Conditions for all photochemical experiments are listed in Table . All experiments were performed in a cylindrical glass photochemical reaction cell with a path length of 15.3 cm and an inner diameter of 5.2 cm . Temperature-controlled experiments were performed in a jacketed cell of the same dimensions. The front window of the cell was made of UV-grade SiO2 (Corning 7980) with greater than 90 % transmittance at wavelengths longer than 190 nm. The window was sealed to the cell with an O-ring and held in place securely with a plastic clamp. Temperature-controlled experiments also utilized a second pre-cell (5.3 cm path length) attached to the front window of the reaction cell and held under vacuum. The purpose of the pre-cell was to thermally insulate the front window and prevent condensation from occurring on the front window during low temperature experiments.

A series of mass-flow controllers controlled the flow rate of gases into the cell. Gas entered the cell through an inlet at the rear of the cell (for temperature experiments) or the front of the cell (for other experiments) and exited through an outlet at the opposite end of the cell. An 8 to 10 cm length of glass tubing packed with glass wool was placed immediately after the cell to trap aerosols formed within the cell. Following the aerosol trap, the gas was made to flow through a proportionating valve to a vacuum pump. A capacitance manometer placed before the entrance to the cell monitored the pressure within the cell. The proportionating valve was used to control the pressure within the cell to within 30 Pa of a set-point pressure, which was usually 101.3 kPa.

Prior to each temperature-controlled experiment, the reaction cell was flushed with nitrogen (N2) for several hours and the chiller was allowed to reach its set-point temperature and equilibrate for at least an hour. The temperature of the reaction cell was calibrated relative to the chiller set-point temperature on two occasions using a series of K-type thermocouples suspended within the cell. During calibrations, N2 (without SO2) was made to flow through the cell at a rate of 3.33 cm3s-1 (200 sccm, standard cubic centimeter per minute). Thermocouples placed at the front and rear of the cell gave consistent measurements to within 5 K, with a higher gradient at lower temperature. No significant differences were observed between the two calibrations. Results for the temperature calibration are shown in Fig. 1.

The temperature effect on SO2 photolysis (190 to 220 nm) was tested using the temperature-controlled reaction cell described in Sect. . Experiments were performed in a nitrogen-flushed glove box to prevent the spectral interference from the Schumann–Runge band of oxygen (O2). A 200 W deuterium (D2) arc lamp (D 200 F, Heraeus Noblelight) was used as the light source without optical filters. The output from the lamp was collimated using a fused silica plano-convex lens. 1000 ppm SO2 (in N2) was made to flow through the cell at a rate of 3.33 cm3s-1 (200 sccm) for all experiments, and pressure within the cell was held constant at 101.3 kPa, giving an SO2 partial pressure of 0.10 kPa within the cell.

Following photolysis experiments, the cell was removed from the glove box and rinsed well with dichloromethane to dissolve any elemental sulfur that was formed. The glass wool in the aerosol trap was also collected and rinsed with dichloromethane. Elemental sulfur was recrystallized from dichloromethane and converted to silver sulfide using the reduced chromium chloride method . Multiple sulfur isotope ratios were measured as described in Sect. .

Photoexcitation experiments were performed in a room air atmosphere using a 150 W UV-enhanced xenon (Xe) arc lamp (Newport Model 6254) housed in a lamp housing (Newport Model 67005), which focused and collimated the light to a 3.3 cm diameter beam. The light was passed through a liquid filter (Newport Model 51945) filled with deionized (18.2 MΩ) water and a 250 nm long-pass filter (Asahi Spectra, ZUL0250).

Following , acetylene (C2H2) was used to trap triplet excited-state SO2 (3SO2). During experiments, 5 % SO2 (in N2), pure C2H2 (atomic absorption grade), and pure N2 (ultra high purity grade) were made to flow through the cell continuously at a rate of 0.67 cm3s-1 (40 sccm), 0.03 cm3s-1 (2 sccm), and 2.63 cm3s-1 (158 sccm), respectively. Pressure in the cell was held constant at 101.3 kPa, giving a total flow rate of 3.33 cm3s-1, an SO2 partial pressure of 1.01 kPa, and a C2H2 partial pressure of 1.01 kPa within the cell during the experiments.

