The CO/Pt(111) Puzzle

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Implementation and Performance

Developing theoretical understanding of complex reactions and processes at interfaces requires using methods that go beyond semilocal density functional theory to accurately describe the interactions between solvent, reactants and substrates. Methods based on many-body perturbation theory, such as the random phase approximation (RPA), have previously been limited due to their computational complexity. However, this is now a surmountable barrier due to the advances in computational power available, in particular through modern GPU-based supercomputers. In this work, we describe the implementation of RPA calculations within BerkeleyGW and show its favorable computational performance on large complex systems relevant for catalysis and electrochemistry applications. Our implementation builds off of the static subspace approximation which, by employing a compressed representation of the frequency dependent polarizability, enables the evaluation of the RPA correlation energy with significant acceleration and systematically controllable accuracy. We find that the computational cost of calculating the RPA correlation energy scales only linearly with system size for systems containing up to 50 thousand bands, and is expected to scale quadratically thereafter. We also show excellent strong scaling results across several supercomputers, demonstrating the performance and portability of this implementation.

Vibrational study of CO, O2, and H2 Adsorbed on the CoCrFeNi (110) High Entropy Alloy Surface

The vibrational properties of CO, O2, and H2 molecularly or dissociatively adsorbed on a CoCrFeNi(110) surface have been probed using high-resolution energy loss spectroscopy (HREELS) and modeled using density functional theory (DFT) calculations. Large (∼20 mm3) single-crystal, quaternary face-centered cubic CoCrFeNi was synthesized via a modified Czochralski technique. We show strong evidence that CO adsorbs primarily on bridge and on-top sites in compositionally varied local environments, which reflect the random, multielemental surface composition inherent in a high entropy alloy. A variation of adsorption sites is also found with oxygen, which exhibits two broad groups of modes. Comparison to previous photoemission and theoretical studies suggests that the higher energy modes consist primarily of local CrO x species, while the lower energy modes are due to oxygen atoms adsorbed on other metal sites. Unlike CO and O2, HREELS upon H2 adsorption shows only two much narrower modes and is consistent with atomic adsorption on 3-fold hollow sites. The hypothesized adsorption sites for all three species are directly corroborated by our DFT calculations.

CO adsorption on Pt(111) studied by periodic coupled cluster theory

We present an application of periodic coupled-cluster theory to the calculation of CO adsorption energies on the Pt(111) surface for different adsorption sites. The calculations employ a range of recently developed theoretical and computational methods. In particular, we use a recently introduced coupled-cluster ansatz, denoted as CCSD(cT), to compute correlation energies of the metallic Pt surface with and without adsorbed CO molecules. The convergence of Hartree-Fock adsorption energy contributions with respect to randomly shifted k-meshes is discussed. Recently introduced basis set incompleteness error corrections make it possible to achieve well-converged correlation energy contributions to the adsorption energies. We show that CCSD(cT) theory predicts the correct order of adsorption energies for the considered adsorption sites. Furthermore, we find that binding of the CO molecule to the top and fcc site is dominated by Hartree-Fock and correlation energy contributions, respectively.

A Comprehensive Investigation of Methanol Electrooxidation on Copper Anodes: Spectroelectrochemical Insights and Energy Conversion in Microfluidic Fuel Cells

Here, we comprehensively investigated methanol electrooxidation on Cu-based catalysts, allowing us to build the first microfluidic fuel cell (μFC) equipped with a Cu anode and a metal-free cathode that converts energy from methanol. We applied a simple, fast, small-scale, and surfactant-free strategy for synthesizing Cu-based nanoparticles at room temperature in steady state (ST), under mechanical stirring (MS), or under ultrasonication (US). The morphology evaluation of the Cu-based samples reveals that they have the same nanoparticle (NP) needle-like form. The elemental mapping composition spectra revealed that pure Cu or Cu oxides were obtained for all synthesized materials. In addition to having more Cu2O on the surface, sample US had more Cu(OH)2 than the others, according to X-ray diffractograms and X-ray photoelectron spectroscopy. The sample US is less carbon-contaminated because of the local heating of the sonic bath, which also enhances the cleanliness of the Cu surface. The activity of the Cu NPs was investigated for methanol electrooxidation in an alkaline medium through electrochemical and spectroelectrochemical measurements. The potentiodynamic and potentiostatic experiments showed higher current densities for the NPs synthesized in the US. In situ FTIR experiments revealed that the three synthesized NP materials eletcrooxidize methanol completely to carbonate through formate. Most importantly, all pathways were led without detectable CO, a poisoning molecule not found at high overpotentials. The reaction path using the US electrode experienced an additional round of formate formation and conversion into carbonate (or CO2 in the thin layer) after 1.0 V (vs. Ag/Ag/Cl), suggesting improved catalysis. The high activity of NPs synthesized in the US is attributed to effective dissociative adsorption of the fuel due to the site's availability and the presence of hydroxyl groups that may fasten the oxidation of adsorbates from the surface. After understanding the surface reaction, we built a mixed-media μFC fed by methanol in alkaline medium and sodium persulfate in acidic medium. The μFC was equipped with Cu NPs synthesized in ultrasonic-bath-modified carbon paper as the anode and metal-free carbon paper as the cathode. Since the onset potential for methanol electrooxidation was 0.45 V and the reduction reaction revealed 0.90 V, the theoretical OCV is 0.45 V, which provides a spontaneous coupled redox reaction to produce power. The μFC displayed 0.56 mA cm-2 of maximum current density and 26 μW cm-2 of peak power density at 100 μL min-1. This membraneless system optimizes each half-cell individually, making it possible to build fuel cells with noble metal-free anodes and metal-free cathodes.

