Vibronic origin of sulfur mass-independent isotope effect in photoexcitation of SO₂ and the implications to the early earth’s atmosphere

Abstract

Signatures of mass-independent isotope fractionation (MIF) are found in the oxygen (¹⁶O,¹⁷O,¹⁸O) and sulfur (³²S, ³³S, ³⁴S, ³⁶S) isotope systems and serve as important tracers of past and present atmospheric processes. These unique isotope signatures signify the breakdown of the traditional theory of isotope fractionation, but the physical chemistry of these isotope effects remains poorly understood. We report the production of large sulfur isotope MIF, with Δ³³S up to 78‰ and Δ³⁶S up to 110‰, from the broadband excitation of SO₂ in the 250–350-nm absorption region. Acetylene is used to selectively trap the triplet-state SO₂ (³B₁), which results from intersystem crossing from the excited singlet (¹A₂/¹B₁) states. The observed MIF signature differs considerably from that predicted by isotopologue-specific absorption cross-sections of SO₂ and is insensitive to the wavelength region of excitation (above or below 300 nm), suggesting that the MIF originates not from the initial excitation of SO₂ to the singlet states but from an isotope selective spin–orbit interaction between the singlet (¹A₂/¹B₁) and triplet (³B₁) manifolds. Calculations based on high-level potential energy surfaces of the multiple excited states show a considerable lifetime anomaly for ³³SO₂ and ³⁶SO₂ for the low vibrational levels of the ¹A₂ state. These results demonstrate that the isotope selectivity of accidental near-resonance interactions between states is of critical importance in understanding the origin of MIF in photochemical systems.

Stable isotope fractionation theory predicts that the magnitude of stable isotope fractionation scales with the differences in isotopic mass (1, 2). Almost all physical, chemical, and biological processes in nature follow this mass-dependent scaling law, resulting in nearly all terrestrial materials with oxygen having δ¹⁷O = 0.52 × δ¹⁸O, whereas those with sulfur have δ³³S = 0.515 × δ³⁴S and δ³⁶S = 1.90 × δ³⁴S.^† Significant deviations from these mass-dependent scaling laws are referred to as mass-independent fractionation (MIF), and serve as important tracers in the earth and planetary sciences (see refs. 3–5).

Early studies suggested that MIF could result only from nucleosynthetic processes (6), and the earliest measurements of oxygen MIF in calcium–aluminum inclusions of meteorites originally were interpreted to be nucleosynthetic in origin (7). It eventually was suggested (8) that chemical processes, such as tunneling or processes associated with predissociation, also might produce MIF. The first experimental evidence for a chemical origin of MIF came from ozone generated by an electric discharge or UV radiation (9, 10). The discovery of oxygen MIF in stratospheric ozone (11) soon triggered intense research into the physiochemical origin of MIF in the ozone system (see refs. 12–14). The possible chemical origins of MIF signatures still are poorly understood.

For the sulfur isotope system (³²S, ³³S, ³⁴S, and ³⁶S), Farquhar et al. (15) made the remarkable discovery that mass-independent sulfur isotope fractionation (S-MIF) is prevalent in sedimentary rocks older than ca. 2.4 Ga but absent in rocks from subsequent periods. The disappearance of S-MIF at about 2.4 Ga (16, 17) signifies a fundamental change in the earth’s surface sulfur cycles, and generally is linked to the suppression of both SO₂ photolysis and the formation of elemental sulfur aerosols by the rise of atmospheric oxygen levels (15, 18, 19). The Archean S-MIF is considered the most compelling evidence for an anoxic early atmosphere and constrains Archean oxygen levels to be less than 10⁻⁵ of present levels (19). This model of oxygen evolution, however, depends critically on the assumption that UV photolysis of SO₂ by ∼200 nm radiation is the ultimate source of the anomalous sulfur isotope signature (18). Constraining the source of the S-MIF requires a thorough understanding of the physiochemical origins of S-MIF during the photochemistry of SO₂.

