Scaled and Dynamic Optimizations of Nudged Elastic Bands

Assessing plasmon-induced reactions by a combined quantum chemical-quantum/classical hybrid approach

Plasmon-driven reactions on metal nanoparticles feature rich and complex mechanistic contributions, involving a manifold of electronic states, near-field enhancement, and heat, among others. Although localized surface plasmon resonances are believed to initiate these reactions, the complex reactivity demands deeper exploration. This computational study investigates factors influencing chemical processes on plasmonic nanoparticles, exemplified by protonation of 4-mercaptopyridine (4-MPY) on silver nanoparticles. We examine the impact of molecular binding modes and molecule-molecule interactions on the nanoparticle's surface, near-field electromagnetic effects, and charge-transfer phenomena. Two proton sources were considered at ambient conditions, molecular hydrogen and water. Our findings reveal that the substrate's binding mode significantly affects not only the energy barriers governing the thermodynamics and kinetics of the reaction but also determine the directionality of light-driven charge-transfer at the 4-MPY-Ag interface, pivotal in the chemical contribution involved in the reaction mechanism. In addition, significant field enhancement surrounding the adsorbed molecule is observed (eletromagnetic contribution) which was found insufficient to modify the ground state thermodynamics. Instead, it initiates and amplifies light-driven charge-transfer and thus modulates the excited states' reactivity in the plasmonic-molecular hybrid system. This research elucidates protonation mechanisms on silver surfaces, highlighting the role of molecular-surface and molecule-molecule-surface orientation in plasmon-catalysis.

Emerging Atomistic Modeling Methods for Heterogeneous Electrocatalysis

Heterogeneous electrocatalysis lies at the center of various technologies that could help enable a sustainable future. However, its complexity makes it challenging to accurately and efficiently model at an atomic level. Here, we review emerging atomistic methods to simulate the electrocatalytic interface with special attention devoted to the components/effects that have been challenging to model, such as solvation, electrolyte ions, electrode potential, reaction kinetics, and pH. Additionally, we review relevant computational spectroscopy methods. Then, we showcase several examples of applying these methods to understand and design catalysts relevant to green hydrogen. We also offer experimental views on how to bridge the gap between theory and experiments. Finally, we provide some perspectives on opportunities to advance the field.

Computational analysis of R-X oxidative addition to Pd nanoparticles

Oxidative addition (OA) is a necessary step in mechanisms of widely used synthetic methodologies such as the Heck reaction, cross-coupling reactions, and the Buchwald-Hartwig amination. This study pioneers the exploration of OA of aryl halide to palladium nanoparticles (NPs), a process previously unaddressed in contrast to the activity of well-studied Pd(0) complexes. Employing DFT modeling and semi-empirical metadynamics simulations, the oxidative addition of phenyl bromide to Pd nanoparticles was investigated in detail. Energy profiles of oxidative addition to Pd NPs were analyzed and compared to those involving Pd(0) complexes forming under both ligand-stabilized (phosphines) and ligandless (amine base) conditions. Metadynamics simulations highlighted the edges of the (1 1 1) facets of Pd NPs as the key element of oxidative addition activity. We demonstrate that OA to Pd NPs is not only kinetically facile at ambient temperatures but also thermodynamically favorable. This finding accentuates the necessity of incorporating OA to Pd NPs in future investigations, thus providing a more realistic view of the involved catalytic mechanisms. These results enhance the understanding of aryl halide (cross-)coupling reactions, reinforcing the concept of a catalytic "cocktail". This concept posits dynamic interconversions between diverse active and inactive centers, collectively affecting the outcome of the reaction. High activity of Pd NPs in direct C-X activation paves the way for novel approaches in catalysis, potentially enhancing the field and offering new catalytic pathways to consider.

The Importance of Reaction Energy in Predicting Chemical Reaction Barriers with Machine Learning Models

Improving our fundamental understanding of complex heterocatalytic processes increasingly relies on electronic structure simulations and microkinetic models based on calculated energy differences. In particular, calculation of activation barriers, usually achieved through compute-intensive saddle point search routines, remains a serious bottleneck in understanding trends in catalytic activity for highly branched reaction networks. Although the well-known Brønsted-Evans-Polyani (BEP) scaling - a one-feature linear regression model - has been widely applied in such microkinetic models, they still rely on calculated reaction energies and may not generalize beyond a single facet on a single class of materials, e. g., a terrace sites on transition metals. For highly branched and energetically shallow reaction networks, such as electrochemical CO2 reduction or wastewater remediation, calculating even reaction energies on many surfaces can become computationally intractable due to the combinatorial explosion of states that must be considered. Here, we investigate the feasibility of activation barrier prediction without knowledge of the reaction energy using linear and nonlinear machine learning (ML) models trained on a new database of over 500 dehydrogenation activation barriers. We also find that inclusion of the reaction energy significantly improves both classes of ML models, but complex nonlinear models can achieve performance similar to the simplest BEP scaling when predicting activation barriers on new systems. Additionally, inclusion of the reaction energy significantly improves generalizability to new systems beyond the training set. Our results suggest that the reaction energy is a critical feature to consider when building models to predict activation barriers, indicating that efforts to reliably predict reaction energies through, e. g., the Open Catalyst Project and others, will be an important route to effective model development for more complex systems.

