Elemental sulfur aerosol-forming mechanismManoj Kumara and Joseph S. Franciscoa,1

aDepartment of Chemistry, University of Nebraska-Lincoln, Lincoln, NE 68588

Contributed by Joseph S. Francisco, December 21, 2016 (sent for review November 13, 2016; reviewed by James Lyons and Hua-Gen Yu)

Elemental sulfur aerosols are ubiquitous in the atmospheres of Venus,ancient Earth, and Mars. There is now an evolving body of evidencesuggesting that these aerosols have also played a role in the evolutionof early life on Earth. However, the exact details of their formationmechanism remain an open question. The present theoretical calcula-tions suggest a chemical mechanism that takes advantage of the in-teraction between sulfur oxides, SOn (n = 1, 2, 3) and hydrogen sulfide(nH2S), resulting in the efficient formation of a Sn+1 particle. Interest-ingly, the SOn + nH2S → Sn+1 + nH2O reactions occur via low-energypathways under water or sulfuric acid catalysis. Once the Sn+1 particlesare formed, they may further nucleate to form larger polysulfur aero-sols, thus providing a chemical framework for understanding the for-mation mechanism of S0 aerosols in different environments.

sulfur aerosols | catalysis | planetary environment | nonphotochemical |hydrogen sulfide

Sulfur chemistry is a ubiquitous component in the atmo-spheres of Venus, early Earth, and Mars (1). The different

forms of sulfur (e.g., S2−, S−, S0, S2O3

2−, SO32−, SO4

2−) provideenergy for different types of sulfur metabolisms in different en-vironments. The sulfur cycle in the Archean atmosphere is alsobelieved to have played a role in the early evolution of life onEarth (2–7). The emerging photochemical picture suggests thatreduced elemental sulfur (S0) and sulfate (SO4) are the dominantsulfur species in the Archean (2–9). However, the latest isotopesignatures of microscopic sulfides in marine sulfate deposits indicatethat the ultimate source for this metabolic sulfur cycling was at-mospherically derived S0 (10). One of the most important sources ofsulfur into the atmosphere is from volcanoes, and the most abun-dant sulfur gases are SO2 and H2S. The photochemistry of thesegases in the atmosphere yields elemental sulfur, sulfur particles,sulfuric acid, and oceanic sulfate. Scheme 1 illustrates the chemicalprocesses suggested to be important in the photochemical oxidationof volcanic sulfur species in the early atmosphere of Earth.The S0 aerosols are not only involved in the Archean life, but

are also implicated in other environments (1, 11–19). For example,polysulfur (Sx = S2→8) aerosols are thought to exist in clouds ofVenus and their role as the unknown UV absorber in its loweratmosphere has been discussed in the literature (14). The S8particles are also observed in the marine troposphere (15). Finally,the role of S8 aerosols in explaining the early climate of Marsatmosphere has also been debated (16).Despite being of broad appeal, the formation mechanism of S0

aerosols remains an open question. The photolysis of SO2 and SOby UV light with λ < 220 nm has generally been invoked to explainthe mass-independent fractionation (MIF) of isotope effects in thesulfur cycle during the Archean (2–9). However, the contribution ofother mass-independent chemical reactions to this geologic recordremains unclear. To fully understand the sulfur cycle, it is necessaryto identify all sources of sulfur compounds and account for allspecies which can occur in the atmosphere.

Results and DiscussionSOn (n = 1, 2, 3) + nH2S Potential Energy Surface. As can be seenfrom Scheme 1, which summarizes the current state of sulfurchemistry in the atmosphere, there is a gap in our understandingof the connection between sulfur oxide chemistry and sulfuraerosol formation. Herein, we describe a nonphotochemical

reaction mechanism that may possibly convert the SOn + nH2S(n = 1, 2, 3) chemistries into the S8 aerosol in the gas phase(Scheme S1). It is the thermodynamics of these processes, andtheir catalysis by water and sulfuric acid, that we investigate here.This mechanism may not only help in better understanding therole of sulfur cycle involving SOn, S8, and H2S as the potential SMIF carrier from the atmosphere to the ocean surface, but mayalso provide deeper insight into the formation mechanism of S0

