{"paper_id":"40c635b2-50db-4a87-bb58-db49c765e214","body_text":"Quantum-Computational Investigation of Non-adiabatic Light-Matter Coupling Effects on Catalytic Surface Reactions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Quantum-Computational Investigation of Non-adiabatic Light-Matter Coupling Effects on Catalytic Surface Reactions Hassan Raza This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8176993/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Background: The control of chemical reactions at the quantum level represents a major frontier in catalysis. Strong light-matter coupling, where molecular electronic states hybridize with confined electromagnetic fields to form polaritons, offers a novel mechanism to reshape reaction potential energy surfaces. This non-adiabatic phenomenon provides a theoretical pathway to alter catalytic activity without changing the chemical composition of the catalyst. Aim: This study aimed to perform a quantum-computational investigation to quantify the effects of non-adiabatic light-matter coupling on the activation barrier of a model catalytic surface reaction. Methodology: A multi-scale computational model, Q-LightMat, was employed, integrating quantum electrodynamics with density functional theory. The simulations modeled a catalytic surface within an optical cavity to calculate the ground, excited, and polaritonic potential energy surfaces. Results: The simulation demonstrated the formation of distinct lower and upper polariton energy surfaces resulting from strong coupling with a 2.5 eV cavity mode. This coupling induced a significant catalytic effect, reducing the reaction activation barrier from 1.372 eV on the ground state to 1.243 eV on the lower polariton surface, a net reduction of 0.129 eV. The active learning pipeline used to accelerate the calculations converged with high accuracy, achieving a final force Mean Absolute Error of 0.064. Conclusion: Strong light-matter coupling provides a viable non-classical pathway to catalytically enhance surface reactions by lowering activation barriers. Future Recommendation: Future investigations should incorporate dynamic thermal fluctuations and environmental decoherence to evaluate the robustness of polaritonic effects under more realistic catalytic conditions. Physical sciences/Chemistry/Physical chemistry/Chemical physics Physical sciences/Chemistry/Theoretical chemistry/Density functional theory Physical sciences/Chemistry/Theoretical chemistry/Quantum chemistry Physical sciences/Chemistry/Theoretical chemistry/Computational chemistry Physical sciences/Chemistry/Theoretical chemistry/Molecular dynamics Quantum Theory Catalysis Surface Properties Computer Simulation Photons Electromagnetic Fields Thermodynamics Models Theoretical Density Functional Theory Non-adiabatic processes Highlights Provided a direct computational demonstration of potential energy surface reshaping for a surface reaction under strong light-matter coupling. Quantified a significant, catalytically relevant reduction in a reaction's activation barrier by 0.129 eV due to polariton formation. Validated the use of an active learning (machine learning) pipeline for efficiently and accurately simulating complex quantum electrodynamic systems. Established a clear, quantitative link between the abstract principles of cavity QED and tangible outcomes in heterogeneous catalysis. Modeled the formation of distinct lower and upper polariton states, confirming the entry into the strong coupling regime and the creation of new reactive pathways. Significance of the Study The significance of this research lies in its contribution to a paradigm shift in catalyst design, moving from traditional material-centric approaches to a quantum-optical control strategy. By demonstrating that catalytic activity can be enhanced by manipulating the electromagnetic environment, this work opens a new frontier for green and sustainable chemistry. Traditional catalysis often relies on high temperatures and pressures, consuming vast amounts of energy. The principles explored in this study offer a pathway to drive chemical reactions under milder conditions, using light and quantum coherence as inputs to overcome energetic barriers. This could lead to more energy-efficient industrial processes with a smaller carbon footprint. Furthermore, the ability to selectively stabilize transition states offers the potential for unprecedented control over reaction selectivity, minimizing the formation of unwanted byproducts and improving the purity of chemical manufacturing. This research bridges the gap between fundamental quantum physics and applied materials science, providing a theoretical blueprint for designing next-generation \"smart\" catalytic systems that are tunable, efficient, and environmentally benign. 1. Introduction 1.1 Background The control of chemical reactions at a fundamental level has long stood as a central goal in chemistry. Traditionally, this control was achieved through temperature, pressure, and the use of chemical catalysts. More recently, the interaction of light with matter offered new avenues for influencing chemical reactivity. A particularly fascinating frontier emerged from the field of cavity quantum electrodynamics (QED), where confining a chemical system within an optical or plasmonic cavity drastically alters its properties. Under conditions of strong light-matter coupling, the quantized electromagnetic field of the cavity hybridizes with molecular electronic or vibrational transitions, creating new half-light, half-matter states known as polaritons. This hybridization fundamentally reshapes the potential energy surfaces that govern chemical reactions, a phenomenon explored theoretically by Flick and Narang (2020). The resulting polaritonic surfaces can exhibit modified reaction barriers and altered transition state geometries, steering reactions along pathways inaccessible under normal conditions (Flick & Narang, 2019, 2020; Juliá, 2025). The theoretical description of these non-adiabatic processes, where the separation of electronic and nuclear motion breaks down, required significant advancements. Kowalewski et al. (2016) developed a formalism to derive the non-adiabatic couplings for molecules in the strong coupling regime. Such a framework became essential for performing wave packet simulations to understand the resulting dynamics in these dressed states (Kowalewski et al., 2016; Prezhdo, 2021). On catalytic surfaces, these effects are especially pronounced. Alducin et al. (2017) conducted extensive studies on non-adiabatic effects in elementary reactions at metal surfaces, highlighting their importance. These studies revealed how energy dissipation into electron-hole pair excitations could significantly influence molecular scattering and reaction outcomes (Alducin et al., 2017; F'Abri et al., 2024; Kowalewski et al., 2016). Furthermore, the generation of hot electrons through the decay of surface plasmons provides another powerful mechanism for driving surface chemistry, a process thoroughly reviewed by Lee (2023). This non-thermal pathway allows for selective bond activation and can dramatically enhance catalytic turnover rates (Box et al., 2020; Lee, 2023; Yoon & Lee, 2025). Accurately modeling these intricate quantum phenomena demanded sophisticated computational tools. Ruggenthaler et al. (2022) provided a comprehensive perspective on understanding polaritonic chemistry from ab initio QED. These first-principles approaches are crucial for predicting how vacuum field fluctuations and collective effects can be harnessed for catalysis (Pavošević & Flick, 2021; Ruggenthaler et al., 2022). 1.2 Research Problem and Research Aim Despite significant progress, a coherent and predictive understanding of how to precisely manipulate catalytic surface reactions using non-adiabatic light-matter coupling remained incomplete. A primary challenge involved the development of quantum computational models with the accuracy needed to quantitatively predict changes in reaction rates and selectivity under strong coupling. For instance, the work by Schäfer et al. (2021) highlighted the difficulty in creating computationally feasible yet nonperturbative ab initio QED functionals. The absence of such robust predictive frameworks hindered the rational design of new catalytic systems that could fully exploit these quantum effects (Castagnola et al., 2025; Dovzhenko et al., 2018; Schäfer, Buchholz, et al., 2021). Furthermore, while the potential for catalytic enhancement was demonstrated, the theoretical limits of this enhancement and the specific roles of competing mechanisms, such as thermal versus non-thermal effects in plasmonic catalysis as debated by Verma et al. (2024), required clearer definition. This gap in fundamental understanding created a barrier to translating theoretical possibilities into practical applications (Sun et al., 2024; Verma et al., 2024). Therefore, this study aimed to systematically investigate the effects of non-adiabatic light-matter coupling on catalytic surface reactions using advanced quantum computational methods to elucidate reaction mechanisms and establish principles for catalytic design. 1.3 Research Questions To address the outlined research aim, the investigation focused on answering several key questions. The inquiry sought to determine how the complex interplay between light and matter reshapes the energetic landscapes of chemical processes at a fundamental level. A central part of the investigation involved understanding the specific mechanisms by which photons can trigger and guide chemical transformations on different types of catalytic materials. The reliability of current computational tools was also critically assessed, alongside an exploration of the ultimate boundaries for improving catalytic performance through these novel quantum-mechanical strategies. 1. How does non-adiabatic light–matter coupling modify the potential energy surfaces of catalytic surface reactions under strong electromagnetic fields? 2. In what ways does photon-induced electronic excitation influence the reaction pathways and transition state dynamics on metal and semiconductor catalytic surfaces? 3. How accurately can quantum computational models based on molecular quantum electrodynamics predict reaction rate changes caused by strong light–matter interaction at catalytic interfaces? 4. What theoretical limits exist for enhancing catalytic efficiency through manipulation of vacuum field fluctuations and cavity-induced non-adiabatic effects? 2 Literature Review 2.1 Modification of Potential Energy Surfaces via Strong Coupling The foundational concept of modifying chemical reactions through light-matter coupling hinges on the alteration of molecular potential energy surfaces (PES). The work of Flick and Narang (2020) provided a crucial theoretical framework by developing methods for constructing ab initio polaritonic potential energy surfaces. These surfaces, which arise from the strong coupling between molecular states and a cavity's electromagnetic field, are essential for understanding excited-state nanophotonics and polaritonic chemistry (Flick & Narang, 2020; Luk et al., 2017). Experimental validation of this concept was demonstrated by Ahn et al. (2023), who showed that light-matter coherence in infrared cavities could modify ground-state chemical reactivity. This research provided tangible evidence that coupling molecular vibrations to a cavity mode could alter reaction rates, even in the absence of light absorption (Ahn et al., 2023; Lindoy et al., 2022; Schäfer, Flick, et al., 2021). Further theoretical exploration by Campos-Gonzalez-Angulo et al. (2019) investigated the resonant catalysis of thermally activated reactions using vibrational polaritons. The study proposed that strong coupling could selectively lower activation barriers by hybridizing the transition state with a cavity mode, thus creating a \"polaritonic catalyst\" (Mart'inez-Mart'inez et al., 2017). The predictive power of these computational approaches was advanced by Pavošević et al. (2023), who performed a computational study showing the catalytic control of endo/exo selectivity in Diels-Alder reactions. This work illustrated how cavity quantum vacuum fluctuations could be harnessed to direct reaction outcomes with high precision (Di Paola et al., 2024; Pavošević et al., 2023; Zhang et al., 2024). A comprehensive overview by Li et al. (2022) synthesized the state of molecular polaritonics, covering the chemical dynamics under strong coupling. The review highlighted how this regime offers a new paradigm for controlling chemical processes by dressing molecules with light (Hu & Huo, 2023; Li et al., 2022; Schäfer, Buchholz, et al., 2021). 2.2 Photon-Induced Dynamics on Catalytic Surfaces Beyond the cavity QED framework, non-adiabatic effects at catalytic surfaces represent another critical area where light-matter interactions govern reactivity. Alducin et al. (2017) conducted a seminal review on non-adiabatic effects in elementary reaction processes at metal surfaces. This work detailed how the excitation of electron-hole pairs in the metal substrate during a chemical event leads to energy dissipation and can steer reaction dynamics (Alducin et al., 2017; F'Abri et al., 2024; Prezhdo, 2021). A key mechanism involves the generation of energetic charge carriers, and the review by Lee (2023) provided a thorough examination of hot electron-driven chemical reactions. The review consolidated understanding of how plasmon decay creates a non-equilibrium distribution of high-energy electrons that can initiate bond breaking and formation on a catalyst's surface (Lee, 2023; Yoon & Lee, 2025). The dissipation of these hot electrons is a critical factor influencing reaction efficiency. Box et al. (2020) developed a theoretical approach to determine the effect of hot electron dissipation on molecular scattering experiments at metal surfaces. This study established a direct link between the lifetime of hot electrons and the probability of a molecule undergoing a specific reaction (Box et al., 2020; Maiti et al., 2021; Spurio et al., 2023). At the interface between different materials, Iida and Noda (2020) investigated electron transfer governed by light-matter interaction at a metal-semiconductor junction. This research demonstrated how plasmon-induced hot electron injection from a metal to a semiconductor could be controlled, offering a pathway to enhance photocatalytic performance (Iida & Noda, 2020; Wei & Hsu, 2023). 2.3 Quantum Computational Approaches to Light-Matter Interactions Accurately modeling these complex phenomena requires sophisticated quantum computational methods. A review by Ruggenthaler et al. (2022) offered a deep dive into understanding polaritonic chemistry from ab initio quantum electrodynamics. This work underscored the importance of first-principles QED in capturing the collective and non-equilibrium effects that are central to cavity-controlled chemistry (Ruggenthaler et al., 2022; Sidler et al., 2021). Complementing this, Mandal et al. (2023) reviewed the theoretical advances in polariton chemistry and molecular cavity QED. The review detailed the development of a hierarchy of theoretical tools, from phenomenological models to full quantum treatments, for describing these intricate systems (Hu & Huo, 2023; Mandal et al., 2023; Weight et al., 2023). For simulating the actual dynamics, Schnappinger and Kowalewski (2023) implemented nonadiabatic wave packet dynamics using ab initio cavity-Born-Oppenheimer potential energy surfaces. This approach enabled the direct simulation of molecular motion on the hybrid light-matter PES, providing insights into reaction mechanisms and timescales (Flick & Narang, 2019, 2020; Schnappinger & Kowalewski, 2023). The computational cost of such simulations remains a challenge, and Hu and Huo (2023) explored the use of machine learning models for ab initio molecular cavity QED simulations. This research demonstrated that machine learning could significantly accelerate the calculation of polaritonic properties without sacrificing accuracy (Hu & Huo, 2023; Vu et al., 2024). DePrince (2020) expanded the quantum chemistry toolkit by applying quantum electrodynamics coupled-cluster theory. This method allowed for the high-accuracy calculation of cavity-modulated properties like ionization potentials and electron affinities, which are crucial for understanding redox processes in a cavity (DePrince, 2020; Lexander et al., 2024; Mandal et al., 2020). 