Improving Molecule-Metal Surface Reaction Networks Using the Meta-Generalized Gradient Approximation: CO2 Hydrogenation

Density functional theory is widely used to gain insights into molecule-metal surface reaction networks, which is important for a better understanding of catalysis. However, it is well-known that generalized gradient approximation (GGA) density functionals (DFs), most often used for the study of reaction networks, struggle to correctly describe both gas-phase molecules and metal surfaces. Also, GGA DFs typically underestimate reaction barriers due to an underestimation of the self-interaction energy. Screened hybrid GGA DFs have been shown to reduce this problem but are currently intractable for wide usage. In this work, we use a more affordable meta-GGA (mGGA) DF in combination with a nonlocal correlation DF for the first time to study and gain new insights into a catalytically important surface reaction network, namely, CO2 hydrogenation on Cu. We show that the mGGA DF used, namely, rMS-RPBEl-rVV10, outperforms typical GGA DFs by providing similar or better predictions for metals and molecules, as well as molecule-metal surface adsorption and activation energies. Hence, it is a better choice for constructing molecule-metal surface reaction networks.

Self-Consistent Convolutional Density Functional Approximations: Application to Adsorption at Metal Surfaces

The exchange-correlation (XC) functional in density functional theory is used to approximate multi-electron interactions. A plethora of different functionals are available, but nearly all are based on the hierarchy of inputs commonly referred to as "Jacob's ladder." This paper introduces an approach to construct XC functionals with inputs from convolutions of arbitrary kernels with the electron density, providing a route to move beyond Jacob's ladder. We derive the variational derivative of these functionals, showing consistency with the generalized gradient approximation (GGA), and provide equations for variational derivatives based on multipole features from convolutional kernels. A proof-of-concept functional, PBEq, which generalizes the PBE α ${\alpha }$ framework with α ${\alpha }$ being a spatially-resolved function of the monopole of the electron density, is presented and implemented. It allows a single functional to use different GGAs at different spatial points in a system, while obeying PBE constraints. Analysis of the results underlines the importance of error cancellation and the XC potential in data-driven functional design. After testing on small molecules, bulk metals, and surface catalysts, the results indicate that this approach is a promising route to simultaneously optimize multiple properties of interest.

Bond Selective Photochemistry at Metal Nanoparticle Surfaces: CO Desorption from Pt and Pd

The use of visible photon fluxes to influence catalytic reactions on metal nanoparticle surfaces has attracted attention based on observations of reaction mechanisms and selectivity not observed under equilibrium heating. These observations suggest that photon fluxes can selectively impact the rates of certain elementary steps, creating nonequilibrium energy distributions among various reaction pathways. However, quantitative studies validating these hypotheses on metal nanoparticle surfaces are lacking. We examine the influence of continuous wave visible photon fluxes on the CO desorption rates from 1 to 2 nm diameter Pt and Pd nanoparticle surfaces supported on γ-Al2O3. Temperature-programmed desorption measurements quantified via diffuse reflectance infrared Fourier transform spectroscopy demonstrate that visible photon fluxes significantly enhanced the rate of CO desorption from Pt nanoparticles in a wavelength-dependent manner. 440 nm photons most efficiently promoted CO desorption from Pt nanoparticle surfaces, aligning with the excitation energy for the interfacial electronic transition within the Pt-CO bond. Conversely, visible photon fluxes had no measurable influence on CO desorption rates from Pd nanoparticle surfaces after accounting for photon-induced heating. Density functional theory calculations demonstrate that the Pt-CO bond exhibits a narrower LUMO resonance, stronger coupling between the photoexcitation and forces induced on the metal-C bond, and vibrational energy dissipation that more effectively couples to desorption as compared to Pd-CO. These results demonstrate the specificity photons provide in facilitating chemical reactions on metal nanoparticle surfaces and substantiate the idea that photon fluxes can steer processes and outcomes of catalytic reactions in ways not achievable by equilibrium heating.

Multiscale Investigation of the Mechanism and Selectivity of CO2 Hydrogenation over Rh(111)

CO2 hydrogenation over Rh catalysts comprises multiple reaction pathways, presenting a wide range of possible intermediates and end products, with selectivity toward either CO or methane being of particular interest. We investigate in detail the reaction mechanism of CO2 hydrogenation to the single-carbon (C1) products on the Rh(111) facet by performing periodic density functional theory (DFT) calculations and kinetic Monte Carlo (kMC) simulations, which account for the adsorbate interactions through a cluster expansion approach. We observe that Rh readily facilitates the dissociation of hydrogen, thus contributing to the subsequent hydrogenation processes. The reverse water-gas shift (RWGS) reaction occurs via three different reaction pathways, with CO hydrogenation to the COH intermediate being a key step for CO2 methanation. The effects of temperature, pressure, and the composition ratio of the gas reactant feed are considered. Temperature plays a pivotal role in determining the surface coverage and adsorbate composition, with competitive adsorption between CO and H species influencing the product distribution. The observed adlayer configurations indicate that the adsorbed CO species are separated by adsorbed H atoms, with a high ratio of H to CO coverage on the Rh(111) surface being essential to promote CO2 methanation.

Interrogating site dependent kinetics over SiO2-supported Pt nanoparticles

A detailed knowledge of reaction kinetics is key to the development of new more efficient heterogeneous catalytic processes. However, the ability to resolve site dependent kinetics has been largely limited to surface science experiments on model systems. Herein, we can bypass the pressure, materials, and temperature gaps, resolving and quantifying two distinct pathways for CO oxidation over SiO2-supported 2 nm Pt nanoparticles using transient pressure pulse experiments. We find that the pathway distribution directly correlates with the distribution of well-coordinated (e.g., terrace) and under-coordinated (e.g., edge, vertex) CO adsorption sites on the 2 nm Pt nanoparticles as measured by in situ DRIFTS. We conclude that well-coordinated sites follow classic Langmuir-Hinshelwood kinetics, but under-coordinated sites follow non-standard kinetics with CO oxidation being barrierless but conversely also slow. This fundamental method of kinetic site deconvolution is broadly applicable to other catalytic systems, affording bridging of the complexity gap in heterogeneous catalysis.

