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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Dynamic Species Reduction for Multi-Cycle CFD Simulations (Final Technical Report)

This project primarily sought to address some of the computational cost concerns of detailed simulations by developing improved methods of handling species transport, and chemical kinetics evaluation in a commercial 3D Computational Fluid Dynamics (CFD) environment. Secondary goals were to apply these techniques to fuels and conditions of interest to better understand the key species and reactions required to adequately capture cycle to cycle coupling. Improved modeling will lead to better understanding of these combustion modes and their dependence on fuel composition, which can then enable more clean and efficient engines, ultimately benefiting the consumer as well as the general public. Two approaches were used to address the computational cost. A “Dynamic Species Reduction” (DSR) procedure was developed to remove chemical species from the simulation during periods when chemical reactions were not expected to be important, particularly during gas exchange when temperatures are low and little fuel remains. This modelling procedure automatically detects relevant species to retain in the simulation domain based on their local concentration, removes species below a specified concentration threshold, and then adjusts the remaining species mass to conserve not only the number of H, C, and O atoms in each cell, but also the relative proportions between species and the heating value of the mixture in every cell. The second procedure was a “Product Directed Remapping” (PDR) updates the algorithm used to group individual computational cells for chemical kinetics evaluation to account for non-uniform temperature distributions and the CO to CO 2 ratio in the cells. The model techniques developed in this work successfully demonstrated computational performance improvements for a range of conditions relevant for Highly Dilute SI and HCCI engine operation. Runtime reductions of 10% were observed for small mechanisms, with further reductions of up to 36% observed for larger mechanisms. Improvements were primarily related to reducing the number of chemical species tracked during the gas exchange process using the Dynamic Species Reduction method. With smaller benefits observed from changes to the kinetics binning and evaluation strategy in the post combustion region using the PDR method. The results of this work show the potential for improved computational runtime for complicated simulations. They can and should be extended to additional conditions and new bio-derived and renewable fuels as they are developed and new kinetic mechanisms become available.

10 SYNTHETIC FUELS↗
DOE OSTI2020

Investigating biomass composition and size effects on fast pyrolysis using global sensitivity analysis and CFD simulations

It is notoriously difficult to build an accurate universal model for biomass pyrolysis due to its sensitivity to a wide number of critical material attributes such as chemical species and physical sizes. In this work, a biomass pyrolysis kinetics with 32 heterogeneous reactions and 59 species was implemented in an open-source multiphase computational fluid dynamics (CFD) software MFiX and validated against two different experimental pyrolysis data sets that provided detailed data describing chemical component yields. The reaction scheme was then used to build a surrogate model and assess the sensitivity of pyrolysis yields to feedstock compositions. The sensitivity analysis determined that the yield of bio-char showed a strong positive sensitivity to the carbon-rich lignin and tannin pseudo-species in the reaction scheme while the bio-oil and bio-gas were correlated to oxygen-rich lignin pseudo-species. The reaction scheme was then integrated into a coarse-grained discrete element model to simulate fast pyrolysis in a bubbling fluidized bed over a range of feedstock particle sizes. The reactor simulations showed further sensitivity to particle size and hydrodynamics. Notably, particles under 0.5 mm have small heat transfer limitations but left the reactor before completely converting and thus reduced the bio-oil yield. Results from this study can be used to guide future development of highly accurate models for fast pyrolysis reactors with a variety of feedstock properties and operating conditions.

09 BIOMASS FUELS↗
DOE OSTI2025

High-pressure reduction of carbon dioxide in reactive liquid mixtures

Density-functional theory based molecular-dynamics simulations were used to investigate high-pressure chemical reactions in liquid mixtures of CO 2 with several elements (Si, Mn, and Fe) at high temperatures of 2000-3000 K. Our ab initio simulations indicate that these reactant elements can reduce CO 2 to C at high pressures (20 GPa) leading to the formation of C-C chains, with Si by far the most effective carbon-reducing agent. A combined chemical analysis using Bader charge analysis and Crystal Orbital Hamilton Population (COHP) on simulation snapshots shows that significant charge transfer from the reducing element to the C atoms creates instability in the C-O covalent bonds. COHP analysis further shows that Mn/Fe-O and Mn/Fe-C bonding interactions are weaker compared to the Si counterparts. These results further our understanding of the redox chemistry of CO 2 at conditions relevant to planetary mantle interiors and demonstrate the effectiveness of high pressure in the reduction of CO 2 directly to solid carbon.

