Long-Range Uniform Deposition of Ag Nanoseed on Cu Current Collector for High-Performance Lithium Metal Batteries.

Uniform lithium deposition is essential to hinder dendritic growth. Achieving this demands even seed material distribution across the electrode, posing challenges in correlating the electrode's surface structure with the uniformity of seed material distribution. In this study, the effect of periodic surface and facet orientation on seed distribution is investigated using a model system consisting of a wrinkled copper (Cu)/graphene structure with a [100] facet orientation. A new methodology is developed for uniformly distributed silver (Ag) nanoparticles over a large area by controlling the surface features of Cu substrates. The regularly arranged Ag nanoparticles, with a diameter of 26.4 nm, are fabricated by controlling the Cu surface condition as [100]-oriented wrinkled Cu. The wrinkled Cu guides a deposition site for spherical Ag nanoparticles, the [100] facet determines the Ag morphology, and the presence of graphene leads to spacings of Ag seeds. This patterned surface and high lithiophilicity, with homogeneously distributed Ag nanoparticles, lead to uniform Li+ flux and reduced nucleation energy barrier, resulting in excellent battery performance. The electrochemical measurements exhibit improved cyclic stability over 260 cycles at 0.5 mA cm-2 and 100 cycles at 1.0 mA cm-2 and enhanced kinetics even under a high current density of 5.0 mA cm-2.

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.

A nearsighted force-training approach to systematically generate training data for the machine learning of large atomic structures.

A challenge of atomistic machine-learning (ML) methods is ensuring that the training data are suitable for the system being simulated, which is particularly challenging for systems with large numbers of atoms. Most atomistic ML approaches rely on the nearsightedness principle ("all chemistry is local"), using information about the position of an atom's neighbors to predict a per-atom energy. In this work, we develop a framework that exploits the nearsighted nature of ML models to systematically produce an appropriate training set for large structures. We use a per-atom uncertainty estimate to identify the most uncertain atoms and extract chunks centered around these atoms. It is crucial that these small chunks are both large enough to satisfy the ML's nearsighted principle (that is, filling the cutoff radius) and are large enough to be converged with respect to the electronic structure calculation. We present data indicating when the electronic structure calculations are converged with respect to the structure size, which fundamentally limits the accuracy of any nearsighted ML calculator. These new atomic chunks are calculated in electronic structures, and crucially, only a single force-that of the central atom-is added to the growing training set, preventing the noisy and irrelevant information from the piece's boundary from interfering with ML training. The resulting ML potentials are robust, despite requiring single-point calculations on only small reference structures and never seeing large training structures. We demonstrated our approach via structure optimization of a 260-atom structure and extended the approach to clusters with up to 1415 atoms.

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.

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.

On the Coupling of Electron Transfer to Proton Transfer at Electrified Interfaces.

Many electrochemical processes are governed by the transfer of protons to the surface, which can be coupled with electron transfer; this electron transfer is in general non-integer and unknown a priori, but is required to hold the potential constant. In this study, we employ a combination of surface spectroscopic techniques and grand-canonical electronic-structure calculations in order to rigorously understand the thermodynamics of this process. Specifically, we explore the protonation/deprotonation of 4-mercaptobenzoic acid as a function of the applied potential. Using grand-canonical electronic-structure calculations, we directly infer the coupled electron transfer, which we find to be on the order of 0.1 electron per proton; experimentally, we also access this quantity via the potential-dependence of the pKa. We show a striking agreement between the potential-dependence of the measured pKa and that calculated with electronic-structure calculations. We further employ a simple electrostatics-based model to show that this slope can equivalently be interpreted to provide information on the degree of coupled electron transfer or the potential change at the point of the charged species.

Anisotropic Strain Tuning of L10 Ternary Nanoparticles for Oxygen Reduction.

Tuning the performance of nanoparticle (NP) catalysts by controlling the NP surface strain has evolved as an important strategy to optimize NP catalysis in many energy conversion reactions. Here, we present our new study on using an eigenforce model to predict and experiments to verify the strain-induced catalysis enhancement of the oxygen reduction reaction (ORR) in the presence of L10-CoMPt NPs (M = Mn, Fe, Ni, Cu, Ni). The eigenforce model allowed us to predict anisotropic (that is, two-dimensional) strain levels on distorted Pt(111) surfaces. Experimentally, by preparing a series of 5 nm L10-CoMPt NPs, we could push the ORR catalytic activity of these NPs toward the optimum region of the theoretical two-dimensional volcano plot predicted for L10-CoMPt. The best ORR catalyst in the alloy NP series we studied is L10-CoNiPt, which has a mass activity of 3.1 A/mgPt and a specific activity of 9.3 mA/cm2 at room temperature with only 15.9% loss of mass activity after 30 000 cycles at 60 °C in 0.1 M HClO4.