Following the experiments, the interior walls of the cell and the window were rinsed with ethanol and water to dissolve any organosulfur products formed. The glass wool in the aerosol trap was also collected. The organosulfur products were converted to silver sulfide using the Raney nickel hydrodesulfurization method of . Multiple sulfur isotope ratios were measured as described in Sect. .

The photochemistry of SO2+O2 with ultraviolet radiation was studied using a reaction cell at room temperature. The 150 W Xe arc lamp (described in Sect. ) was used as the light source without the liquid filter. Several experiments were performed with a 200±35 nm bandpass filter (Model 200-B, Acton Research, Acton, MA), a 250 nm long-pass filter (Asahi Spectra, ZUL0250), or a 280 nm (285 nm cut-on) long-pass filter (Newport Model FSR-WG280) to isolate particular absorption bands of SO2, but most experiments were performed with the Xe lamp and no filters (Table ).

Following experiments, the cell was rinsed well first with dichloromethane then with water. Although sulfate was the dominant product, the cell was rinsed well with dichloromethane first to ensure the removal of elemental sulfur. For two experiments performed with no oxygen, elemental sulfur was recovered. After rinsing the cell with water, 5.0 cm3 of a 1.0 moldm-3 solution of barium chloride (BaCl2) was added to the water used to rinse the cell to precipitate sulfate as barium sulfate. Barium sulfate was rinsed several times with deionized water and dried. The glass wool inside the aerosol trap was combined with the barium sulfate and all sulfate was converted to silver sulfide using the method of . Multiple sulfur isotopes were measured as described in Sect. .

Photochemical products were converted to silver sulfide (Ag2S). Ag2S was rinsed well three to four times with deionized water and then dried completely at 353 K. Dried Ag2S was weighed for total yield and about 8 µmol of Ag2S was weighed into an aluminum foil capsule for isotope analysis. Capsules were loaded into nickel reaction chambers and reacted under approximately 7.3 kPa of fluorine gas (F2) for at least 8 h at 573 K. The resultant SF6 was purified cryogenically and by gas chromatography. Isotope ratios of pure SF6 were measured as SF5+ ions using a Thermo Scientific MAT 253 Isotope Ratio Mass Spectrometer. For sample where less than 1.6 µmol of Ag2S was recovered, a microvolume (0.4 cm3 volume) cold finger was used to concentrate the sample for analysis.

Replicate analyses (N=28) of the reference material IAEA-S-1 gave 2σ standard deviations of 0.26 ‰ for δ34S, 0.014 ‰ for Δ33S, and 0.19 ‰ for Δ36S for standard isotope ratio mass spectrometry analysis. Microvolume analyses for smaller samples gave 2σ standard deviations for replicate analyses of IAEA-S-1 (N=14) of 0.9 ‰ for δ34S, 0.08 ‰ for Δ33S, and 0.8 ‰ for Δ36S. Replicate experiments performed under identical conditions had differences larger than the analytical uncertainty, suggesting experimental variability was the dominant source of uncertainty in our measurements.

To test the feasibility of Reaction (), ab initio energy calculations at multiple levels of theory were performed to search important stationary points on the SO3 PESs. The lowest SO(3Σ-)+O2(3Σg-) asymptote of the SO3 PESs involves three degenerate states, namely the singlet, triplet, and quintet states. The singlet state corresponds to the ground state of the SO3 molecule (1A1′), but does not dissociate to the ground state products SO2(1A1) + O(3P) but to SO2(1A1) + O(1D). The triplet surface corresponds to the ground state products but is adiabatically associated with a higher energy excited-state (triplet) SO3. The quintet state is much higher in energy than the other two states except at the SO(3Σ-)+O2(3Σg-) asymptote and will thus not be considered in this study.

The B3LYP density functional was initially used to optimize each minimum and/or transition state on the singlet and triplet PESs. Single point calculations at these stationary points were then carried out using an explicitly correlated version of the unrestricted coupled cluster method with single, double, and perturbative triple excitations (UCCSD(T)-F12a) .

