Icosahedron Structure Research Articles

Symmetry Reduction upon Size Mismatch: The Non‐Icosahedral Intermetalloid Cluster [Co@Ge12]3−

AbstractA new complex comprising [Co@Ge12]3– cluster core was synthesized through the reaction of CoMe(PMe3)4 and K4Ge9 in ethylenediamine solution. The pseudo‐D5d geometry of this cluster can be viewed as structurally derived from an icosahedral cage via Jahn‐Teller effect, leading to notable bonding differences from Ih‐[M@E12]q− clusters (E = Sn, Pb with q = 2, 3). The [Co@Ge12]3– cluster represents a structural conundrum. On the basis of the geometric considerations it could be viewed as a sandwich complex. However, chemical bonding analysis revealed that there is a direct covalent multicenter bonding between the two pentagons, thus indicating that the structure should be viewed as an elongated icosahedron. Further theoretical calculations on [M@Ge12]3− (M = Rh, Ir, Mt) indicate that similar compounds of larger‐size metal atoms can drive the complete transformation of [M@Ge12]3− clusters from icosahedron structure to a sandwich one.

A molecular dynamics study: Structures and thermal stability of PdmPt(13−m)Ag42 ternary nanoalloys

Structural optimization of ternary PdmPt[Formula: see text]Ag[Formula: see text] nanoalloys was performed using the basin-hopping algorithm, and the Gupta many-body potential was adopted to model interatomic interaction. The optimization results show that all compositions have a structure based on icosahedron with a core–shell segregation. While the Ag atoms prefer to segregate to the surface, Pd and Pt atoms were located at the core of the cluster due to the higher surface and cohesive energy. The single platinum atom with the highest cohesive energy in Pd[Formula: see text]Pt1Ag[Formula: see text] nanoalloy was located at the center of the cluster. Also in all other compositions except Pd[Formula: see text]Ag[Formula: see text], Pd atoms occupy the second shell position of the icosahedron structure. We used classical molecular dynamics (MD) simulations in canonical ensemble conditions (NVT) to investigate the melting temperatures of ternary PdmPt[Formula: see text]Ag[Formula: see text] nanoalloys with the interatomic interactions modeled by the same potential with optimizations. The icosahedral structures were taken as the initial configurations for MD simulations. We obtained caloric curves and Lindemann indexes to investigate the melting transitions. The simulation results showed that varying the composition gives rise to a fluctuation in melting temperatures. The highest melting temperature belongs to the Pd9Pt4Ag[Formula: see text] nanoalloy cluster within the other compositions. However, the relative stability investigation indicates the Pd8Pt5Ag[Formula: see text] nanoalloy cluster as the most stable composition. The Lindemann indexes obtained for the second and third shell of icosahedral structures show that the melting takes place as a whole without any surface premelting.

Structures and Electronic Properties of Ni–Al Alloy Clusters from First-Principles Calculations

Using the density functional theory calculations with the PBE exchange–correlation energy functional, we have studied the low-energy structures and electronic properties of Ni–Al alloy clusters for adsorbing or doping an aluminum atom to Nin (n = 13, 19, 23, 26, 29 and 55) clusters. The most stable structures of NinAl are viewed as adding an Al atom at the hollow triangle and rhombus site of the icosahedron (n = 13, 55) and double-icosahedron (n = 19, 23, 26 and 29) structures, respectively. For Nin−1Al, it can be seen that an Al atom gradually moves from surface (n = 13, 19, 23 and 26) to the interior site (n = 29, 55) in the most stable structures. The electronic properties of the Ni–Al alloy clusters including binding energies, magnetic properties, charge transfer and density of states have also been studied.

Density functional investigation of the adsorption effects of PH3 and SH2 on the structure stability of the Au55 and Pt55 nanoclusters.

