The Role of Perturbations in the B-X UV Spectrum of S2 in a Temperature Dependent Mechanism for S-MIF Alex Hull, Robert W Field, Shuhei Ono MIT Department of Chemistry

Sulfur isotope ratios in rocks follow simple mathematical relationships… Stable Sulfur Isotopes: 32S (94.99%) 34S (4.25%) 33S (0.75%) 36S (0.01%) δx = ( [𝑥𝑆] [32𝑆] )sample – ( [𝑥𝑆] [32𝑆] )ref ( [𝑥𝑆] [32𝑆] )ref Kinetics and thermodynamics tell us that: δ33 = 0.515 δ34 δ36 = 1.90 δ34 Following these rules = Mass Dependent Fractionation (MDF)

Best guess: pO2 < 10-6 atm Oxygenated Atmosphere …But not always Anoxic Atmosphere Best guess: pO2 < 10-6 atm (Pavlov and Kasting, 2002) Oxygenated Atmosphere ∆𝟑𝟑=(δ33 − 0.515 δ34)1000 Mass Independent Fractionation (S - MIF) Johnston, 2011

Sulfur in Anoxic Atmosphere Volcanism HSO3 Troposphere OH O2, O H2S hν O HCO O3, NO2 SO2 SO3 HS HSO O2, HO2 hν hν HCO NO, O HS HCO hν SO H2O S hν hν HS, S S2 H2SO4 aerosol O hν S2 S4 hν S4 Reduced Pathway Oxidized Pathway S8 aerosol Ocean FeS Ba2+ Adapted from: Pavlov and Kasting (2002) and Lyons (2009) Sediment FeS2 BaSO4

Sulfur in Modern Atmosphere Volcanism HSO3 Troposphere OH O2, O H2S hν O HCO O3, NO2 SO2 SO3 HS HSO O2, HO2 hν hν HCO NO, O HS HCO hν SO H2O S hν hν HS, S S2 H2SO4 aerosol O hν S2 S4 Reduced Pathway hν S4 Oxidized Pathway S8 aerosol Ocean FeS Ba2+ Adapted from: Pavlov and Kasting (2002) and Lyons (2009) Sediment FeS2 BaSO4

B-X UV Transition in S2 Green and Western (1996) Avg. lifetime: ~30 ns Avg. lifetime: ~4 μs

Hypothesis: Isotope shifts change location where the B and B” curves intersect Perturbations (randomly) occur at J’s with significant ground state population for one isotopologue, but not the other. Collisions with inert gases can move population to states with even longer lifetimes (chemistry) Temperature dependent effect B (bright) B” 3234 (dark) Red Term Value Doorway B” 3232 (dark) J(J+1) Thermally Accessible Region

Hypothesis: Higher temperature Isotope shifts change location where the B and B” curves intersect Perturbations (randomly) occur at J’s with significant ground state population for one isotopologue, but not the other. Collisions with inert gases can move population to states with even longer lifetimes (chemistry) Temperature dependent effect B (bright) Doorway B” 3234 (dark) Red Term Value Doorway B” 3232 (dark) J(J+1) Thermally Accessible Region

Some Organization: |Ψ > 𝑢𝑝𝑝𝑒𝑟 = 𝛼 |𝜓 𝐵 >+β| ψ 𝐵" > My program calculates ~200,000 transitions. Each transition is characterized by its upper state. |Ψ > 𝑢𝑝𝑝𝑒𝑟 = 𝛼 |𝜓 𝐵 >+β| ψ 𝐵" > Each transition is sorted by the |β|2 of its upper state eigenvector For bins 0.9 < |β|2 < 1.0, 0.8 < |β|2 < 0.9, etc… calculate 𝑖 𝜎 𝑖, 3232 − 𝑖 𝜎 𝑖, 3234 , i ϵ all transitions in a given bin

Total Intensity 3232 – 3234 /arb. units 200 K More 3232 intensity Bin (|beta|^2) Total Intensity 3232 – 3234 /arb. units 32 35 39 45 54 66 84 117 Lifetime (ns) 191 525 More 3234 Intensity

Total Intensity 3232 – 3234 /arb. units 200 K More 3232 intensity Bin (|beta|^2) Total Intensity 3232 – 3234 /arb. units 32 35 39 117 45 54 66 84 Lifetime (ns) 191 525 More 3234 Intensity

Potential Fractionation! Total Intensity 3232 – 3234 /arb. units 200 K ~3% of total intensity Potential Fractionation! Bin (|beta|^2) Total Intensity 3232 – 3234 /arb. units 32 35 39 45 54 66 84 117 Lifetime (ns) 191 525

Total Intensity 3232 – 3234 /arb. units Upper state vibrational level Bin FC Factors V’