Face-centered tetragonal (FCT) Fe and Co alloys of Pt as catalysts for the oxygen reduction reaction (ORR): A DFT study.

Proton exchange membrane fuel cells (PEMFCs) are promising candidates for alternate energy conversion devices owing to their various advantages including high efficiency, reliability, and environmental friendliness. The performance of PEMFCs is fundamentally limited by the sluggish kinetics of the oxygen reduction reaction (ORR) at the cathode. Various studies have addressed myriads of Pt-based alloys as potential catalysts for ORR. However, most of these studies only focus on the cubic-structured Pt-based alloys which require further improvements especially in terms of stability and required loading. In this work, we perform first-principle density functional theory calculations to explore Fe and Co alloys of Pt in a different face centered tetragonal (L10) geometry as potential catalysts for ORR. The work focuses on understanding the reaction mechanism of ORR by both dissociative and associative mechanisms on L10-FePt/Pt(111) and L10-CoPt/Pt(111) surfaces. The binding pattern of each reaction intermediate is studied along with the complete reaction free energy landscape as a function of Pt overlayers. The L10-FePt/Pt(111) and L10-CoPt/Pt(111) surfaces show higher calculated surface activity for ORR as compared to the native fcc Pt(111) surface. The decrease in the required overpotential (η) for the alloys with respect to the unstrained Pt(111) surface is found to be in the range (0.04 V-0.25 V) assuming the dissociative mechanism and (0.02 V-0.10 V) assuming the associative mechanism, where the variation depends on the thickness of Pt overlayers. We further correlate the binding behavior of the reaction intermediates to the applied biaxial strain on the Pt(111) surface with the help of a mechanical eigenforce model. The eigenforce model gives a (semi-) quantitative prediction of the binding energies of the ORR intermediates under applied biaxial strain. The numerical values of the limiting potential (UL) obtained from the eigenforce model are found to be very close to ones obtained from electronic structure calculations (less than 0.1 V difference). The eigenforce model is further used to predict the ideal equi-biaxial strain range required on Pt(111) surfaces for optimum ORR activity.

The potential for machine learning in hybrid QM/MM calculations.

Hybrid quantum-mechanics/molecular-mechanics (QM/MM) simulations are popular tools for the simulation of extended atomistic systems, in which the atoms in a core region of interest are treated with a QM calculator and the surrounding atoms are treated with an empirical potential. Recently, a number of atomistic machine-learning (ML) tools have emerged that provide functional forms capable of reproducing the output of more expensive electronic-structure calculations; such ML tools are intriguing candidates for the MM calculator in QM/MM schemes. Here, we suggest that these ML potentials provide several natural advantages when employed in such a scheme. In particular, they may allow for newer, simpler QM/MM frameworks while also avoiding the need for extensive training sets to produce the ML potential. The drawbacks of employing ML potentials in QM/MM schemes are also outlined, which are primarily based on the added complexity to the algorithm of training and re-training ML models. Finally, two simple illustrative examples are provided which show the power of adding a retraining step to such "QM/ML" algorithms.

Addressing uncertainty in atomistic machine learning.

Machine-learning regression has been demonstrated to precisely emulate the potential energy and forces that are output from more expensive electronic-structure calculations. However, to predict new regions of the potential energy surface, an assessment must be made of the credibility of the predictions. In this perspective, we address the types of errors that might arise in atomistic machine learning, the unique aspects of atomistic simulations that make machine-learning challenging, and highlight how uncertainty analysis can be used to assess the validity of machine-learning predictions. We suggest this will allow researchers to more fully use machine learning for the routine acceleration of large, high-accuracy, or extended-time simulations. In our demonstrations, we use a bootstrap ensemble of neural network-based calculators, and show that the width of the ensemble can provide an estimate of the uncertainty when the width is comparable to that in the training data. Intriguingly, we also show that the uncertainty can be localized to specific atoms in the simulation, which may offer hints for the generation of training data to strategically improve the machine-learned representation.

