Assessing Exchange-Correlation Functionals for Heterogeneous Catalysis of Nitrogen Species.

Increasing interest in the sustainable synthesis of ammonia, nitrates, and urea has led to an increase in studies of catalytic conversion between nitrogen-containing compounds using heterogeneous catalysts. Density functional theory (DFT) is commonly employed to obtain molecular-scale insight into these reactions, but there have been relatively few assessments of the exchange-correlation functionals that are best suited for heterogeneous catalysis of nitrogen compounds. Here, we assess a range of functionals ranging from the generalized gradient approximation (GGA) to the random phase approximation (RPA) for the formation energies of gas-phase nitrogen species, the lattice constants of representative solids from several common classes of catalysts (metals, oxides, and metal-organic frameworks (MOFs)), and the adsorption energies of a range of nitrogen-containing intermediates on these materials. The results reveal that the choice of exchange-correlation functional and van der Waals correction can have a surprisingly large effect and that increasing the level of theory does not always improve the accuracy for nitrogen-containing compounds. This suggests that the selection of functionals should be carefully evaluated on the basis of the specific reaction and material being studied.

Electrocatalysts for Inorganic and Organic Waste Nitrogen Conversion.

Anthropogenic activities have disrupted the natural nitrogen cycle, increasing the level of nitrogen contaminants in water. Nitrogen contaminants are harmful to humans and the environment. This motivates research on advanced and decarbonized treatment technologies that are capable of removing or valorizing nitrogen waste found in water. In this context, the electrocatalytic conversion of inorganic- and organic-based nitrogen compounds has emerged as an important approach that is capable of upconverting waste nitrogen into valuable compounds. This approach differs from state-of-the-art wastewater treatment, which primarily converts inorganic nitrogen to dinitrogen, and organic nitrogen is sent to landfills. Here, we review recent efforts related to electrocatalytic conversion of inorganic- and organic-based nitrogen waste. Specifically, we detail the role that electrocatalyst design (alloys, defects, morphology, and faceting) plays in the promotion of high-activity and high-selectivity electrocatalysts. We also discuss the impact of wastewater constituents. Finally, we discuss the critical product analyses required to ensure that the reported performance is accurate.

Overcoming the Chemical Complexity Bottleneck in on-the-Fly Machine Learned Molecular Dynamics Simulations.

We develop a framework for on-the-fly machine learned force field molecular dynamics simulations based on the multipole featurization scheme that overcomes the bottleneck with the number of chemical elements. Considering bulk systems with up to 6 elements, we demonstrate that the number of density functional theory calls remains approximately independent of the number of chemical elements, in contrast to the increase in the smooth overlap of the atomic positions scheme.

The Open DAC 2023 Dataset and Challenges for Sorbent Discovery in Direct Air Capture.

Direct air capture (DAC) of CO2 with porous adsorbents such as metal-organic frameworks (MOFs) has the potential to aid large-scale decarbonization. Previous screening of MOFs for DAC relied on empirical force fields and ignored adsorbed H2O and MOF deformation. We performed quantum chemistry calculations overcoming these restrictions for thousands of MOFs. The resulting data enable efficient descriptions using machine learning.

Model-Based Design of Experiments for Temporal Analysis of Products (TAP): A Simulated Case Study in Oxidative Propane Dehydrogenation.

Temporal analysis of products (TAP) reactors enable experiments that probe numerous kinetic processes within a single set of experimental data through variations in pulse intensity, delay, or temperature. Selecting additional TAP experiments often involves an arbitrary selection of reaction conditions or the use of chemical intuition. To make experiment selection in TAP more robust, we explore the efficacy of model-based design of experiments (MBDoE) for precision in TAP reactor kinetic modeling. We successfully applied this approach to a case study of synthetic oxidative propane dehydrogenation (OPDH) that involves pulses of propane and oxygen. We found that experiments identified as optimal through the MBDoE for precision generally reduce parameter uncertainties to a higher degree than alternative experiments. The performance of MBDoE for model divergence was also explored for OPDH, with the relevant active sites (catalyst structure) being unknown. An experiment that maximized the divergence between the three proposed mechanisms was identified and provided evidence that improved the mechanism discrimination. However, reoptimization of kinetic parameters eliminated the ability to discriminate between models. The findings yield insight into the prospects and limitations of MBDoE for TAP and transient kinetic experiments.

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.

Kohn-Sham accuracy from orbital-free density functional theory via Δ-machine learning.

