1. 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

2. 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 = δ34
δ36 = 1.90 δ34
Following these rules = Mass Dependent Fractionation (MDF)

3. 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 − δ34)1000
Mass Independent Fractionation (S - MIF)
Johnston, 2011

4. 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

5. 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

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

7. 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

8. 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

9. 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, − 𝑖 𝜎 𝑖, , i ϵ all transitions in a given bin

10. 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

11. 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

12. 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

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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

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