The Homopolyatomic Sulfur Cation [S₂₀]²⁺

Abstract

Homopolyatomic cations of the main group elements and of the element sulfur, in particular, are used as tutorial examples to teach structure and bonding in inorganic chemistry. So far, the cations [S₄]²⁺, [S₈]²⁺, [S₁₉]²⁺, [S₅]^•+, and [S₈]^•+ are known experimentally. In this report, the generation and crystal structure determination of the salt Na₂[S₂₀]₂[B₁₂Cl₁₂]₃, containing the new homopolyatomic sulfur cation [S₂₀]²⁺, is reported. The structure of the latter cation consists of two seven-membered homocycles, which are bridged by a six-membered sulfur chain. This structure is strongly related to that of [S₁₉]²⁺. The heptasulfur rings show pronounced bond alternation. Comparison with the experimental structures of [S₇X]⁺ (X = I, Br) and the application of quantum chemical calculations show unambiguously that the observed structural features are intrinsic properties of the cationic cyclo-heptasulfur moieties. The latter can occupy different conformations, which only slightly differ in energy. Charge delocalization and negative hyperconjugation contribute to the stability of the observed structures. The discovery of the [S₂₀]²⁺ cation fits well into range of known homopolyatomic sulfur cations, which can be classified by their averaged oxidation state of sulfur.

1. Introduction

The homopolyatomic cations of the non-metal elements are used as tutorial examples to teach structures and bonding in main group chemistry. They have become important textbook compounds and are reviewed numerous times [1,2,3,4,5,6,7]. In particular, homopolyatomic sulfur cations have fascinated chemists for more than 200 years due to their intense colors [8]. In 1804, Buchholz reported an intense blue color upon dissolving sulfur in oleum [9]. Later on, the origin of this blue color was attributed to the presence of different homopolyatomic cations of the element sulfur [10]. To date, three homopolyatomic sulfur dications, [S₄]²⁺ [11,12,13,14], [S₈]²⁺ [11,14,15,16], and [S₁₉]²⁺ [14,17], and the monocationic radical [S₈]^•+ [18] have been structurally characterized in a solid state. The dication [S₄]²⁺ has a square planar structure. Both eight-membered cations [S₈]²⁺ and [S₈]^•+ consist of an eight-membered sulfur ring in a chair conformation with a distinct transannular sulfur–sulfur contact. The large dication [S₁₉]²⁺ consists of two seven-membered rings connected by a five-membered sulfur chain. Scheme 1 summarizes the homopolyatomic sulfur cations that were experimentally known prior to this work.

In the past, homopolyatomic sulfur cations were typically prepared by the oxidation of elemental sulfur using a strong oxidizing agent (e.g., AsF₅, SbF₅) in superacidic solutions (typical solvents include oleum, HSO₃F, HF, and SO₂) [2]. Following this general procedure, salts containing the dications [S₄]²⁺, [S₈]²⁺, and [S₁₉]²⁺, partnered by fluorinated anions, have been isolated in the solid state [2,6,8].

In contrast, the composition of superacidic solutions of such cations is still not completely understood. Homopolyatomic sulfur compounds cannot be studied by NMR spectroscopy due to the absence of an appropriate NMR nucleus. Based on UV–visible, IR, and, in particular, ESR investigations in solution, the existence of the radicals [S₁₂]^•+, [S₈]^•+, [S₇]^•+, [S₅]^•+, and [S₄]^•+ was proposed [15,19,20]. Later on, [S₅]^•+ was unambiguously identified by ESR experiments using ³³S-enriched sulfur [21]. Krossing and Passmore suggested that the presence of [S₆]²⁺ in solution was responsible for the typical blue color of solutions of homopolyatomic cations [10]. Gillespie et al. demonstrated that the composition of the solution is strongly dependent on their acidity level [17]. A blue solution of the composition [S₈][AsF₆]₂ takes up additional elemental sulfur up to attain a composition corresponding to [S₁₆][AsF₆]₂. At this point, the color changed from blue to red. Gillespie suggested that [S₁₆]²⁺ may exist in equilibrium with [S₈]^•+ in solution [15]. The determination of the crystal structure of the [S₁₉]²⁺ dication changed his opinion and he discarded the existence of [S₁₆]²⁺ [17]. Recently, we reported the crystal structure of a salt indeed containing the [S₈]^•+ radical cation [18]. The determination of the crystal structure of [S₁₉][AsF₆]₂ [14,17] ([S₁₉]²⁺ can be formulated as [cyclo-S₇–S₅–cyclo-S₇]²⁺) led Passmore et al. to the presumption that other related cations of the type [cyclo-S₇–S_x–cyclo-S₇]²⁺ (x = 2–6) might exist as well [22].