Although several studies have been reported for Pt55 and Au55 nanoclusters, our atomistic understanding of the interplay between the adsorbate-surface interactions and the mechanisms that lead to the formation of the distorted reduced core (DRC) structures, instead of the icosahedron (ICO) structure in gas phase, is still far from satisfactory. Here, we report a density functional theory (DFT) investigation of the role of the adsorption effects of PH3 (one lone pair of electrons) and SH2 (two lone pairs) on the relative stability of the Pt55 and Au55 nanoclusters. In gas phase, we found that the DRC structures with 7 and 9 atoms in the core region are about 5.34 eV (Pt55) and 2.20 eV (Au55) lower in energy than the ICO model with Ih symmetry and 13 atoms in the core region. However, the stability of the ICO structure increases by increasing the number of adsorbed molecules from 1 to 18, in which both DRC and ICO structures are nearly degenerate in energy at the limit of 18 ligands, which can be explained as follows. In gas phase, there is a strong compression of the cationic core region by the anionic surface atoms induced by the attractive Coulomb interactions (core+-surface-), and hence, the strain release is obtained by reducing the number of atoms in the cationic core region, which leads to the 55 atoms distorted reduced core structures. Thus, the Coulomb interactions between the core+ and surface- contribute to break the symmetry in the ICO55 structure. On the other hand, the addition of ligands on the anionic surface reduces the charge transfer between the core and surface, which contributes to decrease the Coulomb interactions and the strain on the core region of the ICO structure, and hence, it stabilizes a compact ICO structure. The same conclusion is obtained by adding van der Waals corrections to the plain DFT calculations. Similar results are obtained by the addition of steric effects, which are considered through the adsorption of triphenylphosphine (PPh3) molecules on Au55, in which the relative stability between ICO and DRC is the same as for PH3 and SH2. However, for Pt55, we found an inversion of stability due to the PPh3 ligand effects, where ICO has higher stability than DRC by 2.40 eV. Our insights are supported by several structural, electronic, and energetic analyses.

Ethanol and Water Adsorption on Transition-Metal 13-Atom Clusters: A Density Functional Theory Investigation within van der Waals Corrections.

Transition-metal (TM) nanoparticles supported on oxides or carbon black have attracted much attention as potential catalysts for ethanol steam reforming reactions for hydrogen production. To improve the performance of nanocatalysts, a fundamental understanding of the interaction mechanism between water and ethanol with finite TM particles is required. In this article, we employed first-principles density functional theory with van der Waals (vdW) corrections to investigate the interaction of ethanol and water with TM13 clusters, where TM = Ni, Cu, Pd, Ag, Pt, and Au. We found that both water and ethanol bind via the anionic O atom to onefold TM sites, while at higher-energy structures, ethanol binds also via the H atom from the CH2 group to the TM sites, which can play an important role at real catalysts. The putative global minimum TM13 configurations are only slightly affected upon the adsorption of water or ethanol; however, for few systems, the compact higher-energy icosahedron structure changes its configuration upon ethanol or water adsorption. That is, those configurations are only shallow local minimums in the phase space. Except few deviations, we found similar trends for the magnitude of the adsorption energies of water and ethanol, that is, Ni13 > Pt13 > Pd13 and Cu13 > Au13 > Ag13, which is enhanced by the addition of the vdW correction (i.e., from 4% to 62%); however, the trend is the same. We found that the magnitude of the adsorption energy increases by shifting the center of gravity of the d-states toward the highest occupied molecular orbital. On the basis of the Mulliken and Hirshfeld charge analysis, as well as electron density differences, we identified the location of the charge redistribution and a tiny charge transfer (from 0.01 e to 0.19 e) from the molecules to the TM13 clusters. Our vibrational analysis indicates the red shifts in the OH modes upon binding of both water and ethanol molecules to the TM13 clusters, suggesting a weakening of the O-H bonding.

A basin-hopping Monte Carlo investigation of the structural and energetic properties of 55- and 561-atom bimetallic nanoclusters: the examples of the ZrCu, ZrAl, and CuAl systems