Incorporation of Epoxy Carbon onto CeO2-Supported Pt to Tackle the CO Self-Poisoning Issue

The catalytic oxidation of carbon monoxide (CO) under ambient conditions plays a crucial role in the abatement of indoor CO, which poses risks to human health. Despite the notable activity exhibited by Pt-based catalysts in CO oxidation, their efficacy is usually diminished by the CO self-poisoning issue. In this work, three different Pt/CeO2-based catalysts, which have distinct coordinative environments of Pt but an identical Pt/CeO2 substrate structure, were synthesized by activating the catalyst with CO using different temperatures and durations. Compared with clean and graphite-covered Pt on CeO2, the one modified by epoxy carbon showed higher activity and stability. The combination of characterizations and density functional theory modeling demonstrated that the clean Pt on CeO2 rapidly deactivated due to the CO self-poisoning albeit high initial activity, and conversely, low initial activity was observed for the more stable graphite-covered catalyst due to the obstruction of the Pt site. In contrast, epoxy carbon species on Pt shifted the d-band of Pt to lower energy, weakening the Pt-CO binding strength. Such a modification mitigated the self-poisoning effect while maintaining ample active sites and enabling the complete oxidative removal of CO under ambient conditions. This work may provide a general approach to tackling the self-poisoning issue.

Fabrication of Large-Area Metal-on-Carbon Catalytic Condensers for Programmable Catalysis

Catalytic condensers stabilize charge on either side of a high-k dielectric film to modulate the electronic states of a catalytic layer for the electronic control of surface reactions. Here, carbon sputtering provided for fast, large-scale fabrication of metal-carbon catalytic condensers required for industrial application. Carbon films were sputtered on HfO2 dielectric/p-type Si with different thicknesses (1, 3, 6, and 10 nm), and the enhancement of conductance and capacitance of carbon films was observed upon increasing the carbon thickness following thermal treatment at 400 °C. After Pt deposition on the carbon films, the Pt catalytic condenser exhibited a high capacitance of ∼210 nF/cm2 that was maintained at a frequency ∼1000 Hz, satisfying the requirement for a dynamic catalyst to implement catalytic resonance. Temperature-programmed desorption of carbon monoxide yielded CO desorption peaks that shifted in temperature with the varying potential applied to the condenser (-6 or +6 V), indicating a shift in the binding energy of carbon monoxide on the Pt condenser surface. A substantial increase in capacitance (∼2000 nF/cm2) of the Pt-on-carbon devices was observed at elevated temperatures of 400 °C that can modulate ∼10% of charge per metal atom when 10 V potential was applied. A large catalytic condenser of 42 cm2 area Pt/C/HfO2/Si exhibited a high capacitance of 9393 nF with a low leakage current/capacitive current ratio (<0.1), demonstrating the practicality and versatility of the facile, large-scale fabrication method for metal-carbon catalytic condensers.

Benchmarking the Accuracy of Density Functional Theory against the Random Phase Approximation for the Ethane Dehydrogenation Network on Pt(111)

The Random Phase Approximation (RPA) is conceptually the most accurate Density Functional Approximation method, able to simultaneously predict both adsorbate and surface energies accurately; however, this work questions its superiority over DFT for catalytic application on hydrocarbon systems. This work uses microkinetic modeling to benchmark the accuracy of DFT functionals against that of RPA for the ethane dehydrogenation reaction on Pt(111). Eight different functionals, with and without dispersion corrections, across the GGA, meta-GGA and hybrid classes are evaluated: PBE, PBE-D3, RPBE, RPBE-D3, BEEF-vdW, SCAN, SCAN-rVV10, and HSE06. We show that PBE and RPBE, without dispersion correction, closely model RPA energies for adsorption, transition states, reaction, and activation energies. Next, RPA fails to describe the gas phase energy as unsaturation and chain-length increases in the hydrocarbon. Finally, we show that RPBE has the best accuracy-to-cost ratio, and RPA is likely not superior to RPBE or BEEF-vdW, which also gives a measure of uncertainty.

Averting the Infrared Catastrophe in the Gold Standard of Quantum Chemistry

Coupled-cluster theories can be used to compute ab initio electronic correlation energies of real materials with systematically improvable accuracy. However, the widely used coupled cluster singles and doubles plus perturbative triples [CCSD(T)] method is only applicable to insulating materials. For zero-gap materials the truncation of the underlying many-body perturbation expansion leads to an infrared catastrophe. Here, we present a novel perturbative triples formalism denoted as (cT) that yields convergent correlation energies in metallic systems. Furthermore, the computed correlation energies for the three-dimensional uniform electron gas at metallic densities are in good agreement with quantum Monte Carlo results. At the same time the newly proposed method retains all desirable properties of CCSD(T) such as its accuracy for insulating systems as well as its low computational cost compared to a full inclusion of the triples. This paves the way for ab initio calculations of real metals with chemical accuracy.

Combining Machine Learning and Many-Body Calculations: Coverage-Dependent Adsorption of CO on Rh(111)

Adsorption of carbon monoxide (CO) on transition-metal surfaces is a prototypical process in surface sciences and catalysis. Despite its simplicity, it has posed great challenges to theoretical modeling. Pretty much all existing density functionals fail to accurately describe surface energies and CO adsorption site preference as well as adsorption energies simultaneously. Although the random phase approximation (RPA) cures these density functional theory failures, its large computational cost makes it prohibitive to study the CO adsorption for any but the simplest ordered cases. Here, we address these challenges by developing a machine-learned force field (MLFF) with near RPA accuracy for the prediction of coverage-dependent adsorption of CO on the Rh(111) surface through an efficient on-the-fly active learning procedure and a Δ-machine learning approach. We show that the RPA-derived MLFF is capable to accurately predict the Rh(111) surface energy and CO adsorption site preference as well as adsorption energies at different coverages that are all in good agreement with experiments. Moreover, the coverage-dependent ground-state adsorption patterns and adsorption saturation coverage are identified.