Area-selective atomic layer deposition on 2D monolayer lateral superlattices

The advanced patterning process is the basis of integration technology to realize the development of next-generation high-speed, low-power consumption devices. Recently, area-selective atomic layer deposition (AS-ALD), which allows the direct deposition of target materials on the desired area using a deposition barrier, has emerged as an alternative patterning process. However, the AS-ALD process remains challenging to use for the improvement of patterning resolution and selectivity. In this study, we report a superlattice-based AS-ALD (SAS-ALD) process using a two-dimensional (2D) MoS2-MoSe2 lateral superlattice as a pre-defining template. We achieved a minimum half pitch size of a sub-10 nm scale for the resulting AS-ALD on the 2D superlattice template by controlling the duration time of chemical vapor deposition (CVD) precursors. SAS-ALD introduces a mechanism that enables selectivity through the adsorption and diffusion processes of ALD precursors, distinctly different from conventional AS-ALD method. This technique facilitates selective deposition even on small pattern sizes and is compatible with the use of highly reactive precursors like trimethyl aluminum. Moreover, it allows for the selective deposition of a variety of materials, including Al2O3, HfO2, Ru, Te, and Sb2Se3.

GPAW: An open Python package for electronic structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Impact of palladium/palladium hydride conversion on electrochemical CO2 reduction via in-situ transmission electron microscopy and diffraction

Electrochemical conversion of CO2 offers a sustainable route for producing fuels and chemicals. Pd-based catalysts are effective for converting CO2 into formate at low overpotentials and CO/H2 at high overpotentials, while undergoing poorly understood morphology and phase structure transformations under reaction conditions that impact performance. Herein, in-situ liquid-phase transmission electron microscopy and select area diffraction measurements are applied to track the morphology and Pd/PdHx phase interconversion under reaction conditions as a function of electrode potential. These studies identify the degradation mechanisms, including poisoning and physical structure changes, occurring in PdHx/Pd electrodes. Constant potential density functional theory calculations are used to probe the reaction mechanisms occurring on the PdHx structures observed under reaction conditions. Microkinetic modeling reveals that the intercalation of *H into Pd is essential for formate production. However, the change in electrochemical CO2 conversion selectivity away from formate and towards CO/H2 at increasing overpotentials is due to electrode potential dependent changes in the reaction energetics and not a consequence of morphology or phase structure changes.

Transferable Machine Learning Interatomic Potential for Bond Dissociation Energy Prediction of Drug-like Molecules

We present a transferable MACE interatomic potential that is applicable to open- and closed-shell drug-like molecules containing hydrogen, carbon, and oxygen atoms. Including an accurate description of radical species extends the scope of possible applications to bond dissociation energy (BDE) prediction, for example, in the context of cytochrome P450 (CYP) metabolism. The transferability of the MACE potential was validated on the COMP6 data set, containing only closed-shell molecules, where it reaches better accuracy than the readily available general ANI-2x potential. MACE achieves similar accuracy on two CYP metabolism-specific data sets, which include open- and closed-shell structures. This model enables us to calculate the aliphatic C-H BDE, which allows us to compare reaction energies of hydrogen abstraction, which is the rate-limiting step of the aliphatic hydroxylation reaction catalyzed by CYPs. On the "CYP 3A4" data set, MACE achieves a BDE RMSE of 1.37 kcal/mol and better prediction of BDE ranks than alternatives: the semiempirical AM1 and GFN2-xTB methods and the ALFABET model that directly predicts bond dissociation enthalpies. Finally, we highlight the smoothness of the MACE potential over paths of sp3C-H bond elongation and show that a minimal extension is enough for the MACE model to start finding reasonable minimum energy paths of methoxy radical-mediated hydrogen abstraction. Altogether, this work lays the ground for further extensions of scope in terms of chemical elements, (CYP-mediated) reaction classes and modeling the full reaction paths, not only BDEs.

Fundamental Drivers of Electrochemical Barriers

We find that ion creation and destruction dominate the behavior of electrochemical reaction barriers, through grand-canonical electronic structure calculations of proton deposition on transition metal surfaces. We show that barriers respond to potential in a nonlinear manner and trace this to the continuous degree of electron transfer as an ion is created or destroyed. This explains both Marcus-like curvature and Hammond-like shifts. Across materials, we find the barrier energy to be driven primarily by the charge presented on the surface, which, in turn, is dictated by the native work function, a fundamentally different driving force than in nonelectrochemical systems.

