Ammonium bis­(salicyl­aldehyde thio­semi­car­ba­zonato)ferrate(III), a supra­molecular material containing low-spin Fe^III

The Fe^IIIS₂N₂O₂ chromophore of ammonium bis­[salicyl­aldehyde thio­semi­car­ba­zon­ato(2−)]iron(III) contains two O,N,S-donating salicyl­aldehyde thio­semi­car­ba­zon­ate(2−) ligands in perpendicular planes, with the O and S atoms in cis and the N atoms in trans positions. The Fe^III ion is in the low-spin state at 100 K. Systematic twinning by metric pseudomerohedry is explained by application of the order–disorder (OD) theory.

Abstract

The synthesis and crystal structure (100 K) of the title com­pound, ammonium bis­[salicyl­aldehyde thio­semi­car­ba­zon­ato(2−)-κ³ O,N ¹,S]iron(III), NH₄[Fe(C₈H₇N₃OS)₂], is reported. The asymmetric unit consists of an octa­hedral [Fe^III(thsa)₂]⁻ fragment, where thsa²⁻ is salicyl­aldehyde thio­semi­car­ba­zon­ate(2−), and an NH₄ ⁺ cation. Each thsa²⁻ ligand binds via the thiol­ate S, the imine N and the phenolate O donor atoms, resulting in an Fe^IIIS₂N₂O₂ chromophore. The ligands are orientated in two perpendicular planes, with the O and S atoms in cis and the N atoms in trans positions. The Fe^III ion is in the low-spin state at 100 K. The crystal structure belongs to a category I order–disorder (OD) family. It is a polytype of a maximum degree of order (MDO). Fragments of the second MDO polytype lead to systematic twinning by pseudomerohedry.

Introduction  

The study of the coordination chemistry of thio­semi­car­ba­zones is an attractive research area. Thio­semicarbazones display a wide range of pharmacological uses based, for example, on their anti­neoplastic, anti­bacterial, anti­viral and anti­fungal activities (Beraldo & Gambino, 2004 ▸; Yemeli Tido et al., 2010 ▸). This pharmacological action is often related to coordination of the thio­semicarbazone to metal ions (Farrell, 2002 ▸). On the other hand, the magnetic properties of iron(III) com­pounds of thio­carbazone derivatives have attracted attention, particularly as switching behaviour was displayed for iron(III) bound to particular salicyl­aldehyde thio­semicarbazone derivatives (van Koningsbruggen et al., 2004 ▸; Phonsri et al., 2017 ▸; Powell et al., 2014 ▸, 2015 ▸; Yemeli Tido, 2010 ▸; Zelentsov et al., 1973 ▸, Ryabova et al., 1978 ▸, 1981a ▸,b ▸, 1982 ▸; Floquet et al., 2003 ▸, 2006 ▸, 2009 ▸; Li et al., 2013 ▸).

This type of magnetic inter­conversion between the low-spin (S = ) and high-spin (S = ) state in Fe^III (3d ⁵) systems has now been found to be triggered by a change in temperature or pressure, or by light irradiation (Hayami et al., 2000 ▸, 2009 ▸; van Koningsbruggen et al., 2004 ▸) and may be used in a functional way in research and technology (Létard et al., 2004 ▸; Gütlich et al., 2004 ▸; Gütlich & Goodwin 2004 ▸; van Koningsbruggen et al., 2004 ▸; Nihei et al., 2007 ▸; Halcrow, 2013 ▸; Harding et al., 2016 ▸).