In addition, complete active space self-consistent field (CASSCF) calculations were performed . Multi-reference Rayleigh Schrödinger perturbation theory of second order (RSPT2 or CASPT2) calculations were performed based on the CASSCF wave functions in order to account for part of the dynamical correlation. Calculations including the full valence orbitals would involve 24 electrons in 16 orbitals and were not feasible. Instead, the 2 s orbital for O and the 3s orbital for S were closed, resulting in an active space of 16 electrons in 12 orbitals (16e,12o). Dunning's augmented correlation-consistent polarized valence triplet-zeta (aug-cc-pVTZ) basis set was used in all cases . B3LYP calculations were performed with Gaussian09 and the other calculations were performed using MOLPRO .

Isotopic results will be presented with conventional δ notation: as relative deviations of isotope ratios with respect to reference sulfur.

δxS=xRproductxRreference-1, where x=33, 34, or 36 and xR is the ratio of xS to 32S in the substance. For experimental results all isotope ratios will be normalized to the isotope ratios of the initial SO2. For natural samples (i.e., stratospheric sulfate aerosol samples), the reference is Vienna Canyon Diablo Troilite (V-CDT).

Mass-independent isotope fractionations in 33S/32S and 36S/32S ratios (relative to 34S/32S ratios) will be presented as Δ33S and Δ36S values, respectively. These are defined as Δ33S=(δ33S+1)(δ34S+1)0.515-1 and Δ36S=(δ36S+1)(δ34S+1)1.90-1. Almost all physical, chemical, and biological processes fractionate isotopes mass dependently (i.e., Δ33S and Δ36S are approximately equal to 0). SO2 photochemistry, as well as the photochemistry of other sulfur gases such as CS2, are some of the few exceptions that produce mass-independent fractionation. Therefore, non-zero Δ33S and Δ36S values can be unique tracers of photochemical processes.

Results from the temperature experiments (Sect. ) are shown in Fig. 2. The SO2 photolysis (190 to 220 nm) experiments (Table ) revealed that the magnitude of the isotope effects increase with decreasing temperatures, from 129 to 191 ‰, 5.5 to 9.1 ‰, and -24.1 to -35.8 ‰ for δ34S, Δ33S, and Δ36S, respectively. The relationship between isotopes (i.e., Δ33S vs. δ34S and Δ36S vs. Δ33S) did not change significantly as temperature was decreased (0.04 to 0.05 for Δ33S/δ34S and -3.9 to -4.6 for Δ36S/Δ33S). Variability between duplicate experiments also increased at lower temperatures, highlighting the difficulty of the low temperature experiments and indicating a strong sensitivity to experimental conditions.

SO2 photoexcitation (250 to 350 nm) experiments show decreasing magnitude Δ33S and Δ36S values at lower temperatures (22.8 to 19.0  ‰ and 52.5 to 46.0 ‰ for Δ33S and Δ36S, respectively; Table ). Even at lower temperatures, the product from SO2 photoexcitation experiments show positive Δ33S and Δ36S values, as shown previously in room-temperature experiments . As discussed previously , these signatures do not match predictions from isotopologue-specific absorption cross sections , suggesting an additional isotope effect beyond differences in the initial excitation for different isotopologues.

SO2 photolysis and photoexcitation in the presence of molecular oxygen (O2) produced mass-independent sulfur isotope signatures in sulfate products (Tables  and ). Isotope ratios of this product sulfate are shown in Fig. 3 and compared with stratospheric sulfate aerosol data from ice cores . Strong agreement between Xe lamp data, 200 nm bandpass (200 BP) data, and previous SO2 photolysis data suggest an SO2 photolysis source for the isotope effects during broadband SO2 irradiation with the Xe lamp light source.

Experiments focusing on the photoexcitation band of SO2 using the 250 nm long-pass filter (250 LP) and the 280 nm long-pass filter (280 LP) display a different isotope signature, characterized by positive Δ33S and Δ36S values, whereas sulfate from SO2 photolysis has positive Δ33S and negative Δ36S values. This is consistent with previous findings , and it demonstrates that MIF in this band region is not produced by chemistry related to acetylene or oxygen. However, the magnitude of the sulfur MIF signatures (i.e., Δ33S and Δ36S values) are considerably smaller than previous experiments using C2H2 Table ;. This suggests that a considerable amount of the sulfate in the system is being produced by a mass-dependent process, such as ∗SO2+SO2→SO+SO3 . This would dilute the MIF signature. In addition, there is considerable variability (i.e., a factor of ∼2) between the two 250 nm long-pass filter experiments, despite identical conditions. The cause of this variability is uncertain but could relate to the amount of water vapor within the system.

