Structural insights into heavy chalcogen polycations and their stabilization via (hydrogen)polysulfates

Abstract

We report the preparation and characterization of [Se₄]²⁺, [Te₄]²⁺ and [Te₆]⁴⁺ cations, stabilized as polysulfates, namely [Se₄][S₂O₇], [Se₄][HS₂O₇]₂, [Se₄][HS₃O₁₀]₂, [Te₄][HS₃O₁₀]₂, [Te₆][HS₃O₁₀]₄ and [Te₆][S₄O₁₃]₂. In the case of tellurium compounds, this represents the first stabilization and solid-state investigations of the species from chlorosulfuric acid/sulfur trioxide-based media, although the respective colorful solutions are known for over 200 years. The unusual cation–anion interactions were investigated via density functional theory (DFT) calculations, i.e., MEP surface plots, QTAIM and NBO analyses. The non-covalent interactions (chalcogen bonding (ChB)) within the novel species reveal different binding modes, namely bifurcated (Ch⋯O,O or Ch,Ch⋯O) and standard (Ch⋯O) σ-hole interactions. We show that the [Se₄]²⁺ dication exhibits electrophilic duality, engaging in σ- and π-hole interactions, and that the stabilization of polycationic chalcogens with oxoanions is enhanced by auxiliary Ch⋯O contacts.

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Introduction

The colorful solutions of tellurium and selenium in concentrated sulfuric acid have been known for over 200 years,^1,2 and even nowadays they are still shown in every freshman lecture.^3,4 Remarkably, the study of these solutions began only in the late 1960s, led predominantly by Gillespie and his colleagues.^5–8 Although these first studies were restricted to spectroscopic and conductometric investigations, the authors were already able to distinguish different polycationic species and they made very accurate assumptions on the geometry of the respective species.^9,10 Notably, though several solids were isolated from these media and analyzed via classical quantitative elemental analysis or conductometry, the only crystallographically elucidated species was, and remains to this day, [Se₄][HS₂O₇]₂ (1).¹¹ In the following decades, the stabilization of chalcogen polycations switched from (hydrogen)polysulfates towards halidometalates like [AlCl₄]⁻,^12,13 [PnF₆]⁻ (Pn = As and Sb)^12,14,15 or [MCl₆]⁻ (M = W, Zr, and Hf)^16,17 (see Fig. 1).¹⁸ This is also true for many mixed chalcogen polycations like [Te₂Se_n]²⁺ (n = 2, 4, 6, 8)^19–22 and higher-condensed cations like [Se_n]²⁺ (n = 8, 10).^23–25 It was not until 2016 that Beck and coworkers were able to isolate the species [Te₄]²⁺, [Te₆]⁴⁺ and [Te₈]⁶⁺ with oxoanionic, yet fluorinated, systems like [F₃CSO₃]⁻ or [C(SO₂CF₃)₃]⁻, using electrochemical synthesis.²⁶ In particular, for tellurium, extensive reviews on the accessible polycationic structures and bonding behavior have been published by Beck, Chivers and Laitinen.^27,28

Fig. 1 Timeline showing the crystallographically elucidated [Se₄]²⁺, [Te₄]²⁺ and [Te₆]⁴⁺ systems using main-group-based anions.^11–15,26

While several assumptions for the species existing in solutions of tellurium and selenium in fluorosulfuric acid or oleum were made, e.g. [Se₄][S₄O₁₃]⁵ or [Te₄][HS₃O₁₀]₂,²⁹ the isolation, crystallographic proof and structural analysis of the species that are present in these systems remain unsolved challenges. Their investigation is not only of academic interest to finally elucidate the possible equilibria between cations and anions in these superacidic media but might also bring additional insight for the research on Se/Te species as conductors or battery materials.^30–32