SO₂ exhibits two strong absorption band systems in the UV region: one between 185 nm and 235 nm (¹B₂←¹A₁) and the other from 240 to 350 nm (¹A₂,¹B₁ ←¹A₁) (ref. 20 and references therein); we will refer to them as the photolysis and photoexcitation bands, respectively. Excitation into the photolysis band leads to the predissociation of SO₂ into SO and O below 220 nm. Laboratory experiments by Farquhar et al. (18) showed production of large (Δ³³S up to 70‰) S-MIF by SO₂ photolysis using an ArF (193-nm) excimer laser source. This was used to link the high-energy photolysis band system to Archean S-MIF, and fueled subsequent detailed investigations (e.g., refs. 21–26) into the S-MIF production from photochemistry in this region. However, recent experiments (24–26) using broadband (as opposed to laser) light sources show S-MIF patterns different from the 193-nm experiments by Farquhar et al. (18). Large-magnitude (Δ³³S > 2.5‰) MIF is produced only by experiments with high SO₂ column densities, suggesting a strong contribution from spectroscopic self- and mutual-shielding, although additional mechanisms also may play a role (26). The elemental sulfur products produced by these experiments are characterized by large δ³⁴S fractionations and Δ³⁶S/Δ³³S ratios that differ from those observed in the Archean rock record (24–26). Discrepancies between experimental results and the geological record require a reanalysis of the origin of Archean S-MIF signatures.

SO₂ photochemistry in the photoexcitation (240–350-nm) band also has been shown to produce S-MIF (18, 25, 27, 28) and has been implicated as the source of S-MIF in stratospheric sulfate aerosols trapped in polar ice (28–31). It also has been suggested that SO₂ photochemistry in the photoexcitation band might have made secondary contributions to the S-MIF signatures during some periods of the Archean (25, 32). This band system is associated with the excitation of SO₂ into a mixed ¹A₂/¹B₁ state, which also interacts with lower-lying triplet states (³B₁, possibly also ³A₂) (Fig. 1) (20). Recently published absorption cross-sections of isotopically enriched SO₂ (27) in this region allow the accurate prediction of the MIF produced during the initial excitation step (28). In this study, we focus on the production of S-MIF by SO₂ excited into the photoexcitation band, and compare the results with the measured isotopologue specific cross-sections, to test the importance of chemistry after photoexcitation. Our results show a strong dependence of the S-MIF on the SO₂ and bath gas pressures but not on the detailed spectrum regions of excitation, suggesting that isotopologue selective vibronic coupling produces significant S-MIF independent of absorption cross-section differences. A theoretical model also is presented to test this hypothesis.

Fig. 1.

Photochemistry of SO₂ in the 240–400-nm region. (A) UV absorption cross-section for SO₂ between 240 and 400 nm (from refs. 33 and 34). (B) Vertical lines showing the spectral ranges for the different optical filters tested. (C) Schematic of the photochemistry of the experiments. SO₂ initially is excited into the coupled ¹B₁/¹A₂ states. It vibrationally relaxes (VR) via collisions with the bath gas. At low vibrational levels of the ¹A₂ state, intersystem crossing may lead to irreversible crossing to the ³B₁ state as the result of vibrational relaxation of the ³B₁ state below the origin of the ¹A₂ band. Isotope effects due to near-resonant spin–orbit coupling between the singlet and triplet states in this region may lead to mass-independent isotope anomalies in the resulting triplet-state SO₂. The triplet-state SO₂ finally reacts with acetylene (C₂H₂) to form the organosulfur products analyzed in this study. (D) Potential energy surfaces for the singlet and triplet states of SO₂ as a function of the O'-SO Jacobi distance with the S-O distance and the Jacobi angle optimized.

Methods

A series of SO₂ photochemical experiments were carried out using a flow-through photochemical system to investigate S-MIF signatures as a function of SO₂ [0.1–10 millibars (mbar)] and nitrogen bath gas (260–1,010 mbar) pressures (SI Text, Table S1). A broadband radiation source (150-W Xe arc lamp) was used to excite SO₂ to the mixed ¹A₂/¹B₁ manifold. A 250-nm longpass filter was used to avoid photochemistry from the higher-energy photolysis band (¹B₂← ¹A₁) of SO₂. Photochemistry of SO₂ in the photoexcitation band was studied previously and showed rapid quenching of singlet SO₂ by bath gas (e.g., N₂, CO₂) and reaction of the resulting triplet SO₂ with CO, SO₂, and organic molecules (see ref. 20) (Fig. 1). Experiments were carried out in the presence of acetylene (10 mbar), which efficiently reacts with triplet-state SO₂ (35) and produces organosulfur aerosols, previously characterized as (C₃H₄S₂O₃)₃ (36). These were captured and analyzed for quadruple sulfur isotope ratios using techniques described in Oduro et al. (37) and Ono et al. (26).