In recent years, particular inter­est has focused on Fe^III com­plexes of substituted derivatives of R-salicyl­aldehyde 4R′-thio­semicarbazone (Powell et al., 2014 ▸, 2015 ▸; Yemeli Tido, 2010 ▸; Floquet et al., 2003 ▸, 2006 ▸, 2009 ▸; Li et al., 2013 ▸) for generating Fe^III spin crossover. In solution, free R-salicyl­aldehyde 4R′-thio­semicarbazone (H₂ L) exists in two tautomeric forms, i.e. the thione and thiol forms, as illustrated in Scheme 1. The chemistry of the Fe^III com­pounds is rather com­plicated as it is possible for the tridentate R-salicyl­alde­hyde 4R′-thio­semicarbazone ligand (H₂ L) to exist in tautomeric forms; moreover, the ligand may also be present in its neutral, anionic or dianionic form. However, the formation of a particular type of Fe^III com­plex unit, i.e. neutral, monocationic or monoanionic, can be achieved by tuning the degree of deprotonation of the ligand through pH variation of the reaction solution during the synthesis (Powell et al., 2014 ▸, 2015 ▸; Powell, 2016 ▸; Yemeli Tido, 2010 ▸; Floquet et al., 2009 ▸). We have been particularly skilled in preparing anionic Fe^III com­plexes of the general formula (cation⁺)[Fe(L ²⁻)₂]·x(solvent), for which it became evident that the electronic state of the Fe^III ion is dependent on the nature of the counter-ion, the nature and degree of solvation and the nature of the R,R′-substituted ligands (Powell et al., 2014 ▸, 2015 ▸; Powell, 2016 ▸; Yemeli Tido, 2010 ▸).

We report here a novel Fe^III com­pound, ammonium bis­[salicyl­aldehyde thio­semi­car­ba­zon­ato(2−)-κ³ O,N ¹,S]iron(III), (I) (see Scheme 2), containing two dianionic tridentate ligands, i.e. salicyl­aldehyde thio­semi­car­ba­zon­ate(2−), abbreviated as thsa²⁻, whose structure was determined at 100 K. Ryabova et al. (1981a ▸) reported the crystallographic data of the related com­pound Cs[Fe(thsa)₂] at 103 and 298 K, which contains Fe^III in the high-spin electronic state (S = ). The main difference between NH₄[Fe(thsa)₂] and Cs[Fe(thsa)₂] is the associated outer-sphere cation. This article describes that the variation in the cation leads to a modification of the structure of the Fe^III com­pound, also changing the crystal packing, and being responsible for the Fe^III in the present NH₄[Fe(thsa)₂] com­pound exhibiting the low-spin electronic state (S = ).

Compound (I) systematically crystallizes as twins. The twinning will be inter­preted in the light of order–disorder (OD) theory (Dornberger-Schiff & Grell-Niemann, 1961 ▸). The OD theory was created in the 1950s to explain the common occurrence of polytypism and stacking faults. It has since been developed into a com­prehensive theory of local/partial symmetry. According to OD theory, if a structure is com­posed of layers and the layers are related by partial symmetry that is not valid for the whole structure, then the stacking becomes ambiguous. This means that the layers can be arranged in different ways, which are nevertheless all locally equivalent. Owing to the short range of inter­atomic inter­actions, these different stacking arrangements are also energetically equivalent. Consequently, OD structures often feature stacking faults. In OD twins, such as the title com­pound, the stacking faults lead to domains with different spacial orientations and are sporadic, i.e. the resulting domains are macroscopic and do not diffract coherently.

Experimental  

Spectroscopic measurements  

Room-temperature IR spectra within the range 4000–400 cm⁻¹ were recorded on a PerkinElmer FT–IR spectrometer Spectrum RXI using KBr pellets. Variable-temperature FT–IR spectra were measured with the attenuated total reflectance (ATR) technique using a PerkinElmer spectrum 400 with a Harrick diamond ATR equipped with a thermostatable temperature-control device. ¹H and ¹³C{¹H} NMR spectra were recorded on a Bruker 200 spectrometer with a broadband probe head. All NMR chemical shifts are reported in ppm; ¹H and ¹³C shifts are established on the basis of the residual solvent resonance.

Synthesis and crystallization  

The synthesis of H₂thsa was carried out according to the general procedure described by Yemeli Tido (2010 ▸). Salicyl­aldehyde (49 mmol, 5.98 g) was dissolved in ethanol (80 ml) with constant stirring, and was added to a solution of thio­semicarbazide (49 mmol, 3.68 g) in ethanol (40 ml). The corresponding mixture was refluxed for 120 min. The resulting solution was cooled to room temperature and the solid isolated by filtration, washed with ether and dried in a vacuum for 2 d (yield: 7.75 g, 39.7 mmol, 81.0%; m.p. 491 K). H₂thsa is soluble in methanol, acetone and dimethyl sulfoxide (DMSO). ¹H NMR (200 MHz, DMSO-d ₆): δ (ppm) 11.39 (s, 1H, NH), 9.84 (s, 1H, OH), 8.40 (s, 1H, CH), 8.10 (s, 1H, o-ArCH), 7.87 (d, J = 8.8 Hz, 2H, NH₂), 7.19 (t, J = 7.7 Hz, 1H, p-ArCH), 6.92–6.71 (m, 2H, m-ArCH). ¹³C NMR (50 MHz, DMSO-d ₆): δ (ppm) 177.76 (C=S), 156.52 (C—OH), 140.16 (C=N), 131.31 (ArCH), 126.99 (ArCH), 120.33 (ArCH), 119.48 (ArCH), 116.22 (ArCH). IR (cm⁻¹, KBr): 3445 (νOH), 3175 (νNH), 3319 (νNH₂), 1616 (νC=N), 1540–1603 (νC=C), 1266 (νC—N), 1111 (νC=S).

For the synthesis of NH₄[Fe(thsa)₂], (I), Fe(p-CH₃C₆H₄SO₃)₃·6H₂O (1.0 mmol, 0.68 g) was dissolved in methanol (5 ml). H₂thsa (1.0 mmol, 0.20 g) was dissolved in methanol (25 ml) with the addition of NH₄OH (20 ml, 35 wt% in water). To this mixture, the methano­lic solution of the Fe^III salt was added dropwise with constant stirring. The resulting dark-green solution was stirred and heated to 353 K for approximately 10 min. The solution was then allowed to stand at room temperature until crystals had formed. The dark-green microcrystals were isolated by filtration and dried (yield: 0.10 g, 0.22 mmol, 21.7%). Elemental analysis found/calculated (%) for C₁₆H₁₈FeN₇O₂S₂: C, 41.47/41.47, H 3.90/3.94, N 20.99/21.30, O 8.05/6.95, S 13.87/13.93. IR (cm⁻¹, KBr): 3472, 3240 (νNH), 3016 (νNH₂), 1595 (νC=N), 1546–1509 (νC=C ring), 1278 (νC—O), 1203 (νN—N), 1027 (νC—N), 756 (νC—S).

Refinement  

Crystal data, data collection and structure refinement details are summarized in Table 1 ▸. The crystal was modelled as twinned by reflection at (100). The positions of the H atoms on the amine N atoms were located in difference Fourier maps and were refined with restrained N—H distances of 0.87 (2) Å. The NH₄ ⁺ cation is disordered around a pseudo-twofold axis. The ammonium N atom was refined as disordered about two positions (N7 and N7′). The sum of the occupancy parameters was constrained to 1. The atomic displacement parameters (ADPs) were constrained to the same value, resulting in a significant decrease of the estimated standard uncertainty on the occupancy parameters. Even though residual electron density in the difference Fourier maps could be attributed to the H atoms of the disordered ammonium positions, a reliable refinement was not possible. The ammonium H atoms were therefore ultimately omitted from the refinement. Other H atoms were included in the refinement in calculated positions and allowed to ride on their parent atoms.

Table 1. Experimental details.

Crystal data
Chemical formula	(NH4)[Fe(C8H7N3OS)2]
M r	460.34
Crystal system, space group	Monoclinic, P21/n
Temperature (K)	100
a, b, c (Å)	8.4393 (8), 18.2444 (17), 11.7635 (11)
β (°)	90.052 (4)
V (Å3)	1811.2 (3)
Z	4
Radiation type	Mo Kα
μ (mm−1)	1.09
Crystal size (mm)	0.60 × 0.36 × 0.18
Data collection
Diffractometer	Bruker Kappa APEXII CCD
Absorption correction	Multi-scan (SADABS; Bruker, 2012 ▸)
T min, T max	0.601, 0.746
No. of measured, independent and observed [I > 2σ(I)] reflections	62618, 5355, 4839
R int	0.041
(sin θ/λ)max (Å−1)	0.708
Refinement
R[F 2 > 2σ(F 2)], wR(F 2), S	0.042, 0.110, 1.10
No. of reflections	5355
No. of parameters	274
No. of restraints	4
H-atom treatment	H atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å−3)	0.93, −0.74

Computer programs: APEX2 (Bruker, 2012 ▸), SAINT-Plus (Bruker, 2012 ▸), SUPERFLIP (Palatinus & Chapuis, 2007 ▸), SHELXL2018 (Sheldrick, 2015 ▸) and ORTEP-3 (Farrugia, 2012 ▸).