In this paper, we report the crystal structure of the new homopolyatomic sulfur dication [S₂₀]²⁺ (which corresponds to [cyclo-S₇–S₆–cyclo-S₇]²⁺), which is strongly related to that of the known [S₁₉]²⁺ cation.

2. Results and Discussion

2.1. Generation of Na₂[S₂₀]₂[B₁₂Cl₁₂]₃ Single Crystals

All homopolyatomic sulfur cations isolated in the solid state prior to the start of our work ([S₄]²⁺, [S₈]²⁺, [S₁₉]²⁺) were dications and were partnered by fluorometallate counter anions. For many years, the existence of further homopolyatomic sulfur cations was anticipated. However, despite several attempts, other than the three known homopolyatomic sulfur cations could not be isolated in a solid state using the “classical methods”.

In our group, we have been investigating halogenated closo-dodecaborates [B₁₂X₁₂]²⁻ (X = F − I) as weakly coordinating anions that stabilize reactive cations in the solid state for more than 15 years [23,24,25,26,27,28,29,30,31]. This has led us to develop the idea of bringing a new twist to the old topic of homopolyatomic sulfur cations by changing the fluorometallate counter anions into the chlorinated closo-dodecaborate [B₁₂Cl₁₂]²⁻.

In classical reactions yielding homopolyatomic sulfur cations, elemental sulfur is oxidized by, for instance, AsF₅ [2]. The [AsF₆]⁻ counter anions are formed in situ in these reactions (Equation (1)). The chlorinated closo-dodecaborate [B₁₂Cl₁₂]²⁻ cannot be introduced the same way. Simple metathesis reactions of the soluble salts [S₈][AsF₆]₂ and Na₂[B₁₂Cl₁₂] in liquid sulfur dioxide were unsuccessful because a mixture of the two completely insoluble solids [S₈][B₁₂Cl₁₂] and Na[AsF₆] was obtained (Equation (2)). However, replacing Na⁺ by [NBu₄]⁺ led to the formation of the soluble by-product [NBu₄][AsF₆], which could be removed (Equation (3)).

$${\mathrm{S}}_8+3{\mathrm{AsF}}_5\stackrel{\mathrm{S}{\mathrm{O}}_2}{\to }[{\mathrm{S}}_8][{\mathrm{AsF}}_6{]}_2+{\mathrm{AsF}}_3$$

(1)

$$[{\mathrm{S}}_8][{\mathrm{AsF}}_6{]}_2+{\mathrm{Na}}_2[{\mathrm{B}}_{12}{\mathrm{Cl}}_{12}]\stackrel{\mathrm{S}{\mathrm{O}}_2}{\to }[{\mathrm{S}}_8][{\mathrm{B}}_{12}{\mathrm{Cl}}_{12}]+2\mathrm{Na}[{\mathrm{AsF}}_6]$$

(2)

$$[{\mathrm{S}}_8][{\mathrm{AsF}}_6{]}_2+[{\mathrm{NBu}}_4{]}_2[{\mathrm{B}}_{12}{\mathrm{Cl}}_{12}]\stackrel{\mathrm{S}{\mathrm{O}}_2}{\to }[{\mathrm{S}}_8][{\mathrm{B}}_{12}{\mathrm{Cl}}_{12}]+2[{\mathrm{NBu}}_4][{\mathrm{AsF}}_6]$$