Controlled Electrochemical Barrier Calculations without Potential Control

The knowledge of electrochemical activation energies under applied potential conditions is a prerequisite for understanding catalytic activity at electrochemical interfaces. Here, we present a new set of methods that can compute electrochemical barriers with accuracy comparable to that of constant potential grand canonical approaches, without the explicit need for a potentiostat. Instead, we Legendre transform a set of constant charge, canonical reaction paths. Additional straightforward approximations offer the possibility to compute electrochemical barriers at a fraction of computational cost and complexity, and the analytical inclusion of geometric response highlights the importance of incorporating electronic as well as the geometric degrees of freedom when evaluating electrochemical barriers.

Pynta─An Automated Workflow for Calculation of Surface and Gas-Surface Kinetics

Many important industrial processes rely on heterogeneous catalytic systems. However, given all possible catalysts and conditions of interest, it is impractical to optimize most systems experimentally. Automatically generated microkinetic models can be used to efficiently consider many catalysts and conditions. However, these microkinetic models require accurate estimation of many thermochemical and kinetic parameters. Manually calculating these parameters is tedious and error prone, involving many interconnected computations. We present Pynta, a workflow software for automating the calculation of surface and gas-surface reactions. Pynta takes the reactants, products, and atom maps for the reactions of interest, generates sets of initial guesses for all species and saddle points, runs all optimizations, frequency, and IRC calculations, and computes the associated thermochemistry and rate coefficients. It is able to consider all unique adsorption configurations for both adsorbates and saddle points, allowing it to handle high index surfaces and bidentate species. Pynta implements a new saddle point guess generation method called harmonically forced saddle point searching (HFSP). HFSP defines harmonic potentials based on the optimized adsorbate geometries and which bonds are breaking and forming that allow initial placements to be optimized using the GFN1-xTB semiempirical method to create reliable saddle point guesses. This method is reaction class agnostic and fast, allowing Pynta to consider all possible adsorbate site placements efficiently. We demonstrate Pynta on 11 diverse reactions involving monodenate, bidentate, and gas-phase species, many distinct reaction classes, and both a low and a high index facet of Cu. Our results suggest that it is very important to consider reactions between adsorbates adsorbed in all unique configurations for interadsorbate group transfers and reactions on high index surfaces.

Ultralow reaction barriers for CO oxidation in Cu-Au nanoclusters

Systematic structure prediction of CunAum nanoclusters was carried out for a wide compositional area (n + m ≤ 15) using the evolutionary algorithm USPEX and DFT calculations. The obtained structural data allowed us to assess the local stability of clusters and their suitability for catalysis of CO oxidation. Using these two criteria, we selected several most promising clusters for an accurate study of their catalytic properties. The adsorption energies of reagents, reaction paths, and activation energies were calculated. We found several cases with low activation energies and explained these cases using the patterns of structural change at the moment of CO2 desorption. The unique case is the Cu7Au6 cluster, which has extremely low activation energies for all transition states (below 0.05 eV). We thus showed that higher flexibility due to the binary nature of nanoclusters makes it possible to achieve the maximum catalytic activity. Considering the lower price of copper, Cu-Au nanoparticles are a promising new family of catalysts.

Inverted Region in Electrochemical Reduction of CO2 Induced by Potential-Dependent Pauli Repulsion

Electrochemical CO₂ reduction reaction (eCO₂RR) is of great significance to energy and environmental engineering, while fundamental questions remain regarding its mechanisms. Herein, we formulate a fundamental understanding of the interplay between the applied potential (U) and kinetics of CO₂ activation in eCO₂RR on Cu surfaces. We find that the nature of the CO₂ activation mechanism in eCO₂RR varies with U, and it is the sequential electron-proton transfer (SEPT) mechanism dominant at the working U but switched to the concerted proton-electron transfer (CPET) mechanism at highly negative U. We then identify that the barrier of the electron-transfer step in the SEPT mechanism exhibits an inverted region as U decreases, which originates from the rapidly rising Pauli repulsion in the physisorption of CO₂ with decreasing U. We further demonstrate catalyst designs that effectively suppress the adverse effect of Pauli repulsion. This fundamental understanding may be general for the electrochemical reduction reactions of closed-shell molecules.