We were now able to isolate and structurally elucidate the neat disulfate [Se₄][S₂O₇] (2) and the three novel (poly-)chalcogen hydrogen trisulfates [Se₄][HS₃O₁₀]₂ (3), [Te₄][HS₃O₁₀]₂ (4) and [Te₆][HS₃O₁₀]₄-I (5), the latter one also in a second modification [Te₆][HS₃O₁₀]₄-II(6). This is the first time that the [Te₄]²⁺ and [Te₆]⁴⁺ cations are stabilized in a purely oxoanionic environment, enabling the direct comparison of both cations, as well as the lighter congener [Se₄]²⁺, within the same anionic environment. Additionally, we re-determined the structure of the known compound 1. We present single-crystal X-ray diffraction (SCXRD) data at 100 K to directly compare the differences between the other anions [S₂O₇]²⁻/[HS₃O₁₀]²⁻ and derive potential trends for the stability of the respective systems. Finally, we also isolated the novel tetrasulfate [Te₆][S₄O₁₃]₂ (7), which helps further understand the influence of different Lewis basic oxoanions on the same cation. Our analysis of the interactions within these systems shows σ- and π-hole chalcogen bonding by the respective cations. Interest in non-covalent interactions, i.e., chalcogen bonding (ChB),^33,34 spans from crystal engineering^35,36 to catalysis^37,38 to small molecule uptake, anion transport and supramolecular assembly.^39–42 Since these studies often focus on the interaction of ‘organic’ Lewis basic chalcogen bond acceptors, we wanted to contribute to a better understanding of non-covalent interactions for the stabilization of unusual main-group (poly-)cations within ‘inorganic’ systems.

Results and discussion

Syntheses

[Se₄][HS₂O₇]₂ (compound 1) is readily available via solvothermal synthesis of elemental selenium with neat SO₃ in combination with a suitable proton donor, either ClSO₃H or 1,2-dichloroethane, at 80 °C in closed glass ampoules (detailed experimental information is provided in the SI). The compound forms characteristic bright orange crystals and can be prepared phase pure (verified via PXRD, see SI, Fig. S2). If a mixture of Se, ClSO₃H and SO₃ (in excess) is stored at −20 °C for 3 weeks, bright yellow crystals grow, which were identified as the hydrogen trisulfate [Se₄][HS₃O₁₀]₂ (3).

Compound 3 decomposes, if not stored under an SO₃-rich atmosphere, also in an Ar glovebox, and transforms into the thermodynamically more stable hydrogen disulfate 1 with the release of SO₃, visible by color change from bright yellow to orange. This also occurs upon grinding (see SI, Fig. S9), preventing phase pure powder preparation of compound 3 (see SI, Fig. S10). Both compounds can be discriminated by their Raman spectra, which differ in the amount and intensity of their S–O vibrational modes (see SI, Fig. S26). The formation of the neat disulfate [Se₄][S₂O₇] (2) is more challenging, since the bright yellow [Se₄][S₄O₁₃] always forms when neat selenium, SeO₂ or SeOCl₂ is reacted with SO₃ at elevated temperatures.⁴³ We were able to isolate the [Se₄][S₂O₇] compound as a byproduct from the reaction of elemental bismuth with selenoyl chloride and SO₃.⁴⁴ As for the hydrogen disulfate, the disulfate crystallizes as bright orange blocks. Attempts to differentiate between the formation of several species using ⁷⁷Se NMR experiments (in ClSO₃H/D₂CCl₂) showed no signals within the range of +2100 ppm to −50 ppm. Direct preparation of solutions, e.g., 1, in usual solvents was not possible, in line with the findings of Gillespie.⁷ Solutions of elemental Se in ClSO₃H/D₂CCl₂ are initially dark green, indicating the formation of the [Se₈]²⁺ cation, but transform into yellow within a period of 24 h at r.t. and ∼3 weeks at −20 °C.⁴⁵