(3)

Unfortunately, the blue solid product, which was assumed to be [S₈][B₁₂Cl₁₂], was completely insoluble in liquid sulfur dioxide and in anhydrous hydrogen fluoride. Typical organic solvents are incompatible with homopolyatomic sulfur cations. For instance, they undergo cycloaddition reactions with nitriles [32,33]. The very low solubility of salts like [S₈][B₁₂Cl₁₂] is caused by their high lattice energy. It should be noted that the lattice energy of a salt of the type M²⁺X²⁻ is approximately four times higher than that of a salt of the type M⁺X⁻. The amorphous blue product did not show any pattern in X-ray powder diffraction experiments, did not show a Raman spectrum due to very strong fluorescence, and did not show a decisive IR spectrum. Thus, crystal structure determination was the only way to actually characterize the material. From one crystallization attempt in supercritical sulfur dioxide (T_c = 158 °C, p_c = 77.8 atm) [34,35], we isolated blue single crystals of the composition Cs_0.73Na_0.27[S₈][B₁₂Cl₁₂], which we reported previously [18]. Another attempt starting from material with a composition corresponding to [S₁₀][B₁₂Cl₁₂] ([S₈][B₁₂Cl₁₂] + excess S₈) yielded blue crystals of Na₂[S₂₀]₂[B₁₂Cl₁₂]₃. The latter contained the previously unknown [S₂₀]²⁺ cation. Its structure will be discussed in the following section.

2.2. Crystal Structure of Na₂[S₂₀]₂[B₁₂Cl₁₂]₃

The crystal structure of Na₂[S₂₀]₂[B₁₂Cl₁₂]₃ consists of [B₁₂Cl₁₂]²⁻ dianions, sodium cations, and [S₂₀]²⁺ dications (Figure 1). The B-B and B-Cl bond lengths within the [B₁₂Cl₁₂]²⁻ dianion are identical to those of [B₁₂Cl₁₂]²⁻ anions in other crystal structures [30] and are very different to those in neutral B₁₂Cl₁₂ [24,31]. Thus, it can be concluded that the [B₁₂Cl₁₂]²⁻ is actually a dianion. The sodium cations originate from the compound Na₂[B₁₂Cl₁₂], which has been used to generate the corresponding salt of the homopolyatomic sulfur cation (for experimental details see Section 3). Their presence seems to be important for crystallization.

The [S₂₀]²⁺ dication (Figure 1) consists of two seven-membered sulfur homocycles (S1–S7 and S14–S20), which are bridged by a six-membered chain (S8–S13). This structure is very similar to that of [S₁₉]²⁺ [14,17], in which the bridging sulfur chain has a length of five atoms, and that of the selenium homopolyatomic cation [Se₁₇]²⁺, in which the seven-membered rings are bridged by three selenium atoms (Figure 2) [36,37].

The S–S bond lengths within the [S₂₀]²⁺ cation vary over a very large range from 191 to 239 pm (

Table 1. Selected bond lengths in the [S₂₀]²⁺ dication. The numbering of the atoms refers to Figure 1 ^a.

Bond	Bond Length [pm]	Bond	Bond Length [pm]
S1–S2	209.9(2)	S10–S11	204.34(10)
S2–S3	199.7(2)	S11–S12	208.7(2)
S3–S4	212.7(2)	S12–S13	202.9(2)
S4–S5	196.7(2)	S13–S14	210.0(2)
S5–S6	217.6(2)	S14–S15	219.9(3)
S6–S7	191.4(2)	S15–S16	201.0(3)
S1–S7	239.0(2)	S16–S17	207.3(2)
S1–S8	203.8(2)	S17–S18	202.8(3)
S8–S9	204.9(2)	S18–S19	207.3(3)
S9–S10	205.3(2)	S19–S20	202.7(2)

^a Only bond lengths for the major component are given.

) and deviate substantially from the value for a typical S–S single bond (cf. approx. 205 pm in S₈) [38]. The reasons for the observed bond lengths and the preference for the formation of seven-membered rings will be discussed in Section 2.3.2.

