Far-infrared spectroscopy of the S8 allotropeA cold and diluted molecular beam of neutral sulfur allotropes is generated from sulfur powder. A mass spectrum of the typically generated distribution (Supplementary Fig. 1) recorded after ionization with 118 nm laser light (10.5 eV/photon) shows allotropes from S2 to S8. The sulfur atom is not observed, possibly due to its high ionization energy (10.4 eV), barely below the energy of the ionization light. The possibility that atomic S is present in the molecular beam, however, cannot be excluded. Moreover, we note that in the past sulfur allotropes larger than S8 have also been suggested to be stable, but that these were not observed here30. The present experimental distribution is dominated by the octasulfur allotrope S8, likely because the precursor sulfur powder may be composed largely of α-sulfur, formed by stacks of S8 units. Supplementary Fig. 2 provides the infrared spectrum of solid α-sulfur, supporting this idea. We note that fragmentation of S8 induced by the photoionization is unlikely, given that the sum of ionization and fragmentation energies, discussed later in this contribution, is higher than 10.5 eV.The far-infrared spectrum of neutral S8 in the 150–600 cm−1 (67–17 µm) spectral range is recorded via infrared photodissociation spectroscopy, utilizing the free-electron laser FELIX (Nijmegen, The Netherlands)31. The spectrum, presented in Fig. 1a, is composed by registering fragmentation of S8 into both S5 and S6. It shows three clear bands, centered at 187, 242 and 474 cm−1 (53.5, 41.3 and 21.1 µm).Fig. 1: Infrared spectrum of neutral S8.a Experimental far-infrared spectrum of gas-phase neutral S8. b Harmonic vibrational modes of S8, calculated by density functional theory using the geometry shown as inset, where two views of it are presented. c Far-infrared spectrum of S8 computed using molecular dynamics simulations at 50 K. Source data are provided as a Source Data file.Because this experiment relies on the absorption of more than one photon to achieve fragmentation (with the condition that the energy carried by the photons exceeds the fragmentation energy) and we cannot establish how many photons are absorbed per infrared pulse, the experiment does not allow to obtain absolute absorption cross-sections. Nevertheless, the relative absorption cross-sections are crucial to benchmark computational methods. Previous computational studies exploring the potential energy surface of S8 reported a crown-shaped ring geometry with singlet spin multiplicity as the putative ground state32. Here, we show the harmonic vibrational frequencies of S8 for such a geometry (Fig. 1b). The computed vibrational bands at 191, 243 and 467 cm−1 agree remarkably well with the experimental spectrum, both in line positions and in relative intensities. Because of the high D4d symmetry of S8, the modes at 191 and 467 cm−1 are doubly degenerate, whereas the mode at 241 cm−1 is non-degenerate. Normal mode vectors are depicted in Supplementary Fig. 3. This high symmetry means that S8 has no permanent dipole moment, rendering it invisible to microwave spectroscopy.The spectral bandwidths of the three observed bands (full-width at half-maximum, FWHM) are close to 10 cm−1, and therefore larger than the IR laser bandwidth of FELIX of 1–2 cm−1 at these wavelengths. The observed bandwidths could result from a broadening effect innate to the requirement to absorb > 20 IR photons to reach the fragmentation threshold. To test an alternative scenario of dynamical broadening at finite-temperatures, an ab-initio Born–Oppenheimer molecular dynamics (BOMD) simulation was performed. From such simulations, an IR spectrum can be obtained that includes the intrinsic vibrational linewidths, and directly comprises anharmonic effects. The temperature in previous molecular beam studies in the same experimental instrument was shown to range from 40 to 50 K33, so we took 50 K as an upper limit here. The result of the 5 ps, 0.5 fs step simulation is shown in Fig. 1c. This simulated spectrum also reproduces the three main bands of S8, with only a slightly poorer agreement in band positions than the density functional theory calculation. The dynamics simulations show that the width of these bands is intrinsically larger than the bandwidth of FELIX, as a consequence of the shape fluctuations of S8 at 50 K. They simultaneously demonstrate that