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Cis--Trans Rotational Isomerism of Seleno-, Thio-, and Formic Acids and Their Dimers: Chemical Kinetics under Interstellar Conditions

This study presents chemical kinetic rate constants for the cis-to-trans isomerization of seleno-, thio-, and formic acids and their dimers across a temperature range of 10 to 300 K, utilizing multidimensional gas-phase calculations to guide the understanding of tunneling reactions in cryogenic matrices and interstellar ice grains.

Original authors: Judith Wurmel, John M. Simmie

Published 2026-01-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Judith Wurmel, John M. Simmie

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

Imagine a tiny, invisible dance floor floating in the freezing cold of deep space. On this floor, molecules are constantly spinning and flipping, trying to find the most comfortable position. This paper is about studying how three specific types of "molecular dancers" (Formic acid, Thio-formic acid, and Seleno-formic acid) change their shapes, and how fast they do it.

Here is the story of the research, broken down into simple concepts:

1. The Two Poses: Cis and Trans

Think of these acid molecules like a person holding a heavy backpack.

The "Trans" pose (Z-configuration): The backpack is on the back, and the person is standing straight. This is the comfortable, relaxed, low-energy pose. It's like sitting in a cozy armchair.
The "Cis" pose (E-configuration): The backpack is awkwardly strapped to the front, making the person hunch over. This is the uncomfortable, high-energy pose. It's like trying to sleep in a twisted position.

In the cold of space, molecules naturally want to be in the comfortable "Trans" pose. But sometimes, they get stuck in the awkward "Cis" pose. The big question the scientists asked is: How fast does the molecule flip from the awkward Cis pose back to the comfortable Trans pose?

2. The Magic Trick: Quantum Tunneling

Usually, to flip from Cis to Trans, a molecule needs to climb over a small "hill" (an energy barrier) to get to the other side. In a warm room, molecules have enough energy to run up and over that hill.

But in deep space, it is incredibly cold (near absolute zero). The molecules are too frozen to run up the hill. So, how do they flip?

The paper explains that these molecules use a "magic trick" called Quantum Tunneling. Imagine the hill is a solid wall. Instead of climbing over it, the molecule acts like a ghost and simply phases right through the wall to get to the other side. This happens because, at the quantum level, particles can exist in two places at once.

3. The Three Dancers: Oxygen, Sulfur, and Selenium

The scientists studied three versions of the same molecule, differing only by one atom in the middle:

Formic Acid (Oxygen): The standard version.
Thio-formic Acid (Sulfur): The sulfur version.
Seleno-formic Acid (Selenium): The selenium version.

The Surprise:
You might think the heavier atoms (Sulfur and Selenium) would make the molecule slower. But the paper found something counter-intuitive. The "width" of the hill matters more than its "height."

The Oxygen version has a very narrow hill. Even though it's tall, it's easy to tunnel through because the wall is thin. It flips incredibly fast.
The Sulfur and Selenium versions have wider hills. Even if the hill isn't much taller, the wall is so thick that the "ghost" has a much harder time phasing through it. They flip much, much slower.

4. The Solo Dancer vs. The Dance Pair (Dimers)

The researchers also looked at what happens when two of these molecules hold hands (forming a "dimer").

Solo (Monomer): When dancing alone, the molecule flips very quickly.
Pair (Dimer): When holding hands, the molecules are a bit more stiff. It's harder for them to twist and turn. Consequently, the "pair" flips much slower than the "solo" dancer.

5. The Big Mystery of Space

Here is the main puzzle the paper tries to solve:
Astronomers look at deep space and see a lot of the awkward "Cis" form of Formic Acid. But the scientists' calculations show that in the gas phase (floating freely), the Cis form should flip into the Trans form in less than 10 milliseconds (a blink of an eye).

The Conclusion:
If the Cis form disappears that fast, why do we see it in space?
The paper suggests that the Cis form must be constantly being re-made by some other process (perhaps light from stars hitting the Trans form and flipping it back, or reactions on icy dust grains). If it weren't being constantly re-made, it would vanish instantly.

6. The "Matrix" vs. The "Gas"

The scientists also compared their computer calculations (gas phase) to real experiments done in labs where molecules are frozen in a block of noble gas (like Argon or Nitrogen).

The Finding: In the lab, the molecules flip much slower than in the computer gas calculations. It's like the frozen gas block acts as a "mud" that slows the dancers down.
The Warning: The paper suggests that if we try to study the Sulfur or Selenium versions in these frozen lab blocks, we might not see much happening because they are already so slow to flip on their own.

Summary

This paper is a high-speed race report for molecular shapes in space. It tells us that:

Oxygen-based acids flip shapes almost instantly using quantum tunneling.
Sulfur and Selenium acids are much slower because their "tunnels" are too wide.
Pairs of molecules flip slower than single molecules.
The "Ghost" effect: At the cold temperatures of space, molecules don't climb over barriers; they tunnel through them.
The Mystery: Since the awkward Cis shape disappears so fast, it must be constantly being created by something else in space to explain why we see it.

