1H chemical shift anisotropy: a high sensitivity solid-state NMR dynamics probe for surface studies?

Dynamics play significant roles in chemistry and biochemistry-molecular motions impact both large- and small-scale chemical reactions in addition to biochemical processes. In many systems, including heterogeneous catalysts, the characterization of dynamics remains a challenge. The most common approaches involve the solid-state NMR measurement of anisotropic interactions, in particular 2H quadrupolar coupling and 1H-X dipolar coupling, which generally require isotope enrichment. Due to the high sensitivity of 1H NMR, 1H chemical shift anisotropy (CSA) is a particularly enticing, and underexplored, dynamics probe. We carried out 1H CSA and 1H-13C dipolar coupling measurements in a series of model supported complexes to understand how 1H CSA can be leveraged to gain dynamic information for heterogeneous catalysts. Mathematical descriptions are given for the dynamic averaging of the CSA tensor, and its dependence on orientation and asymmetry. The variability of the orientation of the tensor in the molecular frame, in addition to its magnitude and asymmetry, negatively impacts attempts to extract quantitative dynamic information. Nevertheless, 1H CSA measurements can reveal useful qualitative insights into the motions of a particularly dilute site, such as from a surface species.

Fluorine spillover for ceria- vs silica-supported palladium nanoparticles: A MD study using machine learning potentials.

Supported metallic nanoparticles play a central role in catalysis. However, predictive modeling is particularly challenging due to the structural and dynamic complexity of the nanoparticle and its interface with the support, given that the sizes of interest are often well beyond those accessible via traditional ab initio methods. With recent advances in machine learning, it is now feasible to perform MD simulations with potentials retaining near-density-functional theory (DFT) accuracy, which can elucidate the growth and relaxation of supported metal nanoparticles, as well as reactions on those catalysts, at temperatures and time scales approaching those relevant to experiments. Furthermore, the surfaces of the support materials can also be modeled realistically through simulated annealing to include effects such as defects and amorphous structures. We study the adsorption of fluorine atoms on ceria and silica supported palladium nanoparticles using machine learning potential trained by DFT data using the DeePMD framework. We show defects on ceria and Pd/ceria interfaces are crucial for the initial adsorption of fluorine, while the interplay between Pd and ceria and the reverse oxygen migration from ceria to Pd control spillover of fluorine from Pd to ceria at later stages. In contrast, silica supports do not induce fluorine spillover from Pd particles.

Nucleation-mediated reshaping of facetted metallic nanocrystals: Breakdown of the classical free energy picture.

Shape stability is key to avoiding degradation of performance for metallic nanocrystals synthesized with facetted non-equilibrium shapes to optimize properties for catalysis, plasmonics, and so on. Reshaping of facetted nanocrystals is controlled by the surface diffusion-mediated nucleation and growth of new outer layers of atoms. Kinetic Monte Carlo (KMC) simulation of a realistic stochastic atomistic-level model is applied to precisely track the reshaping of Pd octahedra and nanocubes. Unexpectedly, separate constrained equilibrium Monte Carlo analysis of the free energy profile during reshaping reveals a fundamental failure of the classical nucleation theory (CNT) prediction for the reshaping barrier and rate. Why? Nucleation barriers can be relatively low for these processes, so the system is not locally equilibrated before crossing the barrier, as assumed in CNT. This claim is supported by an analysis of a first-passage problem for reshaping within a master equation framework for the model that reasonably captures the behavior in KMC simulations.

Reaction processes at step edges on S-decorated Cu(111) and Ag(111) surfaces: MD analysis utilizing machine learning derived potentials.

A variety of complexation, reconstruction, and sulfide formation processes can occur at step edges on the {111} surfaces of coinage metals (M) in the presence of adsorbed S under ultra-high vacuum conditions. Given the cooperative many-atom nature of these reaction processes, Molecular Dynamics (MD) simulation of the associated dynamics is instructive. However, only quite restricted Density Functional Theory (DFT)-level ab initio MD is viable. Thus, for M = Ag and Cu, we instead utilize the DeePMD framework to develop machine-learning derived potentials, retaining near-DFT accuracy for the M-S systems, which should have broad applicability. These potentials are validated by comparison with DFT predictions for various key quantities related to the energetics of S on M(111) surfaces. The potentials are then utilized to perform extensive MD simulations elucidating the above diverse restructuring and reaction processes at step edges. Key observations from MD simulations include the formation of small metal-sulfur complexes, especially MS2; development of a local reconstruction at A-steps featuring an S-decorated {100} motif; and 3D sulfide formation. Additional analysis yields further information on the kinetics for metal-sulfur complex formation, where these complexes can strongly enhance surface mass transport, and on the propensity for sulfide formation.