aerosols in various other environments.We first explored the uncatalyzed gas-phase reactions of SOn with

nH2S using quantum-chemical calculations at the coupled clustersingle and double substitution method with a perturbative treatmentof triple excitations [CCSD(T)]/aug-cc-pVTZ//M06-2X/aug-cc-pVTZlevel of theory. We considered both singlet and triplet states for SO.Although the triplet ground state of SO is more stable than its singletstate, the calculations suggest that the 3SO + H2S reaction leads tothe formation of HS and HOS radicals, and is endothermic by33.5 kcal/mol (Fig. S1). By contrast, the 1SO + H2S reaction is highlyexothermic (Fig. S2). The relative energies of the computed transi-tion-state structures and minima for the uncatalyzed 1SO + H2S re-action are shown in Fig. S2. The possible source of 1SO is either thephotolysis of SO2 at λ < 220 nm or the partial oxidation of H2S.There have also been reports that 1SO could be ejected directly fromthe volcanic vent (20). However, the 1SO + H2S reaction would facecompetition from the 1SO + O2 → SO2 + O in atmosphere, sug-gesting that the 1SO + H2S is more likely to happen locally where theconcentration of sulfur gases is expected to be high.The 1SO + H2S reaction results in the stepwise formation of

H2S2O, which involves a barrier of 23.2 kcal/mol and has anexothermicity of 30.1 kcal/mol. The comparative analysis of thepotential energy surfaces for the 1SO and SO2 (Fig. S3) reactionsreveals that the 1SO reaction is relatively more favorable. Al-though the uncatalyzed SO2 + H2S reaction has been previouslycalculated (13), we reexamined the reaction here in greater detailat the same level of theory to facilitate the comparison between

Significance

The elemental sulfur aerosols are an important constituent in theatmospheres of Earth, Mars, and Venus. There is now evidencesuggesting that these aerosols have also played a role in theevolution of early life on Earth. Traditionally, the photolysis ofsulfur gases by UV light is thought to be the main mechanism forthe formation of sulfur particles in these atmospheres. But, inthe theoretical calculations reported here, we propose a non-photochemical mechanism for the formation of elemental sulfuraerosols that takes advantage of the interaction between sulfuroxides and hydrogen sulfide under water or sulfuric acidcatalysis. These results provide a chemical framework forunderstanding the formation mechanism of S0 aerosols inplanetary atmospheres.

Author contributions: M.K. and J.S.F. designed research; M.K. performed research; M.K.analyzed data; and M.K. wrote the paper.

Reviewers: J.L., Arizona State University; and H.-G.Y., Brookhaven National Laboratory.

The authors declare no conflict of interest.1To whom correspondence should be addressed. Email: francisc@purdue.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1620870114/-/DCSupplemental.

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the 1SO and SO2 reactions. The effective barrier for the 1SO re-action is 7.3 kcal/mol lower than that for the SO2 reaction. Theexothermicity of the H2S2O formation is dramatically higher thanthat for the H2S2O2 formation via the SO2 + H2S reaction. Thehigher reactivity of 1SO may provide an alternate mechanisticexplanation as to why SO is rarely observed in the troposphere.Once H2S2O is formed, it can either dehydrate to S2 or de-

hydrogenate to S2O that can subsequently react with H2S, resulting inthe formation of S3. Thus, the overall

1SO+H2S reaction leads to theformation of a S2 or S3 particle. Analogously, the SO2 + 2H2S andSO3 + 3H2S (Fig. S4) chemistries produce S3 or S4 and S4 or S5particles, respectively. The SO3 reaction is predicted to be more fa-vorable than the SO2 one. These mechanistic outcomes point towarda more generalized interaction between a sulfur oxide, SOn and H2S,which can be qualitatively summarized in the form of a reaction, SOn+n/(n+1)H2S → Sn+1 + Sn+2 + n/(n+1)H2O. The formation of Sn+1particle is predicted to be energetically more viable because it onlyinvolves low-barrier dehydration whereas the Sn+2 pathway must alsogo through high-barrier dehydrogenation in addition to low-barrierdehydration. Thus, it is reasonable to suggest that the SOn + nH2S→Sn+1 + nH2O is the most efficient reaction except for n = 1, where theSn+2 formation may also become feasible under certain conditions.