The role of single-atom Rh-dopants in the adsorption properties of OH and CO on stepped Ag(211) surfaces

Several chemical reactions with commercial and environmental importance can benefit from the development of more active or selective heterogeneous catalysts. Particularly, those catalyzed by metallic surfaces are usually impacted by the presence of defects such as kinks and dopants. Here, we employed density functional theory calculations within van der Waals correction to investigate the effects of single-atom Rh-dopants in the adsorption properties of OH and CO on stepped Ag(211) surfaces. From our calculations and analyses, we found that the dopant is more energetically stable when replacing more coordinated (and less exposed to the vacuum) sites of the surface. However, in the presence of both molecules, this trend is inverted, and the dopant is more stable in the least coordinated site (step). While OH presents high adsorption energies on both doped and non-doped silver surfaces, CO binds weakly to the noble metal, and strongly on doped sites. The results are relevant for understanding single-atom catalysts on noble-metal surfaces, where the difference in selectivity and activity between the host metal and dopants is exploited. The charge redistribution caused by the dopant, and the appearance of a sharp peak in the density of states of the surface are used to rationalize the results and provide insights into the interactions involved in the adsorption of both molecules.

Ensemble Effects in Adsorbate-Adsorbate Interactions in Microkinetic Modeling

Adsorbates on a surface experience lateral interactions that result in a distribution of adsorption energies. The adsorbate-adsorbate interactions are known to affect the kinetics of surface reactions, which motivates efforts to develop models that accurately account for the interactions. Here, we use density functional theory (DFT) calculations combined with Monte Carlo simulations to investigate how the distribution of adsorbates affects adsorption and desorption of CO from Pt(111). We find that the mean of the average adsorption energy determines the adsorption process, whereas the desorption process can be described by the low energy part of the adsorbate stability distribution. The simulated results are in very good agreement with calorimetry and temperature-programmed desorption experiments and provide a guideline of how to include adsorbate-adsorbate interactions in DFT-based mean-field kinetic models.

Binding Energy and Diffusion Barrier of Formic Acid on Pd(111)

Velocity-resolved kinetics is used to measure the thermal rate of formic acid desorption from Pd(111) between 228 and 273 K for four isotopologues: HCOOH, HCOOD, DCOOH, DCOOD. Upon molecular adsorption, formic acid undergoes decomposition to CO₂ and H₂ and thermal desorption. To disentangle the contributions of individual processes, we implement a mass-balance-based calibration procedure from which the branching ratio between desorption and decomposition for formic acid is determined. From experimentally derived elementary desorption rate constants, we obtain the binding energy 639 ± 8 meV and the diffusion barrier 370 ± 130 meV using the detailed balance rate model (DBRM). The DBRM explains the observed kinetic isotope effects.

Adsorption energies on transition metal surfaces: towards an accurate and balanced description

Density functional theory predictions of binding energies and reaction barriers provide invaluable data for analyzing chemical transformations in heterogeneous catalysis. For high accuracy, effects of band structure and coverage, as well as the local bond strength in both covalent and non-covalent interactions, must be reliably described and much focus has been put on improving functionals to this end. Here, we show that a correction from higher-level calculations on small metal clusters can be applied to improve periodic band structure adsorption energies and barriers. We benchmark against 38 reliable experimental covalent and non-covalent adsorption energies and five activation barriers with mean absolute errors of 2.2 kcal mol^-1, 2.7 kcal mol^-1, and 1.1 kcal mol^-1, respectively, which are lower than for functionals widely used and tested for surface science evaluations, such as BEEF-vdW and RPBE.

Effect of temperature on CO oxidation over Pt(111) in two-dimensional confinement

Confined catalysis between a two-dimensional (2D) cover and metal surfaces has provided a unique environment with enhanced activity compared to uncovered metal surfaces. Within this 2D confinement, weakened adsorption and lowered activation energies were observed using surface science experiments and density functional theory (DFT) calculations. Computationally, the role of electronic and mechanical factors responsible for the improved activity was deduced only from static DFT calculations. This demands a detailed investigation on the dynamics of reactions under 2D confinement, including temperature effects. In this work, we study CO oxidation on a 2D graphene covered Pt(111) surface at 90 and 593 K using DFT-based ab initio molecular dynamics simulations starting from the transition state configuration. We show that CO oxidation in the presence of a graphene cover is substantially enhanced (2.3 times) at 90 K. Our findings suggest that 2D confined spaces can be used to enhance the activity of chemical reactions, especially at low temperatures.

Carbon-oxygen surface formation enhances secondary electron yield in Cu, Ag and Au

First-principles calculations coupled with Monte Carlo simulations are used to probe the role of a surface CO monolayer formation on secondary electron emission (SEE) from Cu, Ag, and Au (110) materials. It is shown that formation of such a layer increases the secondary electron emission in all systems. Analysis of calculated total density of states (TDOS) in Cu, Ag, and Au, and partial density of states (PDOS) of C and O confirm the formation of a covalent type bonding between C and O atoms. It is shown that such a bond modifies the TDOS and extended it to lower energies, which is then responsible for an increase in the probability density of secondary electron generation. Furthermore, a reduction in inelastic mean free path is predicted for all systems. Our predicted results for the secondary electron yield (SEY) compare very favorably with experimental data in all three materials, and exhibit increases in SEY. This is seen to occur despite increases in the work function for Cu, Ag, and Au. The present analysis can be extended to other absorbates and gas atoms at the surface, and such analyses will be present elsewhere.

