Number Of Generalized Coordinates Research Articles

A novel defective PdMo bimetallene with atomic-scale cavities for highly efficient chemicals-assisted hydrogen production

Introducing defects into Pd-based metallene has been shown to significantly enhance its electrocatalytic performance. In this study, we embedded a new type of atomic-scale cavities into the basal plane of PdMo bimetallene (c-PdMo) through precise etching. These cavities introduced tensile strain and increased the generalized coordination number (CN̅), resulting in superior performance in formate oxidation reaction (FOR) and methanol oxidation reaction (MOR), with mass activities of 5.01 mAμgNM−1 and 5.38 mAμgNM−1, respectively. Notably, a two-electrode system comprising commercial Pt/C and c-PdMo coated on carbon paper achieved cell voltages of only 0.517 V and 0.362 V at 10 mA cm−2 for FOR and MOR, respectively. Additionally, density functional theory calculations revealed that the deliberate lattice tensile strain and enhanced coordination numbers reduced the D-band center of defective PdMo, which improved OH adsorption and reduced CO adsorption, thus optimizing FOR and MOR catalysis on the surface of c-PdMo bimetallene.

Fundamental Understanding of Hydrogen Evolution Reaction on Zinc Anode Surface: A First-Principles Study

HighlightsThe reaction mechanisms of hydrogen evolution reaction (HER) on various crystal surfaces of zinc anode have been systematically investigated by first-principle calculations.Both the thermodynamic and kinetic aspects of HER have been studied to reveal the relative HER activity of several crystal surface of zinc anode.The generalized coordination number of surface Zn atoms are proposed as a key descriptor of HER activity of Zn anode.

The ABC of Generalized Coordination Numbers and Their Use as a Descriptor in Electrocatalysis.

The quest for enhanced electrocatalysts can be boosted by descriptor-based analyses. Because adsorption energies are the most common descriptors, electrocatalyst design is largely based on brute-force routines that comb materials databases until an energetic criterion is verified. In this review, it is shown that an alternative is provided by generalized coordination numbers (denoted by or GCN), an inexpensive geometric descriptor for strained and unstrained transition metals and some alloys. captures trends in adsorption energies on both extended surfaces and nanoparticles and is used to elaborate structure-sensitive electrocatalytic activity plots and selectivity maps. Importantly, outlines the geometric configuration of the active sites, thereby enabling an atom-by-atom design, which is not possible using energetic descriptors. Specific examples for various adsorbates (e.g., *OH, *OOH, *CO, and *H), metals (e.g., Pt and Cu), and electrocatalytic reactions (e.g., O2 reduction, H2 evolution, CO oxidation, and reduction) are presented, and comparisons are made against other descriptors.

Complex ligand adsorption on 3D atomic surfaces of synthesized nanoparticles investigated by machine-learning accelerated ab initio calculation.

Nanoparticle surfaces are passivated by surface-bound ligands, and their adsorption on synthesized nanoparticles is complicated because of the intricate and low-symmetry surface structures. Thus, it is challenging to precisely investigate ligand adsorption on synthesized nanoparticles. Here, we applied machine-learning-accelerated ab initio calculation to experimentally resolved 3D atomic structures of Pt nanoparticles to analyze the complex adsorption behavior of polyvinylpyrrolidone (PVP) ligands on synthesized nanoparticles. Different angular configurations of large-sized ligands are thoroughly investigated to understand the adsorption behavior on various surface-exposed atoms with intrinsic low-symmetry. It is revealed that the ligand binding energy (Eads) of the large-sized ligand shows a weak positive relationship with the generalized coordination number . This is because the strong positive relationship of short-range direct bonding (Ebind) is attenuated by the negative relationship of long-range van der Waals interaction (EvdW). In addition, it is demonstrated that the PVP ligands prefer to adsorb where the long-range vdW interaction with the surrounding surface structure is maximized. Our results highlight the significant contribution of vdW interactions and the importance of the local geometry of surface atoms to the adsorption behavior of large-sized ligands on synthesized nanoparticle surfaces.

Using micro-solvation and generalized coordination numbers to estimate the solvation energies of adsorbed hydroxyl on metal nanoparticles.