Te compounds 4–6 can be isolated as single crystals directly from a mixture of Te, ClSO₃H and SO₃ at 7 °C and are distinguishable by their color, [Te₄]²⁺ being red and [Te₆]⁴⁺ being colorless to slightly yellow, in accordance with the observations of Gillespie.⁴⁶ [Te₄][HS₃O₁₀]₂ (4) and [Te₆][HS₃O₁₀]₄-I/-II (5) + (6), all being colorless, can only be distinguished by very small differences in the crystal habit. They are readily oxidized to Te[S₂O₇]₂ upon heating to 80 °C.⁴⁷ Overoxidation by SO₃ can be partially prevented by using the Te, SOCl₂ and SO₃ system, i.e., working with a ‘solvent’, which leads to the formation of [Te₆][S₄O₁₃]₂ (7) as pale yellow crystals, besides colorless Te[S₂O₇]₂. If lower temperatures are applied, no suitable crystal growth can be realized. The use of SOCl₂ as a solvent or cooling of the reaction does not fully inhibit the total oxidation to Te[S₂O₇]₂, making the phase pure preparation of the tellurium species challenging so far. Due to this, spectroscopic characterization of the respective species was not achieved yet. Nonetheless, all compounds can be reproducibly made and we could identify all species several times using SCXRD.

Solid-state structures

The bond lengths between the chalcogen atoms (Ch) within the cations are in very good agreement with the reported literature values (see Fig. 2).^48,49 The [Se₄]²⁺ cations in 1, 2 and 3 are slightly, but not significantly, different. They all show almost D_4h symmetry, even if the symmetries in the solids are only C_i (1 and 3) and C₁ (2), respectively. Thus, for 1 and 3, two different Se–Se distances are found while four different values are found for the cation in 2. In any case, the distances are in a very narrow range with a mean value of 228.6 pm (see also the SI). Obviously, the distances within the [Se₄]²⁺ cation are essentially independent of the nature of the counter anion. This finding is different from the observations for the [I₄]²⁺ cation, which shows remarkable bond length alteration with respect to the stabilizing anions.⁵⁰ The reason for this observation is that [Se₄]²⁺ is a 6π-aromatic system, while in the rectangular [I₄]²⁺ ions, two [I₂]⁺ cations are linked only by a weak bond. Accordingly, for the [Te₄]²⁺ cation, which is also a 6π-aromatic system, the observed Te–Te distances in 4 are almost identical to the compounds reported so far. This is significantly different for the non-aromatic trigonal prismatic [Te₆]⁴⁺ cation. It consists of two [Te₃] triangles with short Te–Te distances, comparable to those found for the [Te₄]²⁺ ion, combined by longer Te–Te bonds linking the triangles to the trigonal prism. In particular, these longer bonds seem to be very sensitive to the nature of the surrounding anions (Fig. 2).

Fig. 2 Ch–Ch bond lengths (in pm) within the [Se₄]²⁺, [Te₄]²⁺ and [Te₆]⁴⁺ cations in the novel compounds and the literature-known compounds with [S₄O₁₃]²⁻,⁴³ [AlCl₄]⁻,^12,13[AsF₆]⁻,¹⁵ and [F₃CSO₃]⁻²⁶ and calculated values.⁴⁸

Another interesting feature of the presented compounds is polysulfate anions. In particular, the [HS₃O₁₀]⁻ anion has been rarely described in the literature. The bond lengths in the [HS₂O₇]⁻ anion of the low-temperature modification of 1 (see SI, Table S4) are in good agreement with the 293 K data reported by Gillespie. The slight deviations in the terminal S–O bond lengths and the Se⋯O distances can be attributed to the different measuring temperatures and an increased accuracy of the used diffractometer.¹¹ The structure shows hydrogen bonding between the O13 (S–OH) atom of one [HS₂O₇]⁻ unit and the O22 (terminal) oxygen atom of a second [HS₂O₇]⁻ unit (see SI, Fig. S4). The H⋯O and O⋯O distances of 183.1(5) pm and 258.3(2) pm, as well as the O–H–O angle of 167°, indicate a moderate hydrogen bond, according to Steiner.⁵¹ While the terminal, non-coordinating S–O_t bonds, the bridging S–O_br bonds and the S–OH bonds show distances in good agreement with with those of the hydrogen disulfates [M][HS₂O₇] (M = K, Cs, Rb, [NH₄], and [NO]) in the literature,⁵² the terminal coordinating S–O_t bond lengths are elongated (∼1 pm) for compound 1, which indicates slightly increased cation⋯anion interaction. If the S–O bond lengths within [Se₄][HS₂O₇]₂ are compared to those in the disulfate [Se₄][S₂O₇] and the hydrogen trisulfate [Se₄][HS₃O₁₀]₂, significant differences become apparent (see Fig. 3). The increased asymmetry of the S–O–S bridges, which is known for polysulfate systems and can be explained by polysulfate chain growth via Lewis adduct formation,⁵³ can be observed for the hydrogenpolysulfates as well, when comparing the bond lengths of the anions in 1 and 3. Additionally, a pronounced differentiation between the terminal, non-coordinating (S–O_t) and coordinating (S–O_co) bonds can be observed.