Dynamical Study of Adsorbate-Induced Restructuring Kinetics in Bimetallic Catalysts Using the PdAu(111) Model System

Dynamic restructuring of bimetallic catalysts plays a crucial role in their catalytic activity and selectivity. In particular, catalyst pretreatment with species such as carbon monoxide and oxygen has been shown to be an effective strategy for tuning the surface composition and morphology. Mechanistic and kinetic understanding of such restructuring is fundamental to the chemistry and engineering of surface active sites but has remained challenging due to the large structural, chemical, and temporal degrees of freedom. Here, we combine time-resolved temperature-programmed infrared reflection absorption spectroscopy, ab initio thermodynamics, and machine-learning molecular dynamics to uncover previously unidentified timescale and kinetic parameters of in situ restructuring in Pd/Au(111), a highly relevant model system for dilute Pd-in-Au nanoparticle catalysts. The key innovation lies in utilizing CO not only as a chemically sensitive probe of surface Pd but also as an agent that induces restructuring of the surface. Upon annealing in vacuum, as-deposited Pd islands became encapsulated by Au and partially dissolved into the subsurface, leaving behind isolated Pd monomers on the surface. Subsequent exposure to 0.1 mbar CO enabled Pd monomers to repopulate the surface up to 373 K, above which complete Pd dissolution occurred by 473 K, with apparent activation energies of 0.14 and 0.48 eV, respectively. These restructuring processes occurred over the span of ∼1000 s at a given temperature. Such a minute-timescale dynamics not only elucidates the fluxional nature of alloy catalysts but also presents an opportunity to fine-tune the surface under moderate temperature and pressure conditions.

Finite-Size Error Cancellation in Diffusion Monte Carlo Calculations of Surface Chemistry

The accurate prediction of reaction mechanisms in heterogeneous (surface) catalysis is one of the central challenges in computational chemistry. Quantum Monte Carlo methods─Diffusion Monte Carlo (DMC) in particular─are being recognized as higher-accuracy, albeit more computationally expensive, alternatives to Density Functional Theory (DFT) for energy predictions of catalytic systems. A major computational bottleneck in the broader adoption of DMC for catalysis is the need to perform finite-size extrapolations by simulating increasingly large periodic cells (supercells) to eliminate many-body finite-size effects and obtain energies in the thermodynamic limit. Here, we show that it is possible to significantly reduce this computational cost by leveraging the cancellation of many-body finite-size errors that accompanies the evaluation of energy differences when calculating quantities like adsorption (binding) energies and mapping potential energy surfaces. We analyze the cancellation and convergence of many-body finite-size errors in two well-known adsorbate/slab systems, H₂O/LiH(001) and CO/Pt(111). Based on this analysis, we identify strategies for obtaining binding energies in the thermodynamic limit that optimally utilize error cancellation to balance accuracy and computational efficiency. Using one such strategy, we then predict the correct order of adsorption site preference on CO/Pt(111), a challenging problem for a wide range of density functionals. Our accurate and inexpensive DMC calculations are found to unambiguously recover the top > bridge > hollow site order, in agreement with experimental observations. We proceed to use this DMC method to map the potential energy surface of CO hopping between Pt(111) adsorption sites. This reveals the existence of an L-shaped top-bridge-hollow diffusion trajectory characterized by energy barriers that provide an additional kinetic justification for experimental observations of CO/Pt(111) adsorption. Overall, this work demonstrates that it is routinely possible to achieve order-of-magnitude speedups and memory savings in DMC calculations by taking advantage of error cancellation in the calculation of energy differences that are ubiquitous in heterogeneous catalysis and surface chemistry more broadly.

Modeling Electrochemical Processes with Grand Canonical Treatment of Many-Body Perturbation Theory

Electrocatalysis plays a key role in sustainable energy conversion and storage. It is critical to model the grand canonical treatment of electrons, which accounts for the electrochemical potential explicitly, at the atomic scale and understand these reactions at electrified interfaces. However, such a grand canonical treatment for electrocatalytic modeling is in practice restricted to a treatment of electronic structure with density functional theory, and more accurate methods are in many cases desirable. Here, we develop an original workflow combining the grand canonical treatment of electrons with many-body perturbation theory in its random phase approximation (RPA). Using the potential dependent adsorption of carbon monoxide on the copper (100) facet, we show that the grand canonical RPA energetics provide the correct on-top Cu geometry for CO at reducing potential. The match with experimental results is significantly improved compared to the functionals at the generalized gradient approximation level, which is the most commonly used approximation for electrochemical applications. We expect this development to pave the way to further electrochemical applications using RPA.

Improving the Accuracy of Atomistic Simulations of the Electrochemical Interface

Atomistic simulation of the electrochemical double layer is an ambitious undertaking, requiring quantum mechanical description of electrons, phase space sampling of liquid electrolytes, and equilibration of electrolytes over nanosecond time scales. All models of electrochemistry make different trade-offs in the approximation of electrons and atomic configurations, from the extremes of classical molecular dynamics of a complete interface with point-charge atoms to correlated electronic structure methods of a single electrode configuration with no dynamics or electrolyte. Here, we review the spectrum of simulation techniques suitable for electrochemistry, focusing on the key approximations and accuracy considerations for each technique. We discuss promising approaches, such as enhanced sampling techniques for atomic configurations and computationally efficient beyond density functional theory (DFT) electronic methods, that will push electrochemical simulations beyond the present frontier.

Size and structure effects on platinum nanocatalysts: theoretical insights from methanol dehydrogenation

Methanol dehydrogenation on Pt nanoparticles was studied as a model reaction with the focus on size and structure effects employing the density functional theory approach. The effect of cluster morphology is manifested by the higher adsorption energy of COH_x intermediates on vertexes and edges of model nanoparticles compared to closely packed terraces. Moreover, due to the size effect, the adsorption sites of Pt₇₉ nanoparticles (1.2 nm in diameter) exhibit considerably higher adsorption activity than the same sites of Pt₂₀₁ (1.7 nm). Thus, particles with a size of about 1 nm are shown to be more active due to the superposition of two effects: (i) a higher surface fraction of low-coordinated adsorption sites and (ii) higher activity of these sites compared to particles with a size of about 2 nm.

