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A Comprehensive Sulfur Chemistry Network Including Excited S(1D) and SO(1{\Delta}) for the XODIAC Photochemical Model: Accounting for Missing Sulfur Processes in Venus and Exo-Venus Analogs

This study enhances the XODIAC photochemical model for Venus and exo-Venus analogs by computing new kinetic parameters for ground- and excited-state sulfur reactions with CO2 and incorporating a near-surface atomic sulfur source, which collectively resolves discrepancies in S3 and S4 abundances and highlights the critical role of excited states and deep atmospheric sources in shaping sulfur chemistry.

Original authors: Priyankush Ghosh, Namrata Rani, Jeehyun Yang, Karen Willacy, P. B. Rimmer, Liton Majumdar

Published 2026-04-21

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CC BY 4.0

Original authors: Priyankush Ghosh, Namrata Rani, Jeehyun Yang, Karen Willacy, P. B. Rimmer, Liton Majumdar

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Fixing the Recipe for Venus's Atmosphere

Imagine the atmosphere of Venus as a giant, swirling soup. This soup is mostly carbon dioxide (like the gas in a soda can), but it also contains a secret ingredient: Sulfur.

Sulfur is the "spice" of this soup. It's responsible for the thick, yellow clouds that make Venus so hot and bright. Scientists have been trying to write a "recipe book" (a computer model) to predict exactly how this sulfur behaves. They want to know: How much sulfur is there? Where is it? And why does it look the way it does?

The problem is, the old recipe books were missing some crucial steps. They didn't know how sulfur reacts when it gets a little "excited" (energetic) or how it interacts with the carbon dioxide soup at very high temperatures.

This paper is like a team of master chefs (the scientists) who decided to:

Test new ingredients: They simulated how sulfur reacts with carbon dioxide using super-computers.
Add "Super-Sulfur": They included a special version of sulfur that is "excited" (full of energy), which acts differently than normal sulfur.
Taste the soup: They ran their new, improved recipe through a simulation to see if it matched what we actually see when we look at Venus through telescopes and space probes.

The Key Discoveries (The "Aha!" Moments)

1. The "High Wall" Problem

The scientists looked at how normal sulfur (let's call it "Sleepy Sulfur") tries to mix with carbon dioxide.

The Analogy: Imagine trying to push a heavy boulder up a massive, steep hill to get to the other side.
The Result: The "hill" (energy barrier) is so high that "Sleepy Sulfur" rarely makes it across. It's too slow to be a major player in the atmosphere's chemistry.

2. The "Super-Sulfur" Shortcut

Then, they looked at "Excited Sulfur" (Sulfur that has absorbed energy from sunlight).

The Analogy: Imagine the same boulder, but this time it has a rocket booster attached. It doesn't need to climb the hill; it flies right over it.
The Result: This "Super-Sulfur" reacts much faster. The team calculated exactly how fast this happens and added these new "rocket-boosted" reactions to their recipe book.

3. The Missing Ingredient Mystery

Even with the new "rocket-boosted" reactions, the computer model still couldn't explain everything.

The Problem: The model predicted very low amounts of complex sulfur chains (called $S_3$ and $S_4$ ). But when we look at Venus, we see way more of these chains than the model said there should be. It was like the soup tasted like it needed more salt, but the recipe said we had added enough.
The Solution: The scientists realized the recipe was missing a source of sulfur coming from the bottom. They hypothesized that deep down, near the surface of Venus (or perhaps coming out of volcanoes), there is a hidden source of raw sulfur atoms being released.
The Fix: They added a tiny amount of this "hidden sulfur" (1 part per million) to the bottom of their model.
The Result: Bingo! Suddenly, the model produced the right amount of $S_3$ and $S_4$ . It turned out that a small, hidden source at the bottom of the atmosphere is the key to explaining the sulfur clouds we see today.

What About Alien Worlds? (Exo-Venuses)

The scientists didn't just stop at Venus. They asked: "What if we have other planets like Venus orbiting other stars?"

They tested their new recipe on three different types of "Alien Venus" scenarios:

The Chill Alien Venus: Similar to our Venus but with a weird temperature layer high up.
The Roasting Alien Venus: A planet getting 1,000 times more sunlight than Venus (very hot!).
The Super-Roasted Alien Venus: A mix of both.

The Findings:

For the "Chill" ones: The new "Super-Sulfur" reactions didn't change much. The atmosphere was too calm for the excited sulfur to make a big difference.
For the "Roasting" ones: This is where it got interesting. On planets blasted by intense starlight, the "Super-Sulfur" becomes very active.
The "Hidden Source" Effect: Just like on Venus, if these alien planets have a hidden source of sulfur coming from their surface, the whole atmosphere changes. The sulfur chains multiply, and the chemistry gets completely reshaped.

The Takeaway

Think of this paper as a detective story about the atmosphere of Venus and its alien cousins.

The Clue: The old models were missing some sulfur chains.
The Investigation: The scientists built a better microscope (quantum chemistry) to see how sulfur moves and reacts, including its "excited" forms.
The Twist: Even with the better microscope, the mystery wasn't solved until they realized there was a hidden supply line of sulfur coming from the deep, hot bottom of the atmosphere.
The Lesson: To understand these worlds, we can't just look at the top of the clouds. We have to understand the deep, hot chemistry and the hidden sources of ingredients that feed the atmosphere from below.

In short: We found a new way sulfur reacts, but the biggest discovery is that Venus (and its alien twins) likely has a secret sulfur factory at the bottom that we need to account for to understand their skies.

1. Problem Statement

Sulfur chemistry is critical for understanding the atmospheric structure, cloud formation, and evolution of Venus and Venus-like exoplanets (exo-Venuses). However, existing photochemical models suffer from significant limitations:

Incomplete Kinetic Data: Key reactions, particularly those involving ground-state sulfur $S(^3P)$ and excited-state sulfur $S(^1D)$ reacting with carbon dioxide ( $CO_2$ ), lack experimentally measured or high-level quantum chemically computed rate coefficients, especially under high-temperature, $CO_2$ -rich conditions.
Neglect of Excited States: Most models ignore excited-state sulfur species ( $S(^1D)$ ) and excited-state sulfur monoxide ( $SO(^1\Delta)$ ), despite their potential for higher reactivity and their role in opening new photochemical pathways.
Discrepancies in Observations: Current models fail to reproduce the observed abundances of polysulfur species ( $S_3$ and $S_4$ ) in the Venusian atmosphere, suggesting missing sources or reaction pathways.
Uncertainty in Exo-Venus Chemistry: The impact of these missing processes on the atmospheric chemistry of highly irradiated exo-Venus analogs remains unquantified.

2. Methodology

The authors employed a multi-stage computational approach to extend the XODIAC (eXoplanet One-Dimensional Atmospheric Chemistry) photochemical model:

A. Quantum Chemical Calculations

Electronic Structure: The reaction system $[S + CO_2]$ $[S + C O_{2}]$ was investigated for both ground-state $S(^3P)$ $S (^{3} P)$ and excited-state $S(^1D)$ $S (^{1} D)$ .
- Levels of Theory: Geometries were optimized at the WB97X-D/def2-TZVP level. Single-point energies were refined using CCSD(T)/aug-cc-pV(T+d)Z.
- Spin-Orbit Correction: Fine-structure splitting for $S(^3P)$ and excitation energies for $S(^1D)$ and $SO(^1\Delta)$ were applied using experimental values to ensure accuracy.
- Validation: $T_1$ diagnostics confirmed the single-reference character of the stationary points.
Potential Energy Surfaces (PES): The authors mapped reaction pathways, identifying transition states (TS), intermediates (RC, Int), and energy barriers.
Kinetic Modeling: Rate coefficients were calculated using the Master Equation System Solver (MESS) over 150–2000 K and 1 bar pressure.
- Barrierless Channels: Modeled using Phase Space Theory (PST) with a $-C_6/R^6$ long-range potential.
- Fitted Parameters: Temperature-dependent rates were fitted to the Modified Arrhenius equation.

B. Thermochemical Database Expansion

NASA 7-Term Polynomials: Since coefficients for excited states were missing, the authors computed NASA 7-term polynomial coefficients for $S(^1D)$ and $SO(^1\Delta)$ using Arkane (part of the Reaction Mechanism Generator).
Method: Broken-symmetry DFT calculations (UWB97X-D/def2-TZVP) were used to handle the biradical nature of the singlet states, ensuring accurate heat capacity, enthalpy, entropy, and Gibbs free energy data.

C. Photochemical Modeling (XODIAC)

Network Extension: The authors created XODIAC-2025.v2, an updated network incorporating:
- New $S + CO_2$ reactions (ground and excited states).
- Relaxation pathways for $S(^1D)$ and $SO(^1\Delta)$ via collisions with $CO_2$ and $N_2$ .
- New photodissociation channels producing excited states (e.g., $CS_2 + h\nu \rightarrow CS + S(^1D)$ ).
- Statistical branching ratios (25% singlet, 75% triplet) for photodissociation where state-resolved data is unavailable.
Simulation Scenarios:
- Venus: Four models (M0–M3) varying between the base network (v1) and extended network (v2), with and without a 1 ppm lower-boundary atomic sulfur source.
- Exo-Venus Analogs: Six models (M4–M9) testing three atmospheric profiles: (1) Venus-like with a high-altitude isotherm, (2) 1000 $\times$ solar flux, and (3) a hybrid of both. Each was run with and without the 1 ppm sulfur source.