Technical Summary: Cis–Trans Rotational Isomerism of Seleno-, Thio-, and Formic Acids and Their Dimers

Problem Statement
The chemical kinetics of rotational isomerism (cis–trans interconversion) in formic acid (HC(O)OH) and its sulfur (HC(O)SH) and selenium (HC(O)SeH) analogues remain a subject of significant debate within astrochemistry. While the trans-conformer is thermodynamically stable, the cis-conformer has been observed in various interstellar environments, including giant molecular clouds and dark molecular clouds like TMC-1. However, theoretical studies have yielded conflicting results regarding the rate of cis to trans isomerisation. Some calculations suggest rate constants are too low ( $k \le 4 \times 10^{-21} \text{ s}^{-1}$ ) to allow for interconversion within the age of the universe, contradicting observational data. Conversely, laboratory studies on cryogenic noble-gas matrices indicate rapid isomerisation via quantum tunnelling, with half-lives ranging from minutes to hours depending on the matrix environment. A critical gap exists in understanding the intrinsic gas-phase kinetics of these monomers and their dimers to serve as a baseline for interpreting matrix effects and interstellar chemistry.

Methodology
This study employs high-level quantum chemical calculations to determine chemical kinetic rate constants for the cis to trans isomerisation of monomeric and dimeric formic, thioformic, and selenoformic acids over a temperature range of 10 K to 300 K.

Electronic Structure: Geometry optimisations and frequency calculations (harmonic and anharmonic) were performed using the double-hybrid functional B2PLYP with Grimme's D3(BJ) dispersion correction and the def2-TZVP basis set.
Energy Refinement: Higher-level single-point energies were calculated using the DLPNO-CCSD(T) method to ensure accuracy for kinetic purposes. For dimeric species, B3LYP with D3(BJ) dispersion was used for robustness, though Basis Set Superposition Error (BSSE) corrections were neglected for technical reasons.
Kinetic Theory: Rate constants were calculated using Canonical Variational Transition State Theory (CVT) augmented by quantum mechanical tunnelling corrections. Specifically, the study utilised Small-Curvature Tunnelling (SCT), Quantised Reaction States (QRC), and the Interpolated Single-Point Energies (ISPE) algorithm (summarised as CVT/SCT).
Reaction Coordinate: Intrinsic Reaction Coordinate (IRC) computations were generated at the B2PLYP–D3BJ/def2-TZVP level, modulated by the high-level CCSD(T) energies.

Key Results

Monomer Kinetics: The calculated rate constants for the cis to trans isomerisation of the monomers reveal that quantum mechanical tunnelling dominates the reaction at low temperatures.
- At 10 K, the half-life of cis-formic acid is calculated to be approximately 7.6 ms. This is significantly faster than previous gas-phase theoretical predictions (which suggested lifetimes of billions of years) but slower than some cryogenic matrix experiments (which report seconds to hours).
- The reaction is driven by barrier width rather than barrier height. Despite similar barrier heights for HC(O)OH and HC(O)SeH, the narrower barrier width of the oxygen species ( $3.3 \text{ amu}^{1/2}\cdot\text{bohr}$ ) compared to sulfur and selenium ($5.6$ and $6.3 \text{ amu}^{1/2}\cdot\text{bohr}$ , respectively) results in much higher tunnelling efficiency for formic acid. This illustrates a "second-row anomaly" where oxygen behaves differently from heavier Group 16 elements.
- Thio- and seleno-formic acids exhibit slower isomerisation rates than formic acid, with tunnelling becoming the supreme mechanism below 100 K and 75 K, respectively.
Dimer Kinetics: The study also investigated three dimeric species (cyclic and acyclic forms).
- Tunnelling accounts for over 99% of the rate constant at temperatures $\le 150$ K for the dimers.
- The acyclic dimer tc4 $\to$ tt3 isomerises approximately ten times faster than the cyclic dimer tc1 $\to$ tt2 at 10 K. This aligns with experimental argon matrix data where tc4 has a lifetime of 8.0 minutes versus 24 minutes for tc1.
- The cc5 $\to$ tc3 transformation exhibits a looser transition state and intermediate kinetics.
- Dimer rate constants are generally lower than their monomer counterparts, and the selenium analogues are orders of magnitude slower than the oxygen species.
Matrix vs. Gas-Phase: The authors note that their gas-phase results represent an upper limit to the reaction rate. Experimental rates in cryogenic matrices are generally slower (by factors of $10^3$ to $10^4$ for monomers) due to matrix stabilisation and "solvation" effects, which increase the effective barrier or reduce tunnelling probability.

Significance and Claims
The primary contribution of this work is the provision of rigorous gas-phase kinetic data that serves as a guide for interpreting experimental matrix studies and astrochemical models.

Resolution of Discrepancies: The authors claim their calculated rate constants for formic acid ( $k \approx 10^2 \text{ s}^{-1}$ at 10 K) are vastly different (by factors exceeding $10^{22}$ in some comparisons) from previous gas-phase theoretical studies that predicted negligible reactivity. They attribute this to the inclusion of advanced tunnelling corrections (SCT and QRC) which are essential at low temperatures.
Astrochemical Implications: Given the calculated half-life of cis-formic acid of less than 10 ms at 10 K in the gas phase, the authors argue that cis-formic acid should not be detectable in the interstellar medium (ISM) unless it is being continuously regenerated by a mechanism faster than its isomerisation. They suggest that photoswitching (UV excitation) or specific protonation/de-protonation cycles on ice grains may be necessary to explain its observational presence.
Predictive Value: The study concludes that experimental investigations into the isomerisation of sulfur and selenium analogues in standard cryogenic matrices are unlikely to yield productive results due to the extremely slow rates predicted, whereas formic acid remains a viable candidate for such studies.

The paper does not propose new experimental setups but rather provides a theoretical framework to rationalise existing observations and suggests that the rapid gas-phase isomerisation necessitates alternative formation or regeneration pathways for cis-conformers in space.