We report a basin-hopping Monte Carlo investigation within the embedded-atom method of the structural and energetic properties of bimetallic ZrCu, ZrAl, and CuAl nanoclusters with 55 and 561 atoms. We found that unary Zr55, Zr561, Cu55, Cu561, Al55, and Al561 systems adopt the well known compact icosahedron (ICO) structure. The excess energy is negative for all systems and compositions, which indicates an energetic preference for the mixing of both chemical species. The ICO structure is preserved if a few atoms of the host system are replaced by different species, however, the composition limit in which the ICO structure is preserved depends on both the host and new chemical species. Using several structural analyses, three classes of structures, namely ideal ICO, nearly ICO, and distorted ICO structures, were identified. As the amounts of both chemical species change towards a more balanced composition, configurations far from the ICO structure arise and the dominant structures are nearly spherical, which indicates a strong minimization of the surface energy by decreasing the number of atoms with lower coordination on the surface. The average bond lengths follow Vegard’s law almost exactly for ZrCu and ZrAl, however, this is not the case for CuAl. Furthermore, the radial distribution allowed us to identify the presence of an onion-like behavior in the surface of the 561-atom CuAl nanocluster with the Al atoms located in the outermost surface shell, which can be explained by the lower surface energies of the Al surfaces compared with the Cu surfaces. In ZrCu and ZrAl the radial distribution indicates a nearly homogeneous distribution for the chemical species, however, with a slightly higher concentration of Al atoms on the ZrAl surface, which can also be explained by the lower surface energy.

A theoretical investigation of the structural and electronic properties of 55-atom nanoclusters: The examples of Y–Tc and Pt

Several studies have found that the Pt55 nanocluster adopts a distorted reduced core structure, DRC55, in which there are 8-11 atoms in the core and 47-44 atoms in the surface, instead of the compact and high-symmetry icosahedron structure, ICO55, with 13 and 42 atoms in the core and surface, respectively. The DRC structure has also been obtained as the putative global minimum configuration (GMC) for the Zn55 (3d), Cd55 (4d), and Au55 (5d) systems. Thus, the DRC55 structure has been reported only for systems with a large occupation of the d-states, where the effects of the occupation of the valence anti-bonding d-states might play an important role. Can we observe the DRC structure for 55-atom transition-metal systems with non-occupation of the anti-bonding d-states? To address this question, we performed a theoretical investigation of the Y 55, Zr55, Nb55, Mo55, Tc55, and Pt55 nanoclusters, employing density functional theory calculations. For the putative GMCs, we found that the Y 55 adopts the ICO55 structure, while Nb55 and Mo55 adopt a bulk-like fragment based on the hexagonal close-packed structure and Tc55 adopts a face-centered cubic fragment; however, Zr55 adopts a DRC55 structure, like Zn55, Cd55, Pt55, and Au55. Thus we can conclude that the preference for DRC55 structure is not related to the occupation of the anti-bonding d-states, but to a different effect, in fact, a combination of structural and electronic effects. Furthermore, we obtained that the binding energy per atom follows the occupation of the bonding and anti-bonding model, i.e., the stability of the studied systems increases from Y to Tc with a small oscillation for Mo, which also explains the equilibrium bond lengths. We obtained a larger magnetic moment for Y 55 (31 μB) which can be explained by the localization of the d-states in Y at nanoscale, which is not observed for the remaining systems (0-1 μB).

Size effect in the melting and freezing behaviors of Al/Ti core-shell nanoparticles using molecular dynamics simulations**Project supported by the National Natural Science Foundation of China (Grant No. 21401064), the Science & Technology Development Program of Henan Province, China (Grant No. 142300410282), and the Program of Henan Educational Committee, China (Grant No. 13B140986).

The thermal stability of Ti@Al core/shell nanoparticles with different sizes and components during continuous heating and cooling processes is examined by a molecular dynamics simulation with embedded atom method. The thermodynamic properties and structure evolution during continuous heating and cooling processes are investigated through the characterization of the potential energy, specific heat distribution, and radial distribution function (RDF). Our study shows that, for fixed Ti core size, the melting temperature decreases with Al shell thickness, while the crystallizing temperature and glass formation temperature increase with Al shell thickness. Diverse melting mechanisms have been discovered for different Ti core sized with fixed Al shell thickness nanoparticles. The melting temperature increases with the Ti core radius. The trend agrees well with the theoretical phase diagram of bimetallic nanoparticles. In addition, the glass phase formation of Al–Ti nanoparticles for the fast cooling rate of 12 K/ps, and the crystal phase formation for the low cooling rate of 0.15 K/ps. The icosahedron structure is formed in the frozen 4366 Al–Ti atoms for the low cooling rate.