Results of Photochemical Experiments

All experiments produced organosulfur compounds that had minor fractionations in ³⁴S (−7.0‰ < δ³⁴S < 20.8‰), but were highly enriched in both ³³S and ³⁶S (9.1‰ < δ³³S < 87.3‰ and 13.8‰ < δ³⁶S < 135.7‰) (Table S1 and Fig. 2). This resulted in positive Δ³³S (11.9–77.8‰) and Δ³⁶S (24.3–109.8‰) values, and positive Δ³⁶S/Δ³³S ratios of 1.12–2.25. With the exception of our lowest pSO₂ experiment (0.1 mbar), experiments at lower SO₂ pressures produced higher Δ³³S and Δ³⁶S values than experiments at higher SO₂ pressures under the range of conditions studied, suggesting isotopologue self-shielding is not the dominant source of observed S-MIF anomaly. The sensitivity to pSO₂ might reflect energy transfer between mass-independently fractionated singlet or triplet-state SO₂ and mass-dependently fractionated ground-state SO₂. Such energy transfer might dilute the MIF signal by exciting non-MIF SO₂ into the reactive triplet state. In addition to pSO₂ dependence, Δ³³S values increased as total pressure decreased for experiments run at the same SO₂ pressure. Δ³⁶S/Δ³³S ratios were sensitive to the total pressure of the system, with higher values (1.98–2.25) at the highest pressure tested (1,013 mbar) and lower values (1.12–1.27) at the lowest pressure (253 mbar) (Fig. 2A). These results, particularly the positive Δ³⁶S and Δ³³S values and small δ³⁴S values, are consistent with the previous experiments (25) performed with pure SO₂ without N₂ or C₂H_2, suggesting that the observed isotope signature is characteristic of this absorption band system and not a result of the N₂ or C₂H₂ used in the experiment.

Fig. 2.

Isotopic results from experiments and calculations. (A) Results (Δ³⁶S vs. Δ³³S) from experiments using the 250-nm longpass filter for a variety of SO₂ pressures (italics, in millibars) and total pressures (bold, in millibars). (B) Results (Δ³⁶S vs. Δ³³S) from experiments using various combinations of shortpass (SP) and longpass (LP) filters. The 320 LP experiments also used a 350 SP filter, and the 300 SP experiments also used a 250 LP filter. Also in the figure (× symbols) are the results from calculations based on the Danielache et al. (27) cross-sections for the conditions tested here. (C) Results (Δ³³S vs. δ³⁴S) from all experiments, showing the large Δ³³S values associated with small δ³⁴S values. Symbols are the same as in A and B.

To test the sensitivity of the isotope effects to the detailed spectral regions of the excitation, experiments were performed with a series of longpass (250-, 295-, and 305-nm) and shortpass (300- and 350-nm) filters (Fig. S1). The use of optical filters allows testing for S-MIF signals from the high- or low-energy side of the band system (Fig. 1). Experiments performed at the same SO₂ pressure (10 mbar) and total pressure (507 mbar) conditions but with different filters to isolate the 250–300-nm, >295-nm, or >305-nm regions produced remarkably similar isotopic results, with Δ³³S between 30‰ and 36‰ and Δ³⁶S between 49‰ and 66‰ (Fig. 2B). This result suggests that the anomalous enrichment in ³³S and ³⁶S is not a strong function of excitation wavelength within this absorption band, at least within a broadband regime. Several experiments were performed with 320-nm longpass and 350-nm shortpass filters. This wavelength region corresponds to excitation into the ¹A₂ state only; it is below the origin of the ¹B₁ state (38) and above the spin-forbidden ³B₁←¹A₁ transition of SO₂, which lies between 350 and 390 nm (see references in ref. 20). The experiments were carried out at higher SO₂ (50.7 mbar) and acetylene (101 mbar) pressures, but the same total pressure (507 mbar). These produced lower Δ³³S (11.9–13.5‰) and Δ³⁶S (24.3–28.0‰) values, consistent with the higher SO₂ pressure, but with Δ³⁶S/Δ³³S values (2.05–2.08) similar to the rest of the filter experiments (1.61–1.95) (Fig. 2). The presence of S-MIF signatures from excitation exclusively into the ¹A₂ state suggests that vibronic interactions between the two singlet states (¹B₁ and ¹A₂) make a negligible contribution to the observed S-MIF signatures.