Solvent-adsorbate interactions have a great impact on catalytic processes in aqueous systems. Implicit solvent calculations are inexpensive but inaccurate toward hydrogen bonds, while a full incorporation of explicit solvation is computationally demanding. Micro-solvation attempts to break this dilemma by including only those solvent molecules directly interacting with the solute and any nearby interfaces, thereby providing a compromise between accuracy and computational expenses. Here, we show that micro-solvation of *OH and its relation to adsorption sites is largely transferable across late transition metal nanoparticles. Solvation energies for *OH on nanoparticles of Ir, Pd, and Pt range from -0.63 ± 0.04 eV to -0.67 ± 0.12 eV, while those on Au and Ag are -0.75 ± 0.07 eV and -1.01 ± 0.05 eV, respectively. These results enable the use of average solvation corrections for *OH on late transition metal nanostructures.

Beyond single-crystal surfaces: The GAL21 water/metal force field.

Solvent effects are notoriously difficult to describe for metallic nanoparticles (NPs). Here, we introduce GAL21 which is the first pairwise additive force field that is specifically designed to modulate the near chemisorption energy of water as a function of the coordination numbers of the metallic atoms. We find a quadratic dependence to be most suitable for capturing the dependence of the adsorption energy of water on the generalized coordination number (GCN) of the metal atoms. GAL21 has been fitted against DFT adsorption energies for Cu, Ag, Au, Ni, Pd, Pt, and Co on 500 configurations and validated on about 3000 configurations for each metal, constructed on five surfaces with GCNs varying from 2.5 to 11.25. Depending on the metals, the root mean square deviation is found between 0.7kcal mol-1 (Au) to 1.6kcal mol-1 (Ni). Using GAL21, as implemented in the open-source code CP2K, we then evaluate the solvation energy of Au55 and Pt55 NPs in water using thermodynamic integration. The solvation free energy is found to be larger for Pt than for Au and systematically larger than 200kcal mol-1, demonstrating the large impact of solvent on the surface energetics of NPs. Still, given that the amorphous NPs are both, the most stable and the most solvated ones, we do not predict a change in the preferred morphology between the gas-phase and in water. Finally, based on a linear regression on three sizes of NPs (from 38 to 147), the solvation energy for Au and Pt surface atoms is found to be -5.2 and -9.9kcal mol-1, respectively.

C2H2 selective hydrogenation over the single-atom Pt1/Cu catalysts: Unraveling the role of Pt active site type and its coordination environment in regulating catalytic performance

To unravel the role of active site type and its coordination environment in regulating catalytic performance, C2H2 selective hydrogenation over a series of single-atom Pt1/Cu catalysts was fully investigated using DFT calculations and microkinetic modeling. Four types of Pt active site, including the defect, step, corner, and terrace sites with the generalized coordination number (GCN) from 2.5 to 7.5, are examined. Our results indicate that Pt1/Cu catalysts with four types of active sites favor gas phase C2H4 formation in C2H2 hydrogenation process. C2H4 activity has an inverted volcanic-type curve relationship with d-band center and GCN of Pt active site. For the polymerization process, the corner and terrace sites with larger GCN values could prevent green oil. The screened PtGCN3.0 catalyst with corner site exhibits better C2H4 selectivity and activity and prevents green oil. Hence, tuning the type and GCN value of Pt active site well regulate C2H4 activity and selectivity, as well as catalyst stability, which provide useful structure information to rationally design Pt-based catalysts in C2H2 selective hydrogenation.

Theoretical Investigation of the Oxygen Reduction Reaction over Platinum Catalysts Supported by Multi‐Edged Vertically Aligned Carbon Nanofiber for Electrocatalyst Preparation

AbstractVertically aligned carbon nanofibers (VACNFs) are promising supports for oxygen reduction reaction (ORR) electrocatalysts in fuel cells. Although experimentally these catalytic systems have shown great potential, there is lack of molecular understanding of the catalytic sites and reaction mechanisms. This work investigated the origin of the ORR reactivities of the platinum catalysts on multi‐edged VACNFs (Pt/VACNF) using a multiscale modeling approach combining Density Functional Theory (DFT) and classical Molecular Dynamics (MD) simulations. Based on the ReaxFF potential, all nanoscale Pt particles (Pt55, P100, and Pt147) are stabilized by the open edges located axially along the VACNF walls. The calculated first‐shell coordination numbers, , of surface Pt atoms are 6.63, 7.27, and 7.85, respectively, suggesting that the percentage of low coordination sites increases as the particle size decreases. The adsorption energies of OOH, O, and OH on Pt55 were systematically probed using DFT calculations. These adsorption energies retain a linear correlation against the generalized coordination numbers ( ). For Pt nanoparticles supported on VACNF, we found that the OOH and OH bind stronger than on Pt (111) by 0.14 and 0.17 eV, respectively, which can hinder the ORR activity with lower limiting potential than Pt (111). Our theoretical prediction is in good agreement with the linear sweeping voltammetry that revealed a left shift of the half‐wave potential.

