Assessment of the van der Waals, Hubbard U parameter and spin-orbit coupling corrections on the 2D/3D structures from metal gold congeners clusters

Understanding stability and reactivity of transition metal single-atoms on graphene

Recently, single-atom catalysts (SACs) based on transition metals (TMs) have been identified as highly active catalysts with excellent atomic efficiency, reduced consumption of expensive materials, well-defined active centers, and tunable activity and selectivity. Furthermore, when carbon-based supports (including graphene-derived materials) are employed in SACs, their unique structural and electronic properties, such as high electrical conductivity and mechanical strength, can be integrated. However, for this application, the primary objective is to maintain proper stability-reactivity balance, ensuring the system remains stable while preserving its high chemical activity. In this context, we explore the adsorption behavior of TM single atoms (Co, Ni, Rh, Pd, Ir, Pt) on pristine graphene (pGR), hexagonal boron nitride (hBN), and graphene with monovacancies (GRm) using DFT-PBE+D3 calculations. From the adsorption energy trends, we observe weak chemisorption on pGR and physisorption on hBN, with adsorption energies ranging from 0.5 eV (Co/hBN) to 1.80 eV (Rh/pGR). In contrast, the adsorption strength is significantly enhanced on GRm (strong chemisorption), with adsorption energies reaching up to 9.11 eV for Ir/GRm, attributed to the strong defect-induced reactivity and improved orbital overlap. Electronic structure analysis reveals that pGR retains its semimetallic nature, hBN remains an insulator, and GRm transitions to metallic behavior due to the strong interactions between TM-C. Bader charge analysis indicates significant charge transfer in GRm, consistent with its catalytic potential, while hybridization indices show substantial pd orbital mixing, favoring improved TM anchoring. Thus, our results identify GRm as the most promising substrate for SACs, pGR as a balanced platform for controlled reactivity, and hBN as a stable support for selective catalysis or dielectric applications. Finally, defect engineering is a powerful strategy for designing next-generation catalysts, ensuring the right balance between stability and reactivity.

Investigating Molecular Adsorption on Graphene-Supported Platinum Subnanoclusters: Insights from DFT + D3 Calculations

Platinum (Pt) subnanoclusters have become pivotal in nanocatalysis, yet their molecular adsorption mechanisms, particularly on supported versus unsupported systems, remain poorly understood. Our study employs detailed density functional theory (DFT) calculations with D3 corrections to investigate molecular adsorption on Pt subnanoclusters, focusing on CO, NO, N2, and O2 species. Gas-phase and graphene-supported scenarios are systematically characterized to elucidate adsorption mechanisms and catalytic potential. Gas-phase Pt n clusters are first analyzed to identify stable configurations and assess size-dependent reactivity. Transitioning to graphene-supported Pt n clusters, both periodic and nonperiodic models are employed to study interactions with graphene substrates. Strong adsorbate interactions predominantly occur at single top sites, revealing distinct adsorption geometries and stabilization effects for specific molecules on Pt6 clusters. Energy decomposition analysis highlights the paramount role of graphene substrates in enhancing stability and modulating cluster-adsorbate interactions. The interaction energy emerges as a critical criterion within the Sabatier principle, crucial for distinguishing between physisorption and chemisorption. Hybridization indices and charge density flow tendencies establish direct relationships with stabilization processes, underscoring graphene's influence in stabilizing highly reactive subnanoclusters. This comprehensive investigation provides critical insights into molecular adsorption mechanisms and the catalytic potential of graphene-supported Pt nanoclusters. Our findings contribute to a deeper understanding of nanocatalysis, emphasizing the essential role of substrates in optimizing catalytic performance for industrial applications.

Ferromagnetism in Defected TMD (MoX2, X = S, Se) Monolayer and Its Sustainability under O2, O3, and H2O Gas Exposure: DFT Study

Spin-polarized density-functional theory (DFT) has been employed to study the effects of atmospheric gases on the electronic and magnetic properties of a defective transition-metal dichalcogenide (TMD) monolayer, MoX₂ with X = S or Se. This study focuses on three single vacancies: (i) molybdenum "V_Mo"; (ii) chalcogenide "V_X"; and (iii) di-chalcogenide "V_X2". Five different samples of sizes ranging from 4 × 4 to 8 × 8 primitive cells (PCs) were considered in order to assess the effect of vacancy-vacancy interaction. The results showed that all defected samples were paramagnetic semiconductors, except in the case of V_Mo in MoSe₂, which yielded a magnetic moment of 3.99 μ_B that was independent of the sample size. Moreover, the samples of MoSe₂ with V_Mo and sizes of 4 × 4 and 5 × 5 PCs exhibited half-metallicity, where the spin-up state becomes conductive and is predominantly composed of dxy and dz2 orbital mixing attributed to Mo atoms located in the neighborhood of V_Mo. The requirement for the establishment of half-metallicity is confirmed to be the provision of ferromagnetic-coupling (FMC) interactions between localized magnetic moments (such as V_Mo). The critical distance for the existence of FMC is estimated to be dc≅ 16 Å, which allows small sample sizes in MoSe₂ to exhibit half-metallicity while the FMC represents the ground state. The adsorption of atmospheric gases (H₂O, O₂, O₃) can drastically change the electronic and magnetic properties, for instance, it can demolish the half-metallicity characteristics. Hence, the maintenance of half-metallicity requires keeping the samples isolated from the atmosphere. We benchmarked our theoretical results with the available data in the literature throughout our study. The conditions that govern the appearance/disappearance of half-metallicity are of great relevance for spintronic device applications.