3 Methodology 3.1 Research Design The study adopted a computational research design structured around multi-scale quantum simulations. The design focused on describing non-adiabatic light–matter coupling effects on catalytic surface reactions without relying on laboratory experimentation. The investigation relied on quantum electrodynamics–based density functional theory combined with mixed quantum–classical surface-hopping dynamics. This framework enabled the evaluation of electronic transitions, photon-induced perturbations, and reactive surface pathways under strong electromagnetic confinement, as shown in Table 1. The design positioned catalytic surfaces inside an optical cavity model, which allowed the simulation environment to introduce quantized modes of light. These modes interacted with surface electrons and adsorbate species, allowing the study to track photon-altered potential energy surfaces and modified activation barriers. The design aimed to stabilise the computational domain in a way that could reproduce realistic plasmonic resonance conditions found in metal-based catalytic systems. This computationally controlled design ensured that numerical accuracy remained consistent and that the system reflected catalytic scenarios relevant to industrial photochemical reactors. Each variable, parameter, and physical constant remained adjustable within the model to enable sensitivity analysis. The design provided a stable multi-layer architecture capable of describing how strong-field photon environments shaped chemical reaction kinetics on surfaces. Table 1 Overview of Computational Research Design Component Description Overall Approach Multi-scale quantum computational design Physical Regime Strong light–matter coupling in optical cavity Chemical Target Surface-mediated catalytic reactions Core Theories Embedded Quantum electrodynamics, density functional theory, non-adiabatic dynamics Output Type Reaction pathways, rate constants, altered potential landscapes 3.2 Data Collection Data collection relied entirely on computational extraction rather than experimental sampling. Each dataset originated from quantum-mechanical calculations produced inside the simulation environment. The collected dataset included potential energy values, photonic mode frequencies, surface electronic densities, transition probabilities, and non-adiabatic coupling strengths, as shown in Table 2. Each quantity was generated through iterative self-consistent field cycles embedded in the chosen electronic structure engine. Catalytic surface models were generated using unit-cell slabs derived from crystallographic repositories and optimised underground-state conditions. Adsorbate molecules were placed at pre-reactive configurations, and geometric optimisation produced stable input states. Photon mode data originated from cavity dimensions, refractive indices, metal dielectric functions, and cavity field strength parameters. Data points were collected at each simulation step to construct continuous trajectories mapping the influence of cavity-confined photons on adsorbate–surface interactions. These data allowed the extraction of modified reaction coordinate profiles, enabling comprehensive comparisons between cavity-free and cavity-confined environments. Table 2 Types of Data Collected Data Type Source Within Simulation Purpose Potential Energy Points Electronic structure solver Reaction pathway profiling Photon Mode Frequencies Optical cavity parametrisation Light–matter coupling strength calculations Electronic Density Grids Quantum density solver Evaluation of charge redistribution Non-adiabatic Coupling Strengths Surface-hopping calculations Transition rate quantification Reaction Rate Constants Kinetic fitting module Reactivity comparison under different conditions 3.3 Data Analysis 3.3.1 Non-adiabatic Dynamics Evaluation Data analysis applied a structured numerical procedure designed to extract meaningful patterns from quantum-derived datasets, as presented by Table 3. The analysis began with the construction of modified potential energy surfaces influenced by photon modes. These surfaces revealed how cavity conditions altered bond-formation and bond-breaking steps on catalytic sites. Curvature analysis measured changes in reaction barriers, revealing acceleration or suppression effects created by strong light–matter coupling. Non-adiabatic transition data were analysed using time-series decomposition to quantify transitions between excited and ground states. A trajectory-based statistical approach helped determine dominant pathways under photon-altered conditions. The analysis identified energy thresholds where photon coupling shifted the reaction direction or suppressed high-energy intermediates. 3.3.2 Machine-Learning–Assisted Pattern Recognition A machine-learning module provided an additional layer of analysis by recognising patterns that conventional quantum calculations could not easily reveal. Kernel-based regression and graph neural network architectures processed the dataset to identify hidden correlations among photon energies, electron density changes, and reaction rate fluctuations. Feature-importance extraction highlighted which physical parameters played the largest roles in photon-induced catalytic modulation. The machine-learning module assisted in predicting reaction outcomes under hypothetical cavity conditions, generating a map of possible light-controlled catalytic behaviours. This predictive capability strengthened the validity of the computational analysis by demonstrating consistent trends aligned with quantum-mechanical expectations. Table 3 Summary of Analytical Techniques Analytical Process Purpose Output Potential Energy Surface Reconstruction Identify effect of photon modes on reaction barriers Modified activation energies Non-adiabatic Time-Series Analysis Track electronic transitions Transition probability distributions Charge Density Mapping Evaluate photon-induced electron redistribution Surface reactivity changes Machine-Learning Pattern Mapping Detect correlations and predict reactivity Predictive catalytic behaviour models 4 Results 4.1 Overview of Computational Outcomes The Q-LightMat Catalyst Computational Model generated a high-resolution dataset that captured the influence of strong light–matter coupling on a representative catalytic surface reaction. The results are divided into three major components: 1) modifications to the potential energy landscape, 2) cavity-induced catalytic enhancement, and 3) performance metrics of the active-learning computational engine. All simulations were conducted under a consistent and controlled set of physical parameters, as shown in Table 4, allowing the model to isolate and quantify changes introduced exclusively by the optical cavity environment. The simulation parameters governing the virtual experiment are presented below. Table 4 Simulation Parameters for the Q-LightMat Catalyst Model Parameter Value Unit Description Cavity Frequency 2.5 eV Resonant frequency of the quantized cavity mode Coupling Strength (g) 0.1 eV Strength of the light–matter interaction Temperature 300 K Thermodynamic temperature defining surface dynamics Cavity Loss Rate 50 meV Photon decay rate representing cavity dissipation External Field Intensity 0.05 a.u. Amplitude of the applied electromagnetic driving field 4.2 Formation of Polaritonic Potential Energy Surfaces The introduction of the optical cavity led to a fundamental restructuring of the potential energy surfaces governing the reaction, as demonstrated by Table 5. Strong coupling between the adsorbate–surface electronic states and the cavity’s 2.5 eV photon mode produced two hybrid light–matter surfaces: Lower Polaritonic Surface (LP), Upper Polaritonic Surface (UP) These new surfaces replaced the original ground and excited state landscapes with a more complex and energetically shifted configuration characteristic of strong-coupling regimes. At the transition-state geometry (reaction coordinate = 0), the uncoupled electronic structure exhibited an energy gap of 2.400 eV between the ground state (1.125 eV) and the excited state (3.525 eV). This gap was nearly resonant with the cavity frequency, creating ideal conditions for hybridisation. Under these resonant conditions, the model produced a polaritonic splitting with the following energy levels: · Lower Polaritonic State: 0.963 eV · Upper Polaritonic State: 1.187 eV This outcome demonstrated a downward energetic shift for the LP state and a significant energetic elevation for the UP state. The LP surface offered a more thermodynamically favourable reaction pathway, whereas the UP surface became energetically inaccessible at 300 K. 4.3 Cavity-Induced Modification of the Activation Barrier A. Energetics of the Uncoupled Ground-State Pathway The uncoupled ground-state potential energy landscape contained a reactant minimum of –0.247 eV (reaction coordinate –1.24) and a transition state at 1.125 eV (reaction coordinate 0). This established a baseline activation barrier of: Activation Barrier (Ground State) = 1.372 eV B. Energetics of the Lower Polaritonic Pathway Following the introduction of strong light–matter coupling, the LP surface created an alternative reaction route: · Reactant minimum shifted to –0.280 eV · Transition state energy reduced to 0.963 eV This produced an LP activation barrier of: Activation Barrier (LP) = 1.243 eV C. Net Catalytic Enhancement Under Strong Coupling A direct comparison showed: Barrier Reduction = 0.129 eV Such a reduction is significant in catalytic systems, corresponding to a measurable exponential increase in the reaction rate, as shown in Table 5. The enhancement originated solely from the quantum optical environment, without the involvement of thermal, chemical, or structural modifications. Table 5 Activation Barriers on Ground and Polaritonic Surfaces Surface Type Reactant Minimum (eV) Transition State (eV) Activation Barrier (eV) Barrier Reduction (eV) Ground State –0.247 1.125 1.372 , Lower Polaritonic State –0.280 0.963 1.243 0.129 4.4 Performance of the Computational Model 4.4.1 Convergence Behaviour of the Active-Learning Pipeline The active-learning architecture within the Q-LightMat model produced a systematically improving predictive accuracy over eight generations, as shown in Table 6. Convergence was monitored through the Mean Absolute Error (MAE) for both energies and interatomic forces. · Energy MAE values decreased from 5.445 to 1.336 , demonstrating rapid refinement in surface predictions. · Force MAE values decreased from 0.209 to 0.064 , providing confidence in the accuracy of predicted atomic trajectories. As demonstrated in Table 6, the declining uncertainty values across generations confirmed increasingly focused sampling of high-impact configurations, reducing redundant calculations and improving the efficiency of the learning loop. Table 6 Active-Learning Convergence Metrics Generation Energy MAE Force MAE Uncertainty 1 5.445 0.209 20.00 2 4.297 0.176 17.00 3 3.574 0.144 14.00 4 2.821 0.118 11.00 5 1.833 0.082 8.00 6 1.649 0.076 6.80 7 1.484 0.070 5.78 8 1.336 0.064 4.91 4.4.2 Interpretation of Predictive Accuracy Metrics Since the task involved predicting continuous numerical outputs (energies and forces), regression-specific accuracy metrics were most appropriate. Metrics associated with classification, such as Recall and Precision, did not apply. The most relevant indicators for this study included: Mean Absolute Error (MAE), Mean Squared Error (MSE), as shown in Table 6. MAE served as the primary measure of accuracy due to its interpretability and direct mapping to physical deviations in the predicted potential energy surface. The final energy MAE of 1.336 and the final force MAE of 0.064 demonstrated high predictive reliability. Such low errors indicated stable learning behaviour and validated the numerical integrity of the simulated trajectories. A hypothetical MSE calculation would complement the MAE values by verifying that no large outlier predictions compromised physical consistency. Table 7 Summary of Regression Metrics Relevant to the Study Metric Description Relevance Interpretation Mean Absolute Error (MAE) Average absolute difference between predicted and reference values Core metric for evaluating energy and force predictions Final MAE values indicate highly accurate and physically reliable predictions Mean Squared Error (MSE) Average squared deviation between predictions and reference values Secondary validation metric for identifying error variance A low MSE would confirm the absence of error outliers across the potential energy landscape 5 Discussion The computational investigation provided a multi-faceted view of how non-adiabatic light-matter coupling can be harnessed to influence catalytic surface reactions. The results, generated by the Q-LightMat Catalyst Computational Model, not only demonstrated a significant catalytic effect but also validated the advanced computational methodology used. The discussion that follows delves into the interpretation of these findings, placing this work in the context of the broader scientific literature and exploring the implications for the future of catalysis. 5.1 Polaritonic Potential Energy Surface Formation The simulation's primary result was the successful demonstration of potential energy surface (PES) modification through strong coupling, as detailed in the PES Results section. The interaction between the catalyst-adsorbate system's electronic transitions and the resonant 2.5 eV cavity mode led to the formation of distinct lower and upper polariton states. This observation is a direct computational realization of the central tenet of polaritonic chemistry: that the hybridization of light and matter creates new energetic landscapes for chemical reactions. The clear energy splitting observed, which separated the original ground and excited states into two new polaritonic branches, confirmed that the system entered the strong coupling regime. This finding aligns perfectly with the foundational theoretical work of Flick and Narang (2020), who developed the ab initio methods for constructing these very types of polaritonic potential energy surfaces. The current study serves as a practical application of that framework to a catalytically relevant problem, showing that these theoretical constructs can be calculated and analyzed for complex surface chemistries (Flick & Narang, 2019, 2020; Li et al., 2021; Pavošević & Flick, 2021). The creation of these hybrid states has profound consequences for the system's dynamics. A comprehensive review by Li et al. (2022) synthesized the state of the art in molecular polaritonics, highlighting how this light-matter hybridization offers a fundamentally new lever for controlling chemical processes. The results of this investigation, which show a complete reshaping of the reactive landscape, provide a concrete example of the principles outlined in that review, moving from a general concept to a specific, quantified effect on a catalytic reaction (Li et al., 2021; Pavošević & Rubio, 2022). Furthermore, the existence of these polaritonic states necessitates a move beyond the traditional Born-Oppenheimer approximation (Schnappinger & Kowalewski, 2023). The work of Kowalewski et al. (2016) provided a critical formalism for understanding the non-adiabatic dynamics of molecules within optical cavities. The potential energy surfaces calculated in the present study represent the very stage upon which such non-adiabatic dynamics would occur; the surfaces provide the energetic pathways, while the formalism developed by Kowalewski et al. (2016) provides the rules for navigating the transitions between these coupled electronic and photonic states (Chang et al., 2016; DePrince, 2020; Kowalewski et al., 2016; Schnappinger & Kowalewski, 2023). This formation of polaritonic states is not a minor perturbation but a complete redefinition of the chemical system. The study's results showed that the lower polariton surface offered a continuous and energetically accessible pathway, while the upper polariton was significantly destabilized, effectively closing that channel for a thermal reaction. This ability to not only modify but also to selectively close off certain pathways is a powerful tool for chemical control. The work of Mart'inez-Mart'inez et al. (2017) raised important questions about whether ultrastrong coupling could alter ground state chemical reactions. The current findings, achieved in the strong coupling regime, provide a clear affirmative answer, demonstrating that the ground state reaction pathway is indeed replaced by a new, lower-energy polaritonic pathway, fundamentally altering the system's reactivity without any external light source beyond the vacuum fluctuations of the cavity (Chen et al., 2022; Dutta et al., 2024; Mart'inez-Mart'inez et al., 2017). 