Pd8 Cluster: Too Small to Melt? A BOMD Study.

The question of whether a solid-liquid phase transition occurs in small clusters poses a fundamental challenge. In this study, we attempt to elucidate this phenomenon through a thorough examination of the thermal behavior and structural stability of Pd8 clusters employing ab initio simulations. Initially, a systematic global search is carried out to identify the various isomers of the Pd8 cluster. This is accomplished by employing an ab initio basin-hopping algorithm and using the PBE/SDD scheme integrated in the Gaussian code. The resulting isomers are further refined through reoptimization using the deMon2k package. To ensure the structural firmness of the lowest-energy isomer, we calculated normal modes. The structural stability as a function of temperature is analyzed through the Born-Oppenheimer molecular dynamics (BOMD) approach. Multiple BOMD trajectories at distinct simulated temperatures are examined with data clustering analysis to determine cluster isomers. This analysis establishes a connection between the potential energy landscape and the simulated temperature. To address the question of cluster melting, canonical parallel-tempering BOMD runs are performed and analyzed with the multiple-histogram method. A broad maximum in the heat capacity curve indicates a melting transition between 500 and 600 K. To further examine this transition, the mean-squared displacement and the pair-distance distribution function are calculated. The results of these calculations confirm the existence of a solid-liquid phase transition, as indicated by the heat capacity curve.

Structure, Energetics, and Thermal Behavior of Bimetallic Re-Pt Clusters.

Bimetallic Re-Pt is a widely used catalyst in petroleum reforming to obtain high-octane gasoline, but experimental and theoretical information of such systems at the subnanometer scale-namely, as cluster aggregates-is currently lacking. Thus, in this work, we performed a density functional theory-based global optimization study to determine the physicochemical properties of the most stable Re-Pt gas-phase clusters up to six atoms for all compositions. Our results indicate that in these putative global minima (GM) geometries, Re atoms tend to aggregate, while most Pt atoms remain separated from each other. This is even observed in Pt-rich clusters-an indication of the strength of the Re-Re and Re-Pt bonds over pure Pt-Pt ones-due to a strong, directional hybridization of the Re half-filled 5d and the nearly full Pt 5d states. We observe that doping monometallic Pt clusters even with a single Re atom increases their binding energy values and widens the bimetallic cluster highest occupied molecular orbital-lowest unoccupied molecular orbital gap. As catalysis occurs at elevated temperatures, we explore the concept of cluster fluxionality for Re-Pt minima in terms of the calculated isomer occupation probability, P(T). This allows us to quantify the abundance of GM and low-energy isomer configurations as a function of temperature. This is done at size 5 atoms due to the wide isomer observed variety. Our calculations indicate that for pure Re5, the P(T) of the GM configuration substantially decreases after 750 K. Especially, for Re4Pt1, the GM is the dominant structure up to nearly 700 K when the second-energy isomer becomes the stable one. Although no ordering changes are seen for Re3Pt2, Re2Pt3, and Re1Pt4, we do observe a structural transition-between the GM and the second isomer-for pure Pt5 above 1000 K. We expect this type of combined first-principles analysis to add to the overall, continuous understanding of the stability and energetics of ultrafine and highly-dispersed Re-Pt petroleum-reforming catalysts and the scarce available information on this particular bimetallic system.

Cu-Doped KCl Unfolded Band Structure and Optical Properties Studied by DFT Calculations.

The unfolded band structure and optical properties of Cu-doped KCl crystals were computed by first principles within the framework of density functional theory, implemented in the ABINIT software program, utilizing pseudopotential approximation and a plane-wave basis set. From a theoretical point of view, Cu substitution into pristine KCl crystals requires calculation by the supercell (SC) method. This procedure shrinks the Brillouin zone, resulting in a folded band structure that is difficult to interpret. To solve this problem and gain insight into the effect of copper ions (Cu+) on electronic properties, the band structure of SC KCl:Cu was unfolded to make a direct comparison with the band structure of the primitive cell (PC) of pristine KCl. To understand the effect of Cu substitution on optical absorption, we calculated the imaginary part of the dielectric function of KCl:Cu through a sum-over-states formalism and broke it down into different band contributions by partially making an iterated cumulative sum (ICS) of selected valence and conduction bands. Consequently, we identified those interband transitions that give rise to the absorption peaks due to the Cu+ ion. These transitions involve valence and conduction bands formed by the Cu-3d and Cu-4s electronic states.