Molecular adsorption on coinage metal subnanoclusters: A DFT+D3 investigation

Gold and silver subnanoclusters with few atoms are prominent candidates for catalysis-related applications, primarily because of the large fraction of lower-coordinated atoms exposed and ready to interact with external chemical species. However, an in-depth energetic analysis is necessary to characterize the relevant terms within the molecular adsorption process that can frame the interactions within the Sabatier principle. Herein, we investigate the interaction between Ag_n and Au_n subnanoclusters (clu, n = 2-7) and N₂ , NO, CO, and O₂ molecules, using scalar-relativistic density functional theory calculations within van der Waals D3 corrections. The onefold top site is preferred for all chemisorption cases, with a predominance of linear (≈180°) and bent (≈120°) molecular geometries. A larger magnitude of adsorption energy is correlated with smaller distances between molecules and clusters and with the weakening of the adsorbates bond strength represented by the increase of the equilibrium distances and decrease of molecular stretching frequencies. From the energetic decomposition, the interaction energy term was established as an excellent descriptor to classify subnanoclusters in the adsorption/desorption process concomitant with the Sabatier principle. The limiting cases: (i) weak molecular adsorption on the subnanoclusters, which may compromise the reaction activation, where an interaction energy magnitude close to 0 eV is observed (e.g., physisorption in N₂ /Ag₆ ); and (ii) strong molecular interactions with the subnanoclusters, given the interaction energy magnitude is larger than at least one of the individual fragment binding energies (e.g., strong chemisorption in CO/Au₄ and NO/Au₄ ), conferring a decrease in the desorption rate and an increase in the possible poisoning rate. However, the intermediate cases are promising by involving interaction energy magnitudes between zero and fragment binding energies. Following the molecular closed-shell (open-shell) electronic configuration, we find a predominant electrostatic (covalent) nature of the physical interactions for N₂ ⋯clu and CO ⋯clu (O₂ ⋯clu and NO⋯clu), except in the physisorption case (N₂ /Ag₆ ) where dispersive interaction is dominant. Our results clarify questions about the molecular adsorption on subnanoclusters as a relevant mechanistic step present in nanocatalytic reactions.

The effect of different energy portions on the 2D/3D stability swapping for 13-atom metal clusters

The complexity of Cu₁₃, Ag₁₃, and Au₁₃ coinage-metal clusters was investigated through their energy contributions via a density functional theory study, considering improvements in the PBE functional, such as van der Waals (vdW) corrections, spin-orbit coupling (SOC), Hubbard term (+U), and their combinations. Investigating two-dimensional (planar 2D) and three-dimensional (distorted 3D, CUB - cuboctahedral, and ICO - icosahedral) configurations, we found that vdW corrections are dominant in modulating the stability swapping between 2D and ICO (3D) for Ag₁₃ (Au₁₃), whereas for Cu₁₃ its role is increasing the relative stability between 2D (least stable) and 3D (most stable), setting ICO as the reference. Among the energy portions that constitute the relative total energy, the dimensionality difference correlates with the magnitude of the relative dispersion energy (large for 2D/ICO and small for 3D/ICO) as the causal factor responsible for an eventual stability swapping. For instance, empirical vdW corrections may favor Ag₁₃ as ICO, while semi empirical ones tend to swap the stability by favoring 2D. The same tendency is observed for Au₁₃, except when SOC is included, which enlarges the stability of 3D over 2D. Energy decomposition analysis combined with the natural orbitals for the chemical valence approach confirmed the correlations between the dimensionality difference and the magnitude of the relative dispersion energies. Our structural analysis protocol was able to capture the local distortion effects (or even their absence) through the quantification of the Hausdorff chirality measure. Here, ICO, CUB, and 2D are achiral configurations for all coinage-metal clusters, whereas Cu₁₃ as 3D presents a slight chirality when vdW correction based on many body dispersion is used, at the same time Ag₁₃ as 3D turned out to be chiral for all calculation protocols as evidence of the role of the chemical composition.