Asymptotic energies of SO+O2 on each PES were compared with the energies obtained by separate calculations of each species with a certain spin (Table ). The CASSCF results correctly produced degenerate energies for the SO+O2 asymptote on the singlet and triplet states, which exactly match the sum of the energies of the SO(3Σ-) and O2(3Σg-) species calculated separately. The CASPT2 results also showed the correct degenerate behavior but the energies shift slightly from those calculated separately, which presumably arises from the perturbative treatment in CASPT2. On the other hand, the UCCSD(T)-F12a and B3LYP results both attribute SO+O2 on the singlet state to SO(1Δ)+O2(1Δg), and B3LYP even gives a qualitatively incorrect energy for SO+O2 on the triplet state, while UCCSD(T)-F12a attributes the triplet state to SO(Δ)+O2(3Σg-). An important conclusion from these data is that one has to use a multi-reference method if accurate global adiabatic PESs are desired for this system. Otherwise, the asymptotic behavior can be completely wrong. None of the previous studies noticed this, and as a result a single-reference method was always selected . Fortunately, single reference methods can accurately describe the PES away from the SO+O2 region; they are capable of describing several SO3 isomers and the SO2+O product channel reasonably well.

Energies for the stationary points computed using multi-reference approaches are reported relative to that of the SO(3Σ-)+O2(3Σg-) asymptote. However, the active space used in our CASSCF calculations is not sufficient to provide quantitatively accurate results, but a larger archive space is still computationally infeasible. For single-reference calculations, we chose to use the UCCSD(T) energies at optimized B3LYP geometries for the stationary points. To avoid the aforementioned problems in the SO(3Σ-)+O2(3Σg-) asymptote, we have used the UCCSD(T) energy sum of the two reactants with the correct spin calculated separately, which has been shown above to be accurate. The sum of these two energies thus provides the reference for other stationary points on both the singlet and triplet PESs. All energies of stationary points are listed in Tables  and , and the reaction pathways on both PESs are shown graphically in Fig. 4, using the energies of the UCCSD(T)//B3LYP calculations. It is seen from Tables  and that the experimental derived energy differences from between the reactants and products for the SO(3Σ-)+O2(3Σg-)→SO3(1A1′) reaction (-411.29 kJmole-1, the SO(3Σ-)+O2(3Σg-)→SO2(1A1)+O(3P) reaction (-54.56 kJmole-1) and the SO(3Σ-)+O2(3Σg-)→SO2(1A1)+O(1D) reaction (135.27 kJmole-1) are reproduced well by the UCCSD(T)-F12a//B3LYP calculations, while the other methods contain significant errors.

The differences in the photophysics and photochemistry between the photolysis region (190 to 220 nm) and the photoexcitation region (250 to 350 nm) suggest different mechanisms for MIF formation, as discussed previously .

In the 165 to 235 nm wavelength region, SO2 photolysis occurs through pre-dissociation from the bound C̃(1B2) state. Near the dissociation threshold of 218.7 nm , the quantum yield of photolysis is less than unity, although it increases to greater than 0.99 at wavelengths shorter than 215 nm . In the region where the quantum yield is close to unity (i.e., less than 215 nm), the isotope effects due to SO2 photolysis should be determined entirely by the differences in the absorption cross sections between the different isotopologues of SO2 (e.g., by isotopologue specific Franck–Condon coupling) and optical screening effects under high SO2 column densities . In the narrow spectral region from 215 to 218.7 nm, where the quantum yield of photodissociation varies, it is possible that quantum yield differences between isotopologues could potentially produce additional isotope effects beyond those predicted from absorption cross sections. However, in this region, photodissociation occurs primarily via vibronic mixing of the C̃(1B2) state levels with dissociative continuum of the electronic ground, X̃(1A1) state . Due to the high density of vibronic levels for the X̃(1A1) state, it is unlikely that there will be significant isotope effects in the coupling strength between the C̃(1B2) and X̃(1A1) states. Dissociation occurring through mixing with repulsive singlet and triplet states is expected to be small, as is the non-adiabatic coupling of the C̃(1B2) and D̃(1A1) states .

For laboratory experiments, the observed isotope effect for SO2 photolysis is a function not only of differences in the absorption cross sections but also a function of the SO2 column density. This is because the SO2 absorption cross section has significant fine structure, which causes optical screening effects to occur . This optical screening effect produces larger isotope effects at higher SO2 column densities . In addition to the above effects, there appears to be a total (or bath gas) pressure effect on Δ33S values. This manifests as reduced Δ33S values at higher total (i.e., bath gas) pressures, which is observed with He, SO2, and N2 bath gases . The mechanism responsible for these pressure effects is still uncertain, but it could suggest that 33SO2 has a longer excited-state lifetime prior to dissociation than the other isotopologues.

SO2 photoexcitation in the 250 to 350 nm absorption region also produces absorption-based isotope effects due to differences in cross sections and optical screening effects. In addition, it produces isotope effects by a completely different mechanism. SO2 photoexcitation in the 250 to 350 nm region occurs by initial excitation into a coupled Ã(1A2)/B̃(1B1) singlet excited state that undergoes intersystem crossing to the photochemically active triplet ã(3B1) state . Unlike SO2 photolysis, where the quantum yield of reaction (i.e., photolysis) is near unity, the quantum yield for intersystem crossing between the singlet and triplet states is highly variable and state-dependent. Due to the relatively low density of states in the crossing region (Ã(1A2)→ã(3B1)), the branching between quenching to the ground state and intersystem crossing to the triplet state will be a strong function of isotope substitution. argue for this isotope selective intersystem crossing as the origin of part of the isotope effects in photochemical products following SO2 photoexcitation in the 250 to 350 nm absorption region.

Photoexcitation of SO2 in the presence of O2 produces sulfate with positive Δ33S and positive Δ36S signals, similar to the organic sulfur observed in and the elemental sulfur in . This suggests that the anomalous isotope signatures observed from photoexcitation in the previous studies are a result of the photophysics and photochemistry of excited-state SO2 rather than the chemistry of the subsequent reactions (i.e., chemistry with acetylene). Our experimental results show significant discrepancy with isotope effects predicted by isotopologue-specific absorption cross sections for the 250 to 350 nm region . This is expected if isotope selective intersystem crossing is contributing to the isotope signals in addition to cross-section differences and shielding effects.

presented isotopologue-specific absorption cross sections for SO2 in the 190 to 220 nm absorption region by shifting the measured 32SO2 absorption cross sections of by an amount based on the calculated isotope shifts of . It has been unclear whether these absorption cross sections can correctly predict the isotope effects due to SO2 photolysis , as they include only isotope shifts and not other potential differences among isotopologues. Previous comparisons with experimental data showed significant discrepancies (i.e., a factor of ∼2 in δ34S values) between experimental data and that predicted by the cross sections (Whitehill and Ono, 2012; Ono et al., 2013). Such discrepancies were attributed to the difference in temperature between the cross sections, which are based on cross sections measured at 213 K (Freeman et al., 1984) and the temperature of the experiments (298 K). Given the new temperature data in the present study, it is possible to compare calculations based on the cross sections with temperature-dependent experimental isotope data. Calculations were performed as described in previous papers and are compared to experimental data in Fig. 5.

Excellent agreement with the cross sections can be seen when the observed temperature dependence on δ34S is extrapolated back to 213 K. A similar strong agreement is also seen in the Δ36S values. This new data fills in the major gap between predictions based on the cross sections and the room-temperature experimental data, and provides further support to an optical origin of mass-independent fractionation during SO2 photolysis under laboratory conditions .

Despite the strong agreement for δ34S and Δ36S values, the cross sections overpredict the magnitude of the mass-independent isotope anomaly in 33S (i.e., Δ33S values) when compared with experimental data. There are several possible explanations for this. One reason is that there are significant differences between the actual cross sections and those predicted by shifting the 32SO2 cross sections for 33SO2. Measurements by at room temperature suggest that there are some differences between the isotopologue-specific absorption cross sections aside from just the spectral shifts accounted for by . A second possibility is that the high total pressure (101.3 kPa, including the N2 bath gas) of the experiments caused a decrease in the Δ33S value relative to the values observed at lower total pressures. It has been previously observed (Masterson et al., 2011; Whitehill and Ono, 2012; Ono et al., 2013) that Δ33S values decrease in the presence of high bath gas pressures. This pressure-quenching effect is most noticeable for Δ33S and does not affect δ34S or Δ36S values as strongly.