CeO2(111) electronic reducibility tuned by ultra-small supported bimetallic Pt-Cu clusters.

Controlling Ce4+ to Ce3+ electronic reducibility in a rare-earth binary oxide such as CeO2 has enormous applications in heterogeneous catalysis, where a profound understanding of reactivity and selectivity at the atomic level is yet to be reached. Thus, in this work we report an extensive DFT-based Basin Hopping global optimization study to find the most stable bimetallic Pt-Cu clusters supported on the CeO2(111) oxide surface, involving up to 5 atoms in size for all compositions. Our PBE+U global optimization calculations indicate a preference for Pt-Cu clusters to adopt 2D planar geometries parallel to the oxide surface, due to the formation of strong metal bonds to oxygen surface sites and charge transfer effects. The calculated adsorption energy values (Eads) for both mono- and bimetallic systems are of the order of 1.79 up to 4.07 eV, implying a strong metal cluster interaction with the oxide surface. Our calculations indicate that at such sub-nanometer sizes, the number of Ce4+ surface atoms reduced to Ce3+ cations is mediated by the amount of Cu atoms within the cluster, reaching a maximum of three Ce3+ for a supported Cu5 cluster. Our computational results have critical implications on the continuous understanding of the strong metal-support interactions over reducible oxides such as CeO2, as well as the advancement of frontier research areas such as heterogeneous single-atom catalysts (SAC) and single-cluster catalysts (SCC).

CO2 adsorption on gas-phase Cu4-xPtx (x = 0-4) clusters: a DFT study.

Transition and noble metal clusters have proven to be critical novel materials, potentially offering major advantages over conventional catalysts in a range of value-added catalytic processess such as carbon dioxide transformation to methanol. In this work, a systematic computational study of CO2 adsorption on gas-phase Cu4-xPtx (x = 0-4) clusters is performed. An exhaustive potential energy surface exploration is initially performed using our recent density functional theory basin-hopping global optimization implementation. Ground-state and low-lying energy isomers are identified for Cu4-xPtx clusters. Secondly, a CO2 molecule adsorption process is analyzed on the ground-state Cu4-xPtx configurations, as a function of cluster composition. Our results show that the gas-phase linear CO2 molecule is deformed upon adsorption, with its bend angle varying from about 132° to 139°. Cu4-xPtx cluster geometries remain unchanged after CO2 adsorption, with the exception of Cu3Pt1 and Pt4 clusters. For these particular cases, a structural conversion between the ground-state geometry and the corresponding first isomer configurations is found to be assisted by the CO2 adsorption. For all clusters, the energy barriers between the ground-state and first isomer structures are explored. Our calculated CO2 adsorption energies are found to be larger for Pt-rich clusters, exhibiting a volcano-type plot. The overall effect of a hybrid functional including dispersion forces is also discussed.

2D-3D structural transition in sub-nanometer PtN clusters supported on CeO2(111).

Transition metal particles dispersed on oxide supports are used as heterogeneous catalysts in numerous applications. One example is platinum clusters supported on ceria which is used in automotive catalysis. Although control at the nm-scale is desirable to open new technological possibilities, there is limited knowledge both experimentally and theoretically regarding the geometrical structure and stability of sub-nanometer platinum clusters supported on ceria. Here we report a systematic, Density Functional Theory (DFT) study on the growth trends of CeO2(111) supported PtN clusters (N = 1-10). Using a global optimization methodology as a guidance tool to locate putative global minima, our results show a clear preference for 2D planar structures up to size Pt8. It is followed by a structural transition to 3D configurations at larger sizes. This remarkable trend is explained by the subtle competition between the formation of strong Pt-O bonds and the cluster internal Pt-Pt bonds. Our calculations show that the reducibility of CeO2(111) provides a mechanism to anchor PtN clusters where they become oxidized in a two-way charge transfer mechanism: (a) an oxidation process, where Osurface atoms withdraw charge from Pt atoms forming Pt-O bonds, (b) surface Ce4+ atoms are reduced, leading to Ce3+. The active role of the CeO2(111) support in modifying the structural and eventually the chemical properties of sub-nanometer PtN clusters is computationally demonstrated.