Acceleration of saddle-point searches with machine learning.

In atomistic simulations, the location of the saddle point on the potential-energy surface (PES) gives important information on transitions between local minima, for example, via transition-state theory. However, the search for saddle points often involves hundreds or thousands of ab initio force calls, which are typically all done at full accuracy. This results in the vast majority of the computational effort being spent calculating the electronic structure of states not important to the researcher, and very little time performing the calculation of the saddle point state itself. In this work, we describe how machine learning (ML) can reduce the number of intermediate ab initio calculations needed to locate saddle points. Since machine-learning models can learn from, and thus mimic, atomistic simulations, the saddle-point search can be conducted rapidly in the machine-learning representation. The saddle-point prediction can then be verified by an ab initio calculation; if it is incorrect, this strategically has identified regions of the PES where the machine-learning representation has insufficient training data. When these training data are used to improve the machine-learning model, the estimates greatly improve. This approach can be systematized, and in two simple example problems we demonstrate a dramatic reduction in the number of ab initio force calls. We expect that this approach and future refinements will greatly accelerate searches for saddle points, as well as other searches on the potential energy surface, as machine-learning methods see greater adoption by the atomistics community.

The Influence of Elastic Strain on Catalytic Activity in the Hydrogen Evolution Reaction.

Understanding the role of elastic strain in modifying catalytic reaction rates is crucial for catalyst design, but experimentally, this effect is often coupled with a ligand effect. To isolate the strain effect, we have investigated the influence of externally applied elastic strain on the catalytic activity of metal films in the hydrogen evolution reaction (HER). We show that elastic strain tunes the catalytic activity in a controlled and predictable way. Both theory and experiment show strain controls reactivity in a controlled manner consistent with the qualitative predictions of the HER volcano plot and the d-band theory: Ni and Pt's activities were accelerated by compression, while Cu's activity was accelerated by tension. By isolating the elastic strain effect from the ligand effect, this study provides a greater insight into the role of elastic strain in controlling electrocatalytic activity.

Oxygen-induced changes to selectivity-determining steps in electrocatalytic CO2 reduction.

The state of the electrocatalyst surface-including the oxidation state of the catalyst and the presence of spectator species-is investigated on Cu surfaces with density functional theory in order to understand predicted ramifications on the selectivity and efficiency of CO2 reduction. We examined the presence of oxygen-based species, including the fully oxidized Cu2O surface, the partially oxidized Cu(110)-(2 × 1)O surface, and the presence of OH spectators. The relative oxygen binding strength among these surfaces can help to explain the experimentally observed selectivity change between CH4 and CH3OH on these electrodes; this suggests that the oxygen-binding strength may be a key parameter which predicts the thermodynamically preferred selectivity for pathways proceeding through a methoxy (CH3O) intermediate. This study shows the importance of the local surface environment in the product selectivity of electrocatalysis, and suggests a simple descriptor that can aid in the design of improved electrocatalytic materials.

Active and selective conversion of CO2 to CO on ultrathin Au nanowires.

In this communication, we show that ultrathin Au nanowires (NWs) with dominant edge sites on their surface are active and selective for electrochemical reduction of CO2 to CO. We first develop a facile seed-mediated growth method to synthesize these ultrathin (2 nm wide) Au NWs in high yield (95%) by reducing HAuCl4 in the presence of 2 nm Au nanoparticles (NPs). These NWs catalyze CO2 reduction to CO in aqueous 0.5 M KHCO3 at an onset potential of -0.2 V (vs reversible hydrogen electrode). At -0.35 V, the reduction Faradaic efficiency (FE) reaches 94% (mass activity 1.84 A/g Au) and stays at this level for 6 h without any noticeable activity change. Density functional theory (DFT) calculations suggest that the excellent catalytic performance of these Au NWs is attributed both to their high mass density of reactive edge sites (≥16%) and to the weak CO binding on these sites. These ultrathin Au NWs are the most efficient nanocatalyst ever reported for electrochemical reduction of CO2 to CO.

Monodisperse Au nanoparticles for selective electrocatalytic reduction of CO2 to CO.