Results and discussion  

Crystal structure  

The structure of NH₄[Fe(thsa)₂], (I) (Fig. 1 ▸), was determined at 100 K and was found to crystallize in the monoclinic space group P2₁/n. The asymmetric unit consists of one for­mula unit, i.e. NH₄[Fe(thsa)₂], with no atom on a special position. The Fe^III cation is coordinated by two dianionic O,N,S-tridentate chelating thsa²⁻ ligands, displaying a dis­torted octa­hedral Fe^IIIO₂N₂S₂ geometry. Selected geometric parameters are listed in Table 2 ▸. The twofold deprotonated ligands are coordinated to the Fe^III atom via the phenolate O, thiol­ate S and imine N atoms. These donor–Fe^III bonds are located in two perpendicular planes, with the O and S atoms in cis positions, whereby the S1—Fe—S2 and O1—Fe—O2 angles are 92.07 (3) and 88.53 (12)°, respectively. In addition, the N atoms are situated in trans positions, which is evidenced by the N1—Fe—N4 bond angle of 176.71 (11)°. The FeO₂N₂S₂ coordination core is distorted; the Fe–donor atom distances fall within the range expected for Fe^III in the low-spin state (van Koningsbruggen et al., 2004 ▸).

Figure 1.

The mol­ecular structure and atom-numbering scheme for NH₄[Fe(thsa)₂], (I). The N atom of the NH₄ ⁺ cation has been omitted for clarity. Displacement ellipsoids are drawn at the 50% probability level.

Table 2. Selected geometric parameters (Å, °).

Fe1—N1	1.937 (3)	S1—C8	1.745 (3)
Fe1—O1	1.941 (3)	S2—C16	1.747 (3)
Fe1—N4	1.944 (3)	N1—C7	1.295 (4)
Fe1—O2	1.952 (3)	N1—N2	1.398 (4)
Fe1—S1	2.2369 (10)	N4—C15	1.293 (4)
Fe1—S2	2.2377 (10)	N4—N5	1.406 (4)
N1—Fe1—O1	93.08 (11)	C16—S2—Fe1	95.57 (12)
N1—Fe1—N4	176.71 (11)	C2—O1—Fe1	126.5 (2)
O1—Fe1—N4	88.73 (11)	C10—O2—Fe1	126.4 (2)
N1—Fe1—O2	88.97 (11)	C7—N1—Fe1	125.7 (2)
O1—Fe1—O2	88.53 (12)	C8—N2—N1	113.4 (3)
N4—Fe1—O2	93.83 (11)	C15—N4—Fe1	125.0 (2)
N1—Fe1—S1	86.44 (9)	C16—N5—N4	113.7 (3)
O1—Fe1—S1	177.74 (10)	C2—C1—C7	122.4 (3)
N4—Fe1—S1	91.85 (9)	O1—C2—C1	124.5 (3)
O2—Fe1—S1	89.26 (10)	N1—C7—C1	126.9 (3)
N1—Fe1—S2	91.60 (9)	N2—C8—S1	124.7 (2)
O1—Fe1—S2	90.15 (9)	C10—C9—C15	124.2 (3)
N4—Fe1—S2	85.65 (9)	O2—C10—C9	123.6 (3)
O2—Fe1—S2	178.59 (10)	N4—C15—C9	126.4 (3)
S1—Fe1—S2	92.07 (3)	N5—C16—S2	124.0 (3)
C8—S1—Fe1	94.63 (11)

The incorporation of a monovalent NH₄ ⁺ cation could be corroborated by variable-temperature FT–IR spectroscopy, which revealed the sharpening of the N—H stretching vibrational mode of the NH₄ ⁺ cation at 3240 cm⁻¹ upon cooling from ambient temperature to 173 K, which is in line with the freezing of the rotation of the NH₄ ⁺ cation in the cavity.