Source of MIF Signatures

Danielache et al. (27) reported UV cross-sections for isotopically enriched SO₂ (i.e., ³²SO₂, ³³SO₂, ³⁴SO₂, and ³⁶SO₂) in the 250–320-nm region. These cross-sections are measured at 8-cm⁻¹ resolution, at room temperature, and ∼1–7 mbar SO₂, and characterize the magnitude of the isotopic shifts in band positions and intensities. The measured cross-sections (27) were used to predict S-MIF signatures under the experimental conditions (spectral irradiance and SO₂ column densities) tested here and are compared with experimental results in Fig. 2B. The results show that differences in the absorption cross-sections can account for only a small fraction (<25‰) of the large (up to 78‰) Δ³³S values observed in the 250-nm longpass experiments and cannot account for the large positive Δ³⁶S values (up to 110‰) observed. In particular, the cross-sections predict large negative Δ³⁶S values for a variety of broadband light sources (Fig. 2B and figure 7 in ref. 27), in contrast to the large positive values observed. Even accounting for the systematic errors (2.5%) and SEM (5–10%) for the measured cross-sections (see results and discussion in ref. 27), the cross-sections still cannot explain the Δ³⁶S values observed (Fig. 2B).

The above cross-section model also includes the effect of self- and mutual-shielding of absorption lines under experimental conditions. Self-shielding occurs when the major isotopologue line (i.e., ³²SO₂) saturates under optically thick conditions. In this study, large S-MIF signatures are observed even under optically thin conditions. The experiments with the lowest pSO₂ (column density of 4 × 10¹⁶ molecules per cm⁻²) had over 95% optical transmission, where self-shielding is not expected to play a major role. The magnitude of S-MIF increases with decreasing SO₂ pressure, which is opposite from what is expected from self-shielding. We therefore exclude absorption-based effects, such as self-shielding or absorption cross-section differences as the main source of the observed S-MIF signatures.

Other proposed mechanisms of MIF production include nuclear field shift isotope effects, magnetic isotope effects, and symmetry-based isotope effects. The magnitude of nuclear field shift isotope effects has been estimated to be insignificant for the sulfur isotope system because of the small nuclear size difference among isotopologues (39). Magnetic isotope effects would produce anomalies only in ³³S and cannot explain the large Δ³⁶S values observed in the experiments. A symmetry-based isotope effect also is unlikely because of the lack of any intermediates or transition states with symmetrically equivalent sulfur atoms. In addition, a symmetry-based isotope effect would predict positive Δ³³S values and negative Δ³⁶S values (40), whereas positive Δ³³S and positive Δ³⁶S values are observed in the present experiments.

Intersystem Crossing as a Potential Origin of S-MIF

Although isotope substitution shifts the vibrational and rotational energy level spacing in a mass-dependent manner, the magnitudes of the shifts will be different for different excited electronic states. In systems in which the vibration–rotation levels of multiple low-lying electronic states overlap, the interactions between states may exhibit strong and level-specific isotope selectivity. In particular, pairs of levels capable of interacting with each other and that are near-degenerate for one isotopologue may be nondegenerate for other isotopologues. These effects were cited previously as a source of S-MIF during the photopolymerization of CS₂ (41, 42) and oxygen MIF during the photodissociation of CO₂ (43) and CO (44). In these three cases, the anomalous isotope effects have been attributed to differences in intersystem crossing (ISC) rates from an initially excited singlet state to a reactive (or dissociative) triplet state. Similar spin–orbit effects have been shown to cause anomalous LIF intensities in ³⁷ClO₂ vs. ³⁵ClO₂ for particular vibrational bands (45). A recent study by Muskatel et al. (46) demonstrates a theoretical basis for similar isotope effects during the photolysis of N₂. In particular, they note that the accidental overlap between different electronic states of N₂ may cause large isotope effects in certain regions of the spectrum. The importance of accidental degeneracies between interacting states in producing environmentally relevant MIF signatures remains controversial, as it has been suggested that self-shielding might have contributed to the isotope signatures observed during the CS₂ (47) and CO (48–50) (see also ref. 51) experiments. In addition, isotope effects from local interactions are likely to be isolated to narrow spectral regions where the interactions occur.