The formation of high energy density fuel via the hydrogenation of naphthalene over Ni catalyst: The combined DFT and microkinetic analysis

Decalin is the major ingredients of High-energy-density jet fuel JP-900, in which cis-decalin possesses more excellent combustion performance than trans-decalin. The various coordination environments on metal catalysts are crucial to evaluate activity of catalyst and selectivity of cis-decalin, the density functional theory and microkinetic modeling are applied to investigate the effect of various active sites on the process of naphthalene hydrogenation. Active sites with generalized coordination numbers of 7.50, 6.67, 5.57, and 5.50 from four Ni surfaces including Ni(1 1 1), Ni(1 0 0), Ni(1 1 0) and Ni(2 1 1) are built, respectively. To screen surfaces with preferable selectivity to cis-configuration, the four reaction paths are firstly considered including desorption of NA8H, direct hydrogenation of NA8H to cis- or trans-NA9H, and NA8H to trans-NA9H by hydrogen transfer on four surfaces. And the Ni(1 0 0) and Ni(1 1 1) surfaces exhibit optimal selectivity to cis-decalin by comparing energy barrier of the four paths and calculating the energy barrier gap between direct hydrogenation to cis- and H transfer to trans- configuration, which is the result of 9th C atom receiving more electrons in the process of generating trans-decalin. In addition, reaction mechanism of the whole reaction process from naphthalene hydrogenation to decalin was explored and finding that the rate-determining step of reaction lies in the process of the second-ring hydrogenation. Furthermore, the activity of the Ni(1 0 0) surface is not worse than that of Ni(1 1 1) by comparing the energy barrier of the rate-determining step, which is consistent with the analysis of the d-band-center for different surfaces and the adsorption energy for naphthalene. Microkinetic analysis shows that the temperature between 473 K and 553 K favors the selectivity to cis-decalin for metal Ni catalyst. Therefore, this study provides guide for screening surfaces with different coordination numbers with high activity of naphthalene hydrogenation and high selectivity to cis-decalin.

Exploring Structure-Sensitive Relations for Small Species Adsorption Using Machine Learning.

Accurate prediction of adsorption energies on heterogeneous catalyst surfaces is crucial to predicting reactivity and screening materials. Adsorption linear scaling relations have been developed extensively but often lack accuracy and apply to one adsorbate and a single binding site type at a time. These facts undermine their ability to predict structure sensitivity and optimal catalyst structure. Using machine learning on nearly 300 density functional theory calculations, we demonstrate that generalized coordination number scaling relations hold well for oxygen- and high-valency carbon-binding species but fail for others. We reveal that the valency and the electronic coupling of a species with the surface, along with the site type and its coordination environment, are critical for small species adsorption. The model simultaneously predicts the adsorption energy and preferred site and significantly outperforms linear scalings in accuracy. It can expose the structure sensitivity of chemical reactions and enable enhanced catalyst activity via engineering particle shape and facet defects. The generality of our methodology is validated by training the model with transition metal data and transferring it to predict adsorption energies on single-atom alloys.

C2H2 semi-hydrogenation over Cu catalysts: Revealing the influence of Cu active site types on the catalytic performance

The type of active site is a critical factor to determine catalytic performance. Here, DFT calculations are employed to systematically investigate the influence of Cu active site type on C2H2 semi-hydrogenation. Generalized coordination number (GCN) from 2.5 to 7.5 is used as a descriptor to characterize the type of Cu active site, including the corner, defect, step, and terrace sites. Our results showed that GCN can differentiate the type of Cu active site. C2H2 semi-hydrogenation performance closely depends on the type of Cu active site and GCN. Among them, Cu defect site with the moderate GCN of 4.8 is screened out to exhibit the best catalytic performance, which significantly inhibits green oil formation, and presents excellent C2H4 activity and selectivity. This work provides a basis for rational design Cu catalysts with excellent performance by adjusting the type of active site and GCN in C2H2 semi-hydrogenation.

