Structural Chemistry of Halide including Thallides A 8 Tl 11 X 1 − n ( A = K , Rb , Cs ; X = Cl , Br ; n = 0 . 1 – 0 . 9 )

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 Tl11 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 Cs8Tl11Cl0.8, Cs8Tl11Br0.9, Cs5Rb3Tl11Cl0.5, Cs5.7K2.3Tl11Cl0.6 and K4Rb4Tl11Cl0.1. 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/cdav ratio allows to evaluate the degree of distortion of Tl11 clusters.


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 Pb 9 4− 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 Na 2 Tl [9], which contains Tl 4 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 Tl 11 7− cluster which is present in binary materials A 8 Tl 11 [13,14] and A 15 Tl 27 [15] (A = K, Rb, Cs).The A 8 Tr 11 (Tr = group 13 element) structure type was first described in 1991 for the lighter homologue indium in K 8 In 11 [16], of which the crystal structure proved the presence of a naked, pentacapped trigonal prismatic shaped In 11 cluster, which was Crystals 2018, 8, 319 2 of 10 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, Cs 8 Ga 11 Cl by X-ray single crystal structure analysis [18].Powder diffraction experiments suggested the formation of the heavier homologues Rb 8 Ga 11 Cl, Cs 8 Ga 11 X (X = Br, I), Rb 8 In 11 Cl, Cs 8 In 11 Cl, Cs 8 Tl 11 X (X = Cl, Br, I).Recently, continuative studies on halides A 8 Tr 11 (Tr = Ga, In) have been reported [19].However, the formation of Rb 8 Tl 11 Cl was termed as doubtful due to the lack of a significant change in the lattice constants compared to the binary phase Rb 8 Tl 11 , 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 A 8 Tl 11 X compounds.Thereby, we concentrated on the heavier alkali metals K, Rb and Cs as for sodium no experimental evidence of Tl 11 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 Rb 8 Tl 11 Cl? (3) How do mixed cation sites affect the amount of halide incorporation?

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.

Results
All compounds crystallize in the K 8 In 11 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 Crystals 2018, 8, 319 3 of 10 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 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 Cs 8 Tl 11 Cl 0.8 and Cs 8 Tl 11 Br 0.9 we obtained phase pure materials according to the powder diffraction pattern of the bulk material (Figure 1 The well-crystallized Cs 8 Tl 11 X 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 A 15 Tl 27 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 A 8 Tl 11 , 15/27 = 0.55 for A 15 Tl 27 and 7/11 = 0.63 for A 8 Tl 11 X.The formation of less reduced A 15 Tl 27 were completely comprehensible if the higher reduced A 8 Tl 11 X 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 A 8 Tl 11 X.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 A 8 Tl 11 X x happened to form multicrystals together with A 15 Tl 27 and for the reported single crystals (except K 4 Rb 4 Tl 11 Cl 0.1 ) the data quality was worse compared to Cs 8 Tl 11 X phases.Therefore, the splitting of the alkali metal position could only be observed for K 4 Rb 4 Tl 11 Cl 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).
R indices (all data) R1 = 0.0309 wR2 = 0.0629 With only cesium being present in Cs8Tl11Cl0.8 and Cs8Tl11Br0.9 we obtained phase pure materials according to the powder diffraction pattern of the bulk material (Figure 1  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 NE 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 A8Tl11Xx (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 A8Tl11Xx happened to form multicrystals together with A15Tl27 and for the reported single crystals (except K4Rb4Tl11Cl0.1)the data quality was worse compared to Cs8Tl11X phases.Therefore, the splitting of the alkali metal position could only be observed for K4Rb4Tl11Cl0.1,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).

How Does the Geometry of the Thallide Cluster Change on Halide Incorporation?
All A8Tl11 and A8Tl11Xx compounds include Tl11 7− clusters, which are best described as a very   In Tables 2 and 3 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/cdav ratio (cdd: capping distance difference; cdav: average capping distance; (Equation ( 1)) which allowed for a quick estimation of the degree of distortion.The dependence of the cdd/cdav 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.In Tables 2 and 3 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.Despite numerous efforts we did not succeed in producing crystals of Rb 8 Tl 11 Cl 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% (K 8 Tl 11 ) and 3.1% (Rb 8 Tl 11 ) and a tilt angle of 2.4 • (K 8 Tl 11 : 4.7 • , Rb 8 Tl 11 : 4.9 • ) are very similar to the values found in K 4 Rb 4 Tl 11 Cl 0.1 and suggest a minimal involvement of chloride.Therefore, we assume that Rb 8 Tl 11 Cl 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.