While one of the two S7-rings (atoms S1–S7) is perfectly ordered, the second S7-ring (S14–S20) is disordered over two sites (Figure 3). The ratio of the major component (85%, yellow) and the minor component (15%, blue) was freely refined by referring to a single variable.

The ordered part of the cation is completely surrounded by [B₁₂Cl₁₂]²⁻ anions and thus forms only S…Cl contacts with neighboring anions. In contrast, the disordered part shows S…Cl contacts with [B₁₂Cl₁₂]²⁻ anions and S…S intermolecular contacts with neighboring [S₂₀]²⁺ cations (Figure 4a). See Figures S2 and S3 in the Supplementary Material for visualizations of the packing in the solid state.

The positive +2 charge of the cation is delocalized over the entire cation, with a slightly higher positive charge on the bridgehead atoms (Figure 4c). The calculated molecular electrostatic potential also shows only small deviation from an equal charge distribution (Figure 4b). It appears that the almost uniform charge distribution over the entire cation allows for some fluxional behavior of the corresponding S₇-rings. Details of the cation structure are discussed in Section 2.3 with the help of quantum chemical calculations.

The structure of the [S₂₀]²⁺ cation is strongly related to the known crystal structures of [S₁₉]²⁺ and [Se₁₇]²⁺ (Figure 2) [14,17,36,37]. Obviously, all three dications consisting of seven-membered rings bridged by a chain of variable length belong to the same class of homopolyatomic chalcogen cations. Figure 5 visualizes the two independent seven-membered sulfur homocycles in the [S₂₀]²⁺ dication. For the disordered ring, only the major component is shown. Both seven-membered rings occupy a chair conformation but, when arranged in the same way (Figure 5), it becomes obvious that the substitution pattern is different. In the ordered part of the molecule (atoms S1–S7), the sulfur chain is attached to atom S1 (conformation A, left in Figure 5), while in the disordered part (atoms S14–S20 for the main component), the sulfur chain is bonded to an atom of the planar four-membered part of the homocycle (conformation B, right in Figure 5).

2.3. Structure and Bonding in [S₂₀]²⁺

The experimental findings raise a number of questions. Is the observed wide variance of the S–S bond lengths (196 to 239 pm) from the length of a typical single bond (205 pm) real? Why are two different conformations (A and B) of the seven-membered homocycles found? Is there a preference for seven-membered over eight-membered cycles?

A quantum chemical geometry optimization of [S₂₀]²⁺, starting from the experimental structure, yields a structure that is in very close agreement with the experimental structure (Figure S5 in the Supplementary Material). This indicates that the experimentally observed bond lengths in [S₂₀]²⁺ indeed are not an artifact of the experimental crystal structure determination. In the following subsections, the structure of [S₂₀]²⁺ and the bonding in [S₂₀]²⁺ will be discussed in detail.

2.3.1. The Preference for Seven-Membered Cycles in [S₂₀]²⁺

The most stable neutral sulfur allotrope is the cyclo–S₈ crown. Other sulfur allotropes including cyclo–heptasulfur S₇ are known but are much less stable [40,41]. Eight-membered sulfur homocycles are also be found in the [S₈]²⁺ dication [11,14,15,16] and in the open-shell [S₈]^•+ radical cation [18]. However, when it comes to monocationic closed-shell sulfur homocycles, seven-membered rings seem to be preferred. S₇ homocycles have been experimentally found in the cations [S₇X]⁺ (R = Br, I) [12,13,22] and [S₁₉]²⁺ ([cyclo-S₇–S₄–cyclo-S₇]²⁺ [14,17]), as well as in neutral S₇O [42]. Other derivatives of [S₇X]⁺ (X = F, Cl, CN, OCN, SCN, SeCN) have been reported as well, but their crystal structures could not be determined due to their low thermal stability [43,44]. The most simple derivative [S₇H]⁺ was shown to have a branched structure with a six-membered ring ([cyclo-S₆–SH]⁺) by quantum chemical calculations [45]. A similar finding was made for the protonated S₈ molecule, which also prefers a branched [cyclo-S₇–SH]⁺ structure over the protonated S₈ crown [HS₈]⁺, although energy differences are small (see Ref [45] and Figure S9 in the Supplementary Material). In contrast, branched structures are much less stable for neutral sulfur homocycles (cf. cyclo-S₇ vs. cyclo-S₆–S) [46]. The open-shell radical cations [S₇]⁺ and [S₈]⁺ also prefer non-branched structures [18,47].