Reactivity Under Catalysis. Although the formation of a Sn+1 particlevia the SOn + nH2S reaction is more favorable, it still involves anappreciable thermal barrier that seems insurmountable under at-mospheric conditions. However, recent studies (21–24) suggestthat there are certain species in the atmospheres of Earth andVenus that may be able to catalyze these chemistries to such anextent that these processes become accessible. For example, H2Ois the most dominant species in the troposphere and has been

shown to catalyze hydrogen atom transfer (HAT)-based additionreactions (21). Sulfuric acid (H2SO4) is an important constituentin the Venus atmosphere (25) and has been predicted to be one ofthe most efficient catalysts available for the HAT-based reactions(22–24). Building upon these recent developments, we next ex-amined the SOn + nH2S reaction, which also involves an HATreaction, in the presence of H2O and H2SO4.The formation of H2S2O from the 1SO + H2S reaction and its

subsequent dehydration to S2 becomes facile under H2O or H2SO4catalysis (Fig. 1). H2SO4 turns out to be a better catalyst than waterbecause of its ability to stabilize reactants and products by formingsterically more favorable double hydrogen-bonding interactions. Thealternate decomposition pathway for H2S2O, which leads to S2O, isalso significantly impacted under catalysis. However, the barriers forthe S2O-forming decomposition under catalysis are relatively higherthan the dehydration one, suggesting that the probability of this de-composition pathway in water-rich surfaces or acidic environmentsmay be quite low. H2S2O in the 1SO + H2S reaction is formed withan excess energy of 30.1 kcal/mol, which may play a role in making aS2O-based S3 channel accessible under catalytic conditions.On the other hand, we only examined the SO2 + 2H2S → S3 +

2H2O-forming pathway in the presence of a single H2O and H2SO4molecule (Fig. 1). This is because the S4-particle-forming pathwaysare mediated by very high-lying transition states (Fig. S3) and are notexpected to become accessible even under H2O or H2SO4 catalysis.The overall SO2 + 2H2S → S3 + 2H2O reaction is calculated to be5.7 kcal/mol exothermic. The uncatalyzed H2S2O2 formation involvesan effective barrier of 30.5 kcal/mol. Under H2O andH2SO4 catalysis,the reaction barrier is appreciably lowered to 14.6 and 14.7 kcal/mol,respectively. The subsequent dehydration of H2S2O2, which producesS2O, has a barrier of 28.4 kcal/mol and an exothermicity of 2.5 kcal/molthat are significantly impacted under catalysis. H2SO4 producesmore catalytic effect than water in this case; the dehydration barriersfor the H2SO4- and H2O-catalyzed reactions are lowered to 12.1 and15.8 kcal/mol, respectively. The reaction of S2O with H2S and theeventual decomposition of H2S3O into S3 + 2H2O are significantlyinfluenced under catalysis. Although the S3 formation via the SO2 +2H2S reaction is 11.4 kcal/mol less exothermic than that in the 1SO +2H2S reaction, it is still expected to be the favored pathway becauseit bypasses the high-barrier dehydrogenation step, which significantlylowers the energetics of the overall reaction. The effect of catalysison the S4-forming pathway from the SO3 + 3H2S reaction is alsoappreciable; all of the transition states are submerged below theseparated reactants and the overall reaction occurs in a barrierlessmanner (Fig. 1). Moreover, the complexed S4 particle, which is hy-drogen-bonded with catalyst, H2O or H2SO4, is at least 18.0 kcal/molmore stable than SO3 and ∼7.0 kcal/mol more stable than free S4and catalyst. Among all of the sulfur gases considered, the sulfurparticle formation via the SO3 reactions is the most favorable. Fig. 2summarizes the optimum path for the Sn+1 formation from the SOn+nH2S reaction under H2SO4 catalysis. This qualitative profile revealsan interesting reactivity pattern; for a given interaction between SOnand nH2S, there are n high-energy dehydrogenation channels thatmay or may not open up depending upon reaction conditions.