at 50 K, S8 is stable, with only small shape fluctuations of the ground-state geometry, excluding fragmentation or isomeric changes. Finally, smaller features between the main bands are predicted, providing a possible agreement with weaker modes detected close to the experimental noise level. These intrinsic widths of the bands will complicate astronomical observations of free S8, as discussed later.Destruction pathways of neutral sulfur allotropesIn addition to the measurement of the far-IR spectrum of S8, the experiments allow a determination of its destruction pathways induced by IR absorption. Because the infrared-induced fragmentation mechanism is statistical in nature, fragmentation follows the lowest-energy pathways, and is likely the same which follows after the absorption of UV or visible photons. Observed fragmentation patterns are therefore crucial for astrochemical modelling of molecular abundances, so far relying on general assumptions or computations30,34. Figure 2a presents the wavelength-dependent depletion and appearance (the mass-spectral intensity ratios with and without IR laser light) of neutral S8, S6 and S5. As seen from the figure, a decrease in S8 signal (corresponding to laser induced fragmentation) coincides with an increase in S6 and S5 intensities. Such increases are not observed for the S7 and S4 channels. Therefore, it is shown experimentally that S8 fragments via a competition of the channels S8 → S5 + S3 and S8 → S6 + S2. We note that a clear signal increase for S2 and S3 is not observed, possibly because of the larger recoil energy of smaller fragments, making them more difficult to detect.Fig. 2: Fragmentation of sulfur clusters.a Wavenumber dependence of the laser-induced reduction of S8 signal compared with the signal increase detected for S5 and S6. b Fragmentation products after the collision induced dissociation of isolated S8+ clusters. c, d Density functional theory calculated fragmentation energies of S8 and S8+ fragmenting into SM and S8-M, or SM+ and S8-M species, respectively. Source data are provided as a Source Data file.To rationalize the observed fragmentation channels for S8, thermodynamic fragmentation energies for the possible S8 → SM + S8-M (M = 4–7) pathways (Fig. 2c) are calculated. The lowest fragmentation energies are calculated for the channels leading to S5 and S6 products. Although both are observed in the experiment, we note that the experiment favors S5 formation, whereas the fragmentation energy D calculated for forming S6 is lower. The reliability of the density functional theory calculated fragmentation energies are confirmed by single-point coupled-cluster (CCSD(T)) calculations (Supplementary Fig. S4). The seemingly conflicting findings between experiment and computations can be evaluated further by not only taking thermodynamic, but also kinetic factors in the fragmentation reaction into account. During fragmentation, the system will encounter energy barriers, for instance when S–S bonds are broken. The values in Fig. 2c therefore correspond to lower limits of the energy needed to fragment S8. This is explored by calculating the lowest-energy pathway along the potential energy surface describing the S8 → S6 + S2 fragmentation reaction. Supplementary Fig. S5 shows two energy barriers at 2.2 eV above the energy of S8, corresponding to the breaking of the two S-S bonds, placing a higher, kinetic energy limit for fragmentation. Further, it should be considered that fragmentation rates are not only dependent on energetics, but also on the associated entropy change favoring pathways towards trimers over dimer loss35. Nevertheless, the key observations are the experimentally determined fragmentation pathways S8 → S5 + S3 and S8 → S6 + S2.We note that the presence of sulfur in the atmospheres of gas giant exoplanets is used as evidence for photochemistry in an atmosphere that is enhanced in metals. This assumed tracer role of sulfur depends strongly on a non-volatile nature of the sulfur reservoir in planet forming disks. Our study reveals the fragmentation pathways of S8, which lead to more volatile sulfur allotropes, and hence would increase the volatility of sulfur in disks. If S8 is indeed a major reservoir of sulfur in planet forming disks, this would thus imply that sulfur is less reliable as a tracer of the metal content in gas giant atmospheres.Destruction pathways of charged