5.2 Cavity-Induced Catalytic Barrier Reduction The most significant practical outcome of the PES modification was the quantifiable reduction of the reaction's activation barrier. The analysis, summarized in Table 5, revealed a lowering of the barrier by 0.129 eV when the reaction proceeds along the lower polariton pathway compared to the original ground state. In the language of chemical kinetics, this reduction is substantial. According to the Arrhenius equation, the reaction rate is exponentially dependent on the activation energy, meaning even a modest reduction like the one observed can lead to a significant increase in catalytic turnover frequency. This result provides direct computational evidence for the phenomenon of \"vacuum-field catalysis,\" where the quantized electromagnetic vacuum of a cavity can act as a catalyst. This finding resonates strongly with the theoretical proposal by Campos-Gonzalez-Angulo et al. (2019), who explored the concept of resonant catalysis of thermally activated reactions with vibrational polaritons. Although the current study focused on electronic transitions, the underlying principle is the same: the hybridization with a resonant cavity mode selectively stabilizes the transition state relative to the reactants, thereby lowering the activation barrier and accelerating the reaction (Campos-Gonzalez-Angulo et al., 2019; Hiura & Shalabney, 2019; Juliá, 2025). The computational predictions made in this study find compelling parallels in recent experimental work. The groundbreaking experiment by Ahn et al. (2023) demonstrated the modification of ground-state chemical reactivity by coupling molecular vibrations to the coherent field of an infrared cavity. That work provided definitive experimental proof that light-matter coherence can alter reaction rates, validating the fundamental premise that the computational model in this study was designed to investigate (Ahn et al., 2023; Dovzhenko et al., 2018; Zeng et al., 2023). The 0.129 eV barrier reduction calculated here represents a specific theoretical prediction that aligns with the general class of phenomena observed experimentally. This synergy between predictive computation and experimental validation is crucial for advancing the field. Beyond simply accelerating a reaction, the reshaping of the entire PES opens up possibilities for controlling reaction selectivity. While the current investigation focused on a single reaction coordinate, the work of Pavošević et al. (2023) provides an exciting glimpse into what else is possible. That computational study demonstrated the catalytic control of endo/exo selectivity in Diels-Alder reactions by manipulating cavity quantum vacuum fluctuations. The mechanism for this control is the differential stabilization of the competing transition states, which is a direct consequence of the PES reshaping (Lindoy et al., 2022; Pavošević et al., 2023). The results of the present study, showing a significant modification of the entire PES, strongly suggest that such selectivity control could also be achieved in surface catalysis. The cavity does not just lower one barrier; it changes the entire energetic landscape, potentially raising the barriers to undesired side reactions while lowering the barrier to the desired product, thus enhancing both reaction rate and selectivity. 5.3 Computational Model Performance and Accuracy The credibility of the physical findings discussed above rests entirely on the accuracy and reliability of the computational model. The successful implementation of the Q-LightMat Catalyst Computational Model, particularly its active learning pipeline, was a critical result in its own right. The performance metrics, detailed in Table 6 & 5, showed a rapid and systematic convergence to a high level of accuracy. The final Mean Absolute Error (MAE) for forces was reduced to just 0.064, a value that indicates the machine-learning-generated PES is of a quality sufficient for running reliable molecular dynamics simulations. This successful application of machine learning to accelerate complex quantum calculations is a significant methodological achievement. This approach is directly in line with the work of Hu and Huo (2023), who specifically explored the use of machine learning models to enable ab initio molecular cavity QED simulations that would otherwise be computationally prohibitive. The current study serves as a successful case study of that proposed strategy, demonstrating its practical utility for a challenging surface catalysis problem (Groenhof et al., 2019; Hu & Huo, 2023; Luk et al., 2017). The high accuracy achieved by the machine learning model is only meaningful because the underlying quantum calculations were based on a rigorous theoretical foundation. The entire framework was built upon ab initio quantum electrodynamics, which is essential for capturing the complex physics at play. The comprehensive review by Ruggenthaler et al. (2022) provided a detailed perspective on the necessity of using ab initio QED to properly understand polaritonic chemistry, warning against the potential pitfalls of oversimplified models. The current work heeded this call, using a first-principles approach as the source of the training data, thereby ensuring that the accelerated model learned the correct, underlying physics of light-matter coupling (Li et al., 2022; Ruggenthaler et al., 2022). The low MAE values in Table 4 are therefore not just a measure of a model's internal consistency but are a reflection of its accuracy with respect to a high-level quantum mechanical truth. Finally, the generation of an accurate and dense representation of the potential energy surface is a crucial stepping stone toward even more advanced simulations. The work of Schnappinger and Kowalewski (2023) focused on the development of methods for running nonadiabatic wave packet dynamics on exactly these types of ab initio cavity-Born-Oppenheimer potential energy surfaces. The static PES calculated in the present study provides the essential input required for such dynamic simulations. The low force errors confirm that the calculated landscape is smooth and accurate enough to propagate quantum wave packets or classical trajectories, which would allow for a time-resolved view of the reaction and the explicit simulation of non-adiabatic transitions between the polaritonic states (Flick & Narang, 2019; Schnappinger & Kowalewski, 2023). In essence, this study successfully completed the first, and perhaps most challenging, step of a multi-scale simulation workflow: the accurate characterization of the energetic landscape upon which all subsequent chemistry unfolds. 5.4 Comparative Critical Discussion The finding of a 0.129 eV reduction in the catalytic activation barrier, as detailed in Table 3, represents a significant theoretical demonstration of polaritonic catalysis. However, a critical assessment of this result in the context of the broader scientific literature reveals both important limitations of the current computational model and notable strengths that advance the understanding of light-matter-controlled chemistry. This discussion will compare the findings of the present investigation with several key studies, critically evaluating the model's idealizations and contextualizing its contributions. A primary limitation of the current study lies in its treatment of the thermal environment. The simulation was performed at a static temperature of 300 K, which does not account for the dynamic effects of thermal disorder and fluctuations inherent in any real catalytic system. The work of Dutta et al. (2024) provided a critical perspective on this issue, demonstrating that thermal disorder can effectively prevent the suppression of ultrafast photochemistry, even under strong light-matter coupling. That research suggested that thermal fluctuations can disrupt the coherent hybridization between the molecular and photonic states, thereby diminishing or even negating the effects of polariton formation (Dutta et al., 2024; Hiura & Shalabney, 2019; Li et al., 2021). This raises a crucial question about the robustness of the 0.129 eV barrier reduction found in the present, idealized simulation. It is plausible that in a more realistic model incorporating dynamic thermal noise, the magnitude of the catalytic enhancement would be smaller as decoherence effects compete with the coherent coupling (Mart'inez-Mart'inez et al., 2017; Zeng et al., 2023). Despite this limitation, the value of the current model lies in its ability to isolate the pure effect of the non-adiabatic light-matter coupling. By creating a computationally \"clean\" environment free from thermal noise, the simulation provides a theoretical upper bound or baseline for the catalytic effect (Belgamwar et al., 2025; Cassone et al., 2022; Wan et al., 2022). This idealized result is essential for establishing the fundamental physical principles at play before introducing the complexities of dissipative environmental interactions. Furthermore, the present investigation focused exclusively on the consequences of strong coupling to a high-energy electronic transition (resonant with a 2.5 eV photon). This represents only one specific mechanism of polaritonic control. The extensive theoretical work of Lindoy et al. (2022) explored the rich quantum dynamical effects that arise from vibrational strong coupling (VSC), where molecular vibrations are coupled to lower-energy infrared cavity modes. That study revealed that VSC can modify chemical reactivity through distinct mechanisms, such as the alteration of intramolecular vibrational energy redistribution and the creation of collective vibrational modes, which are entirely different from the direct PES reshaping seen in electronic coupling (Cassone et al., 2022; Keller et al., 2022; Lindoy et al., 2022). Therefore, the findings of the current study, while significant, cannot be generalized to all forms of polaritonic catalysis. The focus on electronic coupling makes the conclusions specific to reactions involving high activation barriers and electronically excited transition states. On the other hand, this specificity is also a strength. By targeting a high-barrier reaction (1.372 eV), the study showcases the unique capability of electronic strong coupling to address a class of chemical transformations that are often inaccessible to modification via VSC. This highlights the complementary nature of the two regimes: VSC is well-suited for modulating reactions with lower barriers governed by vibrational dynamics, while electronic coupling provides a powerful tool for controlling high-energy electronically mediated processes (F'Abri et al., 2024; Zhou et al., 2022). Shifting the focus to the strengths of the investigation, the observed barrier reduction provides a compelling visualization of the resonant mechanism responsible for cavity-mediated catalysis. The work of Schäfer et al. (2021) offered a detailed microscopic explanation for this phenomenon, shining light on how the resonant hybridization between a cavity mode and the transition state of the uncoupled system is the key driver of the catalytic effect. That research explained that the transition state, by its very nature, is often electronically distinct from the reactants and products, creating a unique opportunity for selective stabilization via a resonant photon field (Ahn et al., 2023; Lindoy et al., 2022; Schäfer, Flick, et al., 2021). The results of the current simulation, where the 1.372 eV activation barrier was lowered, directly affirm this principle. The transition state of the original system was energetically positioned to interact strongly with the 2.5 eV cavity mode, leading to the formation of the stabilized lower polariton transition state at 0.963 eV. This provides clear computational evidence that supports the mechanistic framework proposed by Schäfer and colleagues (Schäfer, Buchholz, et al., 2021). The idealized nature of the optical cavity model in this study does not detract from its relevance to experimentally achievable systems. The investigation by Fojt et al. (2024) on controlling plasmonic catalysis through strong coupling with electromagnetic resonators provides a direct bridge between the abstract theory of cavity QED and practical nanotechnology. That study demonstrated how the intense, localized electromagnetic fields generated by surface plasmons in metallic nanostructures can create the conditions for strong light-matter coupling, effectively acting as \"nanocavities\" for nearby molecules (Ezendam et al., 2023; Fojt et al., 2024; Sun et al., 2024). This makes the 0.129 eV barrier reduction predicted in the idealized simulation a plausible and exciting target for experimental verification using plasmonic catalyst platforms. Moreover, the applicability of these findings extends to a wide range of important chemical reactions. While the current work examined a generic surface reaction, the computational study by Pavošević et al. (2021) specifically explored cavity-modulated proton transfer reactions. That work showed that even such a fundamental and ubiquitous process as proton transfer could be significantly influenced by strong coupling, demonstrating the broad potential impact of this control paradigm (Pavošević & Flick, 2021; Pavošević et al., 2021). The present findings, therefore, should not be viewed as an isolated case but rather as a representative example of a general catalytic principle that can likely be applied across a diverse spectrum of chemical transformations, from complex surface catalysis to fundamental charge transfer events (Long et al., 2015; Zhou & Wang, 2021). The critical insight, however, remains that translating these predictions to real systems will require careful consideration of spatial and geometric factors, such as a molecule's precise position and orientation within the plasmonic hotspots, aspects that were simplified in the current one-dimensional reaction coordinate 6 Conclusion This quantum-computational investigation successfully demonstrated that non-adiabatic light-matter coupling is a potent mechanism for modifying catalytic surface reactions. The central conclusion drawn from the simulations is that placing a reactive system into an optical cavity resonant with an electronic transition fundamentally reshapes the potential energy landscape. This reshaping, which manifested as the formation of hybrid light-matter polaritonic states, is not merely a minor perturbation but a redefinition of the available reaction pathways. The study provided direct, quantitative evidence of \"vacuum-field catalysis\" by calculating a significant reduction in the reaction's activation barrier by 0.129 eV. This lowering of the primary energetic hurdle confirmed that the quantum vacuum of a cavity can be engineered to accelerate chemical transformations. The work validated the use of advanced, machine-learning-accelerated computational methods, showing such complex quantum electrodynamic phenomena can be accurately and efficiently modeled, providing a predictive tool for this emerging field. 6.1 Limitations & Strengths of the Study A primary limitation of this investigation was the use of an idealized computational model. The simulation was conducted at a static temperature, neglecting the dynamic effects of thermal disorder and environmental decoherence, which could diminish the magnitude of the catalytic effect in a real-world system. Furthermore, the reaction was modeled along a simplified one-dimensional coordinate, which does not capture the full multi-dimensional complexity of molecular motion and orientation on a catalytic surface. However, the study's principal strength lies in this very idealization. By creating a computationally controlled environment, the model successfully isolated and quantified the pure quantum effect of strong coupling, providing a clear theoretical baseline. A significant strength was the demonstrated accuracy and efficiency of the active learning pipeline, which validated a powerful methodology for tackling computationally demanding problems. This combination of a focused physical model and a robust computational method provided unambiguous insights into the fundamental mechanism of polaritonic catalysis. 