Fig. 3 Bond lengths within the anions of compounds 1–7 in pm. t = terminal, co = coordinating, and br = bridging.

Usually, the S–O_co bond length decreases with increasing (hydrogen)polysulfate chain length for the same cation due to the decreased Lewis basicity of the anion. This can be seen when comparing the elongated S–O_co bond lengths of the stronger Lewis basic disulfate [S₂O₇]²⁻ (2), with the slightly shorter ones of the hydrogen disulfate [HS₂O₇]⁻ (1). When increasing the chain length of the (hydrogen)polysulfate anion, its Lewis basicity further decreases, which can be seen when comparing the hydrogen di- and trisulfates (1 and 3).

Nonetheless, the respective bonds in 3 are still elongated by 1–2 pm when compared to those in the alkaline metal hydrogen trisulfates.⁵⁴ The most notable difference in compound 3 is the starkly increased S–OH bond length for the hydrogen trisulfate. With a value of 157.9(4) pm, it is roughly 5 pm longer compared to the findings for 1 and the tellurium hydrogen trisulfates 4–6 and up to 9 pm longer compared to the group I hydrogen trisulfates. The hydrogen bonding between the anions in 3 is stronger compared to 1 (H⋯O = 172.9(3) pm, O⋯O = 255.8(5) pm, and O–H–O = 169°; see SI, Fig. S12). However, this is not a suitable explanation for the increased S–OH bond length, since the hydrogen bonding within the anions of the related tellurium species 4 is comparably strong (H⋯O = 169.3(7) pm, O⋯O = 253.1(5) pm, and O–H–O = 163°; see SI, Fig. S15), but the respective S–OH bond within [Te₄][HS₃O₁₀]₂ is 152.1(3) pm long and thus aligns perfectly with the other hydrogen trisulfate species reported so far ([M][HS₃O₁₀] (M = Na, K, and Rb)⁵⁴) and herein. The S–O bond lengths within compound 7 are in good agreement with the observations for Li₂[S₄O₁₃]⁵³ and Ba[S₄O₁₃]⁵⁵ (see SI, Table S49), highlighting the strong Lewis acidity of [Te₆]⁴⁺, albeit being a cluster cation with a formal charge of +2/3 per Te atom.

The lability of compound 3 towards the release of SO₃ can be explained by the increased terminal bridging S–O–S bond length. For longer chain (hydrogen)polysulfates, we introduced the δ-value as an additional parameter to characterize the strength of the terminally bound SO₃ unit and to estimate the adduct character of a polysulfate.⁵³ The δ-values of compounds 1 and 2 are unexpectedly high (see SI, Table S50 and Fig. S.25), comparable to values found for the disulfate of the highly Lewis acidic [ICl₂]⁺ cation.⁵³ Since the respective O⋯Se distances are comparable to the O⋯I distances in [ICl₂]₂[S₂O₇], whereas the van der Waals volume of selenium is significantly smaller than for iodine, this already indicates that different coordination motifs are present for the [Ch₄]²⁺ species. The δ-values of compounds 3 and 4 are decreased compared to those of the group I hydrogen trisulfates, meaning that the terminal SO₃ units exhibit only a weak degree of pyramidalization and are weakly bound. The δ-values nonetheless align nicely with the general trend visible for other reported [HS₃O₁₀]⁻ compounds. In general, the elongated S–O_br bond and the decreased δ-value indicate weak donor–acceptor (DA) interactions between the anion and the cation. However, within the novel compounds, strong non-covalent interactions (σ- and π-hole chalcogen bonding) are observed. The DA distances within the novel compounds are shown in Fig. 4.