Several previous spectroscopic studies of SO₂ showed isotopologue-specific perturbations in the 250–350-nm absorption region. Analysis of several absorption bands of S¹⁸O₂ corresponding to the Clements “B” and “E” bands (310.9 and 304.4 nm, respectively) revealed that these bands of S¹⁸O₂ were significantly less perturbed than the corresponding bands of S¹⁶O₂ (52), suggesting different coupling strengths for the different isotopologues. Baskin et al. (53) reported a strong ³²SO₂ vibrational peak at 30,995 cm⁻¹ (322.6 nm) that had no corresponding ³⁴SO₂ peak at the expected location. This was attributed to perturbations caused by accidentally near-degenerate vibronic interactions in one isotopic species but not the other.

If the anomalous isotope effects were purely the result of isolated interactions at particular vibrational levels, a strong wavelength selectivity to the anomalous isotope effects would be expected, with certain regions (i.e., around the localized near-degeneracies) producing considerably larger MIF than other regions. One of the features of the present experiments is that the MIF signature shows remarkable similarity in both the higher- (250–300-nm) and lower- (295–350-nm and 305–350-nm) energy regions of the absorption band (Figs. 1 and 2B). Experiments isolating only the 320–350-nm absorption region, which lies below the origin of the ¹B₁ state and corresponds to excitation into only the ¹A₂ state, also produce S-MIF consistent with the other experiments, although with a smaller magnitude, because of the different experimental conditions (i.e., higher SO₂ pressure).

All our experiments were performed at relatively high total pressures (253–1,013 mbar) in the presence of a bath gas (N₂). Under these conditions, the collision lifetime (on the order of nanoseconds) is considerably shorter than the fluorescence lifetime (on the order of microseconds), allowing rapid collision-induced rotational and vibrational relaxation of the excited state (20, 54). Time-resolved fluorescence experiments performed at 1.33 mbar pure SO₂ showed strong resonance fluorescence from the excited level accompanied by significant fluorescence from vibrationally relaxed molecules (55). At higher SO₂ pressures of 26.6 mbar, fluorescence from highly excited states (266 nm) contained no resonance fluorescence, with the dominant fluorescence occurring around 325.5 nm and 370 nm, near the origin of the ¹B₁ and ¹A₂ states, respectively, suggesting rapid and nearly complete collisional vibrational thermalization (56). Although the collision-induced ISC might occur from any state, the rate of collision-induced vibrational relaxation is faster than the rate of collision-induced ISC (55), at least for some states. Thus, at high bath gas pressures, the ISC reaction more likely will occur from lower vibrational levels of the singlet state. This also increases the likelihood of vibrational relaxation of the ³B₁ state below the origin of the ¹A₂ state, preventing crossing back to the singlet manifold. As a result, localized near-degenerate interactions at low vibrational levels of the singlet state will be selectively expressed regardless of the state and vibrational levels initially excited into. This allows a mechanism for the expression of S-MIF from localized near-degenerate spin–orbit interactions, and also may explain the pressure dependence on the relationship between Δ³⁶S and Δ³³S values.

Theoretical Basis for Proposed Mechanism

To better understand the isotope effects during the ISC reaction of SO₂, high-level ab initio calculations of the global potential energy surfaces (PESs) for the low-lying singlet and triplet states of SO₂ were carried out (SI Text). In the Clements bands (57), about 3.5 eV above the ground electronic (¹A₁) state, there are two nonadiabatically coupled singlet ( ¹A₂ and ¹B₁) and three triplet (³B₁, ³A₂, and ³B₂) electronic states (58–60) (Fig. 2D). The ³B₂ state was not included in the present analysis, as it has no interaction with other states because of its symmetry. For each of the remaining states, ∼19,000 symmetric unique points were determined at the internally contracted multireference configuration interaction (MRCI) level (61) with the augmented correlation-consistent polarized valence triple-zeta (aug-cc-pVTZ) basis set (62) for both the sulfur and oxygen atoms. The Davidson correction (Q) (63) was applied to account for the effect of higher excitations and to reduce size-consistency errors. Nonadiabatic couplings between the two singlet states have been determined in a quasi-diabatic representation (64). In addition, the spin–orbit (SO) interactions between the singlet and triplet states has been computed using the unperturbed MRCI wave functions and Breit–Pauli Hamiltonian. As shown in SI Text (Fig. S2), the calculated absorption cross-section for the Clements bands is in good agreement with experiment. Importantly, the potential energy minimum of the ³B₁ state is about 0.2 eV lower than that of the lowest singlet state, facilitating ISC.