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 Cs 8 Tl 11 X 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).

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/cdav 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 K4Rb4Tl11Cl0.1 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.

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). .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 K4Rb4Tl11Cl0.1 (besides the side products (K,Rb)15Tl27 and (K,Rb)Cl).Careful investigation of the data of K4Rb4Tl11Cl0.1 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). .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 K 4 Rb 4 Tl 11 Cl which resulted in crystals of K 4 Rb 4 Tl 11 Cl 0.1 (besides the side products (K,Rb) 15 Tl 27 and (K,Rb)Cl).Careful investigation of the data of K 4 Rb 4 Tl 11 Cl 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 K4Rb4Tl11Cl0.1 are listed in Tables 4 and 5     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  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 K4Rb4Tl11Cl0.1 are listed in Tables 4 and 5     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 K 8 Tl 11 and K 15 Tl 27 phases.The previously stated stability of the halide including A 8 Tr 11 X 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 Tl 11 clusters themselves seem to tolerate any charge between 7 − and 8 − .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 − .

1 .
How Does the Geometry of the Thallide Cluster Change on Halide Incorporation?All A 8 Tl 11 and A 8 Tl 11 X x compounds include Tl 11 7− 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 D 3 .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).

Figure 3 .
Figure 3. Introduction of split positions and free s.o.f.values for the halide in Cs8Tl11Br0.9 results in an improved model (residual electron density maps, generated by Olex2 adapted from [23], with permission from © 2009 Wiley.

Figure 3 .
Figure 3. Introduction of split positions and free s.o.f.values for the halide in Cs 8 Tl 11 Br 0.9 results in an improved model (residual electron density maps, generated by Olex2 [23]).

Figure 4 .
Figure 4. Introduction of split positions and free s.o.f.values for the halide in K4Rb4Tl11Cl0.1 results in an improved model (residual electron density maps, generated by Olex2 adapted from [23], with permission from © 2011 Olex2 Wiley.

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 K4Rb4Tl11Cl0.1.

Figure 4 .
Figure 4. Introduction of split positions and free s.o.f.values for the halide in K 4 Rb 4 Tl 11 Cl 0.1 results in an improved model (residual electron density maps, generated by Olex2 [23]).
(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 Cs 8 Tl 11 X (X = Cl or Br) and K 4 Rb 4 Tl 11 Cl 0.1 are listed in Tables 4 and 5 lists distances as well as s.o.f.values of the mixed occupied sites within Cs 5 Rb 3 Tl 11 Cl 0.5 and Cs 5.7 K 2.3 Tl 11 Cl 0.6 .Crystals 2018, 8, x FOR PEER REVIEW 7 of 10

Figure 4 .
Figure 4. Introduction of split positions and free s.o.f.values for the halide in K4Rb4Tl11Cl0.1 results in an improved model (residual electron density maps, generated by Olex2 adapted from [23], with permission from © 2011 Olex2 Wiley.

Figure 6 .
Figure 6.The unit cell of Cs8Tl11Br0.9 shows the two characteristic components: Tl11 clusters and the distorted cubic arrangement around the halide atom.

Table 1 .
Crystal data and structure refinement details.

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 Cs 8 Tl 11 X (X = Cl or Br) and K 4 Rb 4 Tl 11 Cl 0.1 .

Table 5 .
Distances in [Å] within the cubic arrangement around the halide/void in Cs 5 Rb 3 Tl 11 Cl 0.5 and Cs 5.7 K 2.3 Tl 11 Cl 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 Figure5).

Table 5 .
Distances in [Å] within the cubic arrangement around the halide/void in Cs5Rb3Tl11Cl0.5 and Cs5.7K2.3Tl11Cl0.6.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 Figure5).