The cross sections are semi-empirical in that they take the measured 32SO2 cross sections of and shift them using theoretical isotope shifts predicted by . Although the cross sections are not necessarily accurate, they seem to accurately predict the isotope effects during SO2 photolysis under low temperature (ca. 213 K) conditions, such as those in the stratosphere.

Our results demonstrate that photolysis of SO2 in the presence of molecular oxygen (O2) produces large amounts of sulfate with considerable mass-independent sulfur isotope anomalies. In our experimental system, there are three dominant pathways for SO3 formation: OH oxidation of SO2 (Reactions () and , if water is present), O2 oxidation of SO from SO2 photolysis (Reactions  and ), and O oxidation of SO2 via SO2+O+M→SO3+M. OH and O oxidation of SO2 (Reactions  and ) are mass-dependent . However, oxidation of SO via Reaction () will trap the isotopic composition of SO as SO3 and carry the mass-independent isotope signature from SO2 photolysis ().

We performed a series of experiments at a total pressure of 101.3 kPa, a flow rate of 6.67 cm3s-1 (400 sccm), and an SO2 partial pressure of 0.127 kPa (Table ; Fig. 6). The partial pressure of molecular oxygen was varied from 0 kPa to 19.8 kPa (0 to 19.5 % O2). In all experiments, SO2 was photolyzed via Reaction (). In the experiments with no oxygen, both elemental sulfur (S0) and SO3 aerosols were formed, with the elemental sulfur (S and related species) formed from SO via SO+SO→SO2+S. SO photolysis is expected to be a minor source of S compared to Reaction (). In the absence of oxygen, SO3 is formed primarily via O oxidation of SO2 (), which is mass dependent .

At 5.1 kPa O2 and above, elemental sulfur formation was shut off and SO3 was the major product. Under these conditions, oxidation of SO (to SO2 or SO3 via Reactions () or ()) competes with SO disproportionation Reaction ().

By comparing the Δ33S value of elemental sulfur in the absence of O2 (0 kPa O2) with the Δ33S value of sulfate in the presence of O2 (5.1 to 19.8 kPa O2), it is possible to estimate the fraction of sulfate formed through Reaction (). In particular, fR6=Δ33Ssulfate, with O2Δ33SS0, noO2, where fR6 is the fraction of total SO3 formed that comes from Reaction (). Given the product yields (Table ), the time each experiment was run, and the volume of the reaction cell (approximately 325 cm3), the sulfate formation rate per unit volume per unit time can be calculated. In experiments with 5.1 to 19.8 kPa O2, the sulfate formation rates were between 5.3×1012 moleculescm-3s-1 and 1.2×1013 moleculescm-3s-1. Combining this with the fR6 values calculated from Eq. (), we can estimate the rate of sulfate formation from Reaction () under our experimental conditions. This gave a rate for Reaction () of 3.6×1012 moleculescm-3s-1 to 6.6×1012 moleculescm-3s-1. Assuming Reaction () is a termolecular reaction, the rate for Reaction () can be written as rate R6=kR6[SO][O2][M], where kR6 is the termolecular rate constant for Reaction () and [SO], [O2], and [M] are the concentrations of SO, O2, and total third body gases (M=N2, O2) in the reaction cell. In Eq. (), the [O2] and [M] terms are known from the experimental conditions. The [SO] term is estimated by assuming a photochemical steady state for SO in the cell. SO production via Reaction () is balanced by SO destruction via Reactions () and (). This gives us a steady state SO concentration of [SO]=JSO2[SO2]kR5[O2]+kR6[O2][M], where JSO2 is the photolysis rate constant for Reaction (). This photolysis rate constant was calculated assuming a spectral irradiance for our 150 W Xe arc lamp of F0/mWnm-1=0.11⋅1.6⋅14-9⋅exp⁡(-0.013⋅(λ/nm-200))), where F0 is the spectral irradiance of the xenon lamp at wavelength λ (Ono et al., 2013). This flux might be modified slightly as a function of the distance between the cell and the lamp, due to interferences from the absorption of oxygen. However, sensitivity studies performed here and previously suggest that the effect of the oxygen absorption on the total SO2 photolysis rate is minor compared to the uncertainty in the lamp photon flux. The lamp photon flux data was determined from the manufacturer's data and uncertainty estimates were not available. Despite this, the function used by (Eq. ) was used to obtain an estimate for the total SO2 photolysis rate.

