Low-lying Pt n cluster structures (n = 6–10) from global optimizations based on DFT potential energy surfaces: Sensitivity of the chemical ordering with the functional

Formation of pyramidal structures through mixing gold and platinum atoms: the AuxPty2+ clusters with x + y = 10

The geometric and electronic structures of a small series of mixed gold and platinum AuxPty2+ clusters, with x + y = 10, were investigated using quantum chemical methods. A consistent tetrahedral pyramid structure emerges, displaying two patterns of structural growth by a notable critical point at y = 5. This affects the clusters' electron population, chemical bonding, and stability. For the Pt-doped Au clusters with y values from 2 to 5, the bonds enable Pt atoms to assemble into symmetric line, triangle, quadrangle, and tetragonal pyramidal Pty blocks, respectively. For the Au-doped Pt clusters, with larger values of y > 5, the structures are more relaxed and the d electrons of Pt atoms become delocalized over more centers, leading to lower symmetry structures. A certain aromaticity arising from delocalization of d electrons over the multi-center framework in the doped Pt clusters contributes to their stability, with Pt102+ at y = 10 exhibiting the highest stability. While the ground electronic state of the neutral platinum atom [Xe]. 4f145d96s1 leads to a triplet state (3D3), the total magnetic moments of AuxPty2+ are large increasing steadily from 0 to 10 μB and primarily located on Pt atoms, corresponding to the increase of the number of Pt atoms from 0 to 10 and significantly enhancing the magnetic moments. An admixture of both Au and Pt atoms thus emerges as an elegant way of keeping a small pyramidal structure but bringing in a high and controllable magnetic moment.

Enhancing the Performance of Global Optimization of Platinum Cluster Structures by Transfer Learning in a Deep Neural Network

The global optimization of metal cluster structures is an important research field. The traditional deep neural network (T-DNN) global optimization method is a good way to find out the global minimum (GM) of metal cluster structures, but a large number of samples are required. We developed a new global optimization method which is the combination of the DNN and transfer learning (DNN-TL). The DNN-TL method transfers the DNN parameters of the small-sized cluster to the DNN of the large-sized cluster to greatly reduce the number of samples. For the global optimization of Pt₉ and Pt₁₃ clusters in this research, the T-DNN method requires about 3-10 times more samples than the DNN-TL method, and the DNN-TL method saves about 70-80% of time. We also found that the average amplitude of parameter changes in the T-DNN training is about 2 times larger than that in the DNN-TL training, which rationalizes the effectiveness of transfer learning. The average fitting errors of the DNN trained by the DNN-TL method can be even smaller than those by the T-DNN method because of the reliability of transfer learning. Finally, we successfully obtained the GM structures of Pt_n (n = 8-14) clusters by the DNN-TL method.

Exploring the Potential Energy Surface of Pt6 Sub-Nano Clusters Deposited over Graphene

Catalytic systems based on sub-nanoclusters deposited over different supports are promising for very relevant chemical transformations such as many electrocatalytic processes as the ORR. These systems have been demonstrated to be very fluxional, as they are able to change shape and interconvert between each other either alone or in the presence of adsorbates. In addition, an accurate representation of their catalytic activity requires the consideration of ensemble effects and not a single structure alone. In this sense, a reliable theoretical methodology should assure an accurate and extensive exploration of the potential energy surface to include all the relevant structures and with correct relative energies. In this context, we applied DFT in conjunction with global optimization techniques to obtain and analyze the characteristics of the many local minima of Pt₆ sub-nanoclusters over a carbon-based support (graphene)-a system with electrocatalytic relevance. We also analyzed the magnetism and the charge transfer between the clusters and the support and paid special attention to the dependence of dispersion effects on the ensemble characteristics. We found that the ensembles computed with and without dispersion corrections are qualitatively similar, especially for the lowest-in-energy clusters, which we attribute to a (mainly) covalent binding to the surface. However, there are some significant variations in the relative stability of some clusters, which would significantly affect their population in the ensemble composition.

Structures of Small Platinum Cluster Anions Ptn-: Experiment and Theory

The structures of platinum cluster anions Pt6--Pt13- have been investigated by trapped ion electron diffraction. Structures were assigned by comparing experimental and simulated scattering functions using candidate structures obtained by density functional theory computations, including spin-orbit coupling. We find a structural evolution from planar structures (Pt6-, Pt7-) and amorphous-like structures (Pt7--Pt9-) to structures based on distorted tetrahedra (Pt9--Pt11-). Finally, Pt12- and Pt13- are based on hcp fragments. While the structural parameters are well described by density functional theory computations for all clusters studied, the predicted lowest energy structure is found in the experiment only for Pt6-. For larger clusters, higher energy isomers are necessary to obtain a fit to the scattering data.

How Many Isomers Do Metallic Clusters Have? Case of Magnesium Clusters of up to 55 Atoms

About 9000 structures of magnesium clusters Mg_n (n = 2-13) generated via different methods were optimized at the DFT levels in order to estimate the number of all possible stable structures that can exist for the given cluster size (∼820,000 PES points were explored in total). It was found that the number of possible cluster isomers N quickly grows with a number of atoms n; however, it is significantly lower than the number of possible nonisomorphic graph structures, which can be drawn for the given n. At the DFT potential energy surface, we found only 543 local minima corresponding to the isomers of Mg₂-Mg₁₃. The number of isomers obtained in the DFT optimizations grows with n approximately as n⁴, whereas the N values extrapolated to the infinite generation process grow as n⁸. The cluster geometries obtained from the global DFT optimization were then used to adjust two empirical potentials of Gupta type (GP) and modified Sutton-Chen type (SCG3) describing the interactions between the magnesium atoms. Using these potentials, the extensive sets of structures Mg₂-Mg₅₅ (up to 30,000 clusters for each n) were optimized to obtain the dependence of the cluster isomer count on n in the continuous range of n = 2-30 and for selected n up to n = 55. It was found that the SCG3 potential, which is closer to the DFT results, gives a number of possible isomers growing as approximately n^8.9, whereas GP potential results in the n^4.3 dependence.

From platinum atoms in molecules to colloidal nanoparticles: A review on reduction, nucleation and growth mechanisms

Platinum (Pt) is one of the most studied materials in catalysis today and considered for a wide range of applications: chemical synthesis, energy conversion, air treatment, water purification, sensing, medicine etc. As a limited and non-renewable resource, optimized used of Pt is key. Nanomaterial design offers multiple opportunities to make the most of Pt resources down to the atomic scale. In particular, colloidal syntheses of Pt nanoparticles are well documented and simple to implement, which accounts for the large interest in research and development. For further breakthroughs in the design of Pt nanomaterials, a deeper understanding of the intricate synthesis-structures-properties relations of Pt nanoparticles must be obtained. Understanding how Pt nanoparticles form from molecular precursors is both a challenging and rewarding area of investigation. It is directly relevant to develop improved Pt nanomaterials but is also a source of inspiration to design other precious metal nanostructures. Here, we review the current understanding of Pt nanoparticle formation. This review is aimed at readers with interest in Pt nanoparticles in general and their colloidal syntheses in particular. Readers with a strongest interest on the study of nanomaterial formation will find here the case study of Pt. The preferred model systems and characterization techniques used to perform the study of Pt nanoparticle syntheses are discussed. In light of recent achievements, further direction and areas of research are proposed.

Thermodynamically accessible titanium clusters TiN, N = 2–32

We have performed a genetic algorithm search on the tight-binding interatomic potential energy surface (PES) for small Ti_N (N = 2–32) clusters.