Fig. 4 Donor–acceptor distances (O⋯Ch [Ch = Se and Te]) for compounds 1–5 in pm. The O–Ch coordination within the [Ch₄]²⁺ plane for 1–3 and the O–Ch–Ch–Ch torsion angles are shown above the graph.

Compound 1 shows the shortest O⋯Se distance within all compounds (267.6(2) pm), although the DA distances are more widely distributed than for compound 2, which displays O⋯Se distances between 268.5(2) pm and 280.7(2) pm, as well as for compound 3, showing narrowly distributed DA distances between 270.0(3) pm and 271.2(3) pm. An increase in the DA distance is usually expected for decreasing Lewis basicity when moving from [HS₂O₇]⁻ towards [HS₃O₁₀]⁻ anions. However, the planarity of the cation–anion coordination is greatly increased for the latter, which in turn indicates a stronger DA interaction. The high planarity is also found for the heavier chalcogen polycation [Te₄]²⁺.

All [Ch₄]²⁺ species show a ‘star-shaped’ coordination pattern of the closest coordinating oxoanions, already known from compound 1, which is in good agreement with reported [Ch₄]²⁺ species with other Lewis basic coordination sites, e.g. [Ch₄][AlCl₄]₂ (Ch = Se and Te)^12,13 or different polynitriles (di-/tetracyanobenzenes).⁵⁶ Notably, the terminal SO₃ unit of the hydrogen polysulfate anions within compounds 1, 3 and 4 is coordinatively saturated, with two oxygen atoms being involved in chalcogen bonding while the remaining oxygen atom is part of the hydrogen bond between the anions, forming 2-D chains along the crystallographic b-axis within the [Ch₄]²⁺ compounds (see SI, Fig. S4, 12 and 15) and dimers in the case of the [Te₆]⁴⁺ compounds (see SI, Fig. S18). Since all hydrogen trisulfate species reported herein are prone to overoxidation if elevated temperatures are applied and the respective crystals were isolated at reduced temperatures (7 °C and −20 °C, respectively), we attribute their stabilization to the extensive additional lattice stabilization energy via hydrogen bonding.

For the [Te₆]⁴⁺ species within compounds 5–7, the O⋯Te coordination environment differs compared to the [Se₄]²⁺ species. Due to its non-aromaticity, the cation–anion interactions show increased directionality and the unusual behavior of bi- and even tridentate coordination of a (hydrogen)polysulfate anion (see SI, Fig. S17, S20 and S22).

Although bidentate, directional coordination was proposed from DFT calculations for the [Te₄][OAc]₂ system,⁵⁷ it is not found experimentally within the [Te₄]²⁺ species discussed here. The respective Te–Te bond lengths within the [Te₆]⁴⁺ ions are slightly elongated compared to those of the [AsF₆]⁻ system but are in excellent agreement with the [F₃CSO₃]⁻ salt.^15,26 The [Te₆]⁴⁺ unit within compound 7 is generated due to symmetry, since the Te2 and Te3 atoms are situated on a mirror plane (Wyckoff site 4c of the space group Pnma). Thus, the asymmetric unit (ASU) does not show the complete prismatic [Te₆]⁴⁺ ion but a pseudo ‘[Te₄]²⁺’ rectangle (see SI, Fig. S21). Accordingly, the Te–Te bonds in 7 are highly symmetric and the resulting prism differs from compounds 4 and 5, which show the literature known boat conformation.^58,59 The only other example with similar regular symmetry is [Te₆][AsF₆]₄·2SO₂,¹⁵ while the irregular, one- or two-side elongated prism is more commonly found in both homo- and heteroatomic chalcogen polycations.^60,61 This is a notable difference from the DFT calculations performed on these species, where the elongated-prismatic structure or the boat structure is predicted to be energetically more stable.⁶²

The coordination of the oxoanions towards the [Ch₄]²⁺ and [Te₆]⁴⁺ species seems to slightly deviate from ‘classical’ σ-hole interaction, since the O⋯Ch (Ch = Se, Te) coordination is found towards the center of the Ch–Ch bonds, rather than towards bond extension. In turn, other planar units, e.g., the S₂O₂ and [S–C]₂ units within 2,2,4,4-tetrafluoro-1,3-dithietane, show large π-character of the bonds and the observed electron density indicates that π-hole interactions might be energetically favored over classical σ-hole interactions in these and related systems.⁶³ Since, to our knowledge, no extensive quantum chemical analysis on the coordination behavior and bonding of [Ch₄]²⁺ and [Te₆]⁴⁺ was reported so far, we sought to analyze the herein observed interactions in more detail.