Ab initio molecular dynamics↗
DOE OSTI2021

Fourier-like Thermal Relaxation of Nanoscale Explosive Hot Spots

Hot spots are local regions of high temperature that are widely considered to govern explosive initiation. Hot spot dynamics rests on a delicate balance between heat generation due to chemical reactions and heat loss through thermal conduction, making accurate determinations of the conductivity under extreme conditions a key component of predictive explosive models. We develop here an approach to directly determine the thermal transport properties of explosive hot spots with realistic initial structures through a combination of molecular dynamics (MD) and diffusive heat equation (HEq) modeling. Effective thermal conductivity values are determined by fitting HEq models to MD predictions of long timescale hot spot relaxation. The approach is applied to model hot spots in the molecular crystalline explosive 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) for a range of shock strengths and two limiting cases for impact orientation. Isotropic and anisotropic HEq models yield similar results, despite TATB exhibiting some of the largest and most anisotropic thermal conductivity values for explosive near normal conditions. The conductivity is found to be a strong function of density, which parametrically captures dependence on temperature, pressure, and material state. The associated root-mean-square errors of the fitted HEq models are approximately 5% of MD predicted final equilibrium temperatures. Here, the conductivity values determined here for TATB hot spots are considerably larger than those used in a prior hot spot criticality study, which may significantly impact predictions for critical hot spot sizes. The approach provides a convenient foundation for determining the effective thermal conductivity for hot spot problems in other explosives and directly yields information on reasonable approximations that might be taken in higher-level models for those materials.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Algorithm advances and applications of time‐dependent first‐principles simulations for ultrafast dynamics

Abstract Far from equilibrium phenomenon is a central theme of contemporary material research. Such phenomenon can exhibit itself in atomic structure and dynamics, but very often it also happens as non‐equilibrium phenomenon in the electronic structure. In ab initio material simulation, density functional theory (DFT) has played an essential role in studying electronic ground state problems. For excited states, besides many‐body perturbation theory, another powerful tool is the time dependent DFT (TDDFT) method. In particular, the real‐time TDDFT (rt‐TDDFT) method can be used to simulate many non‐equilibrium phenomena directly. Here we introduce our works on some algorithm advances based on our recently rt‐TDDFT method. This method uses the plane‐wave basis set, and significantly accelerates its efficiency by increasing the time step from 0.1–1 as in traditional methods to 0.2–0.5 fs. The noncollinear magnetic moments and spin–orbit coupling have also been included in our rt‐TDDFT method. Furthermore, a Boltzmann‐TDDFT algorithm has been developed to solve the hot carrier overheating problem in Ehrenfest dynamics, and a natural orbital branching algorithm has been developed to overcome the mean‐field approximation in Ehrenfest dynamics nuclear trajectory, thus allows stochastic multiple paths in chemical reactions. Utilizing these methods, we have studied the photoinduced ultrafast demagnetization, ultrafast phase transition, energy transfer between plasmon and hot carriers, as well as the high‐energy ion implantation and low‐energy atomic diffusion in semiconductors. We believe the tools as the ones introduced here can enable us to study a wide range of phenomena which are of great interest in modern day material research. This article is categorized under: Structure and Mechanism > Computational Materials Science Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory

Liu, Wen‐Hao↗
DOE OSTI2021

Real-time Characterization of the Fine Structure and Dynamics of an Electrical Double Layer at Electrode-electrolyte Interfaces

