New global minimum conformers for the Pt 19 and Pt 20 clusters: low symmetric species featuring different active sites

CONTEXT

The study of platinum (Pt) clusters and nanoparticles is essential due to their extensive range of potential technological applications, particularly in catalysis. The electronic properties that yield optimal catalytic performance at the nanoscale are significantly influenced by the size and structure of Pt clusters. This research aimed to identify the lowest-energy conformers for Pt18 , Pt19 , and Pt20 species using Density Functional Theory (DFT). We discovered new low-symmetry conformers for Pt19 and Pt20 , which are 3.0 and 1.0 kcal/mol more stable, respectively, than previously reported structures. Our study highlights the importance of using density functional approximations that incorporate moderate levels of exact Hartree-Fock exchange, alongside basis sets of at least quadruple-zeta quality. The resulting structures are asymmetric with varying active sites, as evidenced by sigma hole analysis on the electrostatic potential surface. This suggests a potential correlation between electronic structure and catalytic properties, warranting further investigation.

METHODS

An equivariant graph neural network interatomic potential (NequIP) within the Atomic Simulation Environment suite (ASE) was used to provide initial geometries of the aggregates under study. DFT calculations were performed with the ORCA 5 package, using functional approximations that included Generalized Gradient Approximation (PBE), meta-GGA (TPSS, M06-L), hybrid (PBE0, PBEh), meta-GGA hybrid (TPSSh), and range-separated hybrid ( ω B97x) functionals. Def2-TZVP and Def2-QZVP as well as members of the cc-pwCVXZ-PP family to check basis set convergence were used. QTAIM calculations were performed using the AIMAll suite. Structures were visualized with the AVOGADRO code.

An Efficient Growth Pattern Algorithm (GrowPAL) for Cluster Structure Prediction

Identifying the lowest energy isomers in large clusters is a major challenge. Here, we introduce the Growth Pattern Algorithm (GrowPAL), a new approach that generates initial seeds composed of n+1 atoms from the system with n atoms through an interstitial-type addition (I-type) mechanism. We evaluated the effectiveness of GrowPAL on Lennard-Jones (LJ) clusters with up to n = 80 atoms, verifying the algorithm's ability to find challenging minima such as LJ38 and the partially icosahedral LJ69 with fewer optimizations than existing methods. In addition, we discuss the advantages and limitations of GrowPAL using our deconstruction scheme, which identifies "forebears" structures to study growth pathways. Having evaluated the strengths and weaknesses of GrowPAL, we employed it to explore Sutton-Chen clusters containing 5 to 80 atoms, uncovering three new lowest energy forms. We then applied GrowPAL to boron clusters containing 8 to 15 atoms, successfully identifying all reported minima. Overall, GrowPAL offers a practical solution for efficiently identifying global minima in hierarchical systems, thereby reducing computational costs.

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.

Ab initio investigation of the role of the d-states on the adsorption and activation properties of CO2 on 3d, 4d, and 5d transition-metal clusters

We report a theoretical investigation of the adsorption and activation properties of CO2 on eight-atom 3 d, 4 d, and 5 d transition-metal (TM) clusters based on density functional theory calculations. From our results and analyses, in the lowest energy configurations, CO2 binds via a chemisorption mechanism on Fe, Co, Ni, Ru, Rh, Pd, Os, Ir, and Pt (adsorption energy from −0.49 eV on Pt up to −1.40 eV on Os), where CO2 breaks its linearity and adopts an angular configuration due to the charge transfer from the clusters toward the C atom in the adsorbed CO2. In contrast, it binds via physisorption on Cu, Ag, and Au and maintains its linearity due to a negligible charge transfer toward CO2 and has a small adsorption energy (from −0.17 eV on Cu up to −0.18 eV on Ag). There is an energetic preference for twofold bridge TM sites, which favors binding of C with two TM atoms, which enhances the charge transfer ten times than on the top TM sites (onefold). We identified that the strength of the CO2–TM8 interaction increases when the energy values of the highest occupied molecular orbital (HOMO) of the TM8 are closer to the energy values of the lowest unoccupied molecular orbital of CO2, which contributes to maximize the charge transfer toward the molecule. Beyond the energy position of the HOMO states, the delocalization of 5 d orbitals plays an important role in the adsorption strength in TM, especially for the iron group, e.g., the adsorption energies are −1.08 eV (Fe, 3 d), −1.19 eV (Ru, 4 d), and −1.40 eV (Os, 5 d).

Effects of Temperature on Enantiomerization Energy and Distribution of Isomers in the Chiral Cu13 Cluster

In this study, we report the lowest energy structure of bare Cu₁₃ nanoclusters as a pair of enantiomers at room temperature. Moreover, we compute the enantiomerization energy for the interconversion from minus to plus structures in the chiral putative global minimum for temperatures ranging from 20 to 1300 K. Additionally, employing nanothermodynamics, we compute the probabilities of occurrence for each particular isomer as a function of temperature. To achieve that, we explore the free energy surface of the Cu₁₃ cluster, employing a genetic algorithm coupled with density functional theory. Moreover, we discuss the energetic ordering of isomers computed with various density functionals. Based on the computed thermal population, our results show that the chiral putative global minimum strongly dominates at room temperature.

Investigation of the Stability Mechanisms of Eight-Atom Binary Metal Clusters Using DFT Calculations and k-means Clustering Algorithm

Here, we report density functional theory calculations combined with the k-means clustering algorithm and the Spearman rank correlation analysis to investigate the stability mechanisms of eight-atom binary metal AB clusters, where A and B are Fe, Co, Ni, Cu, Ga, Al, and Zn (7 unary and 21 binary clusters). Based on the excess energy analysis, the six most stable binary clusters are NiAl, NiGa, CoAl, FeNi, NiZn, and FeAl, and except for FeNi, their highest energetic stabilities can be explained by the hybridization of the d- and sp-states, which is maximized at the 50% composition, i.e., A₄B₄. Based on the Spearman correlation analysis, the energetic stability of the binary clusters increases with an increase in the highest occupied molecule orbital-lowest unoccupied molecular orbital (HOMO-LUMO) energy separation, which can be considered as a global descriptor. Furthermore, reducing the total magnetic moment values increases the stability for binary clusters without the Fe, Co, and Ni species, while the binary FeB, CoB, and NiB clusters increase their energetic stability with a decrease in the cluster radius, respectively, i.e., an energetic preference for compact structures.

Reply to 'Comment on "Structural characterization, reactivity, and vibrational properties of silver clusters: A new global minimum for Ag16"' by P. V. Nhat, N. T. Si, L. V. Duong and M. T. Nguyen, Phys. Chem. Chem. Phys., 2021, , DOI: D1CP00646K

Recently, P. V. Nhat et al., have discussed and commented on our article (DOI: 10.1039/D0CP04018E) for the case of the most stable structure of Ag15. They have found a new most stable structure (labeled as 15-1) in comparison to the putative global minimum reported by us, which is a four layered 1-4-6-4 stacking structure with a C2v point group (15-2). In this reply, we have performed a larger structure search which allowed us to confirm the results of Nhat et al. The results show the existence of multiple isoenergetic isomers with similar structure motifs for the Ag15 system, increasing the problem complexity to locate the global minimum. The results in regard to the structure and electronic properties of the new lowest energy structure are discussed.