Redefining the Formation Mechanism of S0 Aerosols. The S0 aerosolsin the anoxic atmosphere of Archean are suggested to be producedby the UV photolysis of SO2 at λ< 220 nm (2–9). However, thepresent results suggest a nonphotochemical mechanism for theformation of these S0 aerosols, in which the Sn+1 particle is formedfrom the interaction of H2O- or H2SO4-bound H2S with SOn (Fig.3). This indicates that once S2, S3, or S4 is formed, it could initiate aself-reaction that would build larger S0 particles. The mechanisticbeauty of this aerosol-forming chemical process is that it does notrequire the conventional gas-phase three-body sulfur atom re-combination, S + S, required for forming S2 (5, 26, 27) or the UVphoton-induced reaction between S and SH to form S2 and H (28).It should be noted that several S2–4 allotropes generally have very

Scheme 1. Sulfur photochemistry in an anoxic early atmosphere. Sulfur isemitted to the atmosphere from volcanoes as sulfur dioxide and hydrogensulfide, and is removed by rainout of soluble gases and by formation anddeposition of sulfate and elemental sulfur particles.

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low vapor pressures in planetary atmospheres (7) However, theconsideration of the kinetics of condensation may make these gas-phase sulfur self-reactions important under certain conditions.This mechanism has broad implications. For example, in Venus

clouds, the exact source of polysulfur particle, which absorbs UVlight, is unknown (14). The present calculations suggest that the Sn+1formation is the most favorable under H2SO4 catalysis. The Sn+1particle may then nucleate into the polysulfur particle. Sulfur speciesare abundantly available in the Venus atmosphere. The estimatedconcentration of SO2 lies in the range of 180± 50 ppm (25) and 130±35 ppm (29), whereas the H2S concentration has been predictedto be 80 ± 40 ppm (30). H2SO4 and H2O are present in ∼5- and∼30-ppm amounts, respectively (31), which lends support to sucha mechanism. In a recently studied kinetic model of Venus chemistry(1), the SO3 mixing ratio in the 40–45-km altitude inversely correlateswith the sulfur particle mixing ratio. The reaction of SO3 with 3H2Sto form S4 may explain this inverse correlation. The SO3 + H2S re-action involves a relatively smaller barrier than that of SO2 +H2S. In35–45-km altitude, the H2SO4 mixing ratio is ∼5 ppm, implying that a

significant fraction of H2SO4 may exist as a van der Waals complexwith H2S, and thus may catalyze the SO3+H2S chemistry by invokinga bimolecular reaction between SO3 and H2SO4••H2S.The CCSD(T) calculated binding energy of H2SO4••H2S complex

is 5.3 kcal/mol. The equilibrium constants for the H2SO4••H2Scomplex calculated at various temperatures are collected in Table 1.The SO3 +H2SO4••H2S reaction occurs in a low-energy manner andis strongly exothermic. Note that the SO2 mixing ratio in the middleatmosphere is the highest among the sulfur gases (17, 18) implyingthat the SO2 + H2SO4••H2S reaction would also make an impor-tant contribution toward the overall elemental sulfur production viaSOn + nH2S reaction. These conclusions are consistent with the factthat the sulfur cycles in the middle atmosphere are fast. Althoughchlorosulfane chemistry has been previously proposed to explain theelemental sulfur aerosols (30), the present results suggest a directconnection between the chemistries of sulfur gases and elementalsulfur particles.In a recent Venus model by Zhang et al. (18), a strong anti-

correlation between the sulfur gases (SO3 and SO) and the elemental

Fig. 1. Calculated reaction profiles for the gas-phase reactions of SOn (n = 1, 2, 3) with H2S, (black), H2S–H2O (magenta) and H2S–H2SO4 (green), respectively.Relative energies (kcal mol−1) of minima and transition-state structures are calculated at the CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ level of theory. Notethat the SO reactions have been calculated at the uCCSD(T)/aug-cc-pVTZ//uM06-2X/aug-cc-pVTZ level.