The chemisorption of species from supporting electrolytes on electrode surfaces is ubiquitous in electrochemical systems and affects the dynamics and mechanism of various electrochemical reactions. The understanding of chemical structure and property of the resulting electrical double layer is vital but limited. In this work, we operando probed the electrochemical interface between a gold electrode surface and a common supporting electrolyte, phosphate buffer, using our newly developed in situ liquid secondary ion mass spectrometry. We surprisingly found that on the positively charged gold electrode surface sodium cations were anchored in the stern layer in a partially dehydrated form by formation of compact ion pairs with the accumulated phosphate anions. The resulting strong and dense adsorption phase was further revealed to retard the electro-oxidation reaction of ascorbate. This finding addressed one major gap in the fundamental science of electrode-electrolyte interfaces that where and how the cations reside in the double layer to impose effects on electrochemical reactions, providing insights into engineering of better electrode-electrolyte interfaces in electrochemical processes.

Zhang, Yanyan↗
DOE OSTI2026

Stoichiometrically-informed symbolic regression for extracting chemical reaction mechanisms from data

A data-driven computational method is introduced to extract chemical reaction mechanisms from time series chemical concentration data. It is realized through the use of dynamic symbolic regression in which a sparse analytical form for a dynamical system is discoverable from the underlying data. We specifically develop the stoichiometrically-informed symbolic regression (SISR) method to address a standing challenge in complex chemical reaction networks: given a time-series dataset of concentrations of several components, what is the mechanism and the associated rate constants? SISR finds the optimal mechanism, kinetic equations and rate constants by combining differential optimization with a genetic optimization approach that searches a symbolic space of possible reaction mechanisms. Use of SISR in several paradigmatic examples spanning linear and nonlinear reaction schemes results in excellent agreement between true and predicted mechanisms, including when the method is applied to noisy data. The advantages of a stoichiometrically-informed approach such as SISR to address reaction discovery is illustrated through comparison with the use of generic state-of-the-art data-driven approaches.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Extemporaneous Mechanochemistry: Shock-Wave-Induced Ultrafast Chemical Reactions Due to Intramolecular Strain Energy

We report regions of energy localization referred to as hotspots are known to govern shock initiation and the run-to-detonation in energetic materials. Mounting computational evidence points to accelerated chemistry in hotspots from large intramolecular strains induced via the interactions between the shock wave and microstructure. However, definite evidence mapping intramolecular strain to accelerated or altered chemical reactions has so far been elusive. From a large-scale reactive molecular dynamics simulation of the energetic material 1,3,5-triamino-2,4,6-trinitrobenzene, we map decomposition kinetics to molecular temperature and intramolecular strain energy prior to reaction. Both temperature and intramolecular strain are shown to accelerate chemical kinetics. A detailed analysis of the atomistic trajectory shows that intramolecular strain can induce a mechanochemical alteration of decomposition mechanisms. The results in this paper could inform continuum-level chemistry models to account for a wide range of mechanochemical effects.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Statistical Correlation Between Quantum Entanglement and Spin–Orbit Coupling in Crossed Beam Molecular Dynamics

Non-classical features like interference are already being harnessed to control the output of chemical reactions. However, quantum entanglement which is an equally enigmatic many-body quantum correlation can also be used as a powerful resource yet has eluded explicit attention. In this report, an experimental scheme under the crossed beam molecular dynamical setup, with the F + HD reaction, is proposed aiming to study the possible influence of entanglement within reactant pairs on the angular features of the product distribution. The aforesaid reaction has garnered interest recently, as an unusual horseshoe shape pattern in the product (HF) distribution was observed, which has been attributed to the coupling of spin and orbital degrees of freedom. An experimental scheme is proposed aiming to study the possible influence of entanglement on the necessity for the inclusion of such spin–orbit characteristics, under circumstances wherein the existence of entanglement and spin–orbit interaction is simultaneously detectable. The attainable results are further numerically simulated highlighting specific patterns corresponding to various possibilities. Finally, such studies if extended can provide unforeseen mechanistic insight into analogous reactions, too, from the lens of quantum information.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Prediction of photodynamics of 200 nm excited cyclobutanone with linear response electronic structure and ab initio multiple spawning