The presence of the trivalent iron cation is supported by the coordination of two doubly deprotonated ligands to the Fe^III ion. In addition, the presence of both dianionic ligands is confirmed by the C—S, C—N and N—N bond lengths (Table 2 ▸) obtained for NH₄[Fe(thsa)₂], which show characteristics of a bond order between single and double bonds. Ryabova et al. (1981a ▸) reported the structure of the related high-spin com­pound Cs[Fe(thsa)₂] at 103 and 298 K, which crystallizes in the space group Pna2₁ with an asymmetric unit consisting of a Cs⁺ cation and an [Fe(thsa)₂]⁻ anionic unit. The C—S, C—N and N—N bond lengths [at 103 K: C—S = 1.749 (9) and 1.761 (9) Å; C—N = 1.314 (10) and 1.303 (11) Å; N—N = 1.371 (11) and 1.380 (11) Å; at 298 K: C—S = 1.743 (14) and 1.775 (17) Å; C—N = 1.281 (19) and 1.281 (19) Å; N—N = 1.393 (18) and 1.412 (18) Å] reported by Ryabova et al. (1981a ▸) for Cs[Fe(thsa)₂], correspond to the bond lengths for NH₄[Fe(thsa)₂], (I), at 100 K.

The hydrogen-bonding inter­actions of NH₄[Fe(thsa)₂] are listed in Table 3 ▸ and are displayed in Fig. 2 ▸. The terminal N atoms of the tridentate ligands (N3 and N6), form N6—HN62⋯O2ⁱ and N3—HN32⋯O1ⁱⁱ contacts with the phe­nol­ate donor atoms O1 and O2, respectively. In this manner, successive Fe^III entities are linked in the c direction. The NH₄ ⁺ cations are distributed in between the layers of the Fe^III entities, with alternate separations of the N atoms of the NH₄ ⁺ cation of 3.915 (7) [at (x + 1, y, z), denoted iii] and 4.547 (7) Å [at (x + , −y + , z + ), denoted iv] in the a direction. The Fe^III⋯Fe^III separations in the present com­pound are 8.4393 (8) Å for Fe^III⋯Fe^IIIiii and 9.7134 (13) Å for Fe^III⋯Fe^IIIv [symmetry code: (v) −x, −y + 1, −z + 1]. The Fe^III units in NH₄[Fe(thsa)₂] are linked by hydrogen-bonding inter­actions between the corresponding phenolate O and amino N atoms of the Fe^III units.

Table 3. Hydrogen-bond geometry (Å, °).

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
N3—HN31⋯O1i	0.87 (2)	2.03 (3)	2.879 (4)	164 (6)
N6—HN62⋯O2ii	0.88 (2)	1.96 (2)	2.834 (4)	178 (5)

Symmetry codes: (i) ; (ii) .

Figure 2.

A projection showing the unit cell of NH₄[Fe(thsa)₂], (I). The N atom of the NH₄ ⁺ cation has been omitted for clarity. Displacement ellipsoids are drawn at the 50% probability level. Dashed lines indicate hydrogen bonds. [Symmetry codes: (i) x − , −y + , z − ; (ii) x − , −y + , z + .]

The embedding of the NH₄ ⁺ cation is, therefore, essentially different from that of the Cs⁺ cation in Cs[Fe(thsa)₂] at 103 and 298 K, where the nearest-neighbour coordination sphere of the Cs⁺ cation is constituted by O, N and C atoms, which form a seven-pointed polyhedron with Cs–(ligand donor atom) separations between 3.06 and 3.82 Å (Ryabova et al., 1981a ▸). This feature shows some similarity with the Cs⁺ cation in Cs[Fe(5-Br-thsa)₂] (Powell et al., 2015 ▸) that is at the centre of an irregular seven-donor-atom polyhedron, the donor atoms of which originate from symmetry-related equivalents of both symmetry-independent 5-bromo­salicyl­aldehyde thio­semi­car­ba­zon­ate(2−) (5-Br-thsa) ligands. Several donor atoms coordinated to the Fe^III atom of Cs[Fe(5-Br-thsa)₂] form inter­actions with the Cs⁺ cation in the second coordination sphere; this is likely to modulate the electron density of the Fe–(donor atom) bonds and hence influence the electronic state of the Fe^III cation. The latter is also prone to be affected by the assembly of Fe^III units in the unit cell. The presence of the Br substituent on the salicyl­aldehyde group of the ligand in Cs[Fe(5-Br-thsa)₂] is a factor in determining the crystal packing, as the Br substituent of one Cs[Fe(5-Br-thsa)₂] unit provides a hydrogen-bonding inter­action with an amino group of a neighbouring Fe^III unit, creating ring systems.

Clearly, the variation in cation, ligand substituents and crystal packing is related to the spin state of Fe^III being high-spin in Cs[Fe(thsa)₂] at 103 and 298 K (Ryabova et al., 1981a ▸), low-spin in Cs[Fe(5-Br-thsa)₂] at 293 K (Powell et al., 2015 ▸) and low-spin in the present NH₄[Fe(thsa)₂] at 100 K. Variable-temperature magnetic susceptibility measurements (10–300 K) confirm that the Fe^III ion in NH₄[Fe(thsa)₂] remains in the low-spin state over this temperature range (Powell, 2016 ▸). In addition, within this family of cation(+) bis­[R-salicyl­aldehyde 4R′-thio­semi­car­ba­zon­ato(2−)]ferrate(III) salts, the presence of particular solvent mol­ecules may further affect the crystal packing, with the associated inter­molecular effects influencing the electronic structure of Fe^III, e.g. leading to a low-spin state of Fe^III in Cs[Fe(L)₂]·CH₃OH [L = 3-eth­oxy­salicyl­aldehyde 4-methyl­thio­semi­car­ba­zon­ate(2−)] at 100 K (Powell et al., 2014 ▸). Our further studies of members of this Fe^III family may shed more light on how the spin state of Fe^III may be tuned in these systems.

Systematic twinning and OD theory  

Even though NH₄[Fe(thsa)₂] crystallizes in the monoclinic space group P2₁/n, the lattice is metrically virtually ortho­rhom­bic primitive [oP, β = 90.052 (4)°]. The crystals are systematically twinned by the additional symmetry of the lattice with respect to the 2/m point symmetry of the crystal. Thus, the twin law com­prises the operations {2_[100], m _[100], 2_[001], m _[001]} and the twin point group (Nespolo, 2004 ▸) is 2′/m′2/m2′/m′. Since the reflections of both domains overlap nearly perfectly (twin index 1, twin obliquity ∼0), the twinning can be classified as being by metric pseudomerohedry (Nespolo & Ferraris, 2000 ▸).

A higher point symmetry of the lattice com­pared to the point symmetry of the crystal is often associated with twinning. However, it is not a sufficient precondition for its existence. In fact, many polar structures do not form twins by inversion despite inversion being an intrinsic symmetry of any lattice. One common and often overlooked cause of twinning is partial symmetry, which may lead to a twin inter­face that is locally equivalent to the twin individuals. The order–disorder (OD) theory (Dornberger-Schiff & Grell-Niemann, 1961 ▸) was introduced in the 1950s to deal precisely with these kinds of structures.

In the light of OD theory, the crystal structure of NH₄[Fe(thsa)₂] can be decom­posed into OD layers A_n (n being a sequential number) parallel to (010), which, in this case, also correspond to layers in the crystallochemical sense (Fig. 3 ▸). The crucial point of an OD structure is that partial symmetry operations relate individual layers, yet need not be valid for the whole structure. In the case of NH₄[Fe(thsa)₂], the A_n layers possess (idealized) P2(n)a symmetry (Fig. 4 ▸). In this layer-group notation, which is commonly used in the OD literature, the parentheses indicate the direction missing translational symmetry. The [Fe(thsa)₂]⁻ ions are located on the twofold axes of the A_n layers, whereas the ammonium ions are disordered about these axes.

Figure 3.

The crystal structure of NH₄[Fe(thsa)₂], viewed down [100]. The names of the OD layers are indicated to the right and a dotted line indicates the inter­face between the OD layers, which in this case is not planar.

Figure 4.

A layer in the crystal structure of NH₄[Fe(thsa)₂] projected on the layer plane (010). Symmetry elements are represented by the usual graphical symbols. The indicated unit cell corresponds to the standard origin choice of the P2(n)a layer group (on 2_[100]), not of the overall crystal structure.

The set of partial symmetry operations of any possible stacking of NH₄[Fe(thsa)₂] is described by the OD groupoid family symbol (Dornberger-Schiff & Grell-Niemann, 1961 ▸).

