Ia) undergo a reversible phase transition to the -phase (denoted Ic). No further phase transitions could be observed between 110 and 300 K. The -phase crystallizes in the space group P2 1 as a pseudomerohedral twin (Table 1). Attempts to grow crystals at 273 and 253 K also led to the formation of twins. Data for the -phase were collected at 150 K. The high deviation from the hexagonal metric leads to split reflections and reflections of different domains close to each other (see Fig. S1 of the supporting information). However, the different orientations could not be separated. To take the twinning into account, an HKLF5 file (Sevvana et al., 2019) was produced (SHELXL-2018;Sheldrick, 2015) according to the transition from P6 3 mc to P2 1 ( Table 2). The normal procedure using the TWIN command was not possible, because in SHELXL, only one TWIN command is allowed, but here two twin operations, a threefold and a mirror, are needed. We checked for additional twinning by inversion using now twelve components, but the fractional contributions of the additional six components refined to values close to zero (for details, see the supporting information). Both the tetrathioperrhenate anion (ReS 4 À ) and research papers Table 1 Experimental details. For all phases: (C 8 H 20 N) [ReS 4 ], M r = 444.69. Experiments were carried out with Mo K radiation using an Oxford Diffraction Gemini E Ultra diffractometer with an EOS CCD camera. The absorption correction was analytical [CrysAlis PRO (Agilent, 2013), based on expressions derived by Clark & Reid (1995)]. H-atom parameters were constrained.

Ia
Ib Ic the tetraethylammonium cation are completely ordered (Fig. 1b). However, to stabilize the refinement, distance restraints were used and the cation was only isotropically refined. H atoms were attached to geometrical optimized positions and refined with the riding model. The C-H distances were fixed at 0.98 (CH 3 ) or 0.99 Å (CH 2 ). The U iso (H) values were constrained to 1.5U eq (C) for methyl H atoms and 1.2U eq (C) otherwise. 2.2.3. b-phase. Rapid cooling (>100 K s À1 ) of the -phase (i.e. Ia) to 110-170 K leads to a mixture of the -phase (i.e. Ic) and the -phase (denoted Ib) through a phase transition forming an allotwin. A reciprocal space plot (see Fig. S2 in the supporting information) shows satellites for the reflections with h = 3n and k = 3m. With slow heating (ca 5 K min À1 ) to 200 K, the -phase irreversibly changes to the -phase. We were not able to obtain crystals of the -phase free from the -phase. Such a superposition of reflections of two phases was also found, for example, in Kautny et al. (2017). The a and b axes of the -phase are enlarged by a factor of three compared to the -phase. Therefore, all hkl reflections with h = 3n and k = 3m of the -phase are contaminated with reflections of the -phase. The data collection software (CrysAlis PRO; Oxford Diffraction, 2016) could not split the summed intensity into its two components. Therefore, the hkl reflections with h = 3n and k = 3m had to be removed from the data set. This lowers the completeness to only 88.8%. Including the contaminated reflections raises the R1 value from 0.0354 to 0.0548 and shows F 2 obs values for hkl reflections with h = 3n and k = 3m much bigger than the F 2 calc values (see Table S1 in the supporting information). Even with the ISOR restraint, where atoms are restrained with effective standard deviations so that their U ij components approximate to isotropic behaviour, the anisotropic displacement parameters refine to nonpositive definite values and the residual density increases to 3.45/À3.41 e Å À3 . The C-H distances were fixed at 0.98 (CH 3 ) or 0.99 Å (CH 2 ). The U iso (H) values were constrained to 1.5U eq (C) for methyl H atoms and 1.2U eq (C) otherwise.
In Ib and Ic, the Re atom is displaced from the threefold axis. In Ic, reflections with k = 2n + 1 are as strong as the reflections with k = 2n, while for Ib (as also for Ia), reflections with l = 2n + 1 are much weaker than those with l = 2n (Table 5).
Structurally, Ib is closer to Ia than to Ic. Therefore, Ib is also formed by rapid cooling of Ia, although Ic is thermodynamically more stable. The energy barrier for the conversion of Ib to Ic is relatively large, so that rapid conversion occurs only above 200 K.
In the known structures with ReS 4 À , the Re-S bond length is independent of the cation ( Table 6)      the ReS 4 À anion is very close to the tetrahedral value (109.47 ). The Re-S bond length in ReO 3 S À is very similar to that in ReS 4 À . For ReO 3 S À , the following Re-S bond lengths are known: RbReO 3 S with 2.126 (6) Å (Krebs & Kindler, 1969) and Et 4 NReO 3 S with 2.128 (5) and 2.143 (5) Å (Partyka & Holm, 2004).
In this article, we were able to show that the unit cell of Et 4 NReS 4 is larger at room temperature than previously thought (Mü ller et al., 1986(Mü ller et al., , 1987. In this structure, the Et 4 N + cation is disordered, while the ReS 4 À anion is ordered. At 285 K, there is a phase transition to an ordered structure, where the space group changes from P6 3 mc to P2 1 . The omission of the threefold axis and the mirror plane creates a twin with six components. In addition to this low-temperature phase, a further metastable phase was formed when Ia was cooled rapidly to 110-170 K. This phase crystallizes in the space group P6 3 with a nine times bigger unit cell forming an allotwin with Ib. Table 6 Re-S bond lengths (Å ) and S-Re-S angles ( ) for some compounds with the ReS 4 À anion.  SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL2018 (Sheldrick, 2015); molecular graphics: DIAMOND (Brandenburg, 2001); software used to prepare material for publication: SHELXL2018 (Sheldrick, 2015).