Simulations of photochemical reaction dynamics have been a challenge to the theoretical chemistry community for some time. In an effort to determine the predictive character of current approaches, we predict the results of an upcoming ultrafast diffraction experiment on the photodynamics of cyclobutanone after excitation to the lowest lying Rydberg state (S 2 ). A picosecond of nonadiabatic dynamics is described with ab initio multiple spawning. Herein we use both time dependent density functional theory (TDDFT) and equation-of-motion coupled cluster singles and doubles (EOM-CCSD) theory for the underlying electronic structure theory. We find that the lifetime of the S 2 state is more than a picosecond (with both TDDFT and EOM-CCSD). The predicted ultrafast electron diffraction spectrum exhibits numerous structural features, but weak time dependence over the course of the simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Effects of pore size on water dynamics in mesoporous silica

Water confined in mesoporous silica plays a central role in its many uses ranging from gas sorption to nanoconfined chemical reactions. Here in this paper, the influence of pore diameter (2.5–5.4 nm) on water hydrogen bond (H-bond) dynamics in MCM41 and SBA15 mesoporous silicas is investigated using femtosecond infrared vibrational spectroscopy and molecular dynamics simulations on selenocyanate (SeCN-) anions dissolved in the pores. As shown recently, SeCN- spectral diffusion is a reliable probe of surrounding water H-bond structural motions. Additionally, the long CN stretch vibrational lifetime facilitates measurement of the full range of confined dynamics, which are much slower than in bulk water. The simulations shed light on quantitative details that are inaccessible from the spatially averaged observables. The dependence of SeCN- orientational relaxation and that of spectral diffusion on the distance from the silica interface are quantitatively described with an exponential decay and a smoothed step-function, respectively. The distance-dependence of both quantities is found to be independent of the diameter of the pores, and the spatial distribution of SeCN- is markedly non-uniform, reaching a maximum between the interface and the pore center. The results indicate that the commonly invoked two-state, or core–shell, model is a more appropriate description of spectral diffusion. Using these insights, we model the full time-dependence of the measured dynamics for all pore sizes and extract the “core” and “shell” dynamical correlation functions and SeCN- spatial probability distributions. The results are critically compared to those for water confined in reverse micelles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Atomic dynamics of gas-dependent oxide reducibility

Understanding oxide reduction is critical for advancing metal production, catalysis and energy technologies. Although carbon monoxide (CO) and hydrogen (H 2 ) are widely used reductants, the mechanisms by which they work are often presumed to be similar, both involving lattice oxygen removal. However, because of growing interest in replacing CO with H 2 to lower CO 2 emissions, distinguishing gas-specific reduction pathways is critical. Yet, capturing these atomic-scale processes under reactive gas and high-temperature conditions remains challenging. Here we use environmental transmission electron microscopy, which is capable of real-time, atomic-resolution imaging of gas–solid redox reactions to directly visualize the gas-dependent oxide reduction dynamics in NiO. We show that CO drives surface nucleation and the growth of metallic Ni islands, leading to self-limiting surface metallization. Conversely, H 2 activates a coupled surface-to-bulk transformation, where protons from dissociated H 2 infiltrate the oxide lattice to promote the inward migration of surface-generated oxygen vacancies and enabling bulk metallization. By contrast, oxygen vacancies formed by CO remain confined near the surface, where they rapidly form a metallic Ni layer that inhibits further reduction. Furthermore, these results reveal distinct atomistic pathways for CO and H 2 and provide insights that may guide metallurgical processes and catalyst design.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Capturing Ultrafast Electron Driven Chemical Reactions in Molecules

The goals of this project are to develop experimental tools to investigate the dynamics of dissociative electron attachment (DEA) reactions in real time. In a DEA reaction, the attachment of a low energy electron to a molecule results in bond breaking and the fragmentation of the molecule. A new instrument has been designed and is under construction to perform time-resolved photoelectron and photo-fragment spectroscopy following electron transfer from an iodide anion to a molecule within a mass-selected molecular dimer. Iodide binds only weakly through the dipole interaction with many polar molecules, and such molecules forming a dimer with iodide undergo only small changes from the equilibrium geometry in isolation. When the electron is transferred from the iodide, the iodine atom is no longer bound, so the electron transfer step can be considered analogous to electron attachment and brings the key advantage of ultrafast timing precision. The experiments proposed here will establish the experimental tools to interrogate the dynamics of dissociative electron attachment on the fundamental timescales of the nuclear motion, by simultaneously probing the valence electronic structure and the fragmentation pathways.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