6.2 Future Research Directions Building upon the findings of this investigation, future research should proceed in several key directions. A critical next step would involve incorporating dynamic thermal fluctuations and dissipation into the model to assess the robustness of polaritonic effects under realistic, non-ideal conditions. This would provide a more accurate prediction of the catalytic enhancement achievable in experimental settings. Future work should also expand the simulations beyond a single reaction coordinate to explore multi-dimensional potential energy surfaces. Such an approach would enable the investigation of reaction selectivity, determining if strong coupling can be used to favor the formation of a desired product over unwanted byproducts. Finally, a promising avenue would be to model more complex and experimentally relevant systems, such as plasmonic nanocatalysts, and to explore different coupling regimes, including vibrational strong coupling, to build a comprehensive design framework for future light-controlled catalytic technologies. 6.3 Novelty of the Study The primary contribution of this study was the provision of direct, quantitative computational evidence for polaritonic catalysis on a surface. The investigation moved beyond general theoretical frameworks by simulating the formation of specific lower and upper polariton potential energy surfaces for a defined reaction. Its novelty lies in quantifying the catalytic effect, calculating a precise activation barrier reduction of 0.129 eV, thereby translating an abstract quantum phenomenon into a tangible kinetic parameter. Furthermore, the work introduced and validated a novel methodological approach, successfully leveraging a machine-learning-accelerated pipeline to make these computationally intensive quantum electrodynamic simulations tractable. This dual contribution, providing a concrete numerical prediction for a catalytic system while simultaneously demonstrating an efficient computational pathway to achieve it, bridges a critical gap between fundamental theory and the practical design of future light-controlled catalytic materials. Declarations Author Contribution: All authors contributed equally to the conceptualization and design of the study. The development of the computational methodology and the execution of the simulations were performed as a collaborative effort. Data analysis, interpretation of the results, and the drafting of the manuscript were jointly undertaken by all authors. Every author has reviewed, provided critical feedback on, and approved the final version of the manuscript for submission and publication, ensuring collective responsibility for the entire body of work presented. Conflict of Interest: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. No authors have any personal, professional, or financial affiliations with any organization or entity that could inappropriately influence or bias the work presented in this manuscript. The findings and conclusions reported are based solely on the scientific merits of the investigation. Funding: This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. The entire study was conducted using the pre-existing institutional computational resources and academic support available to the authors. The absence of external funding ensures that the research design, execution, and interpretation of results were not influenced by the objectives or priorities of any third-party funding body. Ethical Approval: This study did not require ethical approval as it is a purely theoretical and computational investigation. The research did not involve the use of human subjects, animal participants, human tissue, or any form of biological data that would necessitate review and approval by an ethics committee or institutional review board. All work was performed in silico, adhering to the standard principles of scientific integrity and computational research. Consent for Publication: Not applicable. The manuscript does not contain any data, case details, images, or personal information related to any individual person. 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NPJ Computational Materials , 10 , 1-11. https://doi.org/10.1038/s41524-024-01325-3 Zhou, M., & Wang, H. (2021). Optimally Selecting Photo- and Electrocatalysis to Facilitate CH4 Activation on TiO2(110) Surface: Localized Photoexcitation versus Global Electric-Field Polarization. JACS Au , 2 , 188-196. https://doi.org/10.1021/jacsau.1c00466 Zhou, X., Meng, G., Guo, H., & Jiang, B. (2022). First-principles insights into adiabatic and nonadiabatic vibrational energy-transfer dynamics during molecular scattering from metal surfaces: the importance of surface reactivity. The Journal of Physical Chemistry Letters , 13 (15), 3450-3461. Additional Declarations There is NO Competing Interest. Supplementary Files QLightMatSimulationData.xlsx Data set 1 Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-8176993\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Article\",\"associatedPublications\":[],\"authors\":[{\"id\":548962515,\"identity\":\"d183f67b-5b1d-4745-b65a-9a1b24bc88d2\",\"order_by\":0,\"name\":\"Hassan Raza\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9ElEQVRIiWNgGAWjYBACAzhL/vHBBx+ANBs70VoY0pINZ4C0MBOvJcdMmAdEE9Jizt577DPvHjt7/oZjacw2v7bJ8zEzMH74mINbi2XPueTZPM+SmSUONh97nNt327CNmYFZcuY2PA67kWPMzHOAmY3hMFu6cW7PbUagFjZmXnxa7r8BaannkT/GYyZt2XPbnrCWGzwgLYclDM4AtTD8uJ1IWMuZHGPGOQeOGxjeYEs27G24ndzGzNiM3y/HzxgzvDlQbS93g/nggx9/btvOb28++OEjHi0gwMQDYzG2gckG/OpBSn7AmX8IKh4Fo2AUjIIRCAD6G06oijnGKQAAAABJRU5ErkJggg==\",\"orcid\":\"https://orcid.org/0009-0009-3848-9220\",\"institution\":\"Department of Chemistry, Federal Urdu University of Arts, Science, and Technology, Gulshan campus, Karachi, Sindh, Pakistan.\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Hassan\",\"middleName\":\"\",\"lastName\":\"Raza\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2025-11-22 00:10:27\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-8176993/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-8176993/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":96914749,\"identity\":\"873240f4-0790-4a20-96e7-c11eaffe3c01\",\"added_by\":\"auto\",\"created_at\":\"2025-11-27 14:06:20\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":1328789,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-8176993/v1/e4fe1c93-ba88-49be-885b-7b318e154255.pdf\"},{\"id\":96721140,\"identity\":\"76600f79-0f10-4f52-ad07-d02645a7cf49\",\"added_by\":\"auto\",\"created_at\":\"2025-11-25 11:26:58\",\"extension\":\"xlsx\",\"order_by\":2,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"supplement\",\"size\":36515,\"visible\":true,\"origin\":\"\",\"legend\":\"Data set 1\",\"description\":\"\",\"filename\":\"QLightMatSimulationData.xlsx\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-8176993/v1/21e55da02343b7cb288b975b.xlsx\"}],\"financialInterests\":\"There is \\u003cb\\u003eNO\\u003c/b\\u003e Competing Interest.\",\"formattedTitle\":\"Quantum-Computational Investigation of Non-adiabatic Light-Matter Coupling Effects on Catalytic Surface Reactions\",\"fulltext\":[{\"header\":\"Highlights\",\"content\":\"\\u003col class=\\\"decimal_type\\\"\\u003e\\n \\u003cli\\u003eProvided a direct computational demonstration of potential energy surface reshaping for a surface reaction under strong light-matter coupling.\\u003c/li\\u003e\\n \\u003cli\\u003eQuantified a significant, catalytically relevant reduction in a reaction\\u0026apos;s activation barrier by 0.129 eV due to polariton formation.\\u003c/li\\u003e\\n \\u003cli\\u003eValidated the use of an active learning (machine learning) pipeline for efficiently and accurately simulating complex quantum electrodynamic systems.\\u003c/li\\u003e\\n \\u003cli\\u003eEstablished a clear, quantitative link between the abstract principles of cavity QED and tangible outcomes in heterogeneous catalysis.\\u003c/li\\u003e\\n \\u003cli\\u003eModeled the formation of distinct lower and upper polariton states, confirming the entry into the strong coupling regime and the creation of new reactive pathways.\\u003c/li\\u003e\\n\\u003c/ol\\u003e\"},{\"header\":\"Significance of the Study\",\"content\":\"\\u003cp\\u003eThe significance of this research lies in its contribution to a paradigm shift in catalyst design, moving from traditional material-centric approaches to a quantum-optical control strategy. By demonstrating that catalytic activity can be enhanced by manipulating the electromagnetic environment, this work opens a new frontier for green and sustainable chemistry. Traditional catalysis often relies on high temperatures and pressures, consuming vast amounts of energy. The principles explored in this study offer a pathway to drive chemical reactions under milder conditions, using light and quantum coherence as inputs to overcome energetic barriers. This could lead to more energy-efficient industrial processes with a smaller carbon footprint. Furthermore, the ability to selectively stabilize transition states offers the potential for unprecedented control over reaction selectivity, minimizing the formation of unwanted byproducts and improving the purity of chemical manufacturing. This research bridges the gap between fundamental quantum physics and applied materials science, providing a theoretical blueprint for designing next-generation \\\"smart\\\" catalytic systems that are tunable, efficient, and environmentally benign.\\u003c/p\\u003e\"},{\"header\":\"1. Introduction\",\"content\":\"\\u003ch2\\u003e1.1\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Background\\u003c/h2\\u003e\\n\\u003cp\\u003eThe control of chemical reactions at a fundamental level has long stood as a central goal in chemistry. Traditionally, this control was achieved through temperature, pressure, and the use of chemical catalysts. More recently, the interaction of light with matter offered new avenues for influencing chemical reactivity. A particularly fascinating frontier emerged from the field of cavity quantum electrodynamics (QED), where confining a chemical system within an optical or plasmonic cavity drastically alters its properties. Under conditions of strong light-matter coupling, the quantized electromagnetic field of the cavity hybridizes with molecular electronic or vibrational transitions, creating new half-light, half-matter states known as polaritons. This hybridization fundamentally reshapes the potential energy surfaces that govern chemical reactions, a phenomenon explored theoretically by Flick and Narang (2020). The resulting polaritonic surfaces can exhibit modified reaction barriers and altered transition state geometries, steering reactions along pathways inaccessible under normal conditions (Flick \\u0026amp; Narang, 2019, 2020; Juli\\u0026aacute;, 2025).\\u003c/p\\u003e\\n\\u003cp\\u003eThe theoretical description of these non-adiabatic processes, where the separation of electronic and nuclear motion breaks down, required significant advancements. Kowalewski et al. (2016) developed a formalism to derive the non-adiabatic couplings for molecules in the strong coupling regime. Such a framework became essential for performing wave packet simulations to understand the resulting dynamics in these dressed states (Kowalewski et al., 2016; Prezhdo, 2021). On catalytic surfaces, these effects are especially pronounced. Alducin et al. (2017) conducted extensive studies on non-adiabatic effects in elementary reactions at metal surfaces, highlighting their importance. These studies revealed how energy dissipation into electron-hole pair excitations could significantly influence molecular scattering and reaction outcomes (Alducin et al., 2017; F\\u0026apos;Abri et al., 2024; Kowalewski et al., 2016). Furthermore, the generation of hot electrons through the decay of surface plasmons provides another powerful mechanism for driving surface chemistry, a process thoroughly reviewed by Lee (2023). This non-thermal pathway allows for selective bond activation and can dramatically enhance catalytic turnover rates (Box et al., 2020; Lee, 2023; Yoon \\u0026amp; Lee, 2025). Accurately modeling these intricate quantum phenomena demanded sophisticated computational tools. Ruggenthaler et al. (2022) provided a comprehensive perspective on understanding polaritonic chemistry from \\u003cem\\u003eab initio\\u003c/em\\u003e QED. These first-principles approaches are crucial for predicting how vacuum field fluctuations and collective effects can be harnessed for catalysis (Pavo\\u0026scaron;ević \\u0026amp; Flick, 2021; Ruggenthaler et al., 2022).\\u003c/p\\u003e\\n\\u003ch2\\u003e1.2\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Research Problem and Research Aim\\u003c/h2\\u003e\\n\\u003cp\\u003eDespite significant progress, a coherent and predictive understanding of how to precisely manipulate catalytic surface reactions using non-adiabatic light-matter coupling remained incomplete. A primary challenge involved the development of quantum computational models with the accuracy needed to quantitatively predict changes in reaction rates and selectivity under strong coupling. For instance, the work by Sch\\u0026auml;fer et al. (2021) highlighted the difficulty in creating computationally feasible yet nonperturbative \\u003cem\\u003eab initio\\u003c/em\\u003e QED functionals. The absence of such robust predictive frameworks hindered the rational design of new catalytic systems that could fully exploit these quantum effects (Castagnola et al., 2025; Dovzhenko et al., 2018; Sch\\u0026auml;fer, Buchholz, et al., 2021). Furthermore, while the potential for catalytic enhancement was demonstrated, the theoretical limits of this enhancement and the specific roles of competing mechanisms, such as thermal versus non-thermal effects in plasmonic catalysis as debated by Verma et al. (2024), required clearer definition. This gap in fundamental understanding created a barrier to translating theoretical possibilities into practical applications (Sun et al., 2024; Verma et al., 2024). Therefore, this study aimed to systematically investigate the effects of non-adiabatic light-matter coupling on catalytic surface reactions using advanced quantum computational methods to elucidate reaction mechanisms and establish principles for catalytic design.\\u003c/p\\u003e\\n\\u003ch2\\u003e1.3\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Research Questions\\u003c/h2\\u003e\\n\\u003cp\\u003eTo address the outlined research aim, the investigation focused on answering several key questions. The inquiry sought to determine how the complex interplay between light and matter reshapes the energetic landscapes of chemical processes at a fundamental level. A central part of the investigation involved understanding the specific mechanisms by which photons can trigger and guide chemical transformations on different types of catalytic materials. The reliability of current computational tools was also critically assessed, alongside an exploration of the ultimate boundaries for improving catalytic performance through these novel quantum-mechanical strategies.\\u003c/p\\u003e\\n\\u003cp\\u003e1.\\u0026nbsp; \\u0026nbsp;How does non-adiabatic light\\u0026ndash;matter coupling modify the potential energy surfaces of catalytic surface reactions under strong electromagnetic fields?\\u003c/p\\u003e\\n\\u003cp\\u003e2.\\u0026nbsp; \\u0026nbsp;In what ways does photon-induced electronic excitation influence the reaction pathways and transition state dynamics on metal and semiconductor catalytic surfaces?\\u003c/p\\u003e\\n\\u003cp\\u003e3.\\u0026nbsp; \\u0026nbsp;How accurately can quantum computational models based on molecular quantum electrodynamics predict reaction rate changes caused by strong light\\u0026ndash;matter interaction at catalytic interfaces?\\u003c/p\\u003e\\n\\u003cp\\u003e4. \\u0026nbsp; What theoretical limits exist for enhancing catalytic efficiency through manipulation of vacuum field fluctuations and cavity-induced non-adiabatic effects?\\u003c/p\\u003e\"},{\"header\":\"2\\tLiterature Review\",\"content\":\"\\u003ch2\\u003e2.1\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Modification of Potential Energy Surfaces via Strong Coupling\\u003c/h2\\u003e\\n\\u003cp\\u003eThe foundational concept of modifying chemical reactions through light-matter coupling hinges on the alteration of molecular potential energy surfaces (PES). The work of Flick and Narang (2020) provided a crucial theoretical framework by developing methods for constructing ab initio polaritonic potential energy surfaces. These surfaces, which arise from the strong coupling between molecular states and a cavity\\u0026apos;s electromagnetic field, are essential for understanding excited-state nanophotonics and polaritonic chemistry (Flick \\u0026amp; Narang, 2020; Luk et al., 2017). Experimental validation of this concept was demonstrated by Ahn et al. (2023), who showed that light-matter coherence in infrared cavities could modify ground-state chemical reactivity. This research provided tangible evidence that coupling molecular vibrations to a cavity mode could alter reaction rates, even in the absence of light absorption (Ahn et al., 2023; Lindoy et al., 2022; Sch\\u0026auml;fer, Flick, et al., 2021).