Obviously, branched structures with a three-coordinated sulfur atom are energetically preferred, when the molecules are closed-shell and carry a positive charge. The majority of the structurally determined cyclo-heptasulfur structures occupy conformation A, but conformation B has also been reported as well. In the following subsections, we will discuss the structural properties and the bonding situation (Section 2.3.2) of cyclo-heptasulfur structures with conformation A and address the energy difference between conformations A and B (Section 2.3.3).

2.3.2. Bonding and Structural Properties in [S₇R]⁺ Moieties

Table 2. Experimental (X-ray) ^a and calculated (GD3BJ + PBE0/def2-TZVPP, in italics) S–S bond lengths [pm] of selected compounds containing the [S₇R]⁺ moiety in conformation A.

Compound	S1–S2	S2–S3	S3–S4	S4–S5	S5–S6	S6–S7	S7–S1
[S7I][SbF6] [22] a	210.4(4) 207.4	200.4(4) 200.0	211.4(4) 210.7	196.3(4) 197.2	218.4(4) 216.9	190.6(4) 190.7	238.9(4) 235.2
S7O [42] a	216.3(2) 214.8	201.4(2) 200.7	212.1(2) 209.9	198.7(2) 197.6	219.6(2) 217.4	195.7(2) 194.4	228.3(2) 227.4
[(S7I)2I][SbF6]3 [13] a	211(1) 207.4	200(1) 200.0	208(1) 210.7	199(2) 197.2	221(1) 216.9	190(1) 190.7	231(1) 235.2
[(S7I)4S4][AsF6]6 [13] a	208(1) 207.4	199(2) 200.0	211(2) 210.7	200(2) 197.2	219(2) 216.9	189(2) 190.7	234(1) 235.2
[S7Br][SbF6] [12] a	211(2) 206.7	200(2) 200.1	211(2) 210.7	196(2) 197.2	218(2) 216.7	193(2) 190.5	234(2) 235.7
[S7Cl][SbF6]	N/A 206.7	N/A 200.3	N/A 210.7	N/A 197.3	N/A 216.6	N/A 190.7	N/A 235.4
[S7F][SbF6]	N/A 201.8	N/A 202.8	N/A 209.9	N/A 197.4	N/A 216.3	N/A 192.0	N/A 228.7
[S7SH][SbF6]	N/A 208.5	N/A 200.0	N/A 211.2	N/A 197.1	N/A 217.2	N/A 190.8	N/A 235.6
[S7SSH][SbF6]	N/A 207.2	N/A 201.2	N/A 210.4	N/A 197.3	N/A 216.8	N/A 191.9	N/A 231.1
Na2[S20]2[B12Cl12]3	209.9(2) 207.8	199.7(2) 200.8	212.7(2) 210.7	196.7(2) 197.3	217.6(2) 216.5	191.4(2) 191.4	239.0(2) 234.4

^a The references refer to experimental crystal structure data.

summarizes experimental and calculated S–S bond lengths in compounds with a [S₇R]⁺ moiety in conformation A. It should be noted that the experimentally measured bond lengths and their deviation from a typical S–S single bond (205 pm) [38] were reproduced very well by DFT calculations for all compounds in this study. Therefore, it can be concluded that the observed structural features are real and intrinsic properties of the cyclo-heptasulfur homocycles.

