Unravelling Morphological and Topological Energy Contributions of Metal Nanoparticles

Abstract

Metal nanoparticles (NPs) are ubiquitous in many fields, from nanotechnology to heterogeneous catalysis, with properties differing from those of single-crystal surfaces and bulks. A key aspect is the size-dependent evolution of NP properties toward the bulk limit, including the adoption of different NP shapes, which may bias the NP stability based on the NP size. Herein, the stability of different Pdn NPs (n = 10–1504 atoms) considering a myriad of shapes is investigated by first-principles energy optimisation, leading to the determination that icosahedron shapes are the most stable up to a size of ca. 4 nm. In NPs larger than that size, truncated octahedron shapes become more stable, yet a presence of larger {001} facets than the Wulff construction is forecasted due to their increased stability, compared with (001) single-crystal surfaces, and the lower stability of {111} facets, compared with (111) single-crystal surfaces. The NP cohesive energy breakdown in terms of coordination numbers is found to be an excellent quantitative tool of the stability assessment, with mean absolute errors of solely 0.01 eV·atom−1, while a geometry breakdown allows only for a qualitative stability screening.

Machine Learning-Driven Discovery of Key Descriptors for CO2Activation over Two-Dimensional Transition Metal Carbides and Nitrides

“…As per the size of the data set, Figure shows the E ads MAE decay with respect to training set size; in other words, the learning curve, regarding that training set considers randomly selected 80% of the samples, while the test set comprises the remaining 20%. For a better analysis, a cross-validation procedure with 100 shuffle splits was carried out, as done in previous analysis, where average MAE is shown in Figure , with areas denoting the standard deviations . Notice on the training set that RFR MAE decay is rather good, 0.16 ± 0.01 eV, rapidly below the 0.2 eV DFT accuracy limit, and especially with an almost negligible standard deviation when having more than ca.…”

Coverage- and Facet-Dependent Multiscale Modeling of O* and H* Adsorption on Pt Catalytic Nanoparticles

“…There are several existing approaches to modeling entire nanoparticles, − each with its own set of pros and cons. Wulff construction models use the orientation-dependent surface free energy of the facets, with the incorporation of thermodynamics and kinetics, to bring alive the catalyst nanoparticle. − The accuracy of this modeling approach reduces significantly when it comes to nonequilibrated structures, systems with large numbers of configurations, and reactions where edge and vertex sites have a significant influence. − Monte Carlo simulations have advantages such as being able to be used in conjunction with a host of other methods, having a wide range of applications outside nanoparticle modeling, and better incorporation of coverage and configuration effects. ,− However, the vast number of DFT calculations required to parameterize all configurations and elementary reactions limit the broad applicability of this approach. − Molecular dynamics (MD) simulations for nanoparticles can handle larger sizes of nanoparticles (up to 100 nm, equivalent to 3 orders of magnitude larger than DFT). However, the accuracy of the MD results can be significantly influenced by the chosen methods, specifically, the force fields.…”

“… 54 − 56 The accuracy of this modeling approach reduces significantly when it comes to nonequilibrated structures, systems with large numbers of configurations, and reactions where edge and vertex sites have a significant influence. 54 − 60 Monte Carlo simulations have advantages such as being able to be used in conjunction with a host of other methods, having a wide range of applications outside nanoparticle modeling, and better incorporation of coverage and configuration effects. 12 , 61 − 63 However, the vast number of DFT calculations required to parameterize all configurations and elementary reactions limit the broad applicability of this approach.…”

Identifying the Structure of Supported Metal Catalysts Using Vibrational Fingerprints from Ab Initio Nanoscale Models

“…Typically, DFT studies reporting on the stretching frequency of CO adsorbed on Pd restrict the analysis to simplified models such as extended Pd terraces [ 15 ] or Pd single atoms and very small clusters on oxide supports. [ 16–18 ] Recently, comprehensive first‐principles computational studies of supported and unsupported Pd nanoparticles have been presented, [ 19–21 ] opening the door to calculations of the stretching frequency of CO adsorbed on such models. However, so far these works have restricted the scope to a single NP morphology and a single CO molecule, usually disregarding the impact of the support.…”

“…Typically, DFT studies reporting on the stretching frequency of CO adsorbed on Pd restrict the analysis to simplified models such as extended Pd terraces [15] or Pd single atoms and very small clusters on oxide supports. [16][17][18] Recently, comprehensive first-principles computational studies of supported and unsupported Pd nanoparticles have been presented, [19][20][21] Identifying active sites of supported noble metal nanocatalysts remains challenging, since their size and shape undergo changes depending on the support, temperature, and gas mixture composition. Herein, the anharmonic infrared spectrum of adsorbed CO is simulated using density functional theory (DFT) to gain insight into the nature of Pd nanoparticles (NPs) supported on ceria.…”