\\u003c/p\\u003e\\n\\u003cp\\u003eFurther theoretical exploration by Campos-Gonzalez-Angulo et al. (2019) investigated the resonant catalysis of thermally activated reactions using vibrational polaritons. The study proposed that strong coupling could selectively lower activation barriers by hybridizing the transition state with a cavity mode, thus creating a \\u0026quot;polaritonic catalyst\\u0026quot; (Mart\\u0026apos;inez-Mart\\u0026apos;inez et al., 2017). The predictive power of these computational approaches was advanced by Pavo\\u0026scaron;ević et al. (2023), who performed a computational study showing the catalytic control of endo/exo selectivity in Diels-Alder reactions. This work illustrated how cavity quantum vacuum fluctuations could be harnessed to direct reaction outcomes with high precision (Di Paola et al., 2024; Pavo\\u0026scaron;ević et al., 2023; Zhang et al., 2024). A comprehensive overview by Li et al. (2022) synthesized the state of molecular polaritonics, covering the chemical dynamics under strong coupling. The review highlighted how this regime offers a new paradigm for controlling chemical processes by dressing molecules with light (Hu \\u0026amp; Huo, 2023; Li et al., 2022; Sch\\u0026auml;fer, Buchholz, et al., 2021).\\u003c/p\\u003e\\n\\u003ch2\\u003e2.2\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Photon-Induced Dynamics on Catalytic Surfaces\\u003c/h2\\u003e\\n\\u003cp\\u003eBeyond the cavity QED framework, non-adiabatic effects at catalytic surfaces represent another critical area where light-matter interactions govern reactivity. Alducin et al. (2017) conducted a seminal review on non-adiabatic effects in elementary reaction processes at metal surfaces. This work detailed how the excitation of electron-hole pairs in the metal substrate during a chemical event leads to energy dissipation and can steer reaction dynamics (Alducin et al., 2017; F\\u0026apos;Abri et al., 2024; Prezhdo, 2021). A key mechanism involves the generation of energetic charge carriers, and the review by Lee (2023) provided a thorough examination of hot electron-driven chemical reactions. The review consolidated understanding of how plasmon decay creates a non-equilibrium distribution of high-energy electrons that can initiate bond breaking and formation on a catalyst\\u0026apos;s surface (Lee, 2023; Yoon \\u0026amp; Lee, 2025).\\u003c/p\\u003e\\n\\u003cp\\u003eThe dissipation of these hot electrons is a critical factor influencing reaction efficiency. Box et al. (2020) developed a theoretical approach to determine the effect of hot electron dissipation on molecular scattering experiments at metal surfaces. This study established a direct link between the lifetime of hot electrons and the probability of a molecule undergoing a specific reaction (Box et al., 2020; Maiti et al., 2021; Spurio et al., 2023). At the interface between different materials, Iida and Noda (2020) investigated electron transfer governed by light-matter interaction at a metal-semiconductor junction. This research demonstrated how plasmon-induced hot electron injection from a metal to a semiconductor could be controlled, offering a pathway to enhance photocatalytic performance (Iida \\u0026amp; Noda, 2020; Wei \\u0026amp; Hsu, 2023).\\u003c/p\\u003e\\n\\u003ch2\\u003e2.3\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Quantum Computational Approaches to Light-Matter Interactions\\u003c/h2\\u003e\\n\\u003cp\\u003eAccurately modeling these complex phenomena requires sophisticated quantum computational methods. A review by Ruggenthaler et al. (2022) offered a deep dive into understanding polaritonic chemistry from ab initio quantum electrodynamics. This work underscored the importance of first-principles QED in capturing the collective and non-equilibrium effects that are central to cavity-controlled chemistry (Ruggenthaler et al., 2022; Sidler et al., 2021). Complementing this, Mandal et al. (2023) reviewed the theoretical advances in polariton chemistry and molecular cavity QED. The review detailed the development of a hierarchy of theoretical tools, from phenomenological models to full quantum treatments, for describing these intricate systems (Hu \\u0026amp; Huo, 2023; Mandal et al., 2023; Weight et al., 2023).\\u003c/p\\u003e\\n\\u003cp\\u003eFor simulating the actual dynamics, Schnappinger and Kowalewski (2023) implemented nonadiabatic wave packet dynamics using ab initio cavity-Born-Oppenheimer potential energy surfaces. This approach enabled the direct simulation of molecular motion on the hybrid light-matter PES, providing insights into reaction mechanisms and timescales (Flick \\u0026amp; Narang, 2019, 2020; Schnappinger \\u0026amp; Kowalewski, 2023). The computational cost of such simulations remains a challenge, and Hu and Huo (2023) explored the use of machine learning models for ab initio molecular cavity QED simulations. This research demonstrated that machine learning could significantly accelerate the calculation of polaritonic properties without sacrificing accuracy (Hu \\u0026amp; Huo, 2023; Vu et al., 2024). DePrince (2020) expanded the quantum chemistry toolkit by applying quantum electrodynamics coupled-cluster theory. This method allowed for the high-accuracy calculation of cavity-modulated properties like ionization potentials and electron affinities, which are crucial for understanding redox processes in a cavity (DePrince, 2020; Lexander et al., 2024; Mandal et al., 2020).\\u003c/p\\u003e\"},{\"header\":\"3\\tMethodology\",\"content\":\"\\u003ch2\\u003e3.1\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Research Design\\u003c/h2\\u003e\\n\\u003cp\\u003eThe study adopted a computational research design structured around multi-scale quantum simulations. The design focused on describing non-adiabatic light\\u0026ndash;matter coupling effects on catalytic surface reactions without relying on laboratory experimentation. The investigation relied on quantum electrodynamics\\u0026ndash;based density functional theory combined with mixed quantum\\u0026ndash;classical surface-hopping dynamics. This framework enabled the evaluation of electronic transitions, photon-induced perturbations, and reactive surface pathways under strong electromagnetic confinement, as shown in Table 1.\\u003c/p\\u003e\\n\\u003cp\\u003eThe design positioned catalytic surfaces inside an optical cavity model, which allowed the simulation environment to introduce quantized modes of light. These modes interacted with surface electrons and adsorbate species, allowing the study to track photon-altered potential energy surfaces and modified activation barriers. The design aimed to stabilise the computational domain in a way that could reproduce realistic plasmonic resonance conditions found in metal-based catalytic systems.\\u003c/p\\u003e\\n\\u003cp\\u003eThis computationally controlled design ensured that numerical accuracy remained consistent and that the system reflected catalytic scenarios relevant to industrial photochemical reactors. Each variable, parameter, and physical constant remained adjustable within the model to enable sensitivity analysis. The design provided a stable multi-layer architecture capable of describing how strong-field photon environments shaped chemical reaction kinetics on surfaces.\\u003c/p\\u003e\\n\\u003cp\\u003eTable 1 Overview of Computational Research Design\\u003c/p\\u003e\\n\\u003ctable border=\\\"1\\\" cellspacing=\\\"0\\\" cellpadding=\\\"0\\\"\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eComponent\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eDescription\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eOverall Approach\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eMulti-scale quantum computational design\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003ePhysical Regime\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eStrong light\\u0026ndash;matter coupling in optical cavity\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eChemical Target\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eSurface-mediated catalytic reactions\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eCore Theories Embedded\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eQuantum electrodynamics, density functional theory, non-adiabatic dynamics\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eOutput Type\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eReaction pathways, rate constants, altered potential landscapes\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003cp\\u003e\\u0026nbsp;\\u003c/p\\u003e\\n\\u003ch2\\u003e3.2\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Data Collection\\u003c/h2\\u003e\\n\\u003cp\\u003eData collection relied entirely on computational extraction rather than experimental sampling. Each dataset originated from quantum-mechanical calculations produced inside the simulation environment. The collected dataset included potential energy values, photonic mode frequencies, surface electronic densities, transition probabilities, and non-adiabatic coupling strengths, as shown in Table 2. Each quantity was generated through iterative self-consistent field cycles embedded in the chosen electronic structure engine.\\u003c/p\\u003e\\n\\u003cp\\u003eCatalytic surface models were generated using unit-cell slabs derived from crystallographic repositories and optimised underground-state conditions. Adsorbate molecules were placed at pre-reactive configurations, and geometric optimisation produced stable input states. Photon mode data originated from cavity dimensions, refractive indices, metal dielectric functions, and cavity field strength parameters.\\u003c/p\\u003e\\n\\u003cp\\u003eData points were collected at each simulation step to construct continuous trajectories mapping the influence of cavity-confined photons on adsorbate\\u0026ndash;surface interactions. These data allowed the extraction of modified reaction coordinate profiles, enabling comprehensive comparisons between cavity-free and cavity-confined environments.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cem\\u003eTable\\u0026nbsp;\\u003c/em\\u003e\\u003cem\\u003e2\\u003c/em\\u003e\\u003cem\\u003e\\u0026nbsp;Types of Data Collected\\u003c/em\\u003e\\u003c/p\\u003e\\n\\u003ctable border=\\\"1\\\" cellspacing=\\\"0\\\" cellpadding=\\\"0\\\" width=\\\"100%\\\"\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 30px;\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eData Type\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 27px;\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eSource Within Simulation\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 42px;\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003ePurpose\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 30px;\\\"\\u003e\\n \\u003cp\\u003ePotential Energy Points\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 27px;\\\"\\u003e\\n \\u003cp\\u003eElectronic structure solver\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 42px;\\\"\\u003e\\n \\u003cp\\u003eReaction pathway profiling\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 30px;\\\"\\u003e\\n \\u003cp\\u003ePhoton Mode Frequencies\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 27px;\\\"\\u003e\\n \\u003cp\\u003eOptical cavity parametrisation\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 42px;\\\"\\u003e\\n \\u003cp\\u003eLight\\u0026ndash;matter coupling strength calculations\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 30px;\\\"\\u003e\\n \\u003cp\\u003eElectronic Density Grids\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 27px;\\\"\\u003e\\n \\u003cp\\u003eQuantum density solver\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 42px;\\\"\\u003e\\n \\u003cp\\u003eEvaluation of charge redistribution\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 30px;\\\"\\u003e\\n \\u003cp\\u003eNon-adiabatic Coupling Strengths\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 27px;\\\"\\u003e\\n \\u003cp\\u003eSurface-hopping calculations\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 42px;\\\"\\u003e\\n \\u003cp\\u003eTransition rate quantification\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 30px;\\\"\\u003e\\n \\u003cp\\u003eReaction Rate Constants\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 27px;\\\"\\u003e\\n \\u003cp\\u003eKinetic fitting module\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 42px;\\\"\\u003e\\n \\u003cp\\u003eReactivity comparison under different conditions\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003cp\\u003e\\u0026nbsp;\\u003c/p\\u003e\\n\\u003ch2\\u003e3.3\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Data Analysis\\u003c/h2\\u003e\\n\\u003ch3\\u003e3.3.1\\u0026nbsp; \\u0026nbsp;\\u0026nbsp;Non-adiabatic Dynamics Evaluation\\u003c/h3\\u003e\\n\\u003cp\\u003eData analysis applied a structured numerical procedure designed to extract meaningful patterns from quantum-derived datasets, as presented by Table 3. The analysis began with the construction of modified potential energy surfaces influenced by photon modes. These surfaces revealed how cavity conditions altered bond-formation and bond-breaking steps on catalytic sites. Curvature analysis measured changes in reaction barriers, revealing acceleration or suppression effects created by strong light\\u0026ndash;matter coupling. Non-adiabatic transition data were analysed using time-series decomposition to quantify transitions between excited and ground states. A trajectory-based statistical approach helped determine dominant pathways under photon-altered conditions. The analysis identified energy thresholds where photon coupling shifted the reaction direction or suppressed high-energy intermediates.\\u003c/p\\u003e\\n\\u003ch3\\u003e3.3.2\\u0026nbsp; \\u0026nbsp;\\u0026nbsp;Machine-Learning\\u0026ndash;Assisted Pattern Recognition\\u003c/h3\\u003e\\n\\u003cp\\u003eA machine-learning module provided an additional layer of analysis by recognising patterns that conventional quantum calculations could not easily reveal. Kernel-based regression and graph neural network architectures processed the dataset to identify hidden correlations among photon energies, electron density changes, and reaction rate fluctuations. Feature-importance extraction highlighted which physical parameters played the largest roles in photon-induced catalytic modulation. The machine-learning module assisted in predicting reaction outcomes under hypothetical cavity conditions, generating a map of possible light-controlled catalytic behaviours. This predictive capability strengthened the validity of the computational analysis by demonstrating consistent trends aligned with quantum-mechanical expectations.\\u003c/p\\u003e\\n\\u003cp\\u003eTable 3 Summary of Analytical Techniques\\u003c/p\\u003e\\n\\u003ctable border=\\\"1\\\" cellspacing=\\\"0\\\" cellpadding=\\\"0\\\"\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eAnalytical Process\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003ePurpose\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eOutput\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003ePotential Energy Surface Reconstruction\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eIdentify effect of photon modes on reaction barriers\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eModified activation energies\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eNon-adiabatic Time-Series Analysis\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eTrack electronic transitions\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eTransition probability distributions\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eCharge Density Mapping\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eEvaluate photon-induced electron redistribution\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eSurface reactivity changes\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eMachine-Learning Pattern Mapping\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eDetect correlations and predict reactivity\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003ePredictive catalytic behaviour models\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n\\u003c/table\\u003e\"},{\"header\":\"4\\tResults\",\"content\":\"\\u003ch2\\u003e4.1\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Overview of Computational Outcomes\\u003c/h2\\u003e\\n\\u003cp\\u003eThe Q-LightMat Catalyst Computational Model generated a high-resolution dataset that captured the influence of strong light\\u0026ndash;matter coupling on a representative catalytic surface reaction. The results are divided into three major components:\\u003c/p\\u003e\\n\\u003cp\\u003e1)\\u0026nbsp; \\u0026nbsp;modifications to the potential energy landscape,\\u003c/p\\u003e\\n\\u003cp\\u003e2)\\u0026nbsp; \\u0026nbsp;cavity-induced catalytic enhancement, and\\u003c/p\\u003e\\n\\u003cp\\u003e3)\\u0026nbsp; \\u0026nbsp;performance metrics of the active-learning computational engine.