Quantum chemical calculations

The solid-state structures of compounds 1–7 exhibit multiple Se⋯O and Te⋯O contacts, respectively, that are formally classified as chalcogen bonds (ChBs). Given the ionic nature of the compounds, the overall crystal packing is primarily established by strong bulk electrostatic (coulombic) effects. However, while these long-range interactions dominate the assembly's energy profile, the final supramolecular architecture is precisely fine-tuned by the specific directionality inherent to the σ-hole interaction. This arises directly from the anisotropy of the charge distribution around the covalently bonded chalcogen atom, where a localized region of positive electrostatic potential (the σ-hole) selectively attracts the nucleophilic oxygen acceptor. To investigate the most electrophilic regions in the cationic fragments [Se₄]²⁺, [Te₄]²⁺, and [Te₆]⁴⁺, we calculated their molecular electrostatic potential (MEP) surfaces, which are presented in Fig. 5.

Fig. 5 Molecular electrostatic potential (MEP) surfaces of the cationic fragments. MEP surfaces mapped onto the 0.001 a.u. electron density isosurface for the (a) [Se₄]²⁺ and (b) [Te₄]²⁺ dications and (c) [Te]₆⁴⁺ tetracation. Color scales for the MEP surfaces are shown below each structure, where blue indicates the regions of maximum positive potential (electrophilic sites) and red indicates less-positive regions.

For the square dications, [Se₄]²⁺ (a) and [Te₄]²⁺ (b), the σ-holes, corresponding to the maximum positive electrostatic potential (V_S,max), are located at the center of each side, along the extension of the Ch–Ch bond. This position of the σ-holes slightly deviates from the highly directional σ-holes usually found in the extension of a bond as known from halogen,^53,64 chalcogen, and pnictogen bonding within organic compounds.⁶⁵ It aligns with a trend that we already analyzed for ChBs within sp³ and sp² hybridized Se or Te species with nitrogen Lewis bases and explains the observed coordination behavior in the solid-state structures.⁶⁶ The deviation of the expected positions of positive MEP and coordination of the oxoanions towards the σ-holes strongly underline the arguments of Politzer that maxima identified via V_S are local maxima and that an increasing non-linearity due to polarization and the influence of secondary interactions can be observed for the non-covalent interactions of group VI atoms in the solid state, compared to isolated gas-phase calculations.^67–69

Intriguingly, the V_S,max of [Se₄]²⁺ (251 kcal mol⁻¹) is more positive than that of the heavier congener [Te₄]²⁺ (224 kcal mol⁻¹). This finding is in contrast to the general trend observed in divalent chalcogen derivatives, where the σ-hole potential typically increases with the polarizability (atomic size) of the chalcogen atom. Additionally, a π-hole is observed over the center of the square ring, with a potential of 231 kcal mol⁻¹ for [Se₄]²⁺ and 203 kcal mol⁻¹ for [Te₄]²⁺. The significantly more intense π-hole in Se₄²⁺ aligns with experimental data, showing the formation of π-hole-mediated ChBs only in the selenium derivative (see SI, Fig. S28) and explains the decreased planarity of the coordination plane of compound 1 mentioned before.