Enhanced Nanostructure Dynamics on Au(111) with Adsorbed Sulfur due to Au-S Complex Formation.

Chemisorbed species can enhance the fluxional dynamics of nanostructured metal surfaces which has implications for applications such as catalysis. Scanning tunneling microscopy studies at room temperature reveal that the presence of adsorbed sulfur (S) greatly enhances the decay rate of 2D Au islands in the vicinity of extended step edges on Au(111). This enhancement is already significant at S coverages, θS , of a few hundredths of a monolayer (ML), and is most pronounced for 0.1-0.3 ML where the decay rate is increased by a factor of around 30. For θS close to saturation at about 0.6 ML, sulfur induces pitting and reconstruction of the entire surface, and Au islands are stabilized. Enhanced coarsening at lower θS is attributed to the formation and diffusion across terraces of Au-S complexes, particularly AuS2 and Au4 S4 , with some lesser contribution from Au3 S4 . This picture is supported by density functional theory analysis of complex formation energies and diffusion barriers.

Reshaping, Intermixing, and Coarsening for Metallic Nanocrystals: Nonequilibrium Statistical Mechanical and Coarse-Grained Modeling.

Self-assembly of supported 2D or 3D nanocrystals (NCs) by vacuum deposition and of 3D NCs by solution-phase synthesis (with possible subsequent transfer to a support) produces intrinsically nonequilibrium systems. Individual NCs can have far-from-equilibrium shapes and composition profiles. The free energy of NC ensembles is lowered by coarsening which can involve Ostwald ripening or Smoluchowski ripening (NC diffusion and coalescence). Preservation of individual NC structure and inhibition of coarsening are key, e.g., for avoiding catalyst degradation. This review focuses on postsynthesis evolution of metallic NCs. Atomistic-level modeling typically utilizes stochastic lattice-gas models to access appropriate time and length scales. However, predictive modeling requires incorporation of realistic rates for relaxation mechanisms, e.g., periphery diffusion and intermixing, in numerous local environments (rather than the use of generic prescriptions). Alternative coarse-grained modeling must also incorporate appropriate mechanisms and kinetics. At the level of individual NCs, we present analyses of reshaping, including sintering and pinch-off, and of compositional evolution in a vacuum environment. We also discuss modeling of coarsening including diffusion and decay of individual NCs and unconventional coarsening processes. We describe high-level modeling integrated with scanning tunneling microscopy (STM) studies for supported 2D epitaxial nanoclusters and developments in modeling for 3D NCs motivated by in situ transmission electron microscopy (TEM) studies.

Structure of chalcogen overlayers on Au(111): Density functional theory and lattice-gas modeling.

Ordering of different chalcogens, S, Se, and Te, on Au(111) exhibit broad similarities but also some distinct features, which must reflect subtle differences in relative values of the long-range pair and many-body lateral interactions between adatoms. We develop lattice-gas (LG) models within a cluster expansion framework, which includes about 50 interaction parameters. These LG models are developed based on density functional theory (DFT) analysis of the energetics of key adlayer configurations in combination with the Monte Carlo (MC) simulation of the LG models to identify statistically relevant adlayer motifs, i.e., model development is based entirely on theoretical considerations. The MC simulation guides additional DFT analysis and iterative model refinement. Given their complexity, development of optimal models is also aided by strategies from supervised machine learning. The model for S successfully captures ordering motifs over a broader range of coverage than achieved by previous models, and models for Se and Te capture the features of ordering, which are distinct from those for S. More specifically, the modeling for all three chalcogens successfully explains the linear adatom rows (also subtle differences between them) observed at low coverages of ∼0.1 monolayer. The model for S also leads to a new possible explanation for the experimentally observed phase with a (5 × 5)-type low energy electron diffraction (LEED) pattern at 0.28 ML and to predictions for LEED patterns that would be observed with Se and Te at this coverage.

Characteristics of sulfur atoms adsorbed on Ag(100), Ag(110), and Ag(111) as probed with scanning tunneling microscopy: experiment and theory.

