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Inelastic Surface Scattering of Vibrationally Excited N2: Role of Multi-Quantum De-Excitations

This study establishes a validated methodology combining first-principles molecular dynamics with plasma kinetic modeling to reveal that multi-quantum vibrational de-excitations during N2 scattering on Ru(0001) are a critical, previously overlooked mechanism that significantly influences plasma chemistry and catalytic performance.

Original authors: Floris van den Bosch, Nick Gerrits, Jörg Meyer

Published 2026-09-10

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CC BY 4.0

Original authors: Floris van den Bosch, Nick Gerrits, Jörg Meyer

Original paper licensed under CC BY 4.0 (https://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

In the world of industrial chemistry, making useful substances from simple gases like nitrogen often requires extreme heat and pressure, a process that consumes vast amounts of energy. To make this more efficient, scientists are turning to a technology called plasma-assisted catalysis. Imagine a gas that has been energized into a state where its molecules are vibrating intensely, holding extra energy that can help break chemical bonds without needing the same crushing heat as traditional methods. However, for this technology to work, scientists must understand exactly what happens when these energetic molecules hit the solid surfaces of the catalysts they are meant to react with. A critical, yet poorly understood, part of this puzzle is how these vibrating molecules lose their energy when they bounce off a metal surface. If they lose too much energy too quickly, the process fails; if they hold onto it, the reaction might proceed efficiently. The question is whether the molecules simply lose a tiny bit of energy with each bounce or if they can dump a massive amount of it in a single collision.

A team of researchers at Leiden University has tackled this question by simulating the collision of nitrogen molecules with a ruthenium surface, a combination relevant to making ammonia. They used powerful computer models to track the movement of individual nitrogen molecules as they approached the metal, bounced off, and flew away. Unlike previous studies that relied on simplified guesses or experiments that could only see the very first step of energy loss, these simulations allowed the scientists to watch the entire process in high definition. They found that the standard way scientists have been modeling these collisions is fundamentally wrong. For years, models assumed that when a vibrating nitrogen molecule hits a surface, it loses energy in small, single steps, like a person taking one step down a staircase at a time. The new simulations reveal that the reality is much more dramatic: the molecules often lose multiple units of vibrational energy all at once, leaping down several steps of the staircase in a single bounce.

The researchers built their computer models using a highly detailed map of how nitrogen and ruthenium atoms interact, a map created from advanced quantum calculations. They sent millions of virtual nitrogen molecules toward the metal surface at different speeds and with different amounts of internal vibration. They then watched closely to see how the molecules behaved. The results showed that for molecules that were already vibrating with high energy, the chance of losing several vibrational units in one go was significant. In fact, for highly excited molecules, these multi-step energy losses were far more likely than the molecules breaking apart or sticking to the surface. This discovery is crucial because it means that the current computer models used to design plasma reactors are likely underestimating how fast these molecules cool down. If the molecules cool down faster than predicted, the plasma might not stay energetic enough to drive the chemical reactions efficiently.

The study also challenged another long-held assumption: that the likelihood of a molecule losing energy increases in a simple, straight-line relationship with how much energy it starts with. The simulations showed this is not true. The probability of losing energy changes in a complex way depending on the specific starting state of the molecule. This means that simply guessing the behavior of highly energetic molecules based on how low-energy ones behave is unreliable. The researchers compared their simulation results with existing laboratory experiments where nitrogen beams were fired at metal surfaces. While there were some differences, likely due to the messy conditions of real-world experiments where other particles might interfere, the simulations successfully reproduced the general trends of how energy is transferred. This gives the scientists confidence that their detailed view of the multi-step energy loss is accurate.

The implications of these findings extend beyond just one chemical reaction. The work suggests that to truly understand and improve plasma catalysis, scientists must stop using simplified rules of thumb for how molecules lose energy on surfaces. Instead, they need to incorporate these detailed, step-by-step probabilities into their models. By doing so, they can better predict how long these energetic molecules will survive in a reactor and how effectively they will drive chemical changes. The study provides a new, more realistic foundation for understanding the microscopic interactions that drive large-scale industrial processes, moving the field from rough approximations to a precise, physics-based understanding of how energy flows between gas and metal.

