Computer simulations suggest that molecular rotation may matter more than bending vibration when carbon dioxide reacts with surface hydrogen on Cu(111). Under the study's modeled conditions, mild rotational excitation was estimated to enhance reaction probability several times, with rotational efficacy estimated at 11.9 to 19.0 relative to vibration and 75.0 to 140.6 relative to translation. Here, efficacy means how strongly a particular energy source changes the reaction probability.
The result addresses a specific question: whether bending-mode excitation alone explains the nozzle-temperature increase in CO2 hydrogenation reactivity on Cu(111), or whether rotational excitation is important. The authors interpret the calculations as showing that the nozzle-temperature trend is largely entangled with a stronger rotational effect, rather than being a purely vibrational signal.
A bent route into the reaction
Researchers represented the reaction with a full-dimensional neural-network potential energy surface, or PES, a computational map of the system's energy trained on density-functional-theory data. They used that map in quasi-classical trajectory simulations to predict thermally averaged and state-resolved reaction probabilities for gaseous CO2 reacting with surface H atoms on Cu(111).
The copper surface was modeled as a four-layer slab with a 4 by 4 unit cell, eight hydrogen atoms and 0.5 ML hydrogen coverage. The reported effects therefore belong to this defined Cu(111) and surface-hydrogen arrangement.
The active-learning PES dataset contained 11,000 energy-and-force data points, randomly split into 90 percent for training and 10 percent for testing. On the held-out test set, the reported root-mean-square errors, a measure of typical prediction error, were 0.54 meV per atom for energy and 33.4 meV per angstrom for atomic force. Product-state analysis also used adsorbate Gaussian binning to reduce the influence of zero-point-energy leakage when calculating quasi-classical trajectory reaction probabilities.
The reaction's association transition state, the fleeting arrangement at the top of the barrier, was bent. Its O-C-O angle was 144.5 degrees and the barrier was 0.599 eV. Conversion from monodentate to bidentate formate was nearly barrierless and exothermic by 0.496 eV.
Vibration helps, but not enough
One benchmark tested whether the model captured the surface-temperature pattern. At a translational energy of 1.97 eV along the surface normal, a nozzle temperature of 1000 K and mean vibrational energy of 142 meV, the calculated initial reaction probability, P0, for formate formation reproduced the experimental independence across surface temperatures from 120 to 220 K.
Vibration was still effective, but its impact depended on the mode. The quasi-classical trajectory mean vibrational efficacy was about 5.8 to 7.4, compared with an experimental estimate of 7.9. All vibrationally excited states apparently enhanced reactivity over the ground state, with efficacy ranges of 1.3 to 1.8 for symmetric stretch, 0.7 to 0.9 for antisymmetric stretch and 3.0 to 3.9 for bending. Bending therefore had the largest state-specific effect among the three listed vibrational motions.
Rotation changes the picture
Rotation changed the comparison. A calculation contrasting fully cooled rotation at 0 K with mild excitation at 5 percent of the nozzle temperature indicated that rotational excitation could raise reactivity several times. It estimated rotational efficacy at 11.9 to 19.0 relative to vibration and 75.0 to 140.6 relative to translation.
A state-specific test sharpened the result. A CO2 state with rotational quantum number J=10 had energy comparable to the mean rotational energy at a rotational temperature of 50 K, enhanced reactivity over the ground state and reached a rotational efficacy of 90.9 to 150.9. This was a calculated state-resolved effect within the simulation.
To examine the alignment behind the effect, the researchers used Sudden Vector Projection, or SVP, an analysis that compares molecular motions with the reaction coordinate. The degenerate bending modes had an average overlap value of 0.46, compared with 0.23 for translation, 0.014 for symmetric stretch and 0.093 for antisymmetric stretch. In this analysis, bending was more closely aligned with the reaction than translation or either stretching mode.
The authors propose that CO2 approaches through a narrow, anisotropic entrance pathway. Rotation-bending coupling and changes in the potential-energy surface's anisotropy could help the molecule reorient in a cartwheel-like motion and reach the transition-state orientation. The paper's conclusion reports rotational efficacies 30 to 40 times higher than vibrational efficacies and attributes the enhancement to that coupling and changing anisotropy.
A prediction with a clear boundary
The result has a clear boundary: it is a model prediction for the H-covered Cu(111) arrangement and the gas-surface, formate-forming reaction described here. The proposed rotational mechanism awaits experimental verification.
Direct state-resolved experiments are needed to test the predicted rotational contribution and cartwheel-like steric effect. The study also leaves open whether similar rotational effects occur in other Eley-Rideal catalytic systems and how the rotational-state distribution realized in experiments would affect realistic reaction rates.
Paper data and sources
Original title: Mode-Specific Dynamics of $\text{CO}_2$ Hydrogenation on Copper: The Hidden Role of Molecular Rotation
Authors: Junfan Xia, Zhikai Jiang, Yaolong Zhang et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
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