Global minimum Pt(13)M(20) (M = Ag, Au, Cu, Pd) dodecahedral core-shell clusters.

In this work, we report finding dodecahedral core-shell structures as the putative global minima of Pt13M20 (M = Ag, Au, Cu, Pd) clusters by using the basin hopping method and the many-body Gupta model potential to model interatomic interactions. These nanoparticles consist of an icosahedral 13-atom platinum core encapsulated by a 20 metal-atom shell exhibiting a dodecahedral geometry (and Ih symmetry). The interaction between the icosahedral platinum core and the dodecahedral shell is analyzed in terms of the increase in volume of the icosahedral core, and the strength and stickiness of M-Pt and M-M interactions. Low-lying metastable isomers are also obtained. Local relaxations at the DFT level are performed to verify the energetic ordering and stability of the structures predicted by the Gupta potential finding that dodecahedral core-shell structures are indeed the putative global minima for Pt13Ag20 and Pt13Pd20, whereas decahedral structures are obtained as the minimum energy configurations for Pt13Au20 and Pt13Cu20 clusters.

Computational study of Au_4 cluster on a carbon nanotube with and without defects using QM/MM methodology.

We use ONIOM (QM/MM) methodology to carry out geometry calculations in a 4-atom nanocluster supported by an (8, 8) armchair carbon nanotube with and without defects employing LSDA/SDD for the QM system and UFF for MM. In two particular cases, defects were added in the carbon nanotube wall. These defects are a double oxygenated vacancy (Vac2O2) and a double vacancy but without oxygen which creates two pentagons and an octagon. Our results show how geometries using QM/MM and energies calculations carried out with QM, change on both the gold nanocluster and the carbon nanotube. In addition, an application of ONIOM methodology in a comparative study to predict behavior of structures as hybrid materials based in carbon nanotubes combined with gold nanoclusters is shown. In this work we examine geometry changes on both the gold nanocluster and the carbon nanotube. A comparison is made with the binding energy resulting values as well as with the orbital energies such as the frontier orbitals HOMO and LUMO.

Tetrahelix conformations and transformation pathways in Pt1Pd12 clusters.

The threshold method is used to explore the potential energy surface of the Pt(1)Pd(12) bimetallic cluster, defined by the Gupta semiempirical potential. A set of helical structures, which follow a Bernal tetrahelix pattern, correspond to local minima for the Pt(1)Pd(12) cluster, characterizing the region of the energy landscape where these structures are present. Both right-handed and left-handed chiral forms were discovered in our searches. Energetic and structural details of each of the tetrahelices are reported as well as the corresponding transition probabilities between these structures and with respect to the icosahedron-shaped global minimum structure via a disconnectivity graph analysis.

Structures and energetics of 98 atom Pd-Pt nanoalloys: potential stability of the Leary tetrahedron for bimetallic nanoparticles.

The energetics of 98 atom bimetallic Pd-Pt clusters are studied using a combination of: a genetic algorithm technique (to explore vast areas of the configurational space); a basin-hopping atom-exchange routine (to search for lowest-energy homotops at fixed composition); and a shell optimisation approach (to search for high symmetry isomers). The interatomic interactions between Pd and Pt are modelled by the Gupta many-body empirical potential. For most compositions, the putative global minima are found to have structures based on defective Marks decahedra, but in the composition range from Pd46Pt52 to Pd63Pt35, the Leary tetrahedron (LT)--a structure previously identified for 98 atom Lennard-Jones clusters--is consistently found as the most stable structure. Based on the excess energy stability criterion, Pd56Pt42 represents the most stable cluster across the entire composition range. This structure, a Td-symmetry LT, exhibits multi-layer segregation with an innermost core of Pd atoms, an intermediate layer of Pt atoms and an outermost Pd surface shell (Pd-Pt-Pd). The stability of the Leary tetrahedron is compared against other low-energy competing structural motifs: the Marks decahedron (Dh-M), a "quasi" tetrahedron (a closed-packed structure) and two other closed-packed structures. The stability of LT structures is rationalized in terms of their spherical shape and the large number of nearest neighbours.