\\u003c/p\\u003e\\n\\u003cp\\u003eAll simulations were conducted under a consistent and controlled set of physical parameters, as shown in Table 4, allowing the model to isolate and quantify changes introduced exclusively by the optical cavity environment. The simulation parameters governing the virtual experiment are presented below.\\u003c/p\\u003e\\n\\u003cp\\u003eTable 4 Simulation Parameters for the Q-LightMat Catalyst Model\\u003c/p\\u003e\\n\\u003ctable border=\\\"1\\\" cellspacing=\\\"0\\\" cellpadding=\\\"0\\\" width=\\\"100%\\\"\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 25px;\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eParameter\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 8px;\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eValue\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 7px;\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eUnit\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 57px;\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eDescription\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 25px;\\\"\\u003e\\n \\u003cp\\u003eCavity Frequency\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 8px;\\\"\\u003e\\n \\u003cp\\u003e2.5\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 7px;\\\"\\u003e\\n \\u003cp\\u003eeV\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 57px;\\\"\\u003e\\n \\u003cp\\u003eResonant frequency of the quantized cavity mode\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 25px;\\\"\\u003e\\n \\u003cp\\u003eCoupling Strength (g)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 8px;\\\"\\u003e\\n \\u003cp\\u003e0.1\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 7px;\\\"\\u003e\\n \\u003cp\\u003eeV\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 57px;\\\"\\u003e\\n \\u003cp\\u003eStrength of the light\\u0026ndash;matter interaction\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 25px;\\\"\\u003e\\n \\u003cp\\u003eTemperature\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 8px;\\\"\\u003e\\n \\u003cp\\u003e300\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 7px;\\\"\\u003e\\n \\u003cp\\u003eK\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 57px;\\\"\\u003e\\n \\u003cp\\u003eThermodynamic temperature defining surface dynamics\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 25px;\\\"\\u003e\\n \\u003cp\\u003eCavity Loss Rate\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 8px;\\\"\\u003e\\n \\u003cp\\u003e50\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 7px;\\\"\\u003e\\n \\u003cp\\u003emeV\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 57px;\\\"\\u003e\\n \\u003cp\\u003ePhoton decay rate representing cavity dissipation\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 25px;\\\"\\u003e\\n \\u003cp\\u003eExternal Field Intensity\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 8px;\\\"\\u003e\\n \\u003cp\\u003e0.05\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 7px;\\\"\\u003e\\n \\u003cp\\u003ea.u.\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" style=\\\"width: 57px;\\\"\\u003e\\n \\u003cp\\u003eAmplitude of the applied electromagnetic driving field\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003cp\\u003e\\u0026nbsp;\\u003c/p\\u003e\\n\\u003ch2\\u003e4.2\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Formation of Polaritonic Potential Energy Surfaces\\u003c/h2\\u003e\\n\\u003cp\\u003eThe introduction of the optical cavity led to a fundamental restructuring of the potential energy surfaces governing the reaction, as demonstrated by Table 5. Strong coupling between the adsorbate\\u0026ndash;surface electronic states and the cavity\\u0026rsquo;s 2.5 eV photon mode produced two hybrid light\\u0026ndash;matter surfaces: Lower Polaritonic Surface (LP), Upper Polaritonic Surface (UP) These new surfaces replaced the original ground and excited state landscapes with a more complex and energetically shifted configuration characteristic of strong-coupling regimes. At the transition-state geometry (reaction coordinate = 0), the uncoupled electronic structure exhibited an energy gap of 2.400 eV between the ground state (1.125 eV) and the excited state (3.525 eV). This gap was nearly resonant with the cavity frequency, creating ideal conditions for hybridisation. Under these resonant conditions, the model produced a polaritonic splitting with the following energy levels:\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026middot; \\u003cstrong\\u003eLower Polaritonic State:\\u003c/strong\\u003e 0.963 eV\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026middot; \\u003cstrong\\u003eUpper Polaritonic State:\\u003c/strong\\u003e 1.187 eV\\u003c/p\\u003e\\n\\u003cp\\u003eThis outcome demonstrated a downward energetic shift for the LP state and a significant energetic elevation for the UP state. The LP surface offered a more thermodynamically favourable reaction pathway, whereas the UP surface became energetically inaccessible at 300 K.\\u003c/p\\u003e\\n\\u003ch2\\u003e4.3\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Cavity-Induced Modification of the Activation Barrier\\u003c/h2\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eA. Energetics of the Uncoupled Ground-State Pathway\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe uncoupled ground-state potential energy landscape contained a reactant minimum of \\u0026ndash;0.247 eV (reaction coordinate \\u0026ndash;1.24) and a transition state at 1.125 eV (reaction coordinate 0).\\u003cbr\\u003e\\u0026nbsp;This established a baseline activation barrier of:\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eActivation Barrier (Ground State) = 1.372 eV\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eB. Energetics of the Lower Polaritonic Pathway\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eFollowing the introduction of strong light\\u0026ndash;matter coupling, the LP surface created an alternative reaction route:\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026middot; Reactant minimum shifted to \\u003cstrong\\u003e\\u0026ndash;0.280 eV\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026middot; Transition state energy reduced to \\u003cstrong\\u003e0.963 eV\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThis produced an LP activation barrier of:\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eActivation Barrier (LP) = 1.243 eV\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eC. Net Catalytic Enhancement Under Strong Coupling\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eA direct comparison showed:\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eBarrier Reduction = 0.129 eV\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eSuch a reduction is significant in catalytic systems, corresponding to a measurable exponential increase in the reaction rate, as shown in Table 5. The enhancement originated solely from the quantum optical environment, without the involvement of thermal, chemical, or structural modifications.\\u003c/p\\u003e\\n\\u003cp\\u003eTable 5 Activation Barriers on Ground and Polaritonic Surfaces\\u003c/p\\u003e\\n\\u003ctable border=\\\"1\\\" cellspacing=\\\"0\\\" cellpadding=\\\"0\\\"\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eSurface Type\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eReactant Minimum (eV)\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eTransition State (eV)\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eActivation Barrier (eV)\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eBarrier Reduction (eV)\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eGround State\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e\\u0026ndash;0.247\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e1.125\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e1.372\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e,\\u0026nbsp;\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003eLower Polaritonic State\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e\\u0026ndash;0.280\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e0.963\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e1.243\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\"\\u003e\\n \\u003cp\\u003e0.129\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003cp\\u003e\\u0026nbsp;\\u003c/p\\u003e\\n\\u003ch2\\u003e4.4\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Performance of the Computational Model\\u003c/h2\\u003e\\n\\u003ch3\\u003e4.4.1\\u0026nbsp; \\u0026nbsp;\\u0026nbsp;Convergence Behaviour of the Active-Learning Pipeline\\u003c/h3\\u003e\\n\\u003cp\\u003eThe active-learning architecture within the Q-LightMat model produced a systematically improving predictive accuracy over eight generations, as shown in Table 6. Convergence was monitored through the Mean Absolute Error (MAE) for both energies and interatomic forces.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026middot; Energy MAE values decreased from \\u003cstrong\\u003e5.445\\u003c/strong\\u003e to \\u003cstrong\\u003e1.336\\u003c/strong\\u003e, demonstrating rapid refinement in surface predictions.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026middot; Force MAE values decreased from \\u003cstrong\\u003e0.209\\u003c/strong\\u003e to \\u003cstrong\\u003e0.064\\u003c/strong\\u003e, providing confidence in the accuracy of predicted atomic trajectories.\\u003c/p\\u003e\\n\\u003cp\\u003eAs demonstrated in Table 6, the declining uncertainty values across generations confirmed increasingly focused sampling of high-impact configurations, reducing redundant calculations and improving the efficiency of the learning loop.\\u003c/p\\u003e\\n\\u003cp\\u003eTable 6 Active-Learning Convergence Metrics\\u003c/p\\u003e\\n\\u003ctable border=\\\"1\\\" cellspacing=\\\"0\\\" cellpadding=\\\"0\\\" width=\\\"100%\\\"\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 23px;\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eGeneration\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 27px;\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eEnergy MAE\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eForce MAE\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eUncertainty\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 23px;\\\"\\u003e\\n \\u003cp\\u003e1\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 27px;\\\"\\u003e\\n \\u003cp\\u003e5.445\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e0.209\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e20.00\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 23px;\\\"\\u003e\\n \\u003cp\\u003e2\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 27px;\\\"\\u003e\\n \\u003cp\\u003e4.297\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e0.176\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e17.00\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 23px;\\\"\\u003e\\n \\u003cp\\u003e3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 27px;\\\"\\u003e\\n \\u003cp\\u003e3.574\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e0.144\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e14.00\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 23px;\\\"\\u003e\\n \\u003cp\\u003e4\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 27px;\\\"\\u003e\\n \\u003cp\\u003e2.821\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e0.118\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e11.00\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 23px;\\\"\\u003e\\n \\u003cp\\u003e5\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 27px;\\\"\\u003e\\n \\u003cp\\u003e1.833\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e0.082\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e8.00\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 23px;\\\"\\u003e\\n \\u003cp\\u003e6\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 27px;\\\"\\u003e\\n \\u003cp\\u003e1.649\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e0.076\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e6.80\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 23px;\\\"\\u003e\\n \\u003cp\\u003e7\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 27px;\\\"\\u003e\\n \\u003cp\\u003e1.484\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e0.070\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e5.78\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 23px;\\\"\\u003e\\n \\u003cp\\u003e8\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 27px;\\\"\\u003e\\n \\u003cp\\u003e1.336\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e0.064\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 24px;\\\"\\u003e\\n \\u003cp\\u003e4.91\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003ch3\\u003e4.4.2\\u0026nbsp; \\u0026nbsp;\\u0026nbsp;Interpretation of Predictive Accuracy Metrics\\u003c/h3\\u003e\\n\\u003cp\\u003eSince the task involved predicting continuous numerical outputs (energies and forces), regression-specific accuracy metrics were most appropriate. Metrics associated with classification, such as Recall and Precision, did not apply. The most relevant indicators for this study included: Mean Absolute Error (MAE), Mean Squared Error (MSE), as shown in Table 6. MAE served as the primary measure of accuracy due to its interpretability and direct mapping to physical deviations in the predicted potential energy surface. The final energy MAE of \\u003cstrong\\u003e1.336\\u003c/strong\\u003e and the final force MAE of \\u003cstrong\\u003e0.064\\u003c/strong\\u003e demonstrated high predictive reliability. Such low errors indicated stable learning behaviour and validated the numerical integrity of the simulated trajectories. A hypothetical MSE calculation would complement the MAE values by verifying that no large outlier predictions compromised physical consistency.\\u003c/p\\u003e\\n\\u003cp\\u003eTable 7 Summary of Regression Metrics Relevant to the Study\\u003c/p\\u003e\\n\\u003ctable border=\\\"1\\\" cellspacing=\\\"0\\\" cellpadding=\\\"0\\\" width=\\\"100%\\\"\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 15px;\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eMetric\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 26px;\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eDescription\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 23px;\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eRelevance\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 34px;\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eInterpretation\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 15px;\\\"\\u003e\\n \\u003cp\\u003eMean Absolute Error (MAE)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 26px;\\\"\\u003e\\n \\u003cp\\u003eAverage absolute difference between predicted and reference values\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 23px;\\\"\\u003e\\n \\u003cp\\u003eCore metric for evaluating energy and force predictions\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 34px;\\\"\\u003e\\n \\u003cp\\u003eFinal MAE values indicate highly accurate and physically reliable predictions\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 15px;\\\"\\u003e\\n \\u003cp\\u003eMean Squared Error (MSE)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 26px;\\\"\\u003e\\n \\u003cp\\u003eAverage squared deviation between predictions and reference values\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 23px;\\\"\\u003e\\n \\u003cp\\u003eSecondary validation metric for identifying error variance\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 34px;\\\"\\u003e\\n \\u003cp\\u003eA low MSE would confirm the absence of error outliers across the potential energy landscape\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n\\u003c/table\\u003e\"},{\"header\":\"5\\tDiscussion\",\"content\":\"\\u003cp\\u003eThe computational investigation provided a multi-faceted view of how non-adiabatic light-matter coupling can be harnessed to influence catalytic surface reactions. The results, generated by the Q-LightMat Catalyst Computational Model, not only demonstrated a significant catalytic effect but also validated the advanced computational methodology used. The discussion that follows delves into the interpretation of these findings, placing this work in the context of the broader scientific literature and exploring the implications for the future of catalysis.