Dual Function of Hypo-d-electronic Transition Metals in the Brewer Intermetallic Phase for the Highly Efficient Electrocatalytic Hydrogen Evolution Reaction in Alkaline Electrolytes

Reported are the synthesis, material characterization, and electrocatalytic hydrogen evolution reaction (HER) in acid and alkaline electrolytes for the Brewer intermetallic phase, Nb₆Co₇ and Mo₆Co₇. It was realized that the overpotential at a current density of 10 mA/cm² (η₁₀) for Nb₆Co₇ (η₁₀ = 62 mV) and Mo₆Co₇ (η₁₀ = 143 mV) are both much lower than that of using a single Co metal (η₁₀ = 253 mV) in alkaline electrolytes. The enhancement of electrocatalytic HER activity of Nb₆Co₇ and Mo₆Co₇ can be attributed to the hypo-hyper-d-electronic interaction between Nb/Mo and Co elements. Based on the result of density functional theory calculation, alloying between Nb/Mo and Co elements will increase the antibonding state population of the Co-Co bond near the Fermi level (E_F), which induces the synergistic effect to influence the adsorption energy of the H atom (ΔG_H) on the surface of Nb₆Co₇ and Mo₆Co₇. Moreover, the role of the Nb element is not only a simple electron donor but is also an anchor position for the OH molecule (i.e., dual function) due to the bonding character of the Nb-Co bond near E_F. It can reduce the OH position effect as well as the activation energy for water dissociation, which rationalizes the high and robust HER performance of Nb₆Co₇ to that of commercial Pt/C (η₁₀ = 67 mV) in alkaline electrolytes.

Electrochemistry from the atomic scale, in the electronically grand-canonical ensemble

The ability to simulate electrochemical reactions from first-principles has advanced significantly in recent years. Here, we discuss the atomistic interpretation of electrochemistry at three scales: from the electronic structure to elementary processes to constant-potential reactions. At each scale, we highlight the importance of the grand-canonical nature of the process and show that the grand-canonical energy is the natural thermodynamic state variable, which has the additional benefit of simplifying calculations. We show that atomic forces are the derivative of the grand-potential energy when the potential is fixed. We further examine the meaning of potential at the atomic scale and its link to the chemical potential and discuss the link between charge transfer and potential in several situations.

Generalizable Trends in Electrochemical Protonation Barriers

Predicting activation energies for reaction steps is essential for modeling catalytic processes, but accurate barrier simulations often require considerable computational expense, especially for electrochemical reactions. Given the challenges of barrier computations and the growing promise of electrochemical routes for various processes, generalizable energetic trends in electrochemistry can significantly aid in analyzing reaction networks and building microkinetic models. Herein, we employ density functional theory and machine learning nudged elastic band models to simulate electrochemical protonation of *C, *N, and *O monatomic adsorbates from hydronium on a series of transition metal surfaces. We observe a consistent trend of decreasing protonation reaction energies yet increasing activation barriers from *O to *N to *C. Analysis of bond orders and reaction pathways provides insight into the origin of the observed trends in protonation energetics. We hypothesize that these results are relevant for polyatomic adsorbates, which can simplify analysis of reaction mechanisms and inform catalyst design.

Modified Single Iteration Synchronous-Transit Approach to Bound Diffusion Barriers for Solid-State Reactions

Herein, we detail an approach to accelerate the computational screening of materials for properties dictated by the kinetics of solid-state diffusion through reliably and rapidly identifying upper and lower bounds to the transition state (TS) energy through our proposed modified single iteration synchronous-transit (MSIST) approach. While this sacrifices providing detailed information of the explicit TS structure, it requires only 30% of the force evaluations of a full nudged elastic band (NEB) TS search and reduces the computational demand to compute estimated diffusion barriers by ∼70% on average. In all 53 cases in which we explicitly compared our results to those of an NEB calculation, the upper and lower bounds identified using this approach bracketed the TS energy calculated with explicit NEB calculations. We use the applications of diffusion of Na⁺ in potential sodium-ion battery electrodes and oxygen vacancy diffusion in solid-oxide fuel cell electrodes and redox mediators for solar thermochemical hydrogen production to demonstrate the power of MSIST for analyzing the kinetics of bulk diffusion. For Na⁺ diffusion through 13 proposed electrode materials in which the average diffusion barrier was 0.28 eV, the average difference between the upper and lower bounds was 0.08 eV. An iterative application of this approach to the three materials with the largest difference between their upper and lower bounds further narrowed the average range of the bounded TS energies to 0.04 eV while still requiring fewer force evaluations than an NEB TS calculation. When applied in a high-throughput manner to study 514 diffusion pathways in 97 different materials, the average difference between the upper and lower bounds was 0.33 eV and the average barrier, as calculated by the average of all upper and lower bounds, was ∼1.7 eV. Because the MSIST approach produces explicit errors, i.e., the difference between the upper and lower bounds energies, even predicted barrier ranges with large errors can be reliably modeled with weighted regression techniques. MSIST enables the analysis of the kinetics of solid-state diffusion across larger sets of materials and can thus efficiently provide data to train statistically learned models of diffusion and to develop physical insights into the diffusion process.