From Coherence to Function: Exploring the Connection in Chemical Systems

The role of quantum mechanical coherences or coherent superposition states in excited state processes has received considerable attention in the last two decades largely due to advancements in ultrafast laser spectroscopy. These coherence effects hold promise for enhancing the efficiency and robustness of functionally relevant processes, even when confronted with energy disorder and environmental fluctuations. Understanding coherence deeply drives us to unravel mechanisms and dynamics controlled by order and synchronization at a quantum mechanical level, envisioning optical control of coherence to enhance functions or create new ones in molecular and material systems. In this frontier, the interplay between electronic and vibrational dynamics, specifically the influence of vibrations in directing electronic dynamics, has emerged as the leading principle. Here, two energetically disparate quantum degrees of freedom work in-sync to dictate the trajectory of an excited state reaction. Moreover, with the vibrational degree being directly related to the structural composition of molecular or material systems, new molecular designs could be inspired by tailoring certain structural elements. In the realm of chemical kinetics, our understanding of the dynamics of chemical transformations is underpinned by fundamental theories, such as transition state theory, activated rate theory, and Marcus theory. These theories elucidate reaction rates by considering the energy barriers that must be overcome for reactants to transform into products. Those barriers are surmounted by the stochastic nature of energy gap fluctuations within reacting systems, emphasizing that the reaction coordinate, the pathway from reactants to products, is not rigidly defined by a specific vibrational motion but encompasses a diverse array of molecular motions. While less is known about the involvement of specific intramolecular vibrational modes, their significance in certain cases cannot be overlooked. In this Account, we summarize key experimental findings that offer deeper insights into the complex electronic–vibrational trajectories encompassing excited states afforded from state-of-the-art ultrafast laser spectroscopy in three exemplary processes: photoinduced electron transfer, singlet–triplet intersystem crossing, and intramolecular vibrational energy flow in molecular systems. We delve into the rapid decoherence, or loss of phase and amplitude correlations, of vibrational coherences along promoter vibrations during subpicosecond intersystem crossing dynamics in a series of binuclear platinum complexes. This rapid decoherence illustrates the vibration-driven reactive pathways from the Franck–Condon state to the curve crossing region. We also explore the generation of new vibrational coherences induced by impulsive reaction dynamics rather than by the laser pulse in these systems, which sheds light on specific energy dissipation pathways and thereby on the progression of the reaction trajectory in the vicinity of the curve crossing on the product side. Another property of vibrational coherences, amplitude, reveals how energy can flow from one vibration to another in the electronic excited state of a terpyridine–molybdenum complex hosting a nonreactive dinitrogen substrate. In conclusion, a slight change in vibrational energy triggers a quasi-resonant interaction, leading to constructive wavepacket interference and ultimately intramolecular vibrational redistribution from a Franck–Condon active terpyridine vibration to a dinitrogen stretching vibration, energizing the dinitrogen bond.

Electrical energy↗
DOE OSTI2020

Mixed quantum–classical approach to model non-adiabatic electron–nuclear dynamics: Detailed balance and improved surface hopping method