In this paper, we report that S atoms on Ag(100) and Ag(110) exhibit a distinctive range of appearances in scanning tunneling microscopy (STM) images, depending on the sample bias voltage, VS. Progressing from negative to positive VS, the atomic shape can be described as a round protrusion surrounded by a dark halo (sombrero) in which the central protrusion shrinks, leaving only a round depression. This progression resembles that reported previously for S atoms on Cu(100). We test whether DFT can reproduce these shapes and the transition between them, using a modified version of the Lang-Tersoff-Hamann method to simulate STM images. The sombrero shape is easily reproduced, but the sombrero-depression transition appears only for relatively low tunneling current and correspondingly realistic tip-sample separation, dT, of 0.5-0.8 nm. Achieving these conditions in the calculations requires sufficiently large separation (vacuum) between slabs, together with high energy cutoff, to ensure appropriate exponential decay of electron density into vacuum. From DFT, we also predict that an analogous transition is not expected for S atoms on Ag(111) surfaces. The results are explained in terms of the through-surface conductance, which defines the background level in STM, and through-adsorbate conductance, which defines the apparent height at the point directly above the adsorbate. With increasing VS, for Ag(100) and Ag(110), we show that through-surface conductance increases much more rapidly than through-adsorbate conductance, so the apparent adsorbate height drops below background. In contrast, for Ag(111) the two contributions increase at more comparable rates, so the adsorbate level always remains above background and no transition is seen.

Sulfur adsorption on coinage metal(100) surfaces: propensity for metal-sulfur complex formation relative to (111) surfaces.

Experimental data from low-temperature Scanning Tunneling Microscopy (LTSTM) studies on coinage metal surfaces with very low coverages of S is providing new insights into metal-S interactions. A previous LTSTM study for Cu(100), and a new analysis reported here for Ag(100), both indicate no metal-sulfur complex formation, but an Au4S5 complex was observed previously on Au(100). In marked contrast, various complexes have been proposed and/or observed on Ag(111) and Cu(111), but not on Au(111). Also, exposure to trace amounts of S appears to enhance mass transport far more dramatically on (111) than on (100) surfaces for Cu and Ag, a feature tied to the propensity for complex formation. Motivated by these observations, we present a comprehensive assessment at the level of DFT to assess the existence and stability of complexes on (100) surfaces, and compare results with previous analyses for (111) surfaces. Consistent with experiment, our DFT analysis finds no stable complexes on Ag(100) and Cu(100), but several exist for Au(100). In addition, we systematically relate stability for adsorbed and gas-phase species within the framework of Hess's law. We thereby provide key insight into the various energetic contributions to stability which in turn elucidates the difference in behavior between (100) and (111) surfaces.

Discontinuous Phase Transitions in Nonlocal Schloegl Models for Autocatalysis: Loss and Reemergence of a Nonequilibrium Gibbs Phase Rule.

We consider Schloegl models (or contact processes) where particles on a square grid annihilate at a rate p and are created at a rate of k_{n}=n(n-1)/[N(N-1)] at empty sites with n particles in a neighborhood Ω_{N} of size N. Simulation reveals a discontinuous transition between populated and vacuum states, but equistable p=p_{eq} determined by the stationarity of planar interfaces between these states depends on the interface orientation and on Ω_{N}. The behavior for large Ω_{N} follows from continuum equations. These also depend on the interface orientation and on Ω_{N} shape, but a unique p_{eq}=0.211 376 320 4 emerges imposing a Gibbs phase rule.

Oxygen and sulfur adsorption on vicinal surfaces of copper and silver: Preferred adsorption sites.

We present an extensive density functional theory (DFT) study of adsorption site energetics for oxygen and sulfur adsorbed on two vicinal surfaces of Cu and Ag, with the goal of identifying the most stable adsorption site(s), identifying trends and common themes, and comparing with experimental work in the literature where possible. We also present benchmark calculations for adsorption on the flat (111) and (100) surfaces. The first vicinal surface is the (211), and results are similar for both metals. We find that the step-doubling reconstruction is favored with both adsorbates and is driven by the creation of a special stable fourfold hollow (4fh) site at the reconstructed step. Zig-zag chain structures consisting of X-M-X units (X = chalcogen, M = metal) at the step edge are considered, in which the special 4fh site is partially occupied. The zig-zag configuration is energetically competitive for oxygen but not sulfur. DFT results for oxygen agree with experiment in terms of the stability of the reconstruction, but contradict the original site assignment. The second vicinal surface is the (410), where again results are similar for both metals. For oxygen, DFT predicts that step sites are filled preferentially even at lowest coverage, followed by terrace sites, consistent with the experiment. For sulfur, in contrast, DFT predicts that terrace sites fill first. Oxygen forms O-M-O rows on the top edge of the step, where it occupies incomplete 4fh sites. This resolves an experimental ambiguity in the site assignment. For both the (211) and (410) surfaces, the interaction energy that stabilizes the X-M-X chain or row correlates with the linearity of the X-M-X unit, which may explain key differences between oxygen and sulfur.