In the trigonal prismatic [Te₆]⁴⁺ cation (c), the MEP values are, as expected for the higher charge density (+4), considerably more positive. The absolute maximum potential (V_S,max = 381 kcal mol⁻¹) is localized at the center of the square faces of the trigonal prism. Conversely, the minimum potential regions are situated over the atoms in the vertices of the triangular faces. We further analyzed the supramolecular assemblies by characterizing the Ch⋯O chalcogen bonds using the Quantum Theory of Atoms-In-Molecules (QTAIM) and the Non-Covalent Interaction (NCI) plot analysis (see SI, section F, Fig. S27). We were able to identify three different primary binding modes, whereby the bifurcated Ch⋯O,O ChBs are the strongest, as confirmed by the reduced density gradient (RDG) isosurfaces. This bifurcation further explains the deviating directionality. Additional ‘auxiliary Ch⋯O contacts’ (coordination by oxygen atoms within the polysulfate chain, which usually have decreased oxoanionic character) can be found for the hydrogen trisulfates, highlighting the potential of these anions for the stabilization of polycationic species bearing different σ- or σ- and π-holes. Subsequently, we analyzed the ChBs in compounds 1–5 and 7 from an orbital perspective, focusing on the orbital donor–acceptor charge transfer (see Fig. 6).

Fig. 6 NBO plots illustrating the key stabilizing charge transfer interactions in compounds 1 (a), 2 (b), 3 (c), 4 (d), 5 (e), and 7 (e). In all cases, the interaction is characterized by electron donation from the LP orbital of the nucleophilic O atom to the antibonding σ* orbital of the chalcogen–chalcogen bond. The second order stabilization energies are indicated.

The main orbital contributions consistently show electron donation from the lone pair (LP) orbitals located on the terminal oxygen atoms of the (hydrogen)polysulfate anions to the Ch–Ch antibonding σ* orbitals of the cations. These charge transfer energies range significantly from 4.9 to 13.5 kcal mol⁻¹, thus quantitatively confirming the strong orbital effects inherent in these ChBs. It is particularly remarkable that the dominant bifurcated Se,Se⋯O ChB in compound 1 (Fig. 6a) results in two almost symmetric electron donations and stabilization energies (4.9 and 5.3 kcal mol⁻¹) to the two opposite σ*(Se–Se) bonds of the [Se₄]²⁺ square. While not fully depicted for simplicity, additional LP(O) → σ*(Ch–Ch) donations are also observed in all other bifurcated bonds, though these are increasingly asymmetric. The universal observation of the LP(O) → σ*(Ch–Ch) donation across all Ch⋯O contacts, combined with the significant stabilization energies, provides the underlying electronic rationale for the observed coordination motifs that dictate the solid-state architecture of compounds 1–7. The symmetric electron donation of the oxoanions into the σ-holes of two chalcogen atoms also explains the deviating coordination geometry.

Lastly, we calculated the frontier molecular orbitals (FMOs) of the [Ch₄]²⁺ and [Te₆]⁴⁺ units to analyze whether the differences observed in V_S,max and the coordination behavior can be directly related to the respective HOMOs and LUMOs (see Fig. 7).

Fig. 7 Frontier molecular orbitals (FMOs) for the isolated [Ch₄]²⁺ and [Te₆]⁴⁺ units and their respective energies in eV.

The increased electrophilicity of the [Se₄]²⁺ unit can be explained by the decreased energy of the LUMO. While the LUMO is basically identical for both [Ch₄]²⁺ cations regarding the AO contributions, the HOMOs are notably different, whereby [Te₄]²⁺ shows some biradical character. The existence of biradicaloid molecular orbitals within the [Ch₄]²⁺ units was only described in the literature concerning the existence of degenerate, non-bonding orbitals.^49,70 The biradicaloid character was reported to increase within the row S < Se < Te.⁷¹ Passmore denoted that the structural chemistry and bonding within [Te₄]²⁺ is more diverse compared to lighter chalcogens due to different molecular orbital contributions.⁷² The 6π aromatic square is predominantly formed with ‘monomeric’, hard counterions as [PnF₆]⁻, while the formation of dimeric [Te₈]⁴⁺ or polymeric [Te₄]²⁺_n species was reported for ‘polymeric’, higher charged anions like [VOCl₄]²⁻.^60,73,74 The di-/polymeric species form one-dimensional chains or two-dimensional folded bands and show Te–Te connectivity, which can be directly correlated with the diradicaloid character. We propose that our novel compound 4 shows a unique transition state between these two states.