The spectral irradiance of the lamp was used to calculate the photon flux entering the cell, accounting for the absorption of the cell windows from measured transmission data. The SO2 absorption cross sections of were used to calculate the photolysis rate in the cell, accounting for optical screening effects from SO2 and O2 within the cell. With an SO2 partial pressure of 0.127 kPa, this provided a photolysis rate constant of JSO2=5.2×10-3 s-1, The rate constant for Reaction (R5) is kR5=8.0×10-37 cm3molecule-1s-1 at room temperature (298 K). Using these values and Eqs. () and (), the rate constant for Reaction () was calculated iteratively. Calculated rate constants ranged from kR6=7.3×10-38 cm6molecule-2s-1 to kR6=1.4×10-37 cm6molecule-2s-1, with an average value of kR6=1.1×10-37 cm6molecule-2s-1 (Table ). This rate estimate is consistent with the upper bound on kR6≤1×10-36 cm6molecule-2s-1 by .

The calculated rate constant (kR6) appears to decrease at 19.8 kPa O2 compared with the calculated rate for lower pO2 values. It is unclear why this behavior is observed. The relatively strong agreement for the other conditions strengthens our confidence that the model is robust.

The derived rate constant carries uncertainty due to a number of sources of error in the rate calculation. One source of error in the calculation is in the spectral irradiance of the xenon lamp, which was fit from the manufacturer's literature and not directly measured. Because the spectral irradiance is likely to change over the lamp's lifetime, the actual spectral irradiance at the time the experiments were performed might be different than the values calculated here. As the spectral irradiance in the high-energy side of the ultraviolet (190 to 220 nm) is likely to decrease over the course of the lamp's lifetime, this makes the calculated SO2 photolysis rate (and resulting SO number density) most likely to be an upper bound. Reducing the SO2 photolysis rate increases the effective rate constant. A second source of error is the assumption that we trapped 100 % of the SO3 formed as sulfate. It is possible that some fraction of the SO3 remained in the gas phase and did not condense as aerosol particles. A third source of error is the assumption that the Reaction () behaves as a termolecular reaction despite the high total pressure (101.3 kPa) of the system. It is possible that the reaction is saturated at (or near) this pressure and is thus behaving as an effective bimolecular reaction In any of these three cases, the estimate of the rate constant for Reaction () would be a lower bound on the actual termolecular rate constant.

It is also important to consider the impact of water vapor within the system. Although attempts were made to minimize the amount of water vapor in the system, there was almost certainly some water vapor in the system during our experiments. This is evidenced by the visible formation of sulfate aerosols from SO3 during the experiments. Unfortunately, we did not have the analytical capability to quantitatively constrain the amount of water vapor in the system during the experiments. The Zero Air and Ultra High Purity Nitrogen used as a source of gas to the cell had maximum of 3 ppm H2O (by volume), but there could be additional water absorbed onto the surfaces of the system while the cell was disassembled. We assume 100 % of the SO3 was trapped as sulfate, giving a lower bound estimate on the rate of Reaction ().

To further constrain the rate of Reaction () (the SO+O2+M→SO3+M reaction), we constructed a kinetic model of the chemistry occurring within the cell. We used the same data and conditions as Sect. , using the cross sections of . Oxygen and ozone photolysis rates were calculated using the cross sections of for O2 and for O3. Quantum yields for O(1D) vs. O(3P) formation from O3 photolysis were parameterized based on the recommendation of . Photolysis rates for HO2 and H2O2 were calculated using the recommended cross sections of . HO2 photolysis was assumed to produce O(1D) and OH as products, and H2O2 photolysis was assumed to produce 2OH.