Franck–Condon transitions with a 250–350-nm photon bring SO₂ from the ground ¹A₁ state to the excited ¹A₂/¹B₁ manifold. As discussed above, we assume that the excited SO₂ is relaxed quickly to low vibrational levels (Table S2) of the lowest singlet ¹A₂ state because of fast nonadiabatic mixing between the two singlet states and efficient collisions with the bath gas. The ISC to the lowest triplet ³B₁ state follows (Table S2), which was modeled using a wave packet method. In particular, the time-dependent Schrödinger equation was solved numerically (65) with the nonadiabatically coupled full-dimensional Hamiltonian for the ¹B₁/¹A₂/³B₁ manifold (J = 0), as described in SI Text. Four (000, 100, 010, and 001) vibrational eigenfunctions on the ¹A₂ state were used as the initial wave packet, and the ³B₁ triplet-state population is artificially absorbed to account for the irreversibility of the ISC as a result of collisional relaxation. The parameters used in our calculations are listed in Table S3.

The lifetime of the ¹A₂ state is extracted from the population decay curve (Table S4) and used to estimate the isotope effects for ISC from each vibrational level. As shown in Fig. 3 and Fig. S3, the results clearly show the decay rates are different among the sulfur isotopologues and are not mass dependent. In particular, the (000), (100), and (001) vibrational levels show large anomalies in the decay rate of ³⁶SO₂, suggesting a strong mass-independent effect in ³⁶S. Similarly, decay from the (010) level shows large MIF in ³³S. Therefore, combined contributions from MIF at the (100) and (010) levels would explain the experimental results of positive Δ³³S and Δ³⁶S values. It is clear that this simple model cannot fully account for the experimental results; a significant number of approximations were involved. For example, the relative energies of various electronic states might not be determined accurately by the ab initio method. In addition, it is likely that the singlet excited-state SO₂ decays from a range of vibrational and rotational levels. Nevertheless, these results clearly demonstrate that there is a very strong, isotope-specific dependence on the excited-state lifetimes from individual vibrational levels.

Fig. 3.

Results for lifetime calculations for ¹A₂ states. (A and B) Decay of singlet populations for several sulfur isotopologues from the (010) and (100) vibrational states, which have rates faster than those of the (000) and (001) states (Table S4). (C and D) Isotope fractionation factor estimated from the lifetime of ¹A₂ state calculated for the four low-lying vibrational levels: and where ^xk are rate constants for ^xSO₂.

Implications to S-MIF Signatures Observed in Nature

The photolysis of SO₂ in the 185–220-nm absorption region currently is considered the most likely source reaction for Archean S-MIF (18, 19, 22–24). However, there are several issues with SO₂ photolysis as a source of the Archean S-MIF signatures. Broadband photolysis of SO₂ under a range of experimental conditions (e.g., SO₂ pressures, bath gas pressures, light sources) produces large δ³⁴S values (up to 212‰) associated with relatively small Δ³³S enrichments (maximum 25‰), resulting in low δ³³S/δ³⁴S ratios of 0.55–0.66 (24–26). In contrast, the Archean record contains large Δ³³S values (from −4 to +12 ‰) associated with high δ³³S/δ³⁴S ratios of up to 1.4 (e.g., refs. 66 and 67). In addition, S-MIF signatures produced during SO₂ photolysis become very small (Δ³³S < 2.5‰) at low SO₂ column densities (26), indicating that the production of large (Δ³³S > 2.5‰) S-MIF anomalies would require the maintenance of high SO₂ column densities in the atmosphere. Sediment digenesis and biological processes in the oceans likely mix sulfides with different Δ³³S values and dilute the S-MIF signal (68) such that the source reaction likely would have produced Δ³³S values much larger than 12‰. Significant questions remain as to whether 185–220-nm photolysis of SO₂ was the source of Archean S-MIF.

