Solid State Polyselenides and Polytellurides: A Large Variety of Se–Se and Te–Te Interactions

A large variety of different interactions between the chalcogen atoms, Q, occur in the solid state structures of polyselenides and polytellurides, including both molecular and infinite units. The simplest motifs are classical Q22– dumbbells and nonlinear Qn2– chains (n = 3, 4, 5, ..), e.g. found in alkali metal polychalcogenides. In addition, nonclassical so-called hypervalent motifs exist in the form of linear Q34– units or within larger units such as Q44– and Q54–. Infinitely extended Q units include zigzag, cis/trans and linear chains, as well as planar and slightly puckered layers. Several of those are susceptible to Peierls distortions, leading to the formation of both commensurate and incommensurate superstructures and anomalies in transport properties, including metal-nonmetal transitions.


Introduction
Solid state materials based on chalcogenides, i.e., sulfides, selenides and tellurides, play a large role in today's society. Examples include semiconductor devices, e.g. in solid state electronics [1], fast-ion conductors [2,3], rechargeable batteries [4], data storage including phase-change materials [5][6][7], chalcogenide glasses [8], and the thermoelectric energy conversion [9][10][11][12]. Polychalcogenides, like the potential thermoelectric material HfTe 5 , are materials that comprise homonuclear bonds between negatively charged chalcogen atoms, e.g. a Se-Se bond within Se 2 2pairs of Rb 2 Se 2 [13]. These bonds occur in chalcogen-rich materials, where the chalcogen atom cannot be reduced to attain the closedshell formation as in Q 2-. For example, Se carries a charge of -1 in Rb 2 Se 2 , like O in SrO 2 , and OPEN ACCESS therefore forms one Se-Se bond. As such, Rb 2 Se 2 is a typical Zintl phase. Zintl phases AX x consist of an electropositive element A (here: Rb) and a more electronegative element X of the later (post transition) main groups (here: Se). Assuming a complete charge transfer of all of A's valence-electrons to X, the cation A z+ possesses a full octet, and the (formal) anion X z/xattains the octet by forming homonuclear X−X bonds in addition to the reduction by A. In most cases, these bonds are classical single bonds (two-center two-electron, 2c-2e), i.e. exactly one bond is formed for each electron missing to complete the octet of X [14][15][16].
The rich structural chemistry in particular of the polyselenides and polytellurides is the scope of this review, going beyond the common 2c-2e bonds: hypervalent interactions as found in XeF 2 [17] or SF 6 [18] are often observed in various fragments of these materials [19]. In addition, weaker fractional bonds or cohesive interactions of different lengths, as in elemental tellurium, render the Se/Te substructures intriguingly complex [20,21], which in turn may be beneficial for the thermoelectric energy conversion [22]. Four reviews about polychalcogenides from the years 1995 to 2000 underline the importance of this field [20,[23][24][25].  [39] and Te 13 2-in Cs 2 Te 13 [40] (Figure 2), and they are oftenas in these two examples -interconnected via longer interchain interactions (here: 3.14 Å and 3.18 Å). These interactions are much shorter than twice the van der Waals radius and will be discussed later in this review.

Oligomeric Q n 4motifs
Since the Q n 4fragments comprise two more valence-electrons than their Q n 2counterparts, they cannot contain the same 2c-2e bonds. n = 2 is a hypothetical case only, as it would correspond to two isolated closed-shell Q 2anions. n = 3 is realized in Se 3 4units of Ba 2 Ag 4 Se 5 [41], and Rb 12 Nb 6 Se 35 [42]. In the former, Se    [44]. Ideally the two I-I distances are equivalent, with a bond angle of 180° as in [Ph 4 As]I 3 (d I-I = 2.90 Å), but deviations from the centrosymmetric arrangement are often found with smaller cations, like in CsI 3 with I-I bonds of 2.84 Å and 3.04 Å and a bond angle of 178°. The linear arrangement is well understood based on Rundle's model [45], which treats the s orbitals as well as the p orbitals of π symmetry as lone pairs. Then the frontier orbital set consists of one filled σ bonding, one filled nonbonding, and one empty σ antibonding molecular orbital, formed by the p z orbitals when z corresponds to the molecular axis. The nonbonding orbital contains a nodal plane at the center of the triatomic unit, resulting in a three-center-four-electron (3c-4e) bond. The validity of Rundle's model was -in principle -confirmed for Se 3 4via Gaussian calculations using the B3LYP functional [41].
Since the 3c-4e bonds are electron deficient, containing only one bonding molecular orbital for two bonds (which is why they are often called "half" bonds), they are longer than the regular 2c-2e bonds. Correspondingly, the I-I single bond in I 2 of 2.76 Å is much shorter than the above-mentioned I-I bonds ( ) 2 is also a closed-shell material [50].
The trans conformation is only known within the tellurides, occurring in NaTe ((Na + ) 6 [56]. These units can polymerize [57], the products of which will be discussed later in this manuscript. Adding two more Te atoms via single bonds, for example, results in bicyclic Te 7 2- [58].