The sulfur–sulfur bonds show a pronounced bond alternation, which is typical for S₇-rings [12,13,14,17,22]. The bonds S1–S2, S2–S3, and S3–S4 show the smallest deviation from the length of an S–S single bond. The bonds S4–S5 and S5–S6 are about 10 pm shorter and longer, respectively, than expected. The largest deviations are found for the bonds S6–S7 and S7–S1. The bond S6–S7 (190 pm on average) is almost 15 pm shorter than a typical single bond and belongs to the shortest S–S bonds reported so far [48,49]. In contrast, the bond S7–S1 is extremely long (235–239 pm) and resembles the S-S bond length in dithionite [S₂O₄]²⁻ [50,51], which roughly corresponds to a bond order of 0.5. This situation is easily described by two mesomeric valence bond structures (Scheme 2). DFT calculations give Wiberg bond indices (Figure S8 in the Supplementary Material) of 0.6 for the S7–S1 bond and 1.4 for the S6–S7 bond and thus are in accord with the valence bond structures.

In the valence bond structures, the positive formal charge is localized on the three-coordinated sulfur atom S1 [46] and on the atom S6, respectively. To obtain a deeper understanding of structure and bonding, we quantum chemically calculated the structure of the branched [cyclo-S₇–SSH]⁺ cation. The substituent –SSH mimics the chain of sulfur atoms in the structure of [S₂₀]²⁺ when capped after two sulfur atoms. These DFT calculations reveal the positive charge in [cyclo-S₇–SSH]⁺ to be delocalized over the entire cation, but the highest positive charge is still located on atoms S1 and S6 (see Figure 6a and Figure S7 in the Supplementary Material).

An NBO [52] analysis was performed in order to identify internal stabilization effects via negative hyperconjugation (Figure 6b and Section S4 in the Supplementary Material) [53,54]. The antibonding σ* orbital of the S7–S1 bond is coplanar to the p-lone pairs on the sulfur atoms S2, S6, and S8. Therefore, they are all able to donate electron density into the S7–S1 σ* orbital. This leads to a delocalization of the positive charge, an occupancy of the antibonding S7–S1 σ* orbital by approximately 0.5 electrons, a shortening of the bonds S1–S2, S6–S7, and S1–S8, an extreme lengthening of the S7–S1 bond up to 231.1 pm, and an overall energetic stabilization of the entire cation. The most important contribution comes from the sulfur atom S6 which reduces its electron density by negative hyperconjugation to reduce repulsive interaction with the coplanar electron pair on the adjacent sulfur atom S5. For neutral cyclo-S₇ in chair conformation, the importance of negative hyperconjugation has been discussed before [6,46]. Thus, the observed structural features in cyclo-heptasulfur cations are the result of intramolecular charge delocalizing and stabilizing donor–acceptor interactions.

2.3.3. The Preference for Conformation A over Conformation B

We calculated the energy difference between conformations A and B for various [S₇X]⁺ cations (Figure 7). The calculated energy differences were generally small (<13 kJ mol⁻¹). For most X, conformation A was slightly preferred. B was only found to be more stable for X = F and –SSH conformations. Interestingly, the energetic order of conformations A and B just switched between the substituents –SH and –SSH. Indeed, conformation B was found experimentally for the selenium derivative [cyclo-Se₇–Se₂Cl]⁺ [55], for [Se₁₇]²⁺ [36,37], and for [S₁₉]²⁺ [14,17].

There seems to be no simple correlation explaining the preference for conformation A or B. In general, the charge delocalization is slightly more pronounced in conformer A as evident from the smaller charge on the three-coordinated sulfur atom as compared to conformer B. Note that seven-membered chalcogen rings in general are highly fluxional, which was shown by ⁷⁷Se-NMR spectroscopy in solution [56]. The preference for conformer A or B is caused by the amount of charge delocalization, negative hyperconjugation, and the repulsion of lone pairs on adjacent sulfur atoms.

Interestingly, the experimental structure of [S₂₀]²⁺ in the solid state does not exactly resemble the calculated minimum structure in the gas phase. A structure with both rings in conformation B was calculated to be lower in energy by 13 kJ mol⁻¹ (Figure S5 in the Supplementary Material). In the solid state, crystal packing (Figures S2 and S3 in the Supplementary Material) and cation–anion contacts (Figure 4a) are also important. In addition, the flexibility of the six-membered chain has to be considered, which is determined by the properties of the S–S single bond [57].