We present a Δ-machine learning model for obtaining Kohn-Sham accuracy from orbital-free density functional theory (DFT) calculations. In particular, we employ a machine-learned force field (MLFF) scheme based on the kernel method to capture the difference between Kohn-Sham and orbital-free DFT energies/forces. We implement this model in the context of on-the-fly molecular dynamics simulations and study its accuracy, performance, and sensitivity to parameters for representative systems. We find that the formalism not only improves the accuracy of Thomas-Fermi-von Weizsäcker orbital-free energies and forces by more than two orders of magnitude but is also more accurate than MLFFs based solely on Kohn-Sham DFT while being more efficient and less sensitive to model parameters. We apply the framework to study the structure of molten Al0.88Si0.12, the results suggesting no aggregation of Si atoms, in agreement with a previous Kohn-Sham study performed at an order of magnitude smaller length and time scales.

Formation of Carbon-Induced Nitrogen-Centered Radicals on Titanium Dioxide under Illumination.

Titanium dioxide is the most studied photocatalytic material and has been reported to be active for a wide range of reactions, including the oxidation of hydrocarbons and the reduction of nitrogen. However, the molecular-scale interactions between the titania photocatalyst and dinitrogen are still debated, particularly in the presence of hydrocarbons. Here, we used several spectroscopic and computational techniques to identify interactions among nitrogen, methanol, and titania under illumination. Electron paramagnetic resonance spectroscopy (EPR) allowed us to observe the formation of carbon radicals upon exposure to ultraviolet radiation. These carbon radicals are observed to transform into diazo- and nitrogen-centered radicals (e.g., CHxN2• and CHxNHy•) during photoreaction in nitrogen environment. In situ infrared (IR) spectroscopy under the same conditions revealed C-N stretching on titania. Furthermore, density functional theory (DFT) calculations revealed that nitrogen adsorption and the thermodynamic barrier to photocatalytic nitrogen fixation are significantly more favorable in the presence of hydroxymethyl or surface carbon. These results provide compelling evidence that carbon radicals formed from the photooxidation of hydrocarbons interact with dinitrogen and suggest that the role of carbon-based "hole scavengers" and the inertness of nitrogen atmospheres should be reevaluated in the field of photocatalysis.

Screening and Discovery of Metal Compound Active Sites for Strong and Selective Adsorption of N2 in Air.

Photocatalytic nitrogen fixation has the potential to provide a greener route for producing nitrogen-based fertilizers under ambient conditions. Computational screening is a promising route to discover new materials for the nitrogen fixation process, but requires identifying "descriptors" that can be efficiently computed. In this work, we argue that selectivity toward the adsorption of molecular nitrogen and oxygen can act as a key descriptor. A catalyst that can selectively adsorb nitrogen and resist poisoning of oxygen and other molecules present in air has the potential to facilitate the nitrogen fixation process under ambient conditions. We provide a framework for active site screening based on multifidelity density functional theory (DFT) calculations for a range of metal oxides, oxyborides, and oxyphosphides. The screening methodology consists of initial low-fidelity fixed geometry calculations and a second screening in which more expensive geometry optimizations were performed. The approach identifies promising active sites on several TiO2 polymorph surfaces and a VBO4 surface, and the full nitrogen reduction pathway is studied with the BEEF-vdW and HSE06 functionals on two active sites. The findings suggest that metastable TiO2 polymorphs may play a role in photocatalytic nitrogen fixation, and that VBO4 may be an interesting material for further studies.

Automated Generation of Microkinetics for Heterogeneously Catalyzed Reactions Considering Correlated Uncertainties.

The study presents an ab-initio based framework for the automated construction of microkinetic mechanisms considering correlated uncertainties in all energetic parameters and estimation routines. 2000 unique microkinetic models were generated within the uncertainty space of the BEEF-vdW functional for the oxidation reactions of representative exhaust gas emissions from stoichiometric combustion engines over Pt(111) and compared to experiments through multiscale modeling. The ensemble of simulations stresses the importance of considering uncertainties. Within this set of first-principles-based models, it is possible to identify a microkinetic mechanism that agrees with experimental data. This mechanism can be traced back to a single exchange-correlation functional, and it suggests that Pt(111) could be the active site for the oxidation of light hydrocarbons. The study provides a universal framework for the automated construction of reaction mechanisms with correlated uncertainty quantification, enabling a DFT-constrained microkinetic model optimization for other heterogeneously catalyzed systems.

A Universal Framework for Featurization of Atomistic Systems.