Technical Summary: Inelastic Surface Scattering of Vibrationally Excited N2: Role of Multi-Quantum De-Excitations

Problem Statement
Non-equilibrium plasmas generate substantial populations of vibrationally excited molecules, which are critical drivers for plasma-assisted catalysis. However, the modeling of vibrational energy transfer at plasma–surface interfaces remains poorly characterized. Current kinetic plasma models typically rely on simplified assumptions for vibrational relaxation, such as single-quantum de-excitation ( $\nu \to \nu-1$ ) or full relaxation to the ground state. These approximations fail to capture the detailed state-to-state scattering probabilities ( $\nu \to \nu'$ ) required to accurately describe energy loss processes, particularly for highly excited molecules prevalent in non-equilibrium plasmas. Experimental characterization of these processes is challenging due to the lack of dipole moments in molecules like N $_2$ , which limits spectroscopic techniques, and the difficulty in generating beams with high vibrational excitation levels comparable to plasma conditions.

Methodology
The authors employ a state-of-the-art quasi-classical trajectory (QCT) method to simulate the scattering of N $_2$ from a Ru(0001) surface. The study utilizes a machine-learned Behler-Parinello high-dimensional neural network potential (HDNNP) trained on 25,000 density functional theory (DFT) data points (RPBE functional) to describe the molecule-surface interaction.

Dynamics: Nuclear dynamics are simulated classically within the microcanonical (NVE) ensemble, while initial rovibrational conditions are set according to quantum mechanical eigenenergies.
Surface Effects: Surface temperature effects (575 K and 900 K) are included via thermal expansion and atomic displacements. Electronic energy dissipation (electron-hole pair excitations) is modeled using electronic friction theory based on the local density approximation (LDFA).
Validation: The simulation framework is benchmarked against molecular beam experiments. Specifically, scattering angles are compared to data from Zaharia et al. (using a DC discharge plasma source), and energy transfer data are compared to REMPI-based measurements by Mortensen et al. (using a thermal nozzle source).
Analysis: State-to-state scattering probabilities are derived by mapping the classical actions of the scattered molecules back to quantum numbers ( $\nu_{cl}, J_{cl}$ ) using histogram binning.

Key Results

Benchmarking: The QCT simulations show semi-quantitative agreement with experimental scattering angle distributions and energy transfer data. Discrepancies at high incidence energies are attributed to potential adatom coverage buildup in experimental setups, which is not present in the zero-coverage simulations.
Energy Transfer: The total average energy exchange ( $\Delta E$ ) between the molecule and surface follows a normal energy scaling law dependent on the incidence angle and energy.
Multi-Quantum De-Excitations: The most significant finding is the prevalence of multi-quantum vibrational de-excitations. The simulations reveal that for highly vibrationally excited N $_2$ $_{2}$ (high $\nu_{in}$ $ν_{in}$ ), transitions involving the loss of multiple vibrational quanta are significant energy loss channels.
- The probability of multi-quantum de-excitation increases with the initial vibrational quantum number.
- The threshold incidence energy for significant multi-quantum contribution decreases as the initial vibrational state increases.
Non-Linearity: The probability of de-excitation does not scale linearly with the initial vibrational quantum number ( $\nu$ ). This contradicts the common assumption in plasma kinetics that $P(\nu \to \nu-1) = \nu P(1 \to 0)$ .
Comparison to Dissociation: At industrially relevant surface temperatures (673 K), multi-quantum vibrational de-excitations are orders of magnitude more probable than dissociative chemisorption, the rate-limiting step in ammonia synthesis.

Significance and Claims
The paper claims to establish a methodology that bridges first-principles surface dynamics with plasma kinetic modeling. By providing experimentally benchmarked, state-to-state scattering probabilities, the work offers a physically grounded alternative to the approximate surface-loss descriptions currently used in plasma models.

The authors assert that the neglect of multi-quantum de-excitations and the assumption of linear scaling in existing plasma kinetic descriptions are inconsistent with atomistic reality. Incorporating these full state-to-state processes is expected to substantially influence predictions of vibrationally excited N $_2$ populations, lifetimes, and consequently, the overall reactivity and performance of plasma-assisted catalytic processes. The study demonstrates that surface-science methodologies can provide the missing atomistic information required to refine plasma-surface interaction models beyond the N $_2$ /Ru(0001) system.

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