Eliminating Delocalization Error to Improve Heterogeneous Catalysis Predictions with Molecular DFT + U

Approximate semilocal density functional theory (DFT) is known to underestimate surface formation energies yet paradoxically overbind adsorbates on catalytic transition-metal oxide surfaces due to delocalization error. The low-cost DFT + U approach only improves surface formation energies for early transition-metal oxides or adsorption energies for late transition-metal oxides. In this work, we demonstrate that this inefficacy arises due to the conventional usage of metal-centered atomic orbitals as projectors within DFT + U. We analyze electron density rearrangement during surface formation and O atom adsorption on rutile transition-metal oxides to highlight that a standard DFT + U correction fails to tune properties when the corresponding density rearrangement is highly delocalized across both metal and oxygen sites. To improve both surface properties simultaneously while retaining the simplicity of a single-site DFT + U correction, we systematically construct multi-atom-centered molecular-orbital-like projectors for DFT + U. We demonstrate this molecular DFT + U approach for tuning adsorption energies and surface formation energies of minimal two-dimensional models of representative early (i.e., TiO₂) and late (i.e., PtO₂) transition-metal oxides. Molecular DFT + U simultaneously corrects adsorption energies and surface formation energies of multilayer models of rutile TiO₂(110) and PtO₂(110) to resolve the paradoxical description of surface stability and surface reactivity of semilocal DFT.

Adsorption Sites on Pd Nanoparticles Unraveled by Machine-Learning Potential with Adaptive Sampling

Catalytic properties of noble-metal nanoparticles (NPs) are largely determined by their surface morphology. The latter is probed by surface-sensitive spectroscopic techniques in different spectra regions. A fast and precise computational approach enabling the prediction of surface-adsorbate interaction would help the reliable description and interpretation of experimental data. In this work, we applied Machine Learning (ML) algorithms for the task of adsorption-energy approximation for CO on Pd nanoclusters. Due to a high dependency of binding energy from the nature of the adsorbing site and its local coordination, we tested several structural descriptors for the ML algorithm, including mean Pd-C distances, coordination numbers (CN) and generalized coordination numbers (GCN), radial distribution functions (RDF), and angular distribution functions (ADF). To avoid overtraining and to probe the most relevant positions above the metal surface, we utilized the adaptive sampling methodology for guiding the ab initio Density Functional Theory (DFT) calculations. The support vector machines (SVM) and Extra Trees algorithms provided the best approximation quality and mean absolute error in energy prediction up to 0.12 eV. Based on the developed potential, we constructed an energy-surface 3D map for the whole Pd₅₅ nanocluster and extended it to new geometries, Pd₇₉, and Pd₈₅, not implemented in the training sample. The methodology can be easily extended to adsorption energies onto mono- and bimetallic NPs at an affordable computational cost and accuracy.

Enhanced Electrocatalytic Oxidation of Small Organic Molecules on Platinum-Gold Nanowires: Influence of the Surface Structure and Pt-Pt/Pt-Au Pair Site Density

The electrochemical oxidation of small organic molecules (SOMs) such as methanol and glucose is a critical process and has relevant applications in fuel cells and sensors. A key challenge in SOM oxidation is the poisoning of the surface by carbon monoxide (CO) and other partially oxidized intermediates, which is attributed to the presence of Pt-Pt pair sites. A promising pathway for overcoming this challenge is to develop catalysts that selectively oxidize SOMs via "direct" pathways that do not form CO as a primary intermediate. In this report, we utilize an ambient, template-based approach to prepare PtAu alloy nanowires with tunable compositions. X-ray photoelectron spectroscopy measurements reveal that the surface composition matches that of the bulk composition after synthesis. Monte Carlo method simulations of the surface structure of PtAu alloys with varying coverage of oxygen adsorbates and varying degrees of oxygen adsorption strength reveal that oxygen adsorption under electrochemical conditions enriches the surface with Pt and a large fraction of Pt-Pt sites remain on the surface even with the Au content of up to 50%. Electrochemical properties and the catalytic performance measurements of the PtAu nanowires for the oxidation of methanol and glucose reveal that the mechanistic pathways that produce CO are suppressed by the addition of relatively small quantities of Au (∼10%), and CO formation can be completely suppressed by 50% Au. The suppression of CO formation with small quantities of Au suggests that the presence of Pt-Au pair sites may be more important in determining the mechanism of SOM oxidation rather than Pt-Pt pair site density.

Reinvestigating oxygen adsorption on Ag(111) by using strongly constrained and appropriately normed semi-local density functional with the revised Vydrov van Voorhis van der Waals force correction

While density functional theory (DFT) at the generalized gradient approximation (GGA) level has made great success in catalysis, it fails in some important systems such as the adsorption of the oxygen molecule on the Ag(111) surface. Previous DFT studies at the GGA level revealed theoretical inconsistencies on the adsorption energies and dissociation barriers of O₂ on Ag(111) in comparison with the experimental conclusion. In this study, the strongly constrained and appropriately normed-revised Vydrov van Voorhis van der Waals correction functional (SCAN-rVV10) method at the meta-GGA level with the nonlocal van der Waals (vdW) force correction was used to reinvestigate the adsorption properties of O₂ on the Ag(111) surface. The SCAN-rVV10 results successfully confirm the experimental observation that both molecular and dissociative adsorptions can exist for oxygen on Ag(111). The calculated adsorption energy for the physisorption state and the relevant dissociation energy barrier are close to the experimental data. It demonstrates that SCAN-rVV10 can outperform functionals at the GGA level for O₂/Ag(111). Therefore, our findings suggest that SCAN-rVV10 can be the desired method for systems where the correct description of intermediate-ranged vdW forces is essential, such as the physisorption of small molecules on the solid surface.