Machine-learning force fields have become increasingly popular because of their balance of accuracy and speed. However, a significant limitation is the use of element-specific features, leading to poor scalability with the number of elements. This work introduces the Gaussian multipole (GMP) featurization scheme that utilizes physically relevant multipole expansions of the electron density around atoms to yield feature vectors that interpolate between element types and have a fixed dimension regardless of the number of elements present. We combine GMP with neural networks and apply these models to the MD17 and QM9 data sets, revealing high computational efficiency, systematically improvable accuracy, and the ability to make reasonable predictions on elements not included in the training set. Finally, we test GMP-based models for the OCP data set, demonstrating comparable performance to graph-convolutional models. The results indicate that this featurization scheme fills a critical gap in the construction of efficient and transferable machine-learned force fields.

Gaussian approximation of dispersion potentials for efficient featurization and machine-learning predictions of metal-organic frameworks.

Energy-related descriptors in machine learning are a promising strategy to predict adsorption properties of metal-organic frameworks (MOFs) in the low-pressure regime. Interactions between hosts and guests in these systems are typically expressed as a sum of dispersion and electrostatic potentials. The energy landscape of dispersion potentials plays a crucial role in defining Henry's constants for simple probe molecules in MOFs. To incorporate more information about this energy landscape, we introduce the Gaussian-approximated Lennard-Jones (GALJ) potential, which fits pairwise Lennard-Jones potentials with multiple Gaussians by varying their heights and widths. The GALJ approach is capable of replicating information that can be obtained from the original LJ potentials and enables efficient development of Gaussian integral (GI) descriptors that account for spatial correlations in the dispersion energy environment. GI descriptors would be computationally inconvenient to compute using the usual direct evaluation of the dispersion potential energy surface. We show that these new GI descriptors lead to improvement in ML predictions of Henry's constants for a diverse set of adsorbates in MOFs compared to previous approaches to this task.

Heterogeneity in susceptibility dictates the order of epidemic models.

The fundamental models of epidemiology describe the progression of an infectious disease through a population using compartmentalized differential equations, but typically do not incorporate population-level heterogeneity in infection susceptibility. Here we combine a generalized analytical framework of contagion with computational models of epidemic dynamics to show that variation strongly influences the rate of infection, while the infection process simultaneously sculpts the susceptibility distribution. These joint dynamics influence the force of infection and are, in turn, influenced by the shape of the initial variability. We find that certain susceptibility distributions (the exponential and the gamma) are unchanged through the course of the outbreak, and lead naturally to power-law behavior in the force of infection; other distributions are often sculpted towards these "eigen-distributions" through the process of contagion. The power-law behavior fundamentally alters predictions of the long-term infection rate, and suggests that first-order epidemic models that are parameterized in the exponential-like phase may systematically and significantly over-estimate the final severity of the outbreak. In summary, our study suggests the need to examine the shape of susceptibility in natural populations as part of efforts to improve prediction models and to prioritize interventions that leverage heterogeneity to mitigate against spread.

Classification of biomass reactions and predictions of reaction energies through machine learning.

Elementary steps and intermediate species of linearly structured biomass compounds are studied. Specifically, possible intermediates and elementary reactions of 15 key biomass compounds and 33 small molecules are obtained from a recursive bond-breaking algorithm. These are used as inputs to the unsupervised Mol2Vec algorithm to generate vector representations of all intermediates and elementary reactions. The vector descriptors are used to identify sub-classes of elementary steps, and linear discriminant analysis is used to accurately identify the reaction type and reduce the dimension of the vectors. The resulting descriptors are applied to predict gas-phase reaction energies using linear regression with accuracies that exceed the commonly employed group additivity approach. They are also applied to quantitatively assess model compound similarity, and the results are consistent with chemical intuition. This workflow for creating vector representations of complex molecular systems requires no input from electronic structure calculations, and it is expected to be applicable to other similar systems where vector representations are needed.

The Role of Adventitious Carbon in Photo-catalytic Nitrogen Fixation by Titania.

Photo-catalytic fixation of nitrogen by titania catalysts at ambient conditions has been reported for decades, yet the active site capable of adsorbing an inert N2 molecule at ambient pressure and the mechanism of dissociating the strong dinitrogen triple bond at room temperature remain unknown. In this work in situ near-ambient-pressure X-ray photo-electron spectroscopy and density functional theory calculations are used to probe the active state of the rutile (110) surface. The experimental results indicate that photon-driven interaction of N2 and TiO2 is observed only if adventitious surface carbon is present, and computational results show a remarkably strong interaction between N2 and carbon substitution (C*) sites that act as surface-bound carbon radicals. A carbon-assisted nitrogen reduction mechanism is proposed and shown to be thermodynamically feasible. The findings provide a molecular-scale explanation for the long-standing mystery of photo-catalytic nitrogen fixation on titania. The results suggest that controlling and characterizing carbon-based active sites may provide a route to engineering more efficient photo(electro)-catalysts and improving experimental reproducibility.