Special details
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. Refinement. Refined as a 2-component inversion twin.
Suitable single crystals of Et 4 NReS 4 were attached to a goniometer head. The data collection was performed using an Oxford Diffraction Gemini E Ultra diffractometer with a 2K × 2K EOS CCD camera, a four-circle goniometer with κ geometry, a sealed-tube Mo radiation source, and an Oxford Instruments Cryojet cooling unit. Processing of the raw data, scaling of the diffraction data and the application of an empirical absorption correction were performed with the CrysAlisPro program (CrysAlis PRO, 2016). The structures were solved by direct methods and refined against F 2 (Sheldrick, 2015(Sheldrick, , 2008. The graphics were prepared with the program Diamond (Brandenburg, 2001). Full details of all structural data (CCDC-1971807 to CCDC-1971809) are presented in Section S of the Supporting Information File.

Special details
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. Refinement. Refined as a 2-component inversion twin.
Suitable single crystals of Et 4 NReS 4 were attached to a goniometer head. The data collection was performed using an Oxford Diffraction Gemini E Ultra diffractometer with a 2K × 2K EOS CCD camera, a four-circle goniometer with κ geometry, a sealed-tube Mo radiation source, and an Oxford Instruments Cryojet cooling unit. Processing of the raw data, scaling of the diffraction data and the application of an empirical absorption correction were performed with the CrysAlisPro program (CrysAlis PRO, 2016). The structures were solved by direct methods and refined against F 2 (Sheldrick, 2015(Sheldrick, , 2008. The graphics were prepared with the program Diamond (Brandenburg, 2001). Full details of all structural data (CCDC-1971807 to CCDC-1971809) are presented in Section S of the Supporting Information File.

Special details
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. Refinement. Refined as a 6-component twin. Suitable single crystals of Et 4 NReS 4 were attached to a goniometer head. The data collection was performed using an Oxford Diffraction Gemini E Ultra diffractometer with a 2K × 2K EOS CCD camera, a four-circle goniometer with κ geometry, a sealed-tube Mo radiation source, and an Oxford Instruments Cryojet cooling unit. Processing of the raw data, scaling of the diffraction data and the application of an empirical absorption correction were performed with the CrysAlisPro program (CrysAlis PRO, 2016). The structures were solved by direct methods and refined against F 2 (Sheldrick, 2015(Sheldrick, , 2008. The graphics were prepared with the program Diamond (Brandenburg, 2001). Full details of all structural data (CCDC-1971807 to CCDC-1971809) are presented in Section S of the Supporting Information File.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å 2 )
x y z U iso */U eq Re 0.0222 (