Planar Clusters Research Articles

Ionization energies, electron affinities, and binding energies of Li-doped gold nanoclusters

Structural and energetic properties of nanoclusters of Au n , Li n , and LiAu n−1 (n = 1–6) were studied employing MP2, M062X, and B3LYP computational methods. The planar (2D) isomers were the most stable structures of the Au n clusters. Binding energy per atom (E b) for the Au n clusters increased with increase in the cluster size and were in the range of 0.9–1.7 eV. The Li n clusters were more unstable, and their E b values were about 0.4–0.6 eV. Lithium-doping of Au n clusters resulted in an increase of E b values and more stable clusters. Also, Li-doping led to stability of the 3D clusters so that the bipyramidal Au4Li isomer became more stable than the planar clusters. It was observed that the electron affinities of the Au n , Li n , and LiAu n−1 clusters increased with cluster sizes. Ionization energies and electron affinities of the Li-doped gold clusters were smaller than those for pure Au n clusters.

First principles Raman study of boron and nitrogen doped planar T-graphene clusters

Tetragonal graphene (TG) is one of the theoretically proposed dynamically stable graphene allotropes. In this study, the Raman spectra, IR spectra and some electronic properties of pristine and doped (single boron (B) and nitrogen (N)) TG have been investigated by first-principles based density functional theory (DFT) at the B3LYP/6-31G(d) level. Formation energy computation indicates that for the pristine structures, stability increases with increasing cluster size. In addition, for a particular cluster size, single B doping introduces some distortion in the system while single N doping increases the stability of it. The Raman spectrum of the N doped system is dominated by a single peak but for the B doped system several intense lines are found. For all the structures low intensity similar breathing-like modes have been observed. Besides, relatively low (high) intensity Raman lines are found for single B (N) doping compared to those of the pristine one. The vibrational study also reveals the existence of a prominent phonon Raman line for pristine clusters which hardly changes its position and nature of vibration with varying cluster size. So this mode can be used for identification of pristine TG structures. Unlike pristine TG, the doped structures possess non-zero finite dipole moments due to asymmetry in charge distribution. Large values of the HOMO–LUMO gap as well as the absence of DOS at the Fermi level lead to the semiconducting nature of all the structures. All these theoretical predictions from DFT calculations may shed light on experimental observations involving TG systems.

Trends in the Reactivity of Molecular O2 with Copper Clusters: Influence of Size and Shape

The adsorption and dissociation of molecular O2 on copper clusters of varying size and morphology (Cun with n = 3–8, 13, and 38 atoms) has been systematically investigated using several DFT approaches. Different modes of adsorption of molecular O2 are found for each atomicity of the copper clusters, with their relative stability depending on the cluster morphology: bridge conformations are stabilized on planar clusters, while hollow h-100 and h-111 modes are preferentially formed on 3D clusters. O2 adsorption energies correlate with the HOMO energy of the isolated copper clusters but not with their atomicity. On the other hand, the degree of activation of the O–O bond, and therefore the activation energy barrier necessary to break it, depends on the charge transferred to the π* MO of O2, which in turn is determined by the mode of adsorption of O2 on the metal. Cluster morphology appears then as the key factor determining the catalytic activity of copper, since the most activating h-111 and h-100 adsorptio...

Understanding the stable boron clusters: A bond model and first-principles calculations based on high-throughput screening.

The unique electronic property induced diversified structure of boron (B) cluster has attracted much interest from experimentalists and theorists. B30-40 were reported to be planar fragments of triangular lattice with proper concentrations of vacancies recently. Here, we have performed high-throughput screening for possible B clusters through the first-principles calculations, including various shapes and distributions of vacancies. As a result, we have determined the structures of Bn clusters with n = 30-51 and found a stable planar cluster of B49 with a double-hexagon vacancy. Considering the 8-electron rule and the electron delocalization, a concise model for the distribution of the 2c-2e and 3c-2e bonds has been proposed to explain the stability of B planar clusters, as well as the reported B cages.

B27−: Appearance of the smallest planar boron cluster containing a hexagonal vacancy

Photoelectron spectroscopy and ab initio calculations have been carried out to probe the structures and chemical bonding of the B27 (-) cluster. Comparison between the experimental spectrum and the theoretical results reveals a two-dimensional (2D) global minimum with a triangular lattice containing a tetragonal defect (I) and two low-lying 2D isomers (II and III), each with a hexagonal vacancy. All three 2D isomers have 16 peripheral boron atoms and 11 inner boron atoms. Isomer I is shown to be mainly responsible for the observed photoelectron spectrum with isomers II and III as minor contributors. Chemical bonding analyses of these three isomers show that they all feature 16 localized peripheral B-B σ-bonds. Additionally, isomer I possesses 16 delocalized σ bonds and nine delocalized π bonds, while isomers II and III each contain 17 delocalized σ bonds and eight delocalized π bonds. It is found that the hexagonal vacancy is associated generally with an increase of delocalized σ bonds at the expense of delocalized π bonds in 2D boron clusters. The hexagonal vacancy, characteristic of borophenes, is found to be a general structural feature for mid-sized boron clusters. The current study shows that B27 (-) is the first boron cluster, where a hexagonal vacancy appears among the low-lying isomers accessible experimentally.

Two luminescent bcu-type metal-organic frameworks constructed from distinct cadmium clusters

Based on linear 1,4-benzeneditetrazol-5-yl ligand, two Cd(II) metal-organic frameworks have been constructed from square planar tetranuclear and linear trinuclear cadmium clusters, respectively, both of which show 8-connected bcu topology and luminescent properties.

Steady activity of microfractures on geological faults loaded by mining stress

Acoustic Emissions (AE) down to MW~–4 were recorded at a site 1km beneath the surface in the Cooke 4 Mine, South Africa. Several planar AE clusters with lateral extent of 10–100m were identified. Most of them were located several tens of meters away from the mining front, and exhibited steady activity during the analysis period of about two months. Some of the clusters coincided with mapped faults. The planar-cluster AEs were sharply aggregated within a thickness of several decimeters, likely delineating the fracture interface of the fault and its higher-order morphology such as branches, bends, and stepovers. The composite focal mechanism evaluated for each cluster was consistent with slip events on the fracture interface. These results imply that numerous shear microfractures occur steadily on a natural fault surface subjected to a mining-related stress increase. The planar clusters consist of very small AEs (99.7% were smaller than MW –2), exhibiting high b-values much exceeding unity. This contrasts with the more usual b-values of the stope-cluster AEs, which were aggregated within 20m of the mining front and exhibited a more scattered distribution. The size distribution of microfractures on a fracture interface may directly reflect fine-scale irregularities of the interface. On the other hand, many other mapped faults near the planar AE clusters were not accompanied by AE activities, despite the fact that these quiet faults were subjected to a similar stress history. The presence or absence of AE activities on a fault may reflect different states of the fault, including stress and strength.

A three-dimensional complex with a one-dimensional cobalt-hydroxyl chain based on planar nonanuclear clusters showing spin-canted antiferromagnetism.

A new three-dimensional magnetic network, [Co9(OH)6(C42H24O18P3N3)2(H2O)8] (1), has been successfully prepared by utilizing the flexible hexacarboxylate ligand derived from cyclotