Structural Chemistry of Halide including Thallides A₈Tl₁₁X_1−n (A = K, Rb, Cs; X = Cl, Br; n = 0.1–0.9)

Abstract

A₈Tl₁₁ (A = alkali metal) compounds have been known since the investigations of Corbett et al. in 1995 and are still a matter of current discussions as the compound includes one extra electron referred to the charge of the Tl₁₁⁷⁻ cluster. Attempts to substitute this additional electron by incorporation of a halide atom succeeded in the preparation of single crystals for the lightest triel homologue of the group, Cs₈Ga₁₁Cl, and powder diffraction experiments for the heavier homologues also suggested the formation of analogous compounds. However, X-Ray single crystal studies on A₈Tl₁₁X to prove this substitution and to provide a deeper insight into the influence on the thallide substructure have not yet been performed, probably due to severe absorption combined with air and moisture sensitivity for this class of compounds. Here, we present single crystal X-Ray structure analyses of the new compounds Cs₈Tl₁₁Cl_0.8, Cs₈Tl₁₁Br_0.9, Cs₅Rb₃Tl₁₁Cl_0.5, Cs_5.7K_2.3Tl₁₁Cl_0.6 and K₄Rb₄Tl₁₁Cl_0.1. It is shown that a (partial) incorporation of halide can also be indirectly determined by examination of the Tl-Tl distances, thereby the newly introduced cdd/cd_av ratio allows to evaluate the degree of distortion of Tl₁₁⁷⁻ clusters.

1. Introduction

Naked cluster anions of the main group elements are well-known for group 14 and 15 elements in solid-state [1,2,3,4]. Most of these compounds can be described in terms of the Zintl-Klemm concept [5,6,7] by formally transferring the valence electrons of the electropositive element to the electronegative under formation of salt-like structures, so called polyanionic salts. Homoatomic group 14 or 15 element polyanions are known since Zintl himself in 1930 stated the existence of Pb₉⁴⁻ during potentiometric titrations in liquid ammonia solutions [5]. In contrast, the existence of naked group 13 element clusters is not self-evident due to lower values for the electron affinity of group 13 elements which results in a predominantly metallic character of the analogous compounds [3,8]. The first naked thallium cluster was described in 1967 by Hansen and Smith in the binary solid-state compound Na₂Tl [9], which contains Tl₄ tetrahedra with a calculated formal charge of −8 by assuming complete electron transfer. These tetrahedral assemblies are related to the structures of ATt (A: alkali metal, Tt: group 14 element) [10,11,12] and white phosphorus due to their formal iso-(valence)-electronic character. The largest (empty) thallide cluster is represented by the Tl₁₁⁷⁻ cluster which is present in binary materials A₈Tl₁₁ [13,14] and A₁₅Tl₂₇ [15] (A = K, Rb, Cs). The A₈Tr₁₁ (Tr = group 13 element) structure type was first described in 1991 for the lighter homologue indium in K₈In₁₁ [16], of which the crystal structure proved the presence of a naked, pentacapped trigonal prismatic shaped In₁₁ cluster, which was assigned a charge of −7. Additionally, one extra-electron per formula unit is present, being responsible for the metallic character. The additional electron, referred to the charge of −7 of the cluster anion, is not necessary for the stability of the clusters [17] and can be replaced by halide atoms, which are located on a −3 void (Wyckoff position 6b) at the origin of the unit cell resulting in a diamagnetic character of the compounds. Halide incorporation was proven for the lighter homologue of the group, Cs₈Ga₁₁Cl by X-ray single crystal structure analysis [18]. Powder diffraction experiments suggested the formation of the heavier homologues Rb₈Ga₁₁Cl, Cs₈Ga₁₁X (X = Br, I), Rb₈In₁₁Cl, Cs₈In₁₁Cl, Cs₈Tl₁₁X (X = Cl, Br, I). Recently, continuative studies on halides A₈Tr₁₁ (Tr = Ga, In) have been reported [19]. However, the formation of Rb₈Tl₁₁Cl was termed as doubtful due to the lack of a significant change in the lattice constants compared to the binary phase Rb₈Tl₁₁, which also is a common problem for the remaining halide including thallides of this structure family. Therefore, well-resolved single crystal X-ray diffraction studies should provide a deeper insight into the involvement and the role of halide in A₈Tl₁₁X compounds. Thereby, we concentrated on the heavier alkali metals K, Rb and Cs as for sodium no experimental evidence of Tl₁₁ clusters is reported.

The questions we wanted to answer were: (1) How does the geometry of the thallide cluster change on halide incorporation; (2) Is there a Rb₈Tl₁₁Cl? (3) How do mixed cation sites affect the amount of halide incorporation?

In Section 3 (Results), we report on the first single crystal X-Ray structure determination of halide including thallides, Cs₈Tl₁₁Cl_0.8, Cs₈Tl₁₁Br_0.9, Cs₅Rb₃Tl₁₁Cl_0.5, Cs_5.7K_2.3Tl₁₁Cl0_.6 and K_3.98Rb_4.02Tl₁₁Cl_0.1. Subsequently, (Section 4, Discussions), the crystal structures are investigated according to the questions listed above.

2. Materials and Methods

All compounds have been synthesized via a stoichiometric approach using high temperature solid state techniques. Cesium and rubidium were produced by the reduction of the corresponding alkali metal halide with elemental calcium [20] and distilled twice, potassium was segregated for purification. Thallium lumps have been stored under inert atmosphere and were used without further purification. The starting materials were enclosed in tantalum crucibles (for stoichiometric approaches see Appendix A) which were subsequently placed in quartz glass ampoules and sealed under argon atmosphere. The same temperature program was used for all compounds: Heating to 700 °C with a heating rate of 50 °C/h, holding for 24 h, cooling to room temperature with a cooling rate of 3 °C/h to allow for crystallization.

All compounds are very sensitive towards moisture and oxygen and degeneration of the crystals was observed (gassing) in dried mineral oil within few hours. Suitable single crystals for X-ray structure analysis were isolated in dried mineral oil and mounted on a Rigaku SuperNova (Rigaku Polska Sp. Z o. o. Ul, Wroclaw, Poland) (Mo-source, Eos detector) using MiTeGen loops. Thereby, the transfer needed to be very quick as the crystals started to decompose as soon as the mineral oil film became too thin. Once being placed on the diffractometer in the nitrogen stream at 123 K the crystals remained stable and data collection was possible.

Powder diffraction samples were measured in sealed capillaries (0.3–0.5 mm) on a Powder on a STOE Stadi P diffractometer (STOE, Darmstadt, Germany) (monochromatic Mo-K_α1 radiation λ = 0.70926 Å) equipped with a Dectris Mythen 1 K detector.

3. Results

All compounds crystallize in the K₈In₁₁ structure type (rhombohedral, spacegroup R−3c) and especially for the mixed alkali metal compounds many of the crystals happened to form typical “multicrystals”. Due to the presence of reverse/obverse twinning a R(obv) filter was applied during data reduction [21]. The materials naturally possess very high absorption coefficients (μ > 60 mm⁻¹), therefore small single crystals have been chosen for the X-ray analyses. However, the data sets still suffer from severe absorption effects which could be reduced by carefully applying numerical absorption correction [21]. Thereby, the adjustment of the correct shape played a dominant role.

Table 1. Crystal data and structure refinement details.

Compound	Cs8Tl11Cl0.80	Cs8Tl11Br0.92	Cs5.13Rb2.87Tl11Cl0.49	Cs5.67K2.33Tl11Cl0.60	K3.98Rb4.02Tl11Cl0.1
CSD number *	434541	434540	434539	434538	1856564
Mr [g·mol−1]	3339.71	3385.20	3192.52	3114.02	2751.04
Crystal system	Trigonal	Trigonal	Trigonal	Trigonal	Trigonal
Space group	R-3c	R−3c	R-3c	R-3c	R-3c
a [Å]	10.4691 (4)	10.5608 (3)	10.3791 (5)	10.3291 (9)	10.0948 (4)
b [Å]	10.4691 (4)	10.5608 (3)	10.3791 (5)	10.3291 (9)	10.0948 (4)
c [Å]	53.297 (3)	53.401(2)	52.437 (3)	51.909 (5)	51.0274 (18)
α [°]	90	90	90	90	90
β [°]	90	90	90	90	90
γ [°]	120	120	120	120	120
V [Å3]	5058.8 (5)	5157.9 (4)	4892.0 (5)	4796.3 (9)	4503.3 (4)
Z	6	6	6	6	6
F(000)	8068.0	8180.0	7726.0	7544.0	6703.0
ρcalc [g·cm−3]	6.578	6.539	6.502	6.469	6.087
μ [mm−1]	60.902	60.745	64.052	61.908	65.822
2θ-range for data collection [°]	7.59 to 58.982	7.558 to 69.266	7.694 to 54.202	7.758 to 54.198	7.91 to 69.18
Reflections collected/independent	79177/1473	12097/2374	3174/1194	3394/1176	5040/1934
Data/restraints/parameters	1473/0/36	2374/0/36	1194/0/34	1176/0/34	1934/1/37
Goodness-of-fit on F2	1.244	1.136	1.089	1.148	1.033
Final R indices [I > 2σ(I)]	R1 = 0.0280 wR2 = 0.0619	R1 = 0.0242 wR2 = 0.0528	R1 = 0.0392 wR2 = 0.0928	R1 = 0.0456 wR2 = 0.0996	R1 = 0.0242 wR2 = 0.0461
R indices (all data)	R1 = 0.0309 wR2 = 0.0629	R1 = 0.0280 wR2 = 0.0541	R1 = 0.0466 wR2 = 0.0970	R1 = 0.0566 wR2 = 0.1034	R1 = 0.0292 wR2 = 0.0478
Rint	0.0497	0.0385	0.0446	0.0449	0.0280
Largest diff. peak/hole [e·Å−3]	2.96/−1.38	1.83/−3.38	4.82/−2.29	3.62/−2.21	1.48/−1.67

* Further details of the crystal structure investigation(s) may be obtained from The Cambridge Crystallographic data centre CCDC on quoting the deposition number CSD-xxxxxx or the the deposition number CCDC-xxxxxxx at https://www.ccdc.cam.ac.uk/structures/?

lists the data for the structure determination. For the chloride including compounds two additional, unresolved but several times reproduced residual electron density peaks (≈1.5 Å beside the chlorine atom, ≈2.2 Å beside cesium; along the c-axis) are present, which we attribute to unresolved absorption effects as this direction is along the thinnest direction of the plate like crystals. For the bromine including compound this effect is not as dominant as for the chlorine including ones but still is observed.

With only cesium being present in Cs₈Tl₁₁Cl_0.8 and Cs₈Tl₁₁Br_0.9 we obtained phase pure materials according to the powder diffraction pattern of the bulk material (Figure 1; refined cell contstants at room temperature: Cs₈Tl₁₁Cl_0.8: a = 10.566 (5) Å, c = 53.67 (3) Å, R−3c; Cs₈Tl₁₁Br_0.9: a = 10.613 (3) Å, c = 53.680 (19) Å).

The well-crystallized Cs₈Tl₁₁X crystals and the resulting good quality single crystal diffraction data allowed the splitting of one alkali metal position according to the site occupancy factor (s.o.f.) of the halide atom (see Section 4.3).

For the mixed alkali metal compounds, we always additionally observed less reduced A₁₅Tl₂₇ phases as a side product. This observation became reasonable when we determined the N_E value (number of electrons per thallium atom) which sums up to a value of 8/11 = 0.72 for A₈Tl₁₁, 15/27 = 0.55 for A₁₅Tl₂₇ and 7/11 = 0.63 for A₈Tl₁₁X. The formation of less reduced A₁₅Tl₂₇ were completely comprehensible if the higher reduced A₈Tl₁₁X_x (x << 1) phases would have formed when the halide content was significantly less than 1, because the overall degree of reduction was given by the stoichiometric approach for A₈Tl₁₁X. If less halide was incorporated, this is according to a higher degree of reduction and consequently, a less reduced phase was formed in addition. The remaining halide re-crystallized as (mixed) AX, of which we also could observe single crystals. The crystals for the mixed alkali metal compounds A₈Tl₁₁X_x happened to form multicrystals together with A₁₅Tl₂₇ and for the reported single crystals (except K₄Rb₄Tl₁₁Cl_0.1) the data quality was worse compared to Cs₈Tl₁₁X phases. Therefore, the splitting of the alkali metal position could only be observed for K₄Rb₄Tl₁₁Cl_0.1, for the remaining mixed alkali compounds splitting positions could not be reasonably introduced. In these cases, we only refined the s.o.f. of the halide (see Section 4.3).

4. Discussions

4.1. How Does the Geometry of the Thallide Cluster Change on Halide Incorporation?

All A₈Tl₁₁ and A₈Tl₁₁X_x compounds include Tl₁₁⁷⁻ clusters, which are best described as a very compressed, fivefold-capped trigonal prism (Figure 2). Three symmetry independent thallium atoms are located on three different Wyckoff positions of space group R-3c: Tl1(12c; 3-fold rotational axis), Tl2 (36f; general position) and Tl3 (18e; 2-fold rotational axis) build a cluster consisting of 11 Tl atoms with point group D₃. The deviations from point group D_3h are very small and are represented by a distortion of the height of the trigonal prism built by Tl3-atoms. This distortion is also reflected in the distances of Tl2–Tl3 (d(Tl2–Tl3): = cd) as there are two crystallographic independent distances present (d(Tl2–Tl3) = d(Tl2–Tl3#5); d(Tl3#3–Tl2) = d(Tl3#2–Tl2)). The degree of distortion decreases with increasing similarity of the capping distances (cd).

In

Table 2. Selected distances in [Å] (numbering scheme according to, values taken from [1,15]), tilt angle and cdd/cd_av value for K₈Tl₁₁ and Rb₈Tl₁₁.

Atom 1	Atom 2	K8Tl11	Rb8Tl11
Tl2	Tl3	3.0476 (4)	3.060
Tl2	Tl33	3.1396 (4)	3.157
Tl1	Tl31	3.1304 (4)	3.147
Tl3	Tl33	3.2054 (7)	3.219
Tilt [°]		4.69 (2)	4.90
cdd/cdav [%]		2.97	3.12

and

Table 3. Selected distances in [Å] (numbering scheme according to), tilt angle and cdd/cd_av value for Cs₈Tl₁₁Cl_0.8, Cs₈Tl₁₁Br_0.9, Cs₅Rb₃Tl₁₁Cl_0.5 and Cs_5.7K_2.3Tl₁₁Cl_0.6 and K₄Rb₄Tl₁₁Cl_0.1.

Atom 1	Atom 2	Cs8Tl11Cl0.8	Cs8Tl11Br0.9	Cs5Rb3Tl11Cl0.5	Cs5.7K2.3Tl11Cl0.6	K4Rb4Tl11Cl0.1
Tl2	Tl3	3.0656 (4)	3.0743 (2)	3.0605 (6)	3.0554 (7)	3.0564 (2)
Tl2	Tl33	3.0632 (4)	3.0766 (2)	3.0896 (6)	3.0656 (4)	3.1298 (3)
Tl1	Tl31	3.0894 (4)	3.1006 (2)	3.1049 (7)	3.0884 (8)	3.1274 (3)
Tl3	Tl33	3.2019 (11)	3.2102 (4)	3.2025 (11)	3.1873 (11)	3.2104 (4)
Tilt [°]		0.12 (2)	0.069 (7)	0.94 (2)	0.34 (5)	2.352 (7)
cdd/cdav [%]		0.08	0.07	0.95	0.32	2.38

the distances as well as the distortion angles are listed and the dependence on the amount of halide incorporation is clearly evident. In contrast, the height of the trigonal prism (Tl3–Tl3) as well as the distance of the capping atom Tl2 to the mean plane built by Tl3 atoms [d(Tl2-plane) = 0.5 Å in all compounds] do not significantly change. Based on these observations we introduced a cdd/cd_av ratio (cdd: capping distance difference; cd_av: average capping distance; (Equation (1)) which allowed for a quick estimation of the degree of distortion. The dependence of the cdd/cd_av ratio on the amount of halide is conspicuous and therefore allows for the evaluation of the involvement of halide atoms by solely analyzing the distances between heavy atom positions.

$$\frac{\mathrm{cdd}}{{\mathrm{cd}}_{\mathrm{av}}}=\frac{|{\mathrm{cd}}_2-{\mathrm{cd}}_1|}{\left(\frac{{\mathrm{cd}}_2+{\mathrm{cd}}_1}{2}\right)};{\mathrm{cd}}_1\le {\mathrm{cd}}_2$$

(1)

4.2. Is There a Rb₈Tl₁₁Cl?

Despite numerous efforts we did not succeed in producing crystals of Rb₈Tl₁₁Cl of sufficient quality for a reliable determination of halide incorporation directly from the electron density maps. The incorporation of halide cannot be completely ruled out at this point as there is some residual electron density at Wyckoff position 6b according to the position of the halide atom in the previously discussed compounds. The s.o.f. for a chlorine atom at this position refined to a value of 0.08. However, the cdd/cd_av ratio of 2.4% compared to 3.0% (K₈Tl₁₁) and 3.1% (Rb₈Tl₁₁) and a tilt angle of 2.4° (K₈Tl₁₁: 4.7°, Rb₈Tl₁₁: 4.9°) are very similar to the values found in K₄Rb₄Tl₁₁Cl_0.1 and suggest a minimal involvement of chloride. Therefore, we assume that Rb₈Tl₁₁Cl does exist, but the amount of incorporated chlorine is less than 10%, which also is in line with the stated observations of Corbett et al. from powder diffraction experiments.

4.3. How Do Mixed Cation Sites Affect the Amount of Halide Incorporation?

It needs to be emphasized that for the preparation of all compounds the same stoichiometric approach was employed and the dependence of the amount of halide incorporation on the cesium content is conspicuous. Therefore, the cation positions needed to be examined more in detail. There are two different cation positions in the asymmetric unit corresponding to Wyckoff position 36f for A1 and Wyckoff position 12c for A2. For Cs₈Tl₁₁X the A2 position showed the previously mentioned splitting. By taking this splitting as well as free s.o.f. values for the halide (later fixed at the s.o.f. value for Cs2A) into account, a significantly improved model could be refined (Figure 3).

For Cs₅Rb₃Tl₁₁Cl_0.5 and Cs_5.7K_2.3Tl₁₁Cl_0.6 the position of A1 is mixed occupied by both alkali metals and the s.o.f. values for cesium on the mixed position are very similar to the s.o.f. values of the halide position. The position of A2 is only occupied by the heavier alkali metal cesium, which is in accordance with the observations of Corbett et al. for the binary A₈Tl₁₁ phases [14]. In summary, this would mean a favored halide incorporation when cesium is present on both crystallographically independent alkali metal positions. To prove this assumption, we investigated the system K-Rb-Tl in a stoichiometric approach to produce K₄Rb₄Tl₁₁Cl which resulted in crystals of K₄Rb₄Tl₁₁Cl_0.1 (besides the side products (K,Rb)₁₅Tl₂₇ and (K,Rb)Cl). Careful investigation of the data of K₄Rb₄Tl₁₁Cl_0.1 showed the splitting of the A2 position, whereby convergence of the refinement was achieved when A1 and one splitting position are mixed occupied by Rb and K. The second splitting position Rb2A is exclusively occupied by Rb. The overall s.o.f. for A2 was fixed at unity using a SUMP restraint. At the max. peak of the residual electron density a chlorine atom was placed of which the s.o.f. refined at 0.103 (13) and was fixed according to the s.o.f. of Rb2A (Figure 4).

The resulting coordination sphere of the halide is best described as distorted cubic, where the longer distances are along the room diagonal of the cubic arrangement from the halide to the position of A2. This distance shortens significantly for X-A2 by introducing split positions (same s.o.f. as halide), resulting in a less distorted cubic arrangement (Figure 5). This cubic arrangement greatly resembles the coordination of the halide in the CsCl structure type (d(Cs-Cl) = 3.573 Å; d(Cs-Br) = 3.718 Å). The distances within the the distorted cubic arrangements as well as the s.o.f. values for the halide/split position in Cs₈Tl₁₁X (X = Cl or Br) and K₄Rb₄Tl₁₁Cl_0.1 are listed in

Table 4. Distances in [Å] within the distorted cubic arrangement around the halide/void and s.o.f. values for the halide/Cs2A (split position) in Cs₈Tl₁₁X (X = Cl or Br) and K₄Rb₄Tl₁₁Cl_0.1.

Position 1–Position 2	Cs8Tl11Br0.9	Cs8Tl11Cl0.8	Position 1–Position 2	K4Rb4Tl11Cl0.1
Cs2A-X1	3.990 (2)	3.991 (9)	Rb2A-X1	3.80 (2)
Cs2B-void	4.388	4.354	K2B/Rb2B-void	4.096 (3)
Cs1-X1/void	3.6705 (4)	3.5876 (7)	K1/Rb1-X1/void	3.5994 (9)
s.o.f. (X1/Cs2A)	0.924 (6)	0.76 (2)	s.o.f. (X1/Rb2A)	0.103 (13)

and

Table 5. Distances in [Å] within the cubic arrangement around the halide/void in Cs₅Rb₃Tl₁₁Cl_0.5 and Cs_5.7K_2.3Tl₁₁Cl_0.6. The s.o.f. values for Cs at the mixed occupied A1 site resemble the s.o.f. values for the halide (numbering scheme according to Figure 5).

Position 1–Position 2	Cs5Rb3Tl11Cl0.5	Cs5.7K2.3Tl11Cl0.6
A2-X1/void	4.099 (2)	4.002
A1-X1/void	3.6160 (13)	3.5492 (2)
s.o.f. (A1 = Cs)	0.521 (12)	0.612 (9)
s.o.f. (X1)	0.50 (4)	0.60 (4)

lists distances as well as s.o.f. values of the mixed occupied sites within Cs₅Rb₃Tl₁₁Cl_0.5 and Cs_5.7K_2.3Tl₁₁Cl_0.6.

The same stoichiometric approach to produce the hitherto presented compounds also was employed by using solely potassium. Here, we only observed well crystallized halide-free K₈Tl₁₁ and K₁₅Tl₂₇ phases. The previously stated stability of the halide including A₈Tr₁₁X phases might not exclusively be caused by the effect of charge balance due to halide incorporation but by the stabilization of a preferably heavier halide atom in a distorted cubic arrangement including cesium preferentially (Figure 6). If less (or no) cesium is involved, then less (or even no) halide will be incorporated. If rubidium is involved as the heaviest alkali metal, then the amount of incorporated halide seems to be limited to approximately 10%. In return, the Tl₁₁ clusters themselves seem to tolerate any charge between 7⁻ and 8⁻.