The rate constants and their sources are given in Table . Effective second-order rate constants (assuming T=298 K and [M]=2.5×1019 moleculecm-3) were used for termolecular reactions. Initial guesses were made for the concentration of species within the system. The system was assumed to be in photochemical steady state and solved iteratively until convergence. Comparisons were made between the data and the calculations for fR6 values (Eq. ). Simulations were performed with values of kR6 of 1.0×10-37, 1.0×10-36, and 1.0×10-35 cm6molecule-2s-1. Since the amount of water vapor in the system was not constrained experimentally, three simulations were performed, with H2O concentrations of 0 ppm (by volume), 10 ppm (by volume), and 100 ppm (by volume), which spans a range of reasonable estimates for water vapor concentration within the system. Although water vapor in the bath gas (N2 and N2/O2) are less than 3 ppm (by volume), additional water could be absorbed onto the inner surfaces of the cell and released during the experiment. Results for 0 ppm H2O and 10 ppm H2O predict rate for Reaction () on the order of 10-36 cm6molecule-2s-1, with predictions for 100 ppm H2O being slightly higher.

There is a discrepancy between model predictions and the observed experimental behavior. In particular, lower O2 fractions produce higher estimated rates and vice versa. In addition, the model predicts rates mostly higher than the previous upper bound on the rate calculated by of 10-36 cm6molecule-2s-1. Helium was used as a bath gas for the experiments, as compared with nitrogen or nitrogen/oxygen used as the bath gas here. Nitrogen (N2) and oxygen (O2) are more efficient third body quenchers than helium. Thus, the rate of the termolecular reaction with nitrogen (or nitrogen/oxygen) as a bath gas could be higher than the maximum constraint suggested by . There is also an order of magnitude discrepancy between predictions here and those in Sect.  , with those in Sect.  being an order of magnitude smaller than those in Sect.  . This could be based on the assumption that 100 % of the SO3 was trapped as sulfate in Sect. , whereas the actual amount might be less than that (implying a higher rate than predicted in Sect. ). However, the model predicts rate constants within an order of magnitude of previous constraints from the literature and within an order of magnitude of predictions from Sect. . Based on this work, we estimate the termolecular rate constant of Reaction () to be on the order of 10-37 to 10-36 cm6molecule-2s-1. Future work is necessary to better constrain the rate of this reaction.

The experimental evidence presented above suggests the formation of SO3 via the SO+O2 reaction. Our theoretical analyses shows that the singlet PES is associated with the ground state of the SO3 molecule, and thus is the primary surface related to the SO(3Σ-)+O2(3Σg-)→SO3(1A1′) reaction (Fig. 4). As shown in Table , four isomers of SO3 are located on the singlet PES. It is predicted that the D3h SO3 isomer is the global minimum, followed by cyclic-OSOO. There are two shallower wells, denoted as trans-OSOO and cis-OSOO, at the CASPT2 and UCCSD(T)-F12a levels, but they appear to be energetically higher than the SO(3Σ-)+O2(3Σg-) asymptote at the B3LYP and CASSCF levels. No barrier was found for the formation of either trans-OSOO or cis-OSOO, but there is a barrier for the isomerization and the barrier height depends upon the level of the ab initio calculation. The rate-determining barrier for the SO(3Σ-)+O2(3Σg-)→SO3(1A1′) reaction is the one connecting cyclic-OSOO and SO3. The lowest barrier height for this reaction (given by CASPT2) is 56.6 kJmole-1. Using the partition function at the B3LYP level, a conventional transition-state theory rate calculation predicts a pressure-saturated (i.e., effective bimolecular) thermal rate constant for Reaction () at 298 K of 2.7×10-24 cm3molecule-1s-1. This is about 8 orders of magnitude lower than the experimental rate constant for Reaction () (8.0×10-17 cm3molecule-1s-1, , ), and about 6 orders of magnitude lower than the predicted effective second-order rate constant for Reaction () at 101.3 kPa total pressure (about 2.5×10-18 cm3molecule-1s-1, calculated assuming kR6=1.0×10-37 cm6molecule-2s-1 and [M]=2.5×1019 moleculescm-3). We thus conclude that the SO(3Σ-)+O2(3Σg-)→SO2(1A1)+O(3P) reaction cannot occur on the singlet surface without invoking the spin-forbidden intersystem crossing between the singlet and triplet surfaces.