Infinite motifs in polyselenides and polytellurides
2.2.1. One-dimensional motifs: chains The above-mentioned fragments Q n 2and Q n 4can form higher dimensional arrays such as infinite chains, ribbons or layers. At least two bonds are required per Q atom in infinite chains, but the Q atoms may only participate in two 2c-2e bonds, when their oxidation state is 0. Such neutral chains exist in the elements selenium and tellurium. On the other hand, Te is especially well known for its ability to form electron deficient multicenter bonds, thereby producing linear Te -] chains. These chains occur in CuTe [59], UTe 2 [60] and Ca 0.66 K 4 Te 3 [61] with typical intrachain distances between 3.0 Å and 3.1 Å. These interactions are delocalized 2c-1e ("half") bonds, wherein one p orbital is halffilled, indicating a one-dimensional metal. Such linear equidistant chains may undergo a Peierls distortion, i.e. exhibit alternating short and long distances, occurring with a metal-insulator transition ( Figure 5) [62]. There are also examples of distorted linear chains of Te atoms with a formal charge of -1 such as in Cs 5 Te 3 [63] or K 5 Te 3 [64]. In these compounds, the Te atom chain features two different Te-Te distances, one of around 2.8 Å and the other larger than 3.5 Å. Thus, a description as Te 2 2-] is more appropriate for these compounds, wherein van der Waals forces connect the pairs to linear chains. The dimorph TlTe is a nice example of a material exhibiting different Te atom chains [65]. The room temperature (RT) modification of TlTe represents an equidistant Te -] chain with Te-Te distances of 3.08 Å. A parallel running, second linear equidistant Te atom chain within the same structure is more complex, as two additional Te atoms are connected to each chain atom via hypervalent bonds of 3.01 Å, yielding a Te 3 3-] chain ( Figure 6). Thus, the RT modification may be written as (Tl + ) 4 Te 3 3-Te -. In the low temperature (LT, 172 K) modification, both chains are distorted.   In LiTe 3 [67], the VEC(Te) within the chain is lowered to 6⅓. Consequently, this chain exhibits parts known from the Te atom chains in Tl 2 Te 3 as well as from elemental Te [68], and can therefore be viewed as (Te 3 )(Te 3 2-)]. The distances within this chain are 2.85 Å for the 2c-2e bonds in the neutral Te 3 part of the chain, 3.02 Å for the 3c-4e bond in the Te 3 2unit and 2.91 Å for the bond connecting these fragments.

One-dimensional motifs: Ribbons
Only very few polychalcogenides exist that contain one-dimensionally extended Q atom substructures with more than two Q-Q bonds per Q atom. The dialkali pentatellurides show two different forms of intercondensation of above-mentioned Te 5 6squares to yield Te 5 2-] ribbons with VEC(Te) = 6.4, namely the cis conformation in Cs 2 Te 5 [69] and the trans conformation in Rb 2 Te 5 [70] ( Figure 8). The distances in these ribbons range from 2.78 Å in Rb 2 Te 5 and 2.77 Å in Cs 2 Te 5 for the 2c-2e bond between the Te 5 units to 3.04 Å in Rb 2 Te 5 and 3.05 Å in Cs 2 Te 5 for the 3c-4e bond within the Te 5 units. In 2 Te 5 [71] possesses a similar unit with a higher VEC(Te) of 6⅔, which causes a distortion, namely an alternation of short and long Te-Te distances of 2.83 Å (solid lines) and 3.36 Å (dashed lines). Therefore it is best described as a one-dimensional arrangement of Te 3 2fragments.

Two-dimensional motifs: Layers
Compounds with hypervalently bonded Te atoms that are arranged in planar or puckered layers are often dominated by T-shaped fragments. These building blocks are then either directly connected to each other or bridged via other Te atoms. An overview of (schematic) T nets was published in the year 2004 [72]. One of the simplest examples of a T network containing Te atoms can be found in the planar layers of NbTe 4 [73]. Each Te atom in this layer is surrounded by three other Te atoms in form of a heavily distorted T. Four-membered rings, exhibiting Te-Te distances of 3.30 Å, are connected to surrounding four-membered rings via shorter bonds of 2.88 Å (Figure 9). This hole-style arrangement in NbTe 4 is subject to a distortion, driven by a charge density wave along the Nb atom chains perpendicular to the layer of interest. Considering the large difference of 0.4 Å between these distances, one could view this layer as loosely connected Te 2 2units. This is in contrast to the Sb atom layer of Hf 5 Sb 9 [74], wherein all bonds are between 2.99 Å and 3.03 Å, i.e. all bonds of that T net are electron deficient multicenter bonds [75]. CsTe 4 [76] also features T-shaped Te atom units forming a layer, which is comprised of a polymerized Te 4 4anion. This anion loses, due to this polymerization, three charges and builds a puckered layer that could be described as Te 4 -]. The distances in the original T-shaped fragment in this layer are 2.92 Å and 3.14 Å for the collinear bonds, and 2.84 Å for the perpendicular bond. The connection between two (similar or different) fragments is slightly shorter (2.76 Å). The majority of the Te atoms are twofold coordinated and provide bonding angles between 96° and 103°. Therefore, the bonds within the Te 4 4fragments could be considered as asymmetric 3c-4e bonds and the remaining bonds as 2c-2e bonds. Cs 3 Te 22 provides an example of an electron-poor layer of Te atoms [77]. Cs 3 Te 22 contains also neutral eight-membered Te rings, and can be described as (Cs + ) 3 (Te 8 ) 2 (Te 4 Te 4/2 ) 3-. Its planar Te 4 Te 4/2 3-] layer consists of two-and threefold connected Te atoms, with the former being linearly coordinated and the latter T-shaped. The linearly bonded atoms interconnect the Te 4 squares comprising the T connected Te atoms. All Te-Te distances are between 3.00 Å and 3.07 Å. Band structure calculations indicate that this layer would be semiconducting with a charge of -4, but its actual charge of -3 renders it metallic [78].

Two-dimensional motifs: Chains connected to layers
The previously discussed lower dimensional fragments can be connected to two-dimensional layers in several ways. The binary chalcogenides UTe 2 [79], U 2 Te 5 [80], α-UTe 3 [81] and ZrQ 3 [82,83] all contain linear chains aligned to form planar layers ( Figure 10). Furthermore, many more complex variants, mostly tellurides, are known in this class, including UTe 5 [84], incommensurately modulated ALn 3 Te 8 (A = K, Rb, Cs; Ln = La -Nd) [85], and LnSeTe 2 (Ln = La -Nd, Sm) [86], which exhibit corrugated chains interconnected to planar or slightly puckered layers. A detailed discussion of all these materials would go beyond the scope of this review; square nets and their distortions were featured in a review published in 2002 [ [88,89] with an interpair distance of 3.50 Å, which is shorter than a van der Waals contact.

Three-dimensional motifs
The only known compound that is comprised of a three-dimensional, covalently bonded network of Te atoms is Cs 4 Te 28 [40]. The Te atom network is similar to the one in Cs 3 Te 22 , but in this case, half of the Te 8 rings are broken into Te 4 units that connect to one of the former linearly bonded atoms ( Figure  12), which then assumes an oxidation state of zero.

Conclusions
An overview of the variety of Se-Se and Te-Te interactions occurring in the solid state of both inorganic and organic polychalcogenides was presented. In contrast to polysulfides, the Se and Te atoms are capable of forming electron deficient multicenter (hypervalent) bonds. This adds significantly to the connectivity possibilities, e.g. the formation of T-shaped Te motifs or linear Se/Te fragments, which in turn increases the complexity of these polychalcogenides, a desired feature for, e.g., thermoelectric materials.
The tendency of Te towards higher coordination numbers is reflected in the higher abundance of complex Te atom layers, compared to Se. However, within the oligomeric units, the selenides and tellurides are quite comparable, so that more polyselenides with related two-dimensional motifs are likely to be uncovered in the near future as well.