Diffusion Barriers for Carbon Monoxide on the Cu(001) Surface Using Many-Body Perturbation Theory and Various Density Functionals

First-principles calculations play a key role in understanding the interactions of molecules with transition-metal surfaces and the energy profiles for catalytic reactions. However, many of the commonly used density functionals are not able to correctly predict the surface energy as well as the adsorption site preference for a key molecule such as CO, and it is not clear to what extent this shortcoming influences the prediction of reaction or diffusion pathways. Here, we report calculations of carbon monoxide diffusion on the Cu(001) surface along the [100] and [110] pathways, as well as the surface energy of Cu(001), and CO-adsorption energy and compare the performance of the Perdew-Burke-Ernzerhof (PBE), PBE + D2, PBE + D3, RPBE, Bayesian error estimation functional with van der Waals correlation (BEEF-vdW), HSE06 density functionals, and the random phase approximation (RPA), a post-Hartree-Fock method based on many-body perturbation theory. We critically evaluate the performance of these methods and find that RPA appears to be the only method giving correct site preference, overall barrier, adsorption enthalpy, and surface energy. For all of the other methods, at least one of these properties is not correctly captured. These results imply that many density functional theory (DFT)-based methods lead to qualitative and quantitative errors in describing CO interaction with transition-metal surfaces, which significantly impacts the description of diffusion pathways. It is well conceivable that similar effects exist when surface reactions of CO-related species are considered. We expect that the methodology presented here will be used to get more detailed insights into reaction pathways for CO conversion on transition-metal surfaces in general and Cu in particular, which will allow us to better understand the catalytic and electrocatalytic reactions involving CO-related species.

Assessment of the van der Waals, Hubbard U parameter and spin-orbit coupling corrections on the 2D/3D structures from metal gold congeners clusters

The coinage-metal clusters possess a natural complexity in their theoretical treatment that may be accompanied by inherent shortcomings in the methodological approach. Herein, we performed a scalar-relativistic density functional theory study, considering Perdew, Burke, and Ernzerhof (PBE) with (empirical and semi empirical) van der Waals (vdW), spin-orbit coupling (SOC), +U (Hubbard term), and their combinations, to treat the Cu 13 , Ag 13 , and Au 13 clusters in different structural motifs. The energetic scenario is given by the confirmation of the 3D lowest energy configurations for Cu 13 and Ag 13 within all approaches, while for Au 13 there is a 2D/3D competition, depending on the applied correction. The 2D geometry is 0.43 eV more stable with plain PBE than the 3D one, the SOC, +U, and/or vdW inclusion decreases the overestimated stability of the planar configurations, where the most surprising result is found by the D3 and D3BJ vdW corrections, for which the 3D configuration is 0.29 and 0.11 eV, respectively, more stable than the 2D geometry (with even higher values when SOC and/or +U are added). The D3 dispersion correction represents 7.9% (4.4%) of the total binding energy for the 3D (2D) configuration, (not) being enough to change the sd hybridization and the position of the occupied d -states. Our predictions are in agreement with experimental results and in line with the best results obtained for bulk systems, as well as with hybrid functionals within D3 corrections. The properties description undergoes small corrections with the different approaches, where general trends are maintained, that is, the average bond length is smaller (larger) for lower (higher)-coordinated structures, since a same number of electrons are shared by a smaller (larger) number of bonds, consequently, the bonds are stronger (weaker) and shorter (longer) and the sd hybridization index is larger (smaller). Thus, Au has a distinct behavior in relation to its lighter congeners, with a complex potential energy surface, where in addition to the relevant relativistic effects, correlation and dispersion effects must also be considered.

How to extract adsorption energies, adsorbate-adsorbate interaction parameters and saturation coverages from temperature programmed desorption experiments

We present a scheme to extract the adsorption energy, adsorbate interaction parameter and the saturation coverage from temperature programmed desorption (TPD) experiments. We propose that the coverage dependent adsorption energy can be fit using a functional form including the configurational entropy and linear adsorbate-adsorbate interaction terms. As one example of this scheme, we analyze TPD of CO desorption on Au(211) and Au(310) surfaces. We determine that under atmospheric CO pressure, the steps of both facets adsorb between 0.4-0.9 ML coverage of CO*. We compare this result against energies obtained from five density functionals, RPBE, PBE, PBE-D3, RPBE-D3 and BEEF-vdW. We find that the energies and equilibrium coverages from RPBE-D3 and PBE are closest to the values determined from the TPD.

vdW-DF-ahcx: a range-separated van der Waals density functional hybrid

Hybrid density functionals replace a fraction of an underlying generalized-gradient approximation (GGA) exchange description with a Fock-exchange component. Range-separated hybrids (RSHs) also effectively screen the Fock-exchange component and thus open the door for characterizations of metals and adsorption at metal surfaces. The RSHs are traditionally based on a robust GGA, such as PBE (Perdew J Pet al1996Phys. Rev. Lett.773865), for example, as implemented in the HSE design (Heyd Jet al2003J. Chem. Phys.1188207). Here we define an analytical-hole (Henderson T Met al2008J. Chem. Phys.128194105) consistent-exchange RSH extension to the van der Waals density functional (vdW-DF) method (Berland Ket al2015Rep. Prog. Phys.78066501), launching vdW-DF-ahcx. We characterize the GGA-type exchange in the vdW-DF-cx version (Berland K and Hyldgaard P 2014Phys. Rev. B89035412), isolate the short-ranged exchange component, and define the new vdW-DF hybrid. We find that the performance vdW-DF-ahcx compares favorably to (dispersion-corrected) HSE for descriptions of bulk (broad molecular) properties. We also find that it provides accurate descriptions of noble-metal surface properties, including CO adsorption.