Although being a classical monomeric 6π aromatic [Te₄]²⁺ unit with a square-planar geometry, it already shows biradicaloid HOMO character. This also highlights that the bonding character of the cation can be gradually influenced via the anion. This is where our systems stand out due to their ability to form ‘auxiliary’ donor–acceptor contacts due to the terminal oxygen atoms of the polysulfate chain.

Conclusion

In summary, we reported the isolation and structural characterization of the novel disulfate salt [Se₄][S₂O₇] (2), the hydrogen trisulfate salts [Se₄][HS₃O₁₀]₂ (3), [Te₄][HS₃O₁₀]₂ (4), [Te₆][HS₃O₁₀]₄ (5) and [Te₆][HS₃O₁₀]₄-II (6) and the tetrasulfate salt [Te₆][S₄O₁₃]₂ (7), as well as the re-investigation of the hydrogen disulfate [Se₄][HS₂O₇]₂ (1). We presented an extensive structural analysis, highlighting the unusual coordination motifs between the oxoanions and the [Ch₄]²⁺ cations, their differing donor–acceptor distances and the formation of supramolecular aggregates. The comprehensive computational analysis, combining MEP surfaces, QTAIM/NCI plots, and NBO analysis, provided compelling electronic evidence, confirming that while the crystal packing of compounds 1–7 is globally governed by strong ionic (coulombic) forces, the final, high-resolution supramolecular architecture is dictated by the directionality of the ChBs through σ-hole interaction. The QTAIM and NCI plot analyses quantified these interactions, revealing strong (−6.1 to −9.4 kcal mol⁻¹) stabilization energies for the primary bifurcated binding modes. Our results indicate the electrophilic duality of [Se₄]²⁺, capable of engaging not only in robust σ-hole interactions but also in a secondary π-hole binding mode confirmed by LP(O) → π*(Se–Se) donation, showing the complex coordination sites of heavy chalcogen polycations. We could show that the stabilization of these species can be achieved by (hydrogen)polysulfates as weakly coordinating anions, which not only show significant primary LP(O) → σ* charge transfer stabilization energies ranging up to 10.2 kcal mol⁻¹ but are also able to develop secondary, auxiliary Ch⋯O contacts via the terminal oxygen atoms within the polysulfate chain.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: experimental details, synthesis, Raman spectra, X-ray powder diffraction, computational details, crystallographic information, and additional characterization data. See DOI: https://doi.org/10.1039/d6dt01115b.

CCDC 2477856 (for [Se4][HS2O7]2), 2504489 (for [Se4][S2O7]), 2476927 (for [Se4][HS3O10]2), 2476926 (for [Te4][HS3O10]2), 2476929 (for [Te6][HS3O10]4), 2476936 (for [Te6][HS3O10]4-II) and 2502407 (for [Te6][S4O13]2) contain the supplementary crystallographic data for this paper.^75a–g

Acknowledgements

The authors would like to thank Silke Kremer for the SCXRD measurements, Katrin Eppers and Arthur Edelmann for the Raman measurements and Daniel Moog for the P-XRD measurements. J. L. thanks Thomas Kasperowicz for helpful discussions and assistance with the Rietveld refinement. J. L. is thankful to the German National Scholarship Foundation (Studienstiftung des deutschen Volkes) for financial support.

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75. (a) CCDC 2477856: Experimental Crystal Structure Determination, 2026,  DOI:10.5517/ccdc.csd.cc2p5dv4; (b) CCDC 2504489: Experimental Crystal Structure Determination, 2026,  DOI:10.5517/ccdc.csd.cc2q23zx; (c) CCDC 2476927: Experimental Crystal Structure Determination, 2026,  DOI:10.5517/ccdc.csd.cc2p4fw5; (d) CCDC 2476926: Experimental Crystal Structure Determination, 2026,  DOI:10.5517/ccdc.csd.cc2p4fv4; (e) CCDC 2476929: Experimental Crystal Structure Determination, 2026,  DOI:10.5517/ccdc.csd.cc2p4fy7; (f) CCDC 2476936: Experimental Crystal Structure Determination, 2026,  DOI:10.5517/ccdc.csd.cc2p4g5h; (g) CCDC 2502407: Experimental Crystal Structure Determination, 2026,  DOI:10.5517/ccdc.csd.cc2pzytg.

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