The S-MIF signatures produced in this study contain large (Δ³³S up to 78‰) MIF associated with small (<25‰) δ³⁴S values. In contrast to the photolysis band, the S-MIF signatures from the excitation band do not require a high SO₂ column density to produce large S-MIF. The major issues with the excitation band as a source of the Archean S-MIF signature are the difficulty in preserving the isotope signatures from excited-state SO₂ (relative to SO produced from SO₂ photolysis) and the positive Δ³⁶S/Δ³³S ratios (Archean rocks have Δ³⁶S/Δ³³S ∼−1.5 to –0.9; see refs. 15, 32, and 67). Several authors (25, 32) have suggested that SO₂ photochemistry from the photoexcitation region might have contributed to the Archean S-MIF signatures, and studies have shown that the UV irradiation of SO₂ in the presence of methane produces organosulfur aerosols (presumably derived from ³SO₂) that might have contributed to preservation of the Archean S-MIF signature (69). The discrepancy in Δ³⁶S/Δ³³S values requires additional study, but our calculations suggest that MIFs in ³³S and ³⁶S are produced from ISC at different vibrational levels, and our experiments demonstrated that the Δ³⁶S/Δ³³S ratio is a function of pN₂ and could potentially produce the Archean ratio under certain conditions. It should be noted that the Δ³⁶S/Δ³³S values produced from experimental photolysis of SO₂ using broadband radiation sources is too low (−1.6 under pure SO₂ but as low as −6.0 with N₂) to explain the Δ³⁶S/Δ³³S ratios observed for the Archean record. As suggested in Whitehill and Ono (25), contributions from both absorption regions might explain the Archean S-MIF signal.

Several authors (e.g., refs. 28–31) have suggested that excited-state photochemistry in the photoexcitation band might be responsible for the S-MIF signatures observed in modern stratospheric sulfate aerosols. Reaction of excited-state SO_2, particularly triplet ³SO₂, with either ground-state SO₂ [i.e., *SO₂+SO₂→SO+SO₃ (29)] or O₂ [i.e., *SO₂+O₂→SO₃+O (28)] theoretically could preserve mass-independently fractionated SO₃, and SO₃ might be hydrolyzed to form stable sulfuric acid aerosols. Whitehill and Ono (25), however, presented isotopic evidence that the *SO₂+SO₂ reaction primarily occurs via O-atom transfer from the excited-state species to the ground-state species, thus producing MIF signatures in SO, but mass-dependently fractionated SO₃. Hattori et al. (28) modeled the modern stratosphere following a large volcanic eruption and suggested that the *SO₂ formed from the photoexcitation band might react with O₂ to form mass-independently fractionated SO₃ (29–31). Their isotopic agreement, however, critically depends on the assumption that the cross-sections of Danielache et al. (27) accurately predict the isotope ratios of the reactive (i.e., triplet) SO₂ species. As we demonstrate here, significant differences between the isotope signatures predicted by the cross-sections and those observed experimentally are the result of vibronic effects after the initial excitation step, which are not taken into account in ref. 28. Ono et al. (26) showed that the isotopic signatures from SO₂ photolysis in a self-shielding regime match those from stratospheric sulfate aerosols, although a mechanism for the preservation of SO in the modern atmosphere requires additional research.

Conclusions

We report the production of very large S-MIF signatures, with Δ³³S up to 78‰ and Δ³⁶S up to 110‰, from SO₂ photochemistry in the 250–350-nm region. The origin of the S-MIF is attributed to ISC at excitation wavelengths below 320 nm. Isotope effects due primarily to absorption, as predicted by isotopologue-specific cross-sections, do not contribute significantly to the large S-MIF observed, particularly in ³⁶S. Rapid vibrational relaxation allows expression of S-MIF signatures from localized accidental degeneracies regardless of the initially excited vibronic level. The same mechanism, however, may not be applied to the 180- and 220-nm band systems of SO₂ because the quantum efficiency of photolysis is near unity below 205 nm (59), and the lifetime is sufficiently short that little vibrational relaxation occurs. Although the S-MIF signatures observed in this study, particularly the Δ³⁶S/Δ³³S ratios, do not match those from the Archean, the photochemistry in the photoexcitation band can produce large mass-independent signatures (i.e., Δ³³S values) with relatively small mass-dependent fractionations (i.e., δ³⁴S values), which is necessary to explain the preservation of large Archean S-MIF signatures. Photochemistry from the 250–350-nm absorption region should be explored further as a possible source for the geological S-MIF signatures.