Communication: Diverse nanoscale cluster dynamics: Diffusion of 2D epitaxial clusters.

The dynamics of nanoscale clusters can be distinct from macroscale behavior described by continuum formalisms. For diffusion of 2D clusters of N atoms in homoepitaxial systems mediated by edge atom hopping, macroscale theory predicts simple monotonic size scaling of the diffusion coefficient, DN ∼ N-ß, with ß = 3/2. However, modeling for nanoclusters on metal(100) surfaces reveals that slow nucleation-mediated diffusion displaying weak size scaling ß < 1 occurs for "perfect" sizes Np = L2 and L(L+1) for integer L = 3,4,… (with unique square or near-square ground state shapes), and also for Np+3, Np+4,…. In contrast, fast facile nucleation-free diffusion displaying strong size scaling ß ≈ 2.5 occurs for sizes Np+1 and Np+2. DN versus N oscillates strongly between the slowest branch (for Np+3) and the fastest branch (for Np+1). All branches merge for N = O(102), but macroscale behavior is only achieved for much larger N = O(103). This analysis reveals the unprecedented diversity of behavior on the nanoscale.

Formation of Two-Dimensional Copper Selenide on Cu(111) at Very Low Selenium Coverage.

Using scanning tunneling microscopy (STM), we observed that adsorption of Se on Cu(111) produced islands with a (√3×√3)R30° structure at Se coverages far below the structure's ideal coverage of 1/3 monolayer. On the basis of density functional theory (DFT), these islands cannot form due to attractive interactions between chemisorbed Se atoms. DFT showed that incorporating Cu atoms into the √3-Se lattice stabilizes the structure, which provided a plausible explanation for the experimental observations. STM revealed three types of √3 textures. We assigned two of these as two-dimensional layers of strained CuSe, analogous to dense planes of bulk klockmannite (CuSe). Klockmannite has a bulk lattice constant that is 11 % shorter than √3 times the surface lattice constant of Cu(111). This offers a rationale for the differences observed between these textures, for which strain limits the island size or distorts the √3 lattice. STM showed that existing step edges adsorb Se and facet toward ⟨12‾ 1⟩, which is consistent with DFT.

Identification of Au-S complexes on Au(100).

Using a combination of scanning tunneling microscopy and density functional theory (DFT) calculations, we have identified a set of related Au-S complexes that form on Au(100), when sulfur adsorbs and lifts the hexagonal surface reconstruction. The predominant complex is diamond-shaped with stoichiometry Au4S5. All of the complexes can be regarded as combinations of S-Au-S subunits. The complexes exist within, or at the edges of, p(2 × 2) sulfur islands that cover the unreconstructed Au regions, and are observed throughout the range of S coverage examined in this study, 0.009 to 0.12 monolayers. A qualitative model is developed which incorporates competitive formation of complexes, Au rafts, and p(2 × 2) sulfur islands, as Au atoms are released by the surface structure transformation.

Comparison of S-adsorption on (111) and (100) facets of Cu nanoclusters.

In order to gain insight into the nature of chemical bonding of sulfur atoms on coinage metal surfaces, we compare the adsorption energy and structural parameters for sulfur at four-fold hollow (4fh) sites on (100) facets and at three-fold hollow (3fh) sites on (111) facets of Cu nanoclusters. Consistent results are obtained from localized atomic orbital and plane-wave based density functional theory using the same functionals. PBE and its hybrid counterpart (PBE0 or HSE06) also give similar results. 4fh sites are preferred over 3fh sites with stronger bonding by ∼0.6 eV for nanocluster sizes above ∼280 atoms. However, for smaller sizes there are strong variations in the binding strength and the extent of the binding site preference. We show that suitable averaging over clusters of different sizes, or smearing the occupancy of orbitals, provide useful strategies to aid assessment of the behavior in extended surface systems. From site-projected density of states analysis using the smearing technique, we show that S adsorbed on a 4fh site has similar bonding interactions with the substrate as that on a 3fh site, but with much weaker antibonding interactions.