Controlling the crystalline phases (FCC, HCP and BCC) of thiolate-protected gold nanoclusters by ligand-based strategies

Significant advances in the research on atomically precise gold nanoclusters have led to crystallographic determination of total structures (i.e. atomic arrangements in the metal core and surface ligands) of nanoclusters. A fundamental question is what types of structures would exist in gold nanoclusters. Research in this field first revealed icosahedral and decahedral structures in gold nanoclusters, which are novel structures since these are not observed in bulk gold. The emergence of such new structures in nanoclusters has gained much attention; on the other hand, a question arises naturally: can ultrasmall gold nanoclusters adopt the face-centered cubic (FCC) packing structure that is exclusive in bulk gold or even the hexagonal-close-packing (HCP) and body-centered-cubic (BCC) structures? This question has been addressed by the recent successes in controlling gold nanoclusters with all the three types of crystalline structures (or phases). The syntheses of these nanoclusters are based on the ligand strategies. The ligand effect on the structure, which was overlooked in earlier works, has now been recognized as an essential factor. In this highlight, we introduce the diverse structures of gold nanoclusters with 30 atoms or so, such as Au38(SR)24, Au36(SR)24, Au30(SR)18, and Au38S2(SR)20 as examples of the icosahedron, FCC, HCP, and BCC structures, respectively. The driving force to form these structures is discussed from the perspective of the major roles of the protecting ligands.

Intriguing structures and magic sizes of heavy noble metal nanoclusters around size 55 governed by relativistic effect and covalent bonding

Nanoclusters usually display exotic physical and chemical properties due to their intriguing geometric structures in contrast to their bulk counterparts. By means of first-principles calculations within density functional theory, we find that heavy noble metal PtN nanoclusters around the size N = 55 begin to prefer an open configuration, rather than previously reported close-packed icosahedron or core-shell structures. Particularly, for PtN, the widely supposed icosahedronal magic cluster is changed to a three-atomic-layered structure with D6h symmetry, which can be well addressed by our recently established generalized Wulff construction principle (GWCP). However, the magic number of PtN clusters around 55 is shifted to a new odd number of 57. The high symmetric three-layered Pt57 motif is mainly stabilized by the enhanced covalent bonding contributed by both spin-orbital coupling effect and the open d orbital (5d(9)6s(1)) of Pt, which result in a delicate balance between the enhanced Pt-Pt covalent bonding of the interlayers and negligible d dangling bonds on the cluster edges. These findings about PtN clusters are also applicable to IrN clusters, but qualitatively different from their earlier neighboring element Os and their later neighboring element Au. The magic numbers for Os and Au are even, being 56 and 58, respectively. The findings of the new odd magic number 57 are the important supplementary of the recently established GWCP.

Analysis of structures and melting properties of the 19-atom Ni–Co clusters

In this paper, by using the classical molecular dynamics method and the GEAM potential, the geometric structure and the melting properties of the 19-atom Ni – Co clusters with different compositions are studied. It is found that all the clusters have the double icosahedron structures although some of the structures are slightly deformed. With the increase of the temperature, a pre-melting phenomenon is observed. The pre-melting temperatures of the pure cobalt and nickel clusters are very close. But on the whole, the pre-melting temperature decreases with the increase of the number of the nickel atom for the mixed clusters. The effects of the substitution atoms on the melting temperature of the clusters are similar to that on the pre-melting temperature although there are some oscillations in the decrease process. The mechanism of these findings are also investigated and analyzed.

Formation and Evolution of Icosahedron during Relaxation of Amorphous Ca<sub>7</sub>Mg<sub>3</sub> Alloy

The molecular dynamics simulation studies on the microstructure evolution properties of amorphous Ca7Mg3 alloy during the isothermal annealing have been performed. The simulated structure factor S(q) of Ca7Mg3 is well agreed with the experimental data. Results indicate that the icosahedron structure plays dominate role in the structure transformation, and the smaller Mg atoms are much more probable to be the central atoms of the basic clusters of icosahedron.

Structure Relaxations during the Isothermal Annealing of Amorphous Ca<sub>7</sub>Mg<sub>3</sub> Alloy

The molecular dynamics simulation studies on the microstructure evolution properties of amorphous Ca7Mg3 alloy during the isothermal annealing have been performed. The simulated structure factor S(q) of Ca7Mg3 is well agreed with the experimental data. Results indicate that the metallic glass of Ca7Mg3 alloy is relaxed into amorphous structure of greater stability in which much more icosahedron structures is formed; interestingly, it is also found that the short short-range order has no change, while the short-range order of the system increases during the isothermal annealing process.