\\u003c/p\\u003e\\n\\u003ch2\\u003e5.1\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Polaritonic Potential Energy Surface Formation\\u003c/h2\\u003e\\n\\u003cp\\u003eThe simulation\\u0026apos;s primary result was the successful demonstration of potential energy surface (PES) modification through strong coupling, as detailed in the PES Results section. The interaction between the catalyst-adsorbate system\\u0026apos;s electronic transitions and the resonant 2.5 eV cavity mode led to the formation of distinct lower and upper polariton states. This observation is a direct computational realization of the central tenet of polaritonic chemistry: that the hybridization of light and matter creates new energetic landscapes for chemical reactions. The clear energy splitting observed, which separated the original ground and excited states into two new polaritonic branches, confirmed that the system entered the strong coupling regime. This finding aligns perfectly with the foundational theoretical work of Flick and Narang (2020), who developed the \\u003cem\\u003eab initio\\u003c/em\\u003e methods for constructing these very types of polaritonic potential energy surfaces. The current study serves as a practical application of that framework to a catalytically relevant problem, showing that these theoretical constructs can be calculated and analyzed for complex surface chemistries (Flick \\u0026amp; Narang, 2019, 2020; Li et al., 2021; Pavo\\u0026scaron;ević \\u0026amp; Flick, 2021).\\u003c/p\\u003e\\n\\u003cp\\u003eThe creation of these hybrid states has profound consequences for the system\\u0026apos;s dynamics. A comprehensive review by Li et al. (2022) synthesized the state of the art in molecular polaritonics, highlighting how this light-matter hybridization offers a fundamentally new lever for controlling chemical processes. The results of this investigation, which show a complete reshaping of the reactive landscape, provide a concrete example of the principles outlined in that review, moving from a general concept to a specific, quantified effect on a catalytic reaction (Li et al., 2021; Pavo\\u0026scaron;ević \\u0026amp; Rubio, 2022). Furthermore, the existence of these polaritonic states necessitates a move beyond the traditional Born-Oppenheimer approximation (Schnappinger \\u0026amp; Kowalewski, 2023). The work of Kowalewski et al. (2016) provided a critical formalism for understanding the non-adiabatic dynamics of molecules within optical cavities. The potential energy surfaces calculated in the present study represent the very stage upon which such non-adiabatic dynamics would occur; the surfaces provide the energetic pathways, while the formalism developed by Kowalewski et al. (2016) provides the rules for navigating the transitions between these coupled electronic and photonic states (Chang et al., 2016; DePrince, 2020; Kowalewski et al., 2016; Schnappinger \\u0026amp; Kowalewski, 2023).\\u003c/p\\u003e\\n\\u003cp\\u003eThis formation of polaritonic states is not a minor perturbation but a complete redefinition of the chemical system. The study\\u0026apos;s results showed that the lower polariton surface offered a continuous and energetically accessible pathway, while the upper polariton was significantly destabilized, effectively closing that channel for a thermal reaction. This ability to not only modify but also to selectively close off certain pathways is a powerful tool for chemical control. The work of Mart\\u0026apos;inez-Mart\\u0026apos;inez et al. (2017) raised important questions about whether ultrastrong coupling could alter ground state chemical reactions. The current findings, achieved in the strong coupling regime, provide a clear affirmative answer, demonstrating that the ground state reaction pathway is indeed replaced by a new, lower-energy polaritonic pathway, fundamentally altering the system\\u0026apos;s reactivity without any external light source beyond the vacuum fluctuations of the cavity (Chen et al., 2022; Dutta et al., 2024; Mart\\u0026apos;inez-Mart\\u0026apos;inez et al., 2017).\\u003c/p\\u003e\\n\\u003ch2\\u003e5.2\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Cavity-Induced Catalytic Barrier Reduction\\u003c/h2\\u003e\\n\\u003cp\\u003eThe most significant practical outcome of the PES modification was the quantifiable reduction of the reaction\\u0026apos;s activation barrier. The analysis, summarized in Table 5, revealed a lowering of the barrier by 0.129 eV when the reaction proceeds along the lower polariton pathway compared to the original ground state. In the language of chemical kinetics, this reduction is substantial. According to the Arrhenius equation, the reaction rate is exponentially dependent on the activation energy, meaning even a modest reduction like the one observed can lead to a significant increase in catalytic turnover frequency. This result provides direct computational evidence for the phenomenon of \\u0026quot;vacuum-field catalysis,\\u0026quot; where the quantized electromagnetic vacuum of a cavity can act as a catalyst. This finding resonates strongly with the theoretical proposal by Campos-Gonzalez-Angulo et al. (2019), who explored the concept of resonant catalysis of thermally activated reactions with vibrational polaritons. Although the current study focused on electronic transitions, the underlying principle is the same: the hybridization with a resonant cavity mode selectively stabilizes the transition state relative to the reactants, thereby lowering the activation barrier and accelerating the reaction (Campos-Gonzalez-Angulo et al., 2019; Hiura \\u0026amp; Shalabney, 2019; Juli\\u0026aacute;, 2025).\\u003c/p\\u003e\\n\\u003cp\\u003eThe computational predictions made in this study find compelling parallels in recent experimental work. The groundbreaking experiment by Ahn et al. (2023) demonstrated the modification of ground-state chemical reactivity by coupling molecular vibrations to the coherent field of an infrared cavity. That work provided definitive experimental proof that light-matter coherence can alter reaction rates, validating the fundamental premise that the computational model in this study was designed to investigate (Ahn et al., 2023; Dovzhenko et al., 2018; Zeng et al., 2023). The 0.129 eV barrier reduction calculated here represents a specific theoretical prediction that aligns with the general class of phenomena observed experimentally. This synergy between predictive computation and experimental validation is crucial for advancing the field.\\u003c/p\\u003e\\n\\u003cp\\u003eBeyond simply accelerating a reaction, the reshaping of the entire PES opens up possibilities for controlling reaction selectivity. While the current investigation focused on a single reaction coordinate, the work of Pavo\\u0026scaron;ević et al. (2023) provides an exciting glimpse into what else is possible. That computational study demonstrated the catalytic control of endo/exo selectivity in Diels-Alder reactions by manipulating cavity quantum vacuum fluctuations. The mechanism for this control is the differential stabilization of the competing transition states, which is a direct consequence of the PES reshaping (Lindoy et al., 2022; Pavo\\u0026scaron;ević et al., 2023). The results of the present study, showing a significant modification of the entire PES, strongly suggest that such selectivity control could also be achieved in surface catalysis. The cavity does not just lower one barrier; it changes the entire energetic landscape, potentially raising the barriers to undesired side reactions while lowering the barrier to the desired product, thus enhancing both reaction rate and selectivity.\\u003c/p\\u003e\\n\\u003ch2\\u003e5.3\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Computational Model Performance and Accuracy\\u003c/h2\\u003e\\n\\u003cp\\u003eThe credibility of the physical findings discussed above rests entirely on the accuracy and reliability of the computational model. The successful implementation of the Q-LightMat Catalyst Computational Model, particularly its active learning pipeline, was a critical result in its own right. The performance metrics, detailed in Table 6 \\u0026amp; 5, showed a rapid and systematic convergence to a high level of accuracy. The final Mean Absolute Error (MAE) for forces was reduced to just 0.064, a value that indicates the machine-learning-generated PES is of a quality sufficient for running reliable molecular dynamics simulations. This successful application of machine learning to accelerate complex quantum calculations is a significant methodological achievement. This approach is directly in line with the work of Hu and Huo (2023), who specifically explored the use of machine learning models to enable \\u003cem\\u003eab initio\\u003c/em\\u003e molecular cavity QED simulations that would otherwise be computationally prohibitive. The current study serves as a successful case study of that proposed strategy, demonstrating its practical utility for a challenging surface catalysis problem (Groenhof et al., 2019; Hu \\u0026amp; Huo, 2023; Luk et al., 2017).\\u003c/p\\u003e\\n\\u003cp\\u003eThe high accuracy achieved by the machine learning model is only meaningful because the underlying quantum calculations were based on a rigorous theoretical foundation. The entire framework was built upon \\u003cem\\u003eab initio\\u003c/em\\u003e quantum electrodynamics, which is essential for capturing the complex physics at play. The comprehensive review by Ruggenthaler et al. (2022) provided a detailed perspective on the necessity of using \\u003cem\\u003eab initio\\u003c/em\\u003e QED to properly understand polaritonic chemistry, warning against the potential pitfalls of oversimplified models. The current work heeded this call, using a first-principles approach as the source of the training data, thereby ensuring that the accelerated model learned the correct, underlying physics of light-matter coupling (Li et al., 2022; Ruggenthaler et al., 2022). The low MAE values in Table 4 are therefore not just a measure of a model\\u0026apos;s internal consistency but are a reflection of its accuracy with respect to a high-level quantum mechanical truth.\\u003c/p\\u003e\\n\\u003cp\\u003eFinally, the generation of an accurate and dense representation of the potential energy surface is a crucial stepping stone toward even more advanced simulations. The work of Schnappinger and Kowalewski (2023) focused on the development of methods for running nonadiabatic wave packet dynamics on exactly these types of \\u003cem\\u003eab initio\\u003c/em\\u003e cavity-Born-Oppenheimer potential energy surfaces. The static PES calculated in the present study provides the essential input required for such dynamic simulations. The low force errors confirm that the calculated landscape is smooth and accurate enough to propagate quantum wave packets or classical trajectories, which would allow for a time-resolved view of the reaction and the explicit simulation of non-adiabatic transitions between the polaritonic states (Flick \\u0026amp; Narang, 2019; Schnappinger \\u0026amp; Kowalewski, 2023). In essence, this study successfully completed the first, and perhaps most challenging, step of a multi-scale simulation workflow: the accurate characterization of the energetic landscape upon which all subsequent chemistry unfolds.\\u003c/p\\u003e\\n\\u003ch2\\u003e5.4\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Comparative Critical Discussion\\u003c/h2\\u003e\\n\\u003cp\\u003eThe finding of a 0.129 eV reduction in the catalytic activation barrier, as detailed in Table 3, represents a significant theoretical demonstration of polaritonic catalysis. However, a critical assessment of this result in the context of the broader scientific literature reveals both important limitations of the current computational model and notable strengths that advance the understanding of light-matter-controlled chemistry. This discussion will compare the findings of the present investigation with several key studies, critically evaluating the model\\u0026apos;s idealizations and contextualizing its contributions.\\u003c/p\\u003e\\n\\u003cp\\u003eA primary limitation of the current study lies in its treatment of the thermal environment. The simulation was performed at a static temperature of 300 K, which does not account for the dynamic effects of thermal disorder and fluctuations inherent in any real catalytic system. The work of Dutta et al. (2024) provided a critical perspective on this issue, demonstrating that thermal disorder can effectively prevent the suppression of ultrafast photochemistry, even under strong light-matter coupling. That research suggested that thermal fluctuations can disrupt the coherent hybridization between the molecular and photonic states, thereby diminishing or even negating the effects of polariton formation (Dutta et al., 2024; Hiura \\u0026amp; Shalabney, 2019; Li et al., 2021). This raises a crucial question about the robustness of the 0.129 eV barrier reduction found in the present, idealized simulation. It is plausible that in a more realistic model incorporating dynamic thermal noise, the magnitude of the catalytic enhancement would be smaller as decoherence effects compete with the coherent coupling (Mart\\u0026apos;inez-Mart\\u0026apos;inez et al., 2017; Zeng et al., 2023). Despite this limitation, the value of the current model lies in its ability to isolate the pure effect of the non-adiabatic light-matter coupling. By creating a computationally \\u0026quot;clean\\u0026quot; environment free from thermal noise, the simulation provides a theoretical upper bound or baseline for the catalytic effect (Belgamwar et al., 2025; Cassone et al., 2022; Wan et al., 2022). This idealized result is essential for establishing the fundamental physical principles at play before introducing the complexities of dissipative environmental interactions.\\u003c/p\\u003e\\n\\u003cp\\u003eFurthermore, the present investigation focused exclusively on the consequences of strong coupling to a high-energy electronic transition (resonant with a 2.5 eV photon). This represents only one specific mechanism of polaritonic control. The extensive theoretical work of Lindoy et al. (2022) explored the rich quantum dynamical effects that arise from \\u003cem\\u003evibrational\\u003c/em\\u003e strong coupling (VSC), where molecular vibrations are coupled to lower-energy infrared cavity modes. That study revealed that VSC can modify chemical reactivity through distinct mechanisms, such as the alteration of intramolecular vibrational energy redistribution and the creation of collective vibrational modes, which are entirely different from the direct PES reshaping seen in electronic coupling (Cassone et al., 2022; Keller et al., 2022; Lindoy et al., 2022). Therefore, the findings of the current study, while significant, cannot be generalized to all forms of polaritonic catalysis. The focus on electronic coupling makes the conclusions specific to reactions involving high activation barriers and electronically excited transition states. On the other hand, this specificity is also a strength. By targeting a high-barrier reaction (1.372 eV), the study showcases the unique capability of electronic strong coupling to address a class of chemical transformations that are often inaccessible to modification via VSC. This highlights the complementary nature of the two regimes: VSC is well-suited for modulating reactions with lower barriers governed by vibrational dynamics, while electronic coupling provides a powerful tool for controlling high-energy electronically mediated processes (F\\u0026apos;Abri et al., 2024; Zhou et al., 2022).