We report selective electrocatalytic reduction of carbon dioxide to carbon monoxide on gold nanoparticles (NPs) in 0.5 M KHCO3 at 25 °C. Among monodisperse 4, 6, 8, and 10 nm NPs tested, the 8 nm Au NPs show the maximum Faradaic efficiency (FE) (up to 90% at -0.67 V vs reversible hydrogen electrode, RHE). Density functional theory calculations suggest that more edge sites (active for CO evolution) than corner sites (active for the competitive H2 evolution reaction) on the Au NP surface facilitates the stabilization of the reduction intermediates, such as COOH*, and the formation of CO. This mechanism is further supported by the fact that Au NPs embedded in a matrix of butyl-3-methylimidazolium hexafluorophosphate for more efficient COOH* stabilization exhibit even higher reaction activity (3 A/g mass activity) and selectivity (97% FE) at -0.52 V (vs RHE). The work demonstrates the great potentials of using monodisperse Au NPs to optimize the available reaction intermediate binding sites for efficient and selective electrocatalytic reduction of CO2 to CO.

Modeling CO2 reduction on Pt(111).

Density functional theory was used to model the electrochemical reduction of CO2 on Pt(111) with an explicit solvation layer and the presence of extra hydrogen atoms to represent a negatively charged electrode. We focused on the electronic energy barriers for the first four lowest energy proton-electron transfer steps for reducing CO2 on Pt(111) beginning with adsorbed *CO2 and continuing with *COOH, *CO + H2O, *COH, and ending with *C + H2O. We find that simple elementary steps in which a proton is transferred to an adsorbate (such as the protonation of *CO to *COH) have small barriers on the order of 0.1 eV. Elementary steps in which a proton is transferred and a C-O bond is simultaneously cleaved show barriers on the order of 0.5 eV. All barriers calculated for these steps show no sign of being insurmountable at room temperature. To explain why these barriers are so small, we analyze the charge density and the density of states plots to see that first, the electron transfer is decoupled from the proton transfer so that in the initial state, the surface and adsorbate are already charged up and can easily accept the proton from solution. Also, we see that in the cases where barriers are on the order of 0.1 eV, electron density in the initial state localizes on the oxygen end of the adsorbate, while electron density is more spread out on the surface for initial states of the C-O bond cleaving elementary steps.

Modeling Surface Vibrations and Their Role in Molecular Adsorption: A Generalized Langevin Approach.

The atomic vibrations of a solid surface can play a significant role in the reactions of surface-bound molecules, as well as their adsorption and desorption. Relevant phonon modes can involve the collective motion of atoms over a wide array of length scales. In this paper, we demonstrate how the generalized Langevin equation can be utilized to describe these collective motions weighted by their coupling to individual sites. Our approach builds upon the generalized Langevin oscillator (GLO) model originally developed by Tully. We extend the GLO by deriving parameters from atomistic simulation data. We apply this approach to study the memory kernel of a model platinum surface and demonstrate that the memory kernel has a bimodal form due to coupling to both low-energy acoustic modes and high-energy modes near the Debye frequency. The same bimodal form was observed across a wide variety of solids of different elemental compositions, surface structures, and solvation states. By studying how these dominant modes depend on the simulation size, we argue that the acoustic modes are frozen in the limit of macroscopic lattices. By simulating periodically replicated slabs of various sizes, we quantify the influence of phonon confinement effects in the memory kernel and their concomitant effect on simulated sticking coefficients.

The importance of surface morphology in controlling the selectivity of polycrystalline copper for CO2 electroreduction.

This communication examines the effect of the surface morphology of polycrystalline copper on electroreduction of CO(2). We find that a copper nanoparticle covered electrode shows better selectivity towards hydrocarbons compared with the two other studied surfaces, an electropolished copper electrode and an argon sputtered copper electrode. Density functional theory calculations provide insight into the surface morphology effect.

Scaled and Dynamic Optimizations of Nudged Elastic Bands.

We present a modified nudged elastic band routine that can reduce the number of force calls by more than 50% for bands with nonuniform convergence. The method, which we call "dyNEB", dynamically and selectively optimizes images on the basis of the perpendicular PES-derived forces and parallel spring forces acting on that region of the band. The convergence criteria are scaled to focus on the region of interest, i.e., the saddle point, while maintaining continuity of the band and avoiding truncation. We show that this method works well for solid state reaction barriers-nonelectrochemical in general and electrochemical in particular-and that the number of force calls can be significantly reduced without loss of resolution at the saddle point.