Coupled polaron-phonon effects on Seebeck coefficient and lattice conductivity of B13C2from first principles

The anomalous temperature-independent behavior of the Seebeck coefficient and the lattice thermal conductivity of B${}_{13}$C${}_{2}$ are explained through polaron and phonon evolutions found using ab initio molecular dynamics (AIMD). Analyses of lattice dynamics show that the unique icosahedron structures dominate the optical phonon modes and CBC intericosahedral bonds dominate the local acoustic vibration. We identify that the temperature-induced Jahn-Teller distortion and electron-phonon coupling in icosahedron structures create small polarons (i.e., charge trapping and phonon softening). We also verify that large-displacement chain atoms scatter heat-conducting phonons. Using equilibrium and nonequilibrium AIMD methods (including entropy and energy analyses), we predict the Seebeck coefficient and its components as well as the lattice thermal conductivity, and we find good agreement with experiments. Softened and localized phonons make a significant vibrational contribution to the Seebeck coefficient and allow for an amorphous-like lattice thermal conductivity.

Geometry, Orbital Interaction, and Oxygen Chemisorption Properties of Chromium-Doped Nickel Clusters

Density functional theory (DFT) for generalized gradient approximation calculations has been applied to study the stability and orbital structures of Ni and Cr-doped nickel clusters varying in the range 2 ≤ n ≤ 13. Moreover, chemisorption of the oxygen atom has also been studied to understand the oxygen reactivity on Ni and Cr-doped nickel clusters. The binding energy per atom gradually increases with the increase of number of atoms for pure nickel and Cr-doped nickel clusters. The icosahedral Ni12Cr cluster is the most stable structure with binding energy of 2.87 eV per atom. This calculation noticed that the chromium atom prefers to exhibit center at the cluster (n ≥ 10) rather than edge. Furthermore, cluster stability has been gradually decreased with the increase of chromium concentration. Icosahedron structures containing more than four chromium atoms are less stable than the Ni13 cluster. Metal atom 3d orbitals have a strong influence on the overall structure stability of these clusters. The interac...

Structures, stabilities and electronic properties of FePb n ( n=1–14) clusters: Density-functional theory investigations

The structures, stabilities and electronic properties of FePb n ( n=1–14) clusters have been studied using the density-functional theory (DFT). Extensive search of the ground-state structures has been carried out by considering a larger number of structural isomers for each cluster size. The Fe atom gradually falls into the interior of the Pb framework as the number of Pb atom increases from 1 to 14. The FePb n clusters at n=3, 5, 10, 12 have relatively higher stability by analyzing the averaged binding energy and the second-order energy difference. Especially, FePb 12 is more stable, owing to its highest symmetrical icosahedron structure. The magnetic moments of FePb n clusters do not quench when Fe atom is encapsulated in the Pb framework and mostly originate from 3d state of Fe atom.

The role of electron localization in the atomic structure of transition-metal 13-atom clusters: the example of Co13, Rh13, and Hf13

The crystalline structure of transition-metals (TM) has been widely known for several decades, however, our knowledge on the atomic structure of TM clusters is still far from satisfactory, which compromises an atomistic understanding of the reactivity of TM clusters. For example, almost all density functional theory (DFT) calculations for TM clusters have been based on local (local density approximation--LDA) and semilocal (generalized gradient approximation--GGA) exchange-correlation functionals, however, it is well known that plain DFT fails to correct the self-interaction error, which affects the properties of several systems. To improve our basic understanding of the atomic and electronic properties of TM clusters, we report a DFT study within two nonlocal functionals, namely, the hybrid HSE (Heyd, Scuseria, and Ernzerhof) and GGA+U functionals, of the structural and electronic properties of the Co(13), Rh(13), and Hf(13) clusters. For Co(13) and Rh(13), we found that improved exchange-correlation functionals decrease the stability of open structures such as the hexagonal bilayer (HBL) and double simple-cubic (DSC) compared with the compact icosahedron (ICO) structure, however, DFT-GGA, DFT-GGA+U, and DFT-HSE yield very similar results for Hf(13). Thus, our results suggest that the DSC structure obtained by several plain DFT calculations for Rh(13) can be improved by the use of improved functionals. Using the sd hybridization analysis, we found that a strong hybridization favors compact structures, and hence, a correct description of the sd hybridization is crucial for the relative energy stability. For example, the sd hybridization decreases for HBL and DSC and increases for ICO in the case of Co(13) and Rh(13), while for Hf(13), the sd hybridization decreases for all configurations, and hence, it does not affect the relative stability among open and compact configurations.