866 | www.pnas.org/cgi/doi/10.1073/pnas.1620870114 Kumar and Francisco

sulfur aerosol profiles below 65 km has also been observed. Thethermal reactions of SO3 and SO with H2SO4••H2S clearly explainthis anticorrelation. These thermal reactions not only provide usefulmechanistic insights into an important sink of sulfur gases below90 km in the Venus atmosphere, but may also help in understandingthe mixing profiles of SO and SO2 at higher altitudes (1, 17, 18, 32–36). At 96-km Venus atmosphere, the rates of the SO3 hydrationand the SO3 photolysis are found to be comparable (17), which issuggestive of the fact that nearly half of the sulfur in H2SO4 goes intoSO3 and produces the inversion layers of SO2 and SO. However, our

calculations on the reactions of SO2 and SO3 with H2X (X = O, andS) suggest that the bimolecular reactions of sulfur gases with H2Sinvolve smaller barriers than the analogous reactions involving H2O(Fig. 4). This indicates that the SO3 + H2S reaction under H2SO4

catalysis may occur even at higher altitude, leading to the formationof elemental sulfur aerosol.In the Venus photochemistry model analyzed byMills (37), the SO

and S2O sulfur gases, in addition to SO2, are present in significantamounts in the middle atmosphere, which makes the low-barrierSO +H2SO4••H2S and S2O +H2SO4••H2S chemistries important forthe S2- and S3-formation mechanisms. A recently observed correla-tion between SO2 depletion and enhancement in UV absorber alsoendorses this nonphotochemical mechanism (33). This mechanismalso opens up a chemical channel for the formation of S8 aerosols inthe Mars atmosphere, which have been shown to play a role in Mars’early climate (16).

Fig. 2. Reaction scheme network showing the optimum path for the sulfuricacid-assisted formation of elemental Sn+1 aerosols from the SOn (n = 1, 2, 3) +nH2S reaction. The blue and green connections represent the favorable path-ways whereas the red connections represent high-energy less likely pathways.

Table 1. Calculated equilibrium constants for the complexes of hydrogen sulfide (H2S) with water (H2O),thiosulfurous acid (H2S2O2), sulfuric acid (H2SO4), and carbonic acid (H2CO3) at various temperatures

Equilibrium constant, Keq, cm3•molecule−1

Temperature, K H2O••H2S (ΔE = −1.36) H2S2O2••H2S(ΔE = −5.32) H2CO3

••H2S(ΔE = −5.07) H2SO4••H2S(ΔE = −6.69)

200 4.35 × 10−22 1.73 × 10−20 6.21 × 10−20 2.79 × 10−18

210 3.71 × 10−22 8.99 × 10−21 3.42 × 10−20 1.26 × 10−18

220 3.23 × 10−22 4.97 × 10−21 1.99 × 10−20 6.17 × 10−19

230 2.85 × 10−22 2.90 × 10−21 1.23 × 10−20 3.22 × 10−19

240 2.56 × 10−22 1.78 × 10−21 7.87 × 10−21 1.78 × 10−19

250 2.32 × 10−22 1.14 × 10−21 5.25 × 10−21 1.03 × 10−19

260 2.13 × 10−22 7.54 × 10−22 3.63 × 10−21 6.28 × 10−20

270 1.98 × 10−22 5.17 × 10−22 2.58 × 10−21 3.97 × 10−20

280 1.85 × 10−22 3.65 × 10−22 1.89 × 10−21 2.60 × 10−20

290 1.74 × 10−22 2.64 × 10−22 1.42 × 10−21 1.76 × 10−20

298.15 1.67 × 10−22 2.07 × 10−22 1.14 × 10−21 1.31 × 10−20

300 1.65 × 10−22 1.96 × 10−22 1.09 × 10−21 1.23 × 10−20

CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ calculated binding energies of the H2S complexes are given in parentheses.