To conclude, the small energy differences between different isomers, the high flexibility of the S-S bond, and packing effects in the solid state explain the observed disorder in the crystal structure of [S₂₀]²⁺.

3. Experimental Section

Experimental details. The starting materials Na₂[B₁₂Cl₁₂] [30] and [S₈][AsF₆]₂ [11] were prepared by published procedures. Elemental sulfur was purified by sublimation. [NBu₄]Br (98%, FLUKA, Buchs, Switzerland) was commercially available and used as received. The solvent sulfur dioxide (99.98%, SCHICK, Vaihingen/Enz, Germany) was dried over CaH₂ (MERCK, Darmstadt, Germany). Reactions using SO₂ were performed in H-shaped glass apparatuses equipped with J. Young valves.

Synthesis of [NBu₄]₂[B₁₂Cl₁₂]. [NBu₄]Br (2.43 g, 10 mmol) and Na₂[B₁₂Cl₁₂] (3.00 g, 5 mmol) were dissolved in deionized water (8 mL). The product [NBu₄]₂[B₁₂Cl₁₂] precipitated as a white solid, which was separated by filtration and washed with small aliquots of water. After drying in vacuum for one day, the product remained a colorless solid (2.98 g, 3.7 mmol, 74%).

Generation of single crystals of Na₂[S₂₀]₂[B₁₂Cl₁₂]₃. [NBu₄]₂[B₁₂Cl₁₂] and [S₈][AsF₆] were dissolved in 1:2 stoichiometry in liquid sulfur dioxide. A dark blue solid precipitated, containing an insoluble blue product and soluble colorless [NBu₄][AsF₆]. The latter could be removed by repeated washing with liquid sulfur dioxide. The dark blue insoluble residue was expected to be [S₈][B₁₂Cl₁₂] based on the stoichiometry conditions used. The crystallization of this product (5 mg, 1 eq.) and S₈ (2 mg, 1 eq.) in a 10 mm glass ampoule (1 week at 165 °C, cooling rate 1 °C/h) yielded blue single crystals, which were identified as Na₂[S₂₀]₂[B₁₂Cl₁₂]₃.

Crystal structure determination. The single-crystal X-ray structure determination was carried out on a BRUKER (Karlsruhe, Germany) Smart Apex-II CCD system using Mo-K_α (0.71073 Å) radiation. The crystal was mounted onto a cryo loop using fluorinated oil and was frozen in the cold nitrogen stream of the goniometer. The structure was solved by direct methods (SHELXS) [58,59] using the crystallography software package OLEX2 [60]. Subsequent least-squares refinement on F² (SHELXL) [58,59] located the positions of the remaining atoms in the electron density maps. All atoms were refined anisotropically. The data were corrected for absorption (semi-empirical from equivalents). The crystal structure showed some disorder of the sulfur rings. Ring flipping is common in crystal structures of sulfur rings [17] and relates to the small energy differences between different conformers [61,62]. The ring flipping was modeled as disorder over two sites. Graphical representations of the structure were prepared with the program DIAMOND 3.2f [63]. Experimental details for the diffraction experiment are given in Section S2 (Supplementary Material). Crystal data for B₃₆Cl₃₆Na₂S₄₀ (M = 2993.74 g/mol) were as follows: triclinic, space group P$\overline{1}$ (no. 2), a = 9.2556(2) Å, b = 10.7509(3) Å, c = 24.9791(6) Å, α = 80.7800(10)°, β = 89.0980(10)°, γ = 86.8860(10)°, V = 2449.77(10) ų, Z = 1, T = 100.15(1) K, μ(MoKα) = 0.71073 mm⁻¹, D_calc = 2.029 g/cm³, 52,233 reflections measured (3.844° ≤ 2Θ ≤ 49.998°), 8562 unique (R_int = 0.0386, R_sigma = 0.0505). These values were used in all calculations. The final R₁ was 0.0432 (I > 2σ(I)) and wR₂ was 0.1150 (all data). Deposition Number 1791488 contains the supplementary crystallographic data for this paper. These data are provided free of charge by the joint Cambridge Crystallographic Data Centre and Fachinformationszentrum Karlsruhe Access Structures service at https://www.ccdc.cam.ac.uk/structures/ (accessed on 9 January 2025).