SURFACE RELAXATION INDUCED STABILITY OF LOW-SYMMYTRIC STRUCTURES OF AG CLUSTERS

The cohesive energies of Ag nanoclusters E c (N) in truncated octahedron (TO), icosahedron (IH) and truncated decahedron (DH) structures are evaluated through both theory and Density Function theory (DFT) simulation where N denotes the atom number. In the theoretical calculation, through relating E c (N) values to the total bond numbers of clusters, E c (N) value of IH structure is found to be the lowest at any N. In DFT simulation, E c (N) values are separately evaluated before and after geometry optimization. IH structure is always favorable to exist when clusters are un-relaxed, agreed with the theoretical calculation. When the clusters are relaxed, the structural stability becomes selective and low-symmetric TO and DH structures are respectively stable at some specific size. The reason of the difference on E c (N) values between two methods is compared. Both methods indicate that Ec(N) values of the clusters are larger than those of the corresponding bulk crystals E cb .

Roles of cysteines Cys115 and Cys201 in the assembly and thermostability of grouper betanodavirus particles

The virus-like particle (VLP) assembled from capsid subunits of the dragon grouper nervous necrosis virus (DGNNV) is very similar to its native T = 3 virion. In order to investigate the effects of four cysteine residues in the capsid polypeptide on the assembly/dissociation pathways of DGNNV virions, we recombinantly cloned mutant VLPs by mutating each cysteine to destroy the specific disulfide linkage as compared with thiol reduction to destroy all S–S bonds. The mutant VLPs of C187A and C331A mutations were similar to wild-type VLPs (WT-VLPs); hence, the effects of Cys187 and Cys331 on the particle formation and thermostability were presumably negligible. Electron microscopy showed that either C115A or C201A mutation disrupted de novo VLP formation significantly. As shown in micrographs and thermal decay curves, β-mercaptoethanol-treated WT-VLPs remained intact, merely resulting in lower tolerance to thermal disruption than native WT-VLPs. This thiol reduction broke disulfide linkages inside the pre-fabricated VLPs, but it did not disrupt the appearance of icosahedrons. Small dissociated capsomers from EGTA-treated VLPs were able to reassemble back to icosahedrons in the presence of calcium ions, but additional treatment with β-mercaptoethanol during EGTA dissociation resulted in inability of the capsomers to reassemble into the icosahedral form. These results indicated that Cys115 and Cys201 were essential for capsid formation of DGNNV icosahedron structure in de novo assembly and reassembly pathways, as well as for the thermal stability of pre-fabricated particles.

Design of Robust and Reactive Nanoparticles with Atomic Precision: 13Ag-Ih and 12Ag−1X (X = Pd, Pt, Au, Ni, or Cu) Core−Shell Nanoparticles

Density functional theory calculations and a modified reaction model confirm that the initial high CO oxidation reactivity of a 13Ag-Ih nanoparticle from an icosahedron (Ih) structure is immediately diminished as the nanoparticle is transformed to an amorphous state by a reaction-driven structural change. The adsorption of O2 and the formation of a four-center intermediate metastable state from coadsorbed CO and O2 positively charge the 13Ag-Ih nanoparticle, and the repulsive force between the Ag atoms causes the reaction-driven structural change of the 13Ag-Ih nanoparticle. When one central Ag atom is substituted with a solute atom, a core−shell type of 12Ag−1X-Ih (X = Pd, Pt, Au, Ni, or Cu) bimetallic nanoparticle is stabilized. Among them, we propose the 12Ag−1Pd nanoparticle as a robust and reactive Ag-based bimetallic nanoparticle for CO oxidation. The results show that the structural fluxionality accounts for the catalytic activity of small nanoparticles.