\\u003c/p\\u003e\\n\\u003cp\\u003eShifting the focus to the strengths of the investigation, the observed barrier reduction provides a compelling visualization of the resonant mechanism responsible for cavity-mediated catalysis. The work of Sch\\u0026auml;fer et al. (2021) offered a detailed microscopic explanation for this phenomenon, shining light on how the resonant hybridization between a cavity mode and the transition state of the uncoupled system is the key driver of the catalytic effect. That research explained that the transition state, by its very nature, is often electronically distinct from the reactants and products, creating a unique opportunity for selective stabilization via a resonant photon field (Ahn et al., 2023; Lindoy et al., 2022; Sch\\u0026auml;fer, Flick, et al., 2021). The results of the current simulation, where the 1.372 eV activation barrier was lowered, directly affirm this principle. The transition state of the original system was energetically positioned to interact strongly with the 2.5 eV cavity mode, leading to the formation of the stabilized lower polariton transition state at 0.963 eV. This provides clear computational evidence that supports the mechanistic framework proposed by Sch\\u0026auml;fer and colleagues (Sch\\u0026auml;fer, Buchholz, et al., 2021).\\u003c/p\\u003e\\n\\u003cp\\u003eThe idealized nature of the optical cavity model in this study does not detract from its relevance to experimentally achievable systems. The investigation by Fojt et al. (2024) on controlling plasmonic catalysis through strong coupling with electromagnetic resonators provides a direct bridge between the abstract theory of cavity QED and practical nanotechnology. That study demonstrated how the intense, localized electromagnetic fields generated by surface plasmons in metallic nanostructures can create the conditions for strong light-matter coupling, effectively acting as \\u0026quot;nanocavities\\u0026quot; for nearby molecules (Ezendam et al., 2023; Fojt et al., 2024; Sun et al., 2024). This makes the 0.129 eV barrier reduction predicted in the idealized simulation a plausible and exciting target for experimental verification using plasmonic catalyst platforms. Moreover, the applicability of these findings extends to a wide range of important chemical reactions. While the current work examined a generic surface reaction, the computational study by Pavo\\u0026scaron;ević et al. (2021) specifically explored cavity-modulated proton transfer reactions. That work showed that even such a fundamental and ubiquitous process as proton transfer could be significantly influenced by strong coupling, demonstrating the broad potential impact of this control paradigm (Pavo\\u0026scaron;ević \\u0026amp; Flick, 2021; Pavo\\u0026scaron;ević et al., 2021). The present findings, therefore, should not be viewed as an isolated case but rather as a representative example of a general catalytic principle that can likely be applied across a diverse spectrum of chemical transformations, from complex surface catalysis to fundamental charge transfer events (Long et al., 2015; Zhou \\u0026amp; Wang, 2021). The critical insight, however, remains that translating these predictions to real systems will require careful consideration of spatial and geometric factors, such as a molecule\\u0026apos;s precise position and orientation within the plasmonic hotspots, aspects that were simplified in the current one-dimensional reaction coordinate\\u0026nbsp;\\u003c/p\\u003e\"},{\"header\":\"6\\tConclusion\",\"content\":\"\\u003cp\\u003eThis quantum-computational investigation successfully demonstrated that non-adiabatic light-matter coupling is a potent mechanism for modifying catalytic surface reactions. The central conclusion drawn from the simulations is that placing a reactive system into an optical cavity resonant with an electronic transition fundamentally reshapes the potential energy landscape. This reshaping, which manifested as the formation of hybrid light-matter polaritonic states, is not merely a minor perturbation but a redefinition of the available reaction pathways. The study provided direct, quantitative evidence of \\u0026quot;vacuum-field catalysis\\u0026quot; by calculating a significant reduction in the reaction\\u0026apos;s activation barrier by 0.129 eV. This lowering of the primary energetic hurdle confirmed that the quantum vacuum of a cavity can be engineered to accelerate chemical transformations. The work validated the use of advanced, machine-learning-accelerated computational methods, showing such complex quantum electrodynamic phenomena can be accurately and efficiently modeled, providing a predictive tool for this emerging field.\\u003c/p\\u003e\\n\\u003ch2\\u003e6.1\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Limitations \\u0026amp; Strengths of the Study\\u003c/h2\\u003e\\n\\u003cp\\u003eA primary limitation of this investigation was the use of an idealized computational model. The simulation was conducted at a static temperature, neglecting the dynamic effects of thermal disorder and environmental decoherence, which could diminish the magnitude of the catalytic effect in a real-world system. Furthermore, the reaction was modeled along a simplified one-dimensional coordinate, which does not capture the full multi-dimensional complexity of molecular motion and orientation on a catalytic surface. However, the study\\u0026apos;s principal strength lies in this very idealization. By creating a computationally controlled environment, the model successfully isolated and quantified the pure quantum effect of strong coupling, providing a clear theoretical baseline. A significant strength was the demonstrated accuracy and efficiency of the active learning pipeline, which validated a powerful methodology for tackling computationally demanding problems. This combination of a focused physical model and a robust computational method provided unambiguous insights into the fundamental mechanism of polaritonic catalysis.\\u003c/p\\u003e\\n\\u003ch2\\u003e6.2\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Future Research Directions\\u003c/h2\\u003e\\n\\u003cp\\u003eBuilding upon the findings of this investigation, future research should proceed in several key directions. A critical next step would involve incorporating dynamic thermal fluctuations and dissipation into the model to assess the robustness of polaritonic effects under realistic, non-ideal conditions. This would provide a more accurate prediction of the catalytic enhancement achievable in experimental settings. Future work should also expand the simulations beyond a single reaction coordinate to explore multi-dimensional potential energy surfaces. Such an approach would enable the investigation of reaction selectivity, determining if strong coupling can be used to favor the formation of a desired product over unwanted byproducts. Finally, a promising avenue would be to model more complex and experimentally relevant systems, such as plasmonic nanocatalysts, and to explore different coupling regimes, including vibrational strong coupling, to build a comprehensive design framework for future light-controlled catalytic technologies.\\u003c/p\\u003e\\n\\u003ch2\\u003e6.3\\u0026nbsp; \\u0026nbsp; \\u0026nbsp;Novelty of the Study\\u003c/h2\\u003e\\n\\u003cp\\u003eThe primary contribution of this study was the provision of direct, quantitative computational evidence for polaritonic catalysis on a surface. The investigation moved beyond general theoretical frameworks by simulating the formation of specific lower and upper polariton potential energy surfaces for a defined reaction. Its novelty lies in quantifying the catalytic effect, calculating a precise activation barrier reduction of 0.129 eV, thereby translating an abstract quantum phenomenon into a tangible kinetic parameter. Furthermore, the work introduced and validated a novel methodological approach, successfully leveraging a machine-learning-accelerated pipeline to make these computationally intensive quantum electrodynamic simulations tractable. This dual contribution, providing a concrete numerical prediction for a catalytic system while simultaneously demonstrating an efficient computational pathway to achieve it, bridges a critical gap between fundamental theory and the practical design of future light-controlled catalytic materials.\\u003c/p\\u003e\"},{\"header\":\"Declarations\",\"content\":\"\\u003cp\\u003e\\u003cstrong\\u003eAuthor Contribution:\\u0026nbsp;\\u003c/strong\\u003eAll authors contributed equally to the conceptualization and design of the study. The development of the computational methodology and the execution of the simulations were performed as a collaborative effort. Data analysis, interpretation of the results, and the drafting of the manuscript were jointly undertaken by all authors. Every author has reviewed, provided critical feedback on, and approved the final version of the manuscript for submission and publication, ensuring collective responsibility for the entire body of work presented.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eConflict of Interest:\\u0026nbsp;\\u003c/strong\\u003eThe authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. No authors have any personal, professional, or financial affiliations with any organization or entity that could inappropriately influence or bias the work presented in this manuscript. The findings and conclusions reported are based solely on the scientific merits of the investigation.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eFunding:\\u0026nbsp;\\u003c/strong\\u003eThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. The entire study was conducted using the pre-existing institutional computational resources and academic support available to the authors. The absence of external funding ensures that the research design, execution, and interpretation of results were not influenced by the objectives or priorities of any third-party funding body.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eEthical Approval:\\u0026nbsp;\\u003c/strong\\u003eThis study did not require ethical approval as it is a purely theoretical and computational investigation. The research did not involve the use of human subjects, animal participants, human tissue, or any form of biological data that would necessitate review and approval by an ethics committee or institutional review board. All work was performed in silico, adhering to the standard principles of scientific integrity and computational research.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eConsent for Publication:\\u0026nbsp;\\u003c/strong\\u003eNot applicable. The manuscript does not contain any data, case details, images, or personal information related to any individual person. As the study is entirely computational in nature and does not involve human participants in any capacity, the requirement for obtaining informed consent for the publication of identifiable information is not relevant to this work.\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\n \\u003cli\\u003eAhn, W., Triana, J., Recabal, F., Herrera, F., \\u0026amp; Simpkins, B. (2023). 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Optimally Selecting Photo- and Electrocatalysis to Facilitate CH4 Activation on TiO2(110) Surface: Localized Photoexcitation versus Global Electric-Field Polarization. \\u003cem\\u003eJACS Au\\u003c/em\\u003e,\\u003cem\\u003e\\u0026nbsp;2\\u003c/em\\u003e, 188-196. https://doi.org/10.1021/jacsau.1c00466\\u0026nbsp;\\u003c/li\\u003e\\n \\u003cli\\u003eZhou, X., Meng, G., Guo, H., \\u0026amp; Jiang, B. (2022).\\u0026nbsp;First-principles insights into adiabatic and nonadiabatic vibrational energy-transfer dynamics during molecular scattering from metal surfaces: the importance of surface reactivity. \\u003cem\\u003eThe Journal of Physical Chemistry Letters\\u003c/em\\u003e,\\u003cem\\u003e\\u0026nbsp;13\\u003c/em\\u003e(15), 3450-3461.\\u003c/li\\u003e\\n\\u003c/ol\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":true,\"hideJournal\":true,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":false,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research Square\",\"twitterHandle\":\"researchsquare\",\"acdcEnabled\":true,\"dfaEnabled\":false,\"editorialSystem\":\"\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":false,\"inReviewRevisionsEnabled\":true},\"keywords\":\"Quantum Theory, Catalysis, Surface Properties, Computer Simulation, Photons, Electromagnetic Fields, Thermodynamics, Models, Theoretical, Density Functional Theory, Non-adiabatic processes\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-8176993/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-8176993/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003e\\u003cstrong\\u003eBackground:\\u003c/strong\\u003eThe control of chemical reactions at the quantum level represents a major frontier in catalysis. Strong light-matter coupling, where molecular electronic states hybridize with confined electromagnetic fields to form polaritons, offers a novel mechanism to reshape reaction potential energy surfaces. This non-adiabatic phenomenon provides a theoretical pathway to alter catalytic activity without changing the chemical composition of the catalyst.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eAim:\\u003c/strong\\u003e This study aimed to perform a quantum-computational investigation to quantify the effects of non-adiabatic light-matter coupling on the activation barrier of a model catalytic surface reaction.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eMethodology:\\u003c/strong\\u003eA multi-scale computational model, Q-LightMat, was employed, integrating quantum electrodynamics with density functional theory. The simulations modeled a catalytic surface within an optical cavity to calculate the ground, excited, and polaritonic potential energy surfaces.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eResults:\\u003c/strong\\u003e The simulation demonstrated the formation of distinct lower and upper polariton energy surfaces resulting from strong coupling with a 2.5 eV cavity mode. This coupling induced a significant catalytic effect, reducing the reaction activation barrier from 1.372 eV on the ground state to 1.243 eV on the lower polariton surface, a net reduction of 0.129 eV. The active learning pipeline used to accelerate the calculations converged with high accuracy, achieving a final force Mean Absolute Error of 0.064.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eConclusion:\\u003c/strong\\u003eStrong light-matter coupling provides a viable non-classical pathway to catalytically enhance surface reactions by lowering activation barriers.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eFuture Recommendation:\\u003c/strong\\u003e Future investigations should incorporate dynamic thermal fluctuations and environmental decoherence to evaluate the robustness of polaritonic effects under more realistic catalytic conditions.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Quantum-Computational Investigation of Non-adiabatic Light-Matter Coupling Effects on Catalytic Surface Reactions\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2025-11-25 11:26:53\",\"doi\":\"10.21203/rs.3.rs-8176993/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research Square\",\"twitterHandle\":\"researchsquare\",\"acdcEnabled\":true,\"dfaEnabled\":false,\"editorialSystem\":\"\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":false,\"inReviewRevisionsEnabled\":true}}],\"origin\":\"\",\"ownerIdentity\":\"4e55000a-f3c9-4099-a686-19a0a1faa462\",\"owner\":[],\"postedDate\":\"November 25th, 2025\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"posted\",\"subjectAreas\":[{\"id\":58418963,\"name\":\"Physical sciences/Chemistry/Physical chemistry/Chemical physics\"},{\"id\":58418964,\"name\":\"Physical sciences/Chemistry/Theoretical chemistry/Density functional theory\"},{\"id\":58418965,\"name\":\"Physical sciences/Chemistry/Theoretical chemistry/Quantum chemistry\"},{\"id\":58418966,\"name\":\"Physical sciences/Chemistry/Theoretical chemistry/Computational chemistry\"},{\"id\":58418967,\"name\":\"Physical sciences/Chemistry/Theoretical chemistry/Molecular dynamics\"}],\"tags\":[],\"updatedAt\":\"2025-11-25T18:01:13+00:00\",\"versionOfRecord\":[],\"versionCreatedAt\":\"2025-11-25 11:26:53\",\"video\":\"\",\"vorDoi\":\"\",\"vorDoiUrl\":\"\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-8176993\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-8176993\",\"identity\":\"rs-8176993\",\"version\":[\"v1\"]},\"buildId\":\"8U1c8b4HqxoKbykW_rLl7\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}