Critical Role of Thermal Fluctuations for CO Binding on Electrocatalytic Metal Surfaces

This work considers the evaluation of density functional theory (DFT) when comparing against experimental observations of CO binding trends on the strong binding Pt(111) and intermediate binding Cu(111) and for weak binding Ag(111) and Au(111) surfaces important in electrocatalysis. By introducing thermal fluctuations using appropriate statistical mechanical NVT and NPT ensembles, we find that the RPBE and B97M-rV DFT functionals yield qualitatively better metal surface strain trends and CO enthalpies of binding for Cu(111) and Pt(111) than found at 0 K, thereby correcting the overbinding by 0.2 to 0.3 eV to yield better agreement with the enthalpies determined from experiment. The importance of dispersion effects are manifest for the weak CO binding Ag(111) and Au(111) surfaces at finite temperatures in which the RPBE functional does not bind CO at all, while the B97M-rV functional shows that the CO-metal interactions are a mixture of chemisorbed and physisorbed species with binding enthalpies that are within ∼0.05 eV of experiment. Across all M(111) surfaces, we show that the B97M-rV functional consistently predicts the correct atop site preference for all metals due to thermally induced surface distortions that preferentially favor the undercoordinated site. This study demonstrates the need to fully account for finite temperature fluctuations to make contact with the binding enthalpies from surface science experiments and electrocatalysis applications.

Molecular Properties and Chemical Transformations Near Interfaces

The properties of bulk water and aqueous solutions are known to change in the vicinity of an interface and/or in a confined environment, including the thermodynamics of ion selectivity at interfaces, transition states and pathways of chemical reactions, and nucleation events and phase growth. Here we describe joint progress in identifying unifying concepts about how air, liquid, and solid interfaces can alter molecular properties and chemical reactivity compared to bulk water and multicomponent solutions. We also discuss progress made in interfacial chemistry through advancements in new theory, molecular simulation, and experiments.

Formation of a Ti-Cu(111) single atom alloy: Structure and CO binding

A single atom Ti-Cu(111) surface alloy can be generated by depositing small amounts of Ti onto Cu(111) at slightly elevated surface temperatures (∼500 to 600 K). Scanning tunneling microscopy shows that small Ti-rich islands covered by a Cu single layer form preferentially on ascending step edges of Cu(111) during Ti deposition below about 400 K but that a Ti-Cu(111) alloy replaces these small islands during deposition between 500 and 600 K, producing an alloy in the brims of the steps. Larger partially Cu-covered Ti-containing islands also form on the Cu(111) terraces at temperatures between 300 and 700 K. After surface exposure to CO at low temperatures, reflection absorption infrared spectroscopy (RAIRS) reveals distinct C-O stretch bands at 2102 and 2050 cm^-1 attributed to CO adsorbed on Cu-covered Ti-containing domains vs sites in the Ti-Cu(111) surface alloy. Calculations using density functional theory (DFT) suggest that the lower frequency C-O stretch band originates specifically from CO adsorbed on isolated Ti atoms in the Ti-Cu(111) surface alloy and predicts a higher C-O stretch frequency for CO adsorbed on Cu above subsurface Ti ensembles. DFT further predicts that CO preferentially adsorbs in flat-lying configurations on contiguous Ti surface structures with more than one Ti atom and thus that CO adsorbed on such structures should not be observed with RAIRS. The ability to generate a single atom Ti-Cu(111) alloy will provide future opportunities to investigate the surface chemistry promoted by a representative early transition metal dopant on a Cu(111) host surface.

NO Binding Energies to and Diffusion Barrier on Pd Obtained with Velocity-Resolved Kinetics

We report nitric oxide (NO) desorption rates from Pd(111) and Pd(332) surfaces measured with velocity-resolved kinetics. The desorption rates at the surface temperatures from 620 to 800 K span more than 3 orders of magnitude, and competing processes, like dissociation, are absent. Applying transition state theory (TST) to model experimental data leads to the NO binding energy E ₀ = 1.766 ± 0.024 eV and diffusion barrier D _T = 0.29 ± 0.11 eV on the (111) terrace and the stabilization energy for (110)-steps ΔE _ST = 0.060_-0.030 ^+0.015 eV. These parameters provide valuable benchmarks for theory.

Perspective on computational reaction prediction using machine learning methods in heterogeneous catalysis

Heterogeneous catalysis plays a significant role in the modern chemical industry. Towards the rational design of novel catalysts, understanding reactions over surfaces is the most essential aspect. Typical industrial catalytic processes such as syngas conversion and methane utilisation can generate a large reaction network comprising thousands of intermediates and reaction pairs. This complexity not only arises from the permutation of transformations between species but also from the extra reaction channels offered by distinct surface sites. Despite the success in investigating surface reactions at the atomic scale, the huge computational expense of ab initio methods hinders the exploration of such complicated reaction networks. With the proliferation of catalysis studies, machine learning as an emerging tool can take advantage of the accumulated reaction data to emulate the output of ab initio methods towards swift reaction prediction. Here, we briefly summarise the conventional workflow of reaction prediction, including reaction network generation, ab initio thermodynamics and microkinetic modelling. An overview of the frequently used regression models in machine learning is presented. As a promising alternative to full ab initio calculations, machine learning interatomic potentials are highlighted. Furthermore, we survey applications assisted by these methods for accelerating reaction prediction, exploring reaction networks, and computational catalyst design. Finally, we envisage future directions in computationally investigating reactions and implementing machine learning algorithms in heterogeneous catalysis.

Semi-grand canonical Monte Carlo simulation of the acrolein induced surface segregation and aggregation of AgPd with machine learning surrogate models

The single atom alloy of AgPd has been found to be a promising catalyst for the selective hydrogenation of acrolein. It is also known that the formation of Pd islands on the surface will greatly reduce the selectivity of the reaction. As a result, the surface segregation and aggregation of Pd on the AgPd surface under reaction conditions of selective hydrogenation of acrolein are of great interest. In this work, we lay out a workflow that can predict the surface segregation and aggregation of Pd on a FCC(111) AgPd surface with and without the presence of acrolein. We use machine learning surrogate models to predict the AgPd bulk energy, AgPd slab energy, and acrolein adsorption energy on AgPd slabs. Then, we use the semi-grand canonical Monte Carlo simulation to predict the surface segregation and aggregation under different bulk Pd concentrations. Under vacuum conditions, our method predicts that only trace amount of Pd will exist on the surface at Pd bulk concentrations less than 20%. However, with the presence of acrolein, Pd will start to aggregate as dimers on the surface at Pd bulk concentrations as low as 6.5%.