P 2 (n) a

n _2,r 2₂ 2_r–1

OD groupoid families are the analogue of space group types in classical crystallography. They abstract from metric parameters and additionally of the particular stacking. The first line of the symbol indicates the layer symmetry, the second line one set of operations relating adjacent layers. Since the intrinsic translations are not limited to those found in space groups, a generalization of the Hermann-Mauguin notation is used. For example, n _2,r represents a glide reflection with the intrinsic translation b/2 + r c/2, whereby r is one of the metric parameters the OD groupoid family abstracts from.

Owing to the partial symmetry, layers can be arranged in different ways while keeping pairs of adjacent layers geometrically equivalent. These stacking possibilities can be enumerated using the NFZ relationship (Ďurovič, 1997 ▸), which reads as Z = N/F = [G_n:G_n∩G_{n +1}]. G_n = P1(1)a is the group of operations of the A_n layer that do not invert A_n with respect to the stacking direction. Since the a-glide planes of adjacent layers do not overlap, G_n∩G_{n +1} = P1(1)1. The possible layer arrangements are determined by coset decom­position of the latter in the former. In other words, given the A_n layer, the adjacent A_{n +1} layer can be placed in Z = [P1(1)a:P1(1)1] = 2 ways, which are related by the a-glide reflection of the A_n layer.

Of the infinity of the thus obtained locally equivalent polytypes, a finite number is especially simple in the sense that they cannot be decom­posed into fragments of even simpler polytypes. In these polytypes, which are said to be of a maximum degree of order (MDO), not only pairs but also triples, quadruples and generally n-tuples of adjacent layers are equivalent (for a more rigorous definition, see Dornberger-Schiff, 1982 ▸). Polytypes of the MDO type play a special role in OD theory, because all other polytypes can be decom­posed into fragments of MDO polytypes. Moreover, experience shows that ordered bulk polytypes are in most cases of the MDO type. The OD family of NH₄[Fe(thsa)₂] contains two MDO polytypes:

MDO₁: P2/b11, b = 2b ₀ + r c

MDO₂: P2₁/n, b = 2b ₀

where b ₀ is the vector perpendicular to the layer lattices with the length of one layer width. Both MDO polytypes are shown schematically in Fig. 5 ▸. The twin individuals of NH₄[Fe(thsa)₂] correspond to the MDO₂ polytype. A fragment of the MDO₁ polytype is located at the twin inter­face.

Figure 5.

Schematic representation of the (top) MDO₁ and (bottom) MDO₂ polytypes of NH₄[Fe(thsa)₂]. [Fe(thsa)₂]⁻ ions are represented by pairs of triangles which are blue on one side and red on the other side. Darker colours indicate a translation by a/2. The geometrical elements of partial sym­metry operations of layers and those relating adjacent layers are represented by the usual graphical symbols for symmetry elements. Screw axes and glide planes with nonstandard intrinsic translations are represented using the symbols for the 2₁ and n symmetry elements. Symbols of operations that are valid for the whole polytype are shown in red.

Thus, the OD theory plausibly explains the formation of the observed twins, as the twin inter­face is geometrically and, if inter­actions over one layer width are ignored, also energetically equivalent to the twin individuals. Moreover, it explains the pseudo-oP metrics of the lattice. Such a metric pseudo-symmetry has often been considered as ‘accidental’. However, here it is clearly very much intrinsic to the structure family.

Finally, it should be noted that an OD description is usually based on a certain degree of idealization. Ordered polytypes are desymmetrized with respect to the ideal description (Ďurovič, 1979 ▸). Indeed, in the actual MDO₂ polytypes of NH₄[Fe(thsa)₂], the symmetry of the A_n layers is reduced by an index of 2 from P2(n)a to P1(n)1. Accordingly, the site symmetry of the [Fe(thsa)₂]⁻ ion is reduced from 2 to 1. Moreover, the unit-cell parameters deviate slightly from ortho­rhom­bic metrics [β = 90.052 (4)°, according to single-crystal diffraction]. Finally, the desymmetrization is also observed by a splitting of the single disordered ammonium position into two independent positions, which are now not forcibly disordered in a 1:1 manner. Indeed, the ratio of the occupancies of both positions refines to 52.7 (9):47.3 (9). However, collectively the deviations from the idealized partial symmetry are minute and the OD description can be considered as correct.

Supplementary Material

CCDC reference: 2003812

Funding Statement

This work was funded by Austrian Science Fund grant P 31076.