We develop a density matrix formalism to describe coupled electron–nuclear dynamics. To this end, we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a classical trajectory of the nuclei. Using this Hamiltonian, we derive equations of motion for the electronic occupation numbers and for the nuclear coordinates and momenta. We show that, in the limit, when the number of nuclear degrees of freedom coupled to a given electronic transition is sufficiently high (i.e., the strong decoherence limit), the equations of motion for the electronic occupation numbers become Markovian. Furthermore, the transition rates in these (rate) equations are asymmetric with respect to the lower-to-higher energy transitions and vice versa. In thermal equilibrium, such asymmetry corresponds to the detailed balance condition. We also study the equations for the electronic occupations in the non-Markovian regime and develop a surface hopping algorithm based on our formalism. To treat the decoherence effects, we introduce additional “virtual” nuclear wave packets whose interference with the “real” (physical) wave packets leads to the reduction in coupling between the electronic states (i.e., decoherence) as well as to the phase shifts that improve the accuracy of the numerical approach. Remarkably, the same phase shifts lead to the detailed balance condition in the strong decoherence limit.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Synergistically Chemical and Thermal Coupling between Graphene Oxide and Graphene Fluoride for Enhancing Aluminum Combustion

Metal combustion reaction is highly exothermic and is used in energetic applications, such as propulsion, pyrotechnics, powering micro- and nano-devices, and nanomaterials synthesis. Aluminum (Al) is attracting great interest in those applications because of its high energy density, earth abundance, and low toxicity. Nevertheless, Al combustion is hard to initiate and progresses slowly and incompletely. On the other hand, ultrathin carbon nanomaterials, such as graphene, graphene oxide (GO), and graphene fluoride (GF), can also undergo exothermic reactions. Herein, we demonstrate that the mixture of GO and GF significantly improves the performance of Al combustion as interactions between GO and GF provide heat and radicals to accelerate Al oxidation. Overall, our experiments and reactive molecular dynamics simulation reveal that GO and GF have strong chemical and thermal couplings through radical reactions and heat released from their oxidation reactions. GO facilitates the dissociation of GF, and GF accelerates the disproportionation and oxidation of GO. When the mixture of GO and GF is added to micron-sized Al particles, their synergistic couplings generate reactive oxidative species, such as CF x and CF x O y , and heat, which greatly accelerates Al combustion. This work demonstrates a new area of using synergistic couplings between ultrathin carbon nanomaterials to accelerate metal combustion and potentially oxidation reactions of other materials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Coherence mapping to identify the intermediates of multi-channel dissociative ionization

Identifying the short-lived intermediates and reaction mechanisms of multi-channel radical cation fragmentation processes remains a current and important challenge to understanding and predicting mass spectra. We find that coherent oscillations in the femtosecond time-dependent yields of several product ions following ultrafast strong-field ionization represent spectroscopic signatures that elucidate their mechanism of formation and identify the intermediate(s) they originate from. Experiments on endo-dicyclopentadiene show that vibrational frequencies from various intermediates are mapped onto their resulting products. Aided by ab initio methods, we identify the vibrational modes of both the cleaved and intact molecular ion intermediates. These results confirm stepwise and concerted fragmentation pathways of the dicyclopentadiene ion. This study highlights the power of tracking the femtosecond dynamics of all product ions simultaneously and sheds further light onto one of the fundamental reaction mechanisms in mass spectrometry, the retro-Diels Alder reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

The role of sub-surface hydrogen on CO 2 reduction and dynamics on Ni(110): An ab initio molecular dynamics study

The catalytic reduction of carbon dioxide is a crucial step in many chemical industrial reactions, such as methanol synthesis, the reverse water-gas shift reaction (rWGS) and formic acid synthesis. Here, we investigate the role of bulk hydrogen, where hydrogen atoms are found deep inside a metal surface as opposed to subsurface ones, upon CO 2 reduction over a Ni(110) surface using density functional theory (DFT) and ab initio molecular dynamics (AIMD) simulations. While it has previously been shown that subsurface hydrogen stabilizes CO 2 and can aid in overcoming reaction barriers, the role of bulk hydrogen is less studied and thus unknown with regard to CO 2 reduction. Furthermore, we find that the presence of bulk hydrogen can significantly alter the electronic structure of the Ni(110) surface, particularly the work function and d-band center, such that CO 2 adsorbs more strongly to the surface and is more easily reduced. Our results show an enhanced CO 2 dissociation in the presence of bulk hydrogen, shedding light on a hitherto underappreciated mechanistic pathway for CO 2 reduction on metal surfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