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.

CO2 activation and conversion on Cu catalysts: Revealing the role of Cu surface defect types in tuning the activity and selectivity

Cu catalysts with different defect types are widely applied in CO2 activation and conversion, however, the underlying role of Cu surface defect types in tuning the activity and selectivity is still unclear due to the complexity of surface defect types. This work constructed a series of Cu catalysts including the perfect surface, as well as the point and line defect surfaces to reveal the role of Cu surface defect types on CO2 activation and conversion using theoretical calculations. The results show that Cu defect types can effectively tune the activity and selectivity of CO2 activation and conversion; the line defect Cu surfaces have higher CO2 activation activity than the point defect and perfect surfaces. Both the line defect Cu(111)LD and (511)LD surfaces are screened out to present the highest activity toward C1 and C2 species formation, respectively. Moreover, Cu surfaces with different defects present an inverted volcano-type curve between d-band center and CO2 activation activity, both Cu(111)LD and (511)LD with excellent activity are attributed to the moderate d-band center. Further, the generalized coordination number (GCN) of Cu surface is proposed and confirmed as an effective descriptor to predict the activity of CO2 activation on different Cu surfaces. The results can provide the valuable structural information for the design and prediction of Cu catalysts with excellent activity and selectivity in CO2 activation and conversion.

Accelerated prediction of Cu-based single-atom alloy catalysts for CO2 reduction by machine learning

Various strategies, including controls of morphology, oxidation state, defect, and doping, have been developed to improve the performance of Cu-based catalysts for CO2 reduction reaction (CO2RR), generating a large amount of data. However, a unified understanding of underlying mechanism for further optimization is still lacking. In this work, combining first-principles calculations and machine learning (ML) techniques, we elucidate critical factors influencing the catalytic properties, taking Cu-based single atom alloys (SAAs) as examples. Our method relies on high-throughput calculations of 2669 CO adsorption configurations on 43 types of Cu-based SAAs with various surfaces. Extensive ML analyses reveal that low generalized coordination numbers and valence electron number are key features to determine catalytic performance. Applying our ML model with cross-group learning scheme, we demonstrate the model generalizes well between Cu-based SAAs with different alloying elements. Further, electronic structure calculations suggest surface negative center could enhance CO adsorption by back donating electrons to antibonding orbitals of CO. Finally, several SAAs, including PCu, AgCu, GaCu, ZnCu, SnCu, GeCu, InCu, and SiCu, are identified as promising CO2RR catalysts. Our work provides a paradigm for the rational design and fast screening of SAAs for various electrocatalytic reactions.

Tricritical behavior of the spin-3/2 anisotropic Heisenberg model with Dzyaloshinskii–Moriya interaction

The spin-3/2 anisotropic Heisenberg model with Dzyaloshinskii–Moriya interaction is studied by using the framework of the two-spin cluster approximation. The formalism is developed for lattices with general coordination number. However, we address our attention to the simple cubic lattice (q=6). The phase diagram of the system reveals the presence of tricritical points and the first and second-order phase transitions are obtained. The critical behavior is discussed and compared with the spin-1/2 and spin-1 Heisenberg systems.

Designing Active Sites for Structure-Sensitive Reactions via the Generalized Coordination Number: Application to Alcohol Dehydrogenation

Identifying the structure of the most active site is essential to improve the performance of supported metal catalysts. For structure-sensitive reactions, in silico design cannot be easily achieved combining the scaling relations and Bronsted–Evans–Polanyi relations, which are only built on energy-based descriptors. We used here the generalized coordination number as a structural descriptor and established that low-coordinated sites are desirable when using Co and Cu to perform the acceptor-less alcohol dehydrogenation reaction.

Selectivity Map for the Late Stages of CO and CO2 Reduction to C2 Species on Copper Electrodes.