Fig. 3. Reaction scheme showing the optimum path for the formation of ele-mental S8 aerosols from the SOn (n = 1, 2, 3) + nH2S reaction. The green con-nections represent the probable pathways whereas the red connectionsrepresent less likely pathways.

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Elemental sulfur deposits are also common at volcanic ventsand fumaroles where high-temperature discharge gas is supersat-urated in sulfur (38) as a result of equilibrium chemical reactionsinvolving a variety of magmatic sulfur gases. The reaction betweenSO2 and H2S has been used to explain these sulfur sediments (39).It is important to note that in Kawah Ijen fumarole discharges

(38), water is the most abundant gas species, followed by carbondioxide (CO2) and sulfur gases, SO2 and H2S. As a result, an ap-preciable fraction of H2O may exist in a complexed form with H2S.This may alter the energetics of the overall elemental sulfur forma-tion by invoking the bimolecular reaction between SO2 andH2O••H2S. Our results indicate that the barrier for the rate-determining step of the reaction between SO2 and H2O••H2S islowered by ∼40% compared with the uncatalyzed SO2 + H2S re-action. Alternatively, H2O may add across either CO2 to form car-bonic acid (H2CO3) or SO2 to form thiosulfurous acid (H2S2O2),which may subsequently influence the SO2 + H2S reaction. BothH2CO3 (–C=O, OH) and H2S2O2 (–S=O, OH) form strong com-plexes with H2S (Table 1) and possess mandatory functionalities toallow the SO2 + H2S reaction to occur under acid catalysis. Consid-ering that these proposed chemical processes are all H2S-based, andno elemental sulfur formation has been seen in the absence of H2S(40), the results could help in better understanding the geochemistryof the magmatic–hydrothermal systems.In summary, we have used electronic structure calculations to

suggest a nonphotochemical mechanism for the formation ofelemental sulfur aerosols in planetary atmospheres. The mech-anistic beauty of this proposal is that the reactions of sulfur ox-ides and hydrogen sulfide under water or sulfuric acid catalysisprovide low-energy pathways for the formation of S2–S4 parti-cles. Interestingly, the uncatalyzed reactions of sulfur oxides andhydrogen sulfide result in the intermediates that are functionallysimilar to sulfuric acid, which points to the fact that these sulfurchemistries could be autocatalyzed.

MethodsThe SOn (n = 1, 2, 3) + nH2S reactions in the gas phase have been examined inthe absence and presence of H2O and H2SO4 catalysts. The uncatalyzed reactionshave been briefly explored whereas the effect of catalysis on the most probablereactions has been examined in detail. In particular, the effect of H2O or H2SO4

catalysis on the H2S addition reactions and the subsequent H2O elimination re-actions have been explored. The effect of catalysis on the dehydrogenation reac-tions has not been examined because these reactions involve very high barriers andare less likely to be important in atmosphere. The impact of catalysis was quantifiedby calculating the reaction profiles for the bimolecular reactions between the H2O-or H2SO4-bound H2S and SOn. All of the reactions have been calculated assumingthe singlet ground state except for the SO reactions, which have been explored forboth the singlet and triplet states. The singlet SO reactions have been examinedbecause the spectroscopic signatures of the direct singlet SO ejection from thevolcanic vent have been detected (20). All calculations were performed withGaussian 09 (41). All geometries were optimized using the density-functional theorymethod, M06-2X (42), and the augmented correlation-consistent basis set, aug-cc-pVTZ (43). Because the open-shell 1SO is more stable than the closed-shell one, thecalculations involving 1SO have been done using the uM06-2X/aug-cc-pVTZ level oftheory. The energetics were further improved by performing single-point calcula-tions at the CCSD(T) (44) and the aug-cc-pVTZ basis set. This level of theory hasbeen found to provide an accurate description of hydrogen atom transfer-basedchemistries in the recent past (23, 24). All stationary points were characterized byfrequency calculations and reported energies include zero-point energy correc-tions (unscaled) from the method used for geometry optimization.

ACKNOWLEDGMENTS. We are grateful to the Holland Computing Center,University of Nebraska-Lincoln for computational support of this work.

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