Transitions between strongly correlated and random steady-states for catalytic CO-oxidation on surfaces at high-pressure.

We explore simple lattice-gas reaction models for CO-oxidation on 1D and 2D periodic arrays of surface adsorption sites with CO adsorption and desorption, dissociative O2 adsorption and recombinative desorption (at low rate), and CO + O reaction to form CO2. Adspecies interactions are neglected, and adspecies diffusion is effectively absent. The models are motivated by studies of CO-oxidation on RuO2(110) at high-pressures. Despite the lack of adspecies interactions, negligible adspecies diffusion results in kinetically induced spatial correlations. A transition occurs from a random primarily CO-populated steady-state at high CO-partial pressure, pCO, to a strongly correlated near-O-covered steady-state for low pCO as noted by Matera et al. [J. Chem. Phys. 134, 064713 (2011)]. In addition, we identify a second transition to a random near-O-covered steady-state at very low pCO. Furthermore, we identify and analyze the slow "diffusive dynamics" for very low pCO and provide a detailed characterization of the crossover to the strongly correlated O-covered steady-state as well as of the spatial correlations in that state.

Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability.

Threshold versions of Schloegl's model on a lattice, which involve autocatalytic creation and spontaneous annihilation of particles, can provide a simple prototype for discontinuous non-equilibrium phase transitions. These models are equivalent to so-called threshold contact processes. A discontinuous transition between populated and vacuum states can occur selecting a threshold of N ≥ 2 for the minimum number, N, of neighboring particles enabling autocatalytic creation at an empty site. Fundamental open questions remain given the lack of a thermodynamic framework for analysis. For a square lattice with N = 2, we show that phase coexistence occurs not at a unique value but for a finite range of particle annihilation rate (the natural control parameter). This generic two-phase coexistence also persists when perturbing the model to allow spontaneous particle creation. Such behavior contrasts both the Gibbs phase rule for thermodynamic systems and also previous analysis for this model. We find metastability near the transition corresponding to a non-zero effective line tension, also contrasting previously suggested critical behavior. Mean-field type analysis, extended to treat spatially heterogeneous states, further elucidates model behavior.

Reconstruction of steps on the Cu(111) surface induced by sulfur.

A rich menagerie of structures is identified at 5 K following adsorption of low coverages (≤0.05 monolayers) of S on Cu(111) at room temperature. This paper emphasizes the reconstructions at the steps. The A-type close-packed step has 1 row of S atoms along its lower edge, where S atoms occupy alternating pseudo-fourfold-hollow (p4fh) sites. Additionally, there are 2 rows of S atoms of equal density on the upper edge, bridging a row of extra Cu atoms, together creating an extended chain. The B-type close-packed step exhibits an even more complex reconstruction, in which triangle-shaped groups of Cu atoms shift out of their original sites and form a base for S adsorption at (mostly) 4fh sites. We propose a mechanism by which these triangles could generate Cu-S complexes and short chains like those observed on the terraces.

Self-organization of S adatoms on Au(111): √3R30° rows at low coverage.

Using scanning tunneling microscopy, we observe an adlayer structure that is dominated by short rows of S atoms, on unreconstructed regions of a Au(111) surface. This structure forms upon adsorption of low S coverage (less than 0.1 monolayer) on a fully reconstructed clean surface at 300 K, then cooling to 5 K for observation. The rows adopt one of three orientations that are rotated by 30° from the close-packed directions of the Au(111) substrate, and adjacent S atoms in the rows are separated by √3 times the surface lattice constant, a. Monte Carlo simulations are performed on lattice-gas models, derived using a limited cluster expansion based on density functional theory energetics. Models which include long-range pairwise interactions (extending to 5a), plus selected trio interactions, successfully reproduce the linear rows of S atoms at reasonable temperatures.

Real-time ab initio KMC simulation of the self-assembly and sintering of bimetallic epitaxial nanoclusters: Au + Ag on Ag(100).

Far-from-equilibrium shape and structure evolution during formation and post-assembly sintering of bimetallic nanoclusters is extremely sensitive to the periphery diffusion and intermixing kinetics. Precise characterization of the many distinct local-environment-dependent diffusion barriers is achieved for epitaxial nanoclusters using density functional theory to assess interaction energies both with atoms at adsorption sites and at transition states. Kinetic Monte Carlo simulation incorporating these barriers then captures structure evolution on the appropriate time scale for two-dimensional core-ring and intermixed Au-Ag nanoclusters on Ag(100).