A Highly Active Molybdenum Phosphide Catalyst for Methanol Synthesis from CO and CO2.

Methanol is a major fuel and chemical feedstock currently produced from syngas, a CO/CO2 /H2 mixture. Herein we identify formate binding strength as a key parameter limiting the activity and stability of known catalysts for methanol synthesis in the presence of CO2 . We present a molybdenum phosphide catalyst for CO and CO2 reduction to methanol, which through a weaker interaction with formate, can improve the activity and stability of methanol synthesis catalysts in a wide range of CO/CO2 /H2 feeds.

To address surface reaction network complexity using scaling relations machine learning and DFT calculations.

Surface reaction networks involving hydrocarbons exhibit enormous complexity with thousands of species and reactions for all but the very simplest of chemistries. We present a framework for optimization under uncertainty for heterogeneous catalysis reaction networks using surrogate models that are trained on the fly. The surrogate model is constructed by teaching a Gaussian process adsorption energies based on group additivity fingerprints, combined with transition-state scaling relations and a simple classifier for determining the rate-limiting step. The surrogate model is iteratively used to predict the most important reaction step to be calculated explicitly with computationally demanding electronic structure theory. Applying these methods to the reaction of syngas on rhodium(111), we identify the most likely reaction mechanism. Propagating uncertainty throughout this process yields the likelihood that the final mechanism is complete given measurements on only a subset of the entire network and uncertainty in the underlying density functional theory calculations.

Intrinsic Selectivity and Structure Sensitivity of Rhodium Catalysts for C(2+) Oxygenate Production.

Synthesis gas (CO + H2) conversion is a promising route to converting coal, natural gas, or biomass into synthetic liquid fuels. Rhodium has long been studied as it is the only elemental catalyst that has demonstrated selectivity to ethanol and other C2+ oxygenates. However, the fundamentals of syngas conversion over rhodium are still debated. In this work a microkinetic model is developed for conversion of CO and H2 into methane, ethanol, and acetaldehyde on the Rh (211) and (111) surfaces, chosen to describe steps and close-packed facets on catalyst particles. The model is based on DFT calculations using the BEEF-vdW functional. The mean-field kinetic model includes lateral adsorbate-adsorbate interactions, and the BEEF-vdW error estimation ensemble is used to propagate error from the DFT calculations to the predicted rates. The model shows the Rh(211) surface to be ∼6 orders of magnitude more active than the Rh(111) surface, but highly selective toward methane, while the Rh(111) surface is intrinsically selective toward acetaldehyde. A variety of Rh/SiO2 catalysts are synthesized, tested for catalytic oxygenate production, and characterized using TEM. The experimental results indicate that the Rh(111) surface is intrinsically selective toward acetaldehyde, and a strong inverse correlation between catalytic activity and oxygenate selectivity is observed. Furthermore, iron impurities are shown to play a key role in modulating the selectivity of Rh/SiO2 catalysts toward ethanol. The experimental observations are consistent with the structure-sensitivity predicted from theory. This work provides an improved atomic-scale understanding and new insight into the mechanism, active site, and intrinsic selectivity of syngas conversion over rhodium catalysts and may also guide rational design of alloy catalysts made from more abundant elements.

Analyzing the Case for Bifunctional Catalysis.

Bifunctional coupling of two different catalytic site types has often been invoked to explain experimentally observed enhanced catalytic activities. We scrutinize such claims with generic scaling-relation-based microkinetic models that allow exploration of the theoretical limits for such a bifunctional gain for several model reactions. For sites at transition-metal surfaces, the universality of the scaling relations between adsorption energies largely prevents any improvements through bifunctionality. Only the consideration of systems that involve the combination of different materials, such as metal particles on oxide supports, offers hope for significant bifunctional gains.

Catalysis. Assessing the reliability of calculated catalytic ammonia synthesis rates.

We introduce a general method for estimating the uncertainty in calculated materials properties based on density functional theory calculations. We illustrate the approach for a calculation of the catalytic rate of ammonia synthesis over a range of transition-metal catalysts. The correlation between errors in density functional theory calculations is shown to play an important role in reducing the predicted error on calculated rates. Uncertainties depend strongly on reaction conditions and catalyst material, and the relative rates between different catalysts are considerably better described than the absolute rates. We introduce an approach for incorporating uncertainty when searching for improved catalysts by evaluating the probability that a given catalyst is better than a known standard.