3. Key Contributions

New Kinetic Data: Provided the first high-level quantum chemical rate coefficients for $S(^3P) + CO_2$ and $S(^1D) + CO_2$ reactions, revealing that the excited-state pathway is significantly faster due to a barrierless entrance complex.
Thermochemical Parameters: Generated and validated NASA 7-term polynomial coefficients for $S(^1D)$ and $SO(^1\Delta)$ , enabling their inclusion in standard photochemical models.
Extended Chemical Network: Developed XODIAC-2025.v2, the first network to comprehensively include excited-state sulfur chemistry and associated photochemical pathways for Venus and exo-Venuses.
Diagnostic of Missing Sources: Systematically tested the hypothesis that a deep-atmosphere or surface source of atomic sulfur is required to explain observed polysulfur abundances.

4. Key Results

A. Reaction Kinetics and Mechanisms

$S(^3P) + CO_2$ : Proceeds via a two-step mechanism with a high entrance barrier (284 kJ/mol), making it kinetically slow under Venusian conditions.
$S(^1D) + CO_2$ : Proceeds via a barrierless formation of a singlet reaction complex ( $^1RC$ ), followed by dissociation to $SO(^1\Delta) + CO$ . This pathway is orders of magnitude faster than the ground-state reaction.
Rate Coefficients: The activation temperatures ( $\gamma$ ) for all pathways are on the order of $10^4$ K, indicating strong temperature dependence.

B. Venusian Atmosphere

Impact of New Chemistry: Incorporating the extended network (v2) into the Venus model produced minor effects above 60 km. The new reactions did not significantly alter the abundances of major species ( $SO, SO_2, OCS$ ) compared to the base network.
The $S_3/S_4$ Discrepancy: Both the base (v1) and extended (v2) networks failed to reproduce observed $S_3$ and $S_4$ abundances, underestimating them by 1–2 orders of magnitude.
The 1 ppm Source Solution: Introducing a 1 ppm atomic sulfur source at the lower boundary (simulating deep-atmosphere or surface release) increased $S_3$ and $S_4$ abundances by 1–2 orders of magnitude, bringing them into agreement with observations. This suggests a missing reduced sulfur flux from below the cloud deck.

C. Exo-Venus Analogs

Isothermal/High-Flux Conditions: Under isothermal conditions (M4), the extended network showed only modest changes. However, under strong irradiation (1000 $\times$ solar flux) combined with a high-altitude isotherm (M6), the inclusion of excited-state chemistry led to pronounced changes.
Excited State Populations: In the high-flux hybrid model (M6), $S(^1D)$ and $SO(^1\Delta)$ reached mixing ratios of $\sim 10^{-9}$ and $\sim 10^{-11}$ , respectively.
Impact of Surface Sulfur Source: In exo-Venus models with a 1 ppm sulfur source (M7–M9), the chemical structure changed drastically compared to Venus.
- Polysulfur abundances increased significantly near the surface.
- Unlike Venus, where the source mainly affected $S_3/S_4$ , in exo-Venuses, the source altered the abundances of $SO, H_2S, H_2SO_4, S_2O,$ and $CO$ throughout the mid-atmosphere.
- The hybrid model (M9) showed the largest deviations, driven by the synergy of intense irradiation and the isothermal profile.

5. Significance and Implications

Resolution of Venusian Chemistry: The study identifies that the "missing sulfur" problem in Venus models is likely due to an unmodeled flux of reduced sulfur from the deep atmosphere or surface, rather than a deficiency in the gas-phase kinetics of excited states alone.
Exoplanet Characterization: The results highlight that for highly irradiated exo-Venuses, excited-state chemistry and deep-atmosphere sources can fundamentally reshape atmospheric composition. Ignoring these factors could lead to incorrect interpretations of spectral features (e.g., $CO_2$ depletion or sulfur species detection).
Future Directions: The work underscores the necessity of:
1. Investigating sulfur release mechanisms from Venus's surface or deep atmosphere (e.g., via the DAVINCI mission).
2. Incorporating excited-state species and deep-source fluxes into future exoplanet atmospheric retrieval models to avoid biases in metallicity and habitability assessments.

In conclusion, while the new excited-state kinetics did not drastically alter the Venusian model on their own, the framework established allows for the identification of missing physical processes (deep sulfur sources) and provides a robust tool for predicting the complex chemistry of Venus-like exoplanets under extreme conditions.