Quantum chemical calculations. Geometry optimizing quantum chemical calculations were performed on the GD3BJ + PBE0/def2-TZVPP level of theory. To obtain accurate energies, single-point calculations were performed at CCSD(T)/aug-cc-pVXZ (X = D, T, Q) [64,65] based on the GD3BJ + PBE0/def2-TZVPP geometries and the self-consistent field energies were extrapolated to the complete basis set limit (CBS) using the exponential three-point extrapolation outlined by Halkier et al. for some structures [66]. All basis sets used were implemented in the program package Gaussian 16, Revision C.02 [67]. We visualized structures, orbitals, and electro-static potential surfaces using the programs GaussView 6.0.16 [68] and Chemcraft 1.8 [69]. NBO analyses were carried out using NBO 3.1 implemented in Gaussian 16, Revision C.02 [70].

4. Conclusions

The crystal structure of Na₂[S₂₀]₂[B₁₂Cl₁₂]₃ containing the new homopolyatomic sulfur dication [S₂₀]²⁺ was determined. The [S₂₀]²⁺ cation consists of two seven-membered sulfur homocycles and a six-membered bridging sulfur chain ([cyclo-S₇–S₆–cyclo-S₇]²⁺). The structure, although unusual at first sight, is related to those of [S₁₉]²⁺ and [S₇X]⁺ cations. Comparison and quantum chemical calculations show that the unusual structural features are typical for this type of cation and are the result of charge delocalization and stabilizing intramolecular donor–acceptor interactions (negative hyperconjugation).

The identification of [S₂₀]²⁺ confirms previous predictions about the existence of previously unknown homopolyatomic sulfur cations and expands the range of known homopolyatomic sulfur cations.

Table 3. A compilation of experimentally known and quantum chemically predicted homopolyatomic sulfur cations ^a.

Avg. Oxidation State of Sulfur	+1/2	+1/3	+1/4	+1/5	+1/8	+1/9.5	+1/10
Monocation				[S5]+	[S8]+
Dication	[S4]2+	[S6]2+	[S8]2+			[S19]2+	[S20]2+
Reference	[11,12,13,14]	[10]	[11,14,15,16]	[21]	[18]	[14,17]	b

^a Black, bold: experimentally known in the solid state (crystal structure). Green: experimentally known in solution (ESR spectrum). Blue, italics: predicted by quantum chemical calculations. ^b This work.

summarizes all known homopolyatomic sulfur cations.

They can be divided into three different classes depending on the averaged oxidation state of sulfur. The highly oxidized cations [S₄]²⁺, [S₆]²⁺, and [S₈]²⁺ form cyclic dications, whose structures are well understood. At medium oxidation states, cyclic radical cations ([S₅]⁺ and [S₈]⁺) are formed. The missing cations in between ([S₆]⁺ and [S₇]⁺) do not exist, because they are unstable with respect to disproportionation [18]. Oxidation states lower than +¹/₈ lead to the formation of dications consisting of two heptasulfur homocycles bridged by a sulfur chain. To date, two examples of the latter class ([S₁₉]²⁺ and [S₂₀]²⁺) are known. We expect that [S₁₇]²⁺ and [S₁₈]²⁺ might exist as well. It should be noted that the selenium cation [Se₁₇]²⁺ has been reported [36,37]. However, it could be very difficult to actually isolate [S₁₇]²⁺ and [S₁₈]²⁺, because the averaged oxidation state is difficult to adjust experimentally. The choice of the counter ion, which will influence the packing in the solid state, will also play a role. Nevertheless, the story of homopolyatomic sulfur cations might well continue into the future.