The electrochemical CO and CO2 reduction reactions (CORR and CO2 RR) using copper catalysts and renewable electricity hold promise as a carbon-neutral route to produce commodity chemicals and fuels. However, the exact mechanisms and structure sensitivity of Cu electrodes toward C2 products are still under debate. Herein, we investigate ethylene oxide reduction (EOR) as a proxy to the late stages of CORR to ethylene, and the results are compared to those of acetaldehyde reduction to ethanol. Density functional theory (DFT) calculations show that ethylene oxide undergoes ring opening before exclusively reducing to ethylene via *OH formation. Based on generalized coordination numbers (CN), a selectivity map for the late stages of CORR and CO2 RR shows that sites with moderate coordination (5.9 < CN < 7.5) are efficient for ethylene production, with pristine Cu(100) being more active than defective surfaces such as Cu(311). In contrast, kinks and edges are more active for ethanol production, while (111) terraces are relatively inert.

Selectivity Map for the Late Stages of CO and CO2 Reduction to C2 Species on Copper Electrodes

AbstractThe electrochemical CO and CO2 reduction reactions (CORR and CO2RR) using copper catalysts and renewable electricity hold promise as a carbon‐neutral route to produce commodity chemicals and fuels. However, the exact mechanisms and structure sensitivity of Cu electrodes toward C2 products are still under debate. Herein, we investigate ethylene oxide reduction (EOR) as a proxy to the late stages of CORR to ethylene, and the results are compared to those of acetaldehyde reduction to ethanol. Density functional theory (DFT) calculations show that ethylene oxide undergoes ring opening before exclusively reducing to ethylene via *OH formation. Based on generalized coordination numbers (CN), a selectivity map for the late stages of CORR and CO2RR shows that sites with moderate coordination (5.9 &lt; CN &lt; 7.5) are efficient for ethylene production, with pristine Cu(100) being more active than defective surfaces such as Cu(311). In contrast, kinks and edges are more active for ethanol production, while (111) terraces are relatively inert.

An Element-Based Generalized Coordination Number for Predicting the Oxygen Binding Energy on Pt3M (M = Co, Ni, or Cu) Alloy Nanoparticles.

We studied the binding energies of O species on face-centered-cubic Pt3M nanoparticles (NPs) with a Pt-skin layer using density functional theory calculations, where M is Co, Ni, or Cu. It is desirable to express the property by structural parameters rather than by calculated electronic structures such as the d-band center. A generalized coordination number (GCN) is an effective descriptor to predict atomic or molecular adsorption energy on Pt-NPs. The GCN was extended to the prediction of highly active sites for oxygen reduction reaction. However, it failed to explain the O binding energies on Pt-skin Pt150M51-NPs. In this study, we introduced an element-based GCN, denoted as GCNA–B, and considered it as a descriptor for supervised learning. The obtained regression coefficients of GCNPt–Pt were smaller than those of the other GCNA–B. With increasing M atoms in the subsurface layer, GCNPt–M, GCNM–Pt, and GCNM–M increased. These factors could reproduce the calculated result that the O binding energies of the Pt-skin Pt150M51-NPs were less negative than those of the Pt201-NPs. Thus, GCNA–B explains the ligand effect of the O binding energy on the Pt-skin Pt150M51-NPs.

Spectroscopic Probe Molecule Selection Using Quantum Theory, First-Principles Calculations, and Machine Learning.

Probe molecule vibrational spectra have a long history of being used to characterize materials including metals, oxides, metal-organic frameworks, and even human proteins. Furthermore, recent advances in machine learning have enabled computationally generated spectra to aid in detailed characterization of complex surfaces with probe molecules. Despite widespread use of probe molecules, the science of probe molecule selection is underdeveloped. Here, we develop physical concepts, including orbital interaction energy and the energy overlap integral, to explain and predict the ability of probe molecules to discriminate structural descriptors. We resolve the crystal orbital overlap population (COOP) to specific molecular orbitals and quantify their bonding character, which directly influences vibrational frequencies. Using only a single adsorbate calculation from density function theory (DFT), we compute the interaction energy of individual adsorbate molecular orbitals with adsorption site atomic orbitals across many different sites. Combining the molecular orbital resolved COOP and changes in orbital interaction energy enables probe molecule selection for improved discrimination of various sites. We demonstrate these concepts by comparing the predicted effectiveness of carbon monoxide (CO), nitric oxide (NO), and ethylene (C2H4) to probe Pt adsorption sites. Finally, using a previously developed machine learning framework, we show that models trained on hundreds of thousands of C2H4 spectra, computed from DFT, which regress surface binding-type and generalized coordination number, outperform those trained using CO and NO spectra. A python package, pDOS_overlap, for implementing the electron density-based analysis on any combination of adsorbates and materials, is also made available.