sulfur allotropesBecause local surroundings determine the charge state of interstellar species, with both neutrals and ions being currently identified in the ISM36, we also investigated negatively and positively charged sulfur allotropes, using a room temperature quadrupole ion trap37. Ions were formed through sublimation at 250 °C and ionization in a plasma corona discharge, before being guided to the He filled ion trap. As shown in Supplementary Fig. S6, this preparation method leads primarily to S8+ in the cationic charge state. For anions, only S4− is observed.Experimental information about the destruction pathways of ionic sulfur allotropes is obtained via collision induced dissociation (CID)38, where a specific allotrope is isolated in the ion trap and the products of fragmentation induced by collisions with He gas are characterized. Isolating and fragmenting the S8+ allotrope leads to the formation of S5+ and S6+ products, in line with previous findings39. This is shown in the mass spectrum of Fig. 2b, where upon collision induced dissociation the intensity of the isolated S8+ decreases, with a concomitant increase in the S5+ and S6+ channels. Therefore, S8+ follows the S8+ → S5+ + S3 and S8+ → S6+ + S2 destruction pathways, like neutral S8. Here as well, calculations of fragmentation energies (Fig. 2d) show the lowest values for the channels forming cationic S5+ and S6+ products, in line with the experimental observations, although the S5+ channel is again not the thermodynamically favored.Following the fragmentation of S8+, the S6+ and S5+ products can be further isolated, allowing also characterization of their fragmentation pathways. S6+ was found to have a unique S6+ → S4+ + S2 destruction pathway, whereas for S5+ there is a competition between the S5+ → S3+ + S2 and S5+ → S2+ + S3 channels. Finally, S4+ and S3+ fragment following S4+ → S2+ + S2 and S3+ → S2+ + S. A summary of calculated fragmentation energies for the different cationic sulfur clusters is presented in Supplementary Fig. 7.Far-infrared spectroscopy of ionic S4
+ and S4
− allotropesIR induced fragmentation of S8+ proved unsuccessful, potentially due to a combination of a high fragmentation threshold, medium strength IR cross sections, large heat capacity, and importantly, the presence of He in the ion trap, acting as a heat bath that prevents reaching the required internal energy for fragmentation.In contrast, for the dominant anionic S4− allotrope, as well as for the generated S4+ fragment, we successfully recorded an IR spectrum. For S4− (Fig. 3a) only a single mode is detected in the 400–800 cm−1 (12.5–25 µm) spectral range covered in the ion trap experiments, centered at 544 cm−1 (18.4 µm). Concomitant calculations yielded a single S4− harmonic vibrational mode at 542 cm−1 (Fig. 3b), showing a near-perfect match with the experiment. The IR spectrum of S4+ (Fig. 3a) has, analogous to the S4− anion, only a single IR band within the 400–800 cm−1 range, centered at 688 cm−1 (14.5 µm). A calculation again finds an almost perfect agreement with the experiment, predicting a single vibration at 685 cm−1 (Fig. 3b). For comparison, the calculated harmonic vibrational spectrum of S8+ shows a much lower IR activity than S4+ and S4−, a potential reason for the failure to observe infrared-induced fragmentation of S8+.Fig. 3: Infrared spectra of charged allotropes.a Experimental far-infrared spectra of S4+ and S4−, measured in a room temperature ion trap. b Density functional theory calculated harmonic vibrational modes of S4+ and S4−, using the shown geometries. Transitions are broadened using Gaussian line shapes, broader than the laser spectral profile, to simulate broadening effects in the experiment. For comparison, the calculated vibrational spectrum of S8+ is also shown. Source data are provided as a Source Data file.IR absorption cross sections of sulfur allotropes and comparison to comet 67 P/Churyumov-GerasimenkoOur experiments reveal IR absorption bands for SN allotropes concentrated in the 15–22 µm range, with a trend of decreasing wavelength for smaller N. Interestingly, this wavelength range coincides with the prominent absorption detected in irradiated laboratory samples that are proposed to be representative of the refractory sulfur-containing organics detected in the comet 67 P/Churyumov-Gerasimenko40. In particular, an absorption peak near 21 µm is close to the 21.1 µm band of S8. Given that S2 and S3 desorption products were detected in the warm-up of the laboratory ices, we suggest that the organic residue also contains sulfur allotropes, including S8. Because of the relatively low fragmentation energies of only a few eV of most allotropes, the detection of S2 and S3 in irradiated sulfur bearing ices may well result from larger sulfur allotropes. We note that S2 and S3 were detected both in comet and in the laboratory residue40, and that S2 is ubiquitous in cometary comae41. This further supports the role of sulfur allotropes as a major sink of sulfur. However, we conjecture that this should be in the form of a distribution, with octasulfur S8 as most stable representative, but subject to fragmentation by external fields. Our results support the notion that the presence of S3 and S4 and a significant fraction of the S2 in the comet 67 P/Churyumov-Gerasimenko12 are due to fragmentation of S8.Based on our results we can estimate the requirements for detecting sulfur allotropes in the ISM using the JWST MIRI instrument. For neutral S8 (Fig. 1a), vibrational modes are experimentally seen at 53.5, 41.3 and 21.1 µm. Of these, only the 21.1 µm band lies within the accessible spectral range42 and therefore, could be targeted for detecting S8 in space. A key question, however, is the absolute cross section of such a band. Given the excellent agreement between the experimental infrared spectrum and the computed vibrational frequencies and relative intensities presented here, we propose the computational results as a reliable source for deducing the cross sections. Under the assumption of a rigid S8 structure, the instrument resolution limited absorption cross-sections for the 21.1 µm band increase from 2.5·10−19 to 8.0·10−19 cm2 when reducing the temperature from 40 to 1 K due to the reduction in population of excited rotational states. Of course, a flexible nature of S8, as inferred from the molecular dynamics simulations, lowers these values. We have simulated IR profiles of JWST/MIRI observations, indicating that the direct detection of cold gas phase S8 in molecular clouds is challenging, based on the required S/N ratio of the 21.1 µm band in the IR profiles, under the assumption that a significant fraction of the sulfur content goes into S8. More details are provided in the Supplementary Figs. 8 and 9. Furthermore, we note that other allotropes have much larger cross sections than S8, such as S8+ with σ = 2.6·10−18 cm2 for the predicted band at 19.7 µm, S4 with σ = 1.4·10−17 cm2 for the predicted band at 15.4 µm, S4+ with σ = 1.4·10−17 cm2 for the measured band at 14.5 µm, and S4− with σ = 3.7·10−17 cm2 for the measured band at 18.4 µm (values calculated at 5 K). A list of cross sections calculated for different sulfur allotropes is presented in Supplementary Table 1. The possibility of detecting other allotropes of course still depends on their abundance in the ISM.Final remarksThe IR spectral properties and photostability of neutral S8 in the cold and isolated conditions of a molecular beam were investigated, underlying its possible presence in cold interstellar environments. Its far-infrared signature reveals a characteristic mode at 21.1 µm, within reach by JWST, as well as clear bands at 41.3 and 53.5 µm. Computations of the IR spectrum of S8, as well as those of S4+ and S4−, measured in a room-temperature ion trap, reveal a near-perfect agreement with experimental results. These benchmark results for the calculations lend credibility to future computational work on other sulfur allotropes. For both neutral S8 and its cationic and anionic counterparts, the destruction pathways demonstrate a pronounced stability consistent with calculated thermodynamic fragmentation energies >1.5 eV that with inclusion of kinetic barriers likely exceed 2 eV. Our data allow direct tests of the presence of sulfur allotropes in space and in laboratory samples studied with infrared spectroscopy. While the direct detection of S8 in space is challenging, the presence of S2, S3 and S4 are signposts of the fragmentation of S8, strengthening the evidence that S8 is a major sink of sulfur in space. The measured IR spectra, together with the observed fragmentation chemistry, provide a key piece for solving the long-standing Sulfur Depletion Puzzle43.
Laboratory infrared spectra and fragmentation chemistry of sulfur allotropes