Max Ground State Population v = 20, Ω = 0 v = 19, Ω = 2 v = 20, Ω = 0 v = 19, Ω = 2 v = 19, Ω = 1 v = 19, Ω = 1 v = 19, Ω = 0 v = 19, Ω = 0 vB = 9 v = 18, Ω = 2 v = 18, Ω = 2 v = 18, Ω = 1 v = 18, Ω = 1 v = 18, Ω = 0 v = 18, Ω = 0 v = 17, Ω = 2 v = 17, Ω = 1 v = 17, Ω = 2 v = 17, Ω = 1 v = 17, Ω = 0 v = 17, Ω = 0 v = 16, Ω = 2 v = 16, Ω = 2 E – 0.05J(J+1) v = 16, Ω = 1 v = 16, Ω = 1 v = 15, Ω = 2 v = 15, Ω = 2 v = 16, Ω = 0 v = 16, Ω = 0 v = 15, Ω = 1 v = 14, Ω = 2 v = 15, Ω = 1 vB = 8 v = 14, Ω = 2 v = 15, Ω = 0 v = 15, Ω = 0 -J(J+1) J(J+1) 400 K 300 K 200 K 100 K 100 K 200 K Max Ground State Population 300 K 400 K 3234 3232

Max Ground State Population v = 20, Ω = 0 v = 19, Ω = 2 v = 20, Ω = 0 v = 19, Ω = 2 v = 19, Ω = 1 v = 19, Ω = 1 v = 19, Ω = 0 v = 19, Ω = 0 vB = 9 v = 18, Ω = 2 v = 18, Ω = 2 v = 18, Ω = 1 v = 18, Ω = 1 v = 18, Ω = 0 v = 18, Ω = 0 v = 17, Ω = 2 v = 17, Ω = 1 v = 17, Ω = 2 v = 17, Ω = 1 v = 17, Ω = 0 v = 17, Ω = 0 v = 16, Ω = 2 v = 16, Ω = 2 E – 0.05J(J+1) v = 16, Ω = 1 v = 16, Ω = 1 v = 15, Ω = 2 v = 15, Ω = 2 v = 16, Ω = 0 v = 16, Ω = 0 v = 15, Ω = 1 v = 14, Ω = 2 v = 15, Ω = 1 vB = 8 v = 14, Ω = 2 v = 15, Ω = 0 v = 15, Ω = 0 -J(J+1) J(J+1) 400 K 300 K 200 K 100 K Max Ground State Population 100 K 200 K 300 K 400 K 3234 3232

Max Ground State Population B state v = 9 E(dark)– E(bright) B” v=18 Ω=1 3232 B” v = 18 Ω=1 3234 B” v=18 Ω=0 3232 B” v=18 Ω=0 3232 J(J+1) 100 K 200 K 300 K 400 K Max Ground State Population

Max Ground State Population v = 20, Ω = 0 v = 19, Ω = 2 v = 20, Ω = 0 v = 19, Ω = 2 v = 19, Ω = 1 v = 19, Ω = 1 v = 19, Ω = 0 v = 19, Ω = 0 vB = 9 v = 18, Ω = 2 v = 18, Ω = 2 v = 18, Ω = 1 v = 18, Ω = 1 v = 18, Ω = 0 v = 18, Ω = 0 v = 17, Ω = 2 v = 17, Ω = 1 v = 17, Ω = 2 v = 17, Ω = 1 v = 17, Ω = 0 v = 17, Ω = 0 v = 16, Ω = 2 v = 16, Ω = 2 E – 0.05J(J+1) v = 16, Ω = 1 v = 16, Ω = 1 v = 15, Ω = 2 v = 15, Ω = 2 v = 16, Ω = 0 v = 16, Ω = 0 v = 15, Ω = 1 v = 14, Ω = 2 v = 15, Ω = 1 vB = 8 v = 14, Ω = 2 v = 15, Ω = 0 v = 15, Ω = 0 J(J+1) Max Ground State Population 400 K 300 K 200 K 100 K 100 K 200 K 300 K 400 K 3234 3232

Ground State Population Maximum B” v=15 Ω=1 3232 B state v = 8 E(dark)– E(bright) B” v=15 Ω=1 3234 B” v=15 Ω=0 3232 J(J+1) 100 K 200 K 300 K 400 K Ground State Population Maximum B” v=15 Ω=0 3234

For these relative energy plots, a few things are consistent: 1) The dark state energies decrease in energy, relative to bright states, with increasing J (Crossings can only occur from above) 2) The 3232 dark states are shifted higher in energy, relative to 3234 dark states Patterns! 3232 3234 3232 3234

Conclusions Next Steps Pattern of greater absorption to long lived states for 3232 relative to 3234 We’ve identified a potential mechanism for Sulfur Mass Independent Fractionation “Random” perturbations aren’t entirely random, so this kind of analysis could be applied to other species. Next Steps Self-Shielding Master Equation Modeling (absorption, collisional transfer, chemistry, etc.) Experiments

Acknowledgements Prof. Bob Field Prof. Shuhei Ono Dr. Colin Western Jun Jiang Trevor Erickson Claire Keenan Dr. David Grimes Tim Barnum Prof. John Muenter Dr. Zhenhui Du Prof. Shuhei Ono Andrew Whitehill Jeehyun Yang Dr. Colin Western

Ground State Population Maximum B” v=15 Ω=1 3232 E(dark)– E(bright) B state v = 8 B” v=15 Ω=1 3234 B” v=15 Ω=0 3232 J(J+1) 100 K 200 K 300 K 400 K Ground State Population Maximum B” v=15 Ω=0 3234

Rocks showing S-MIF FeS2 Reduced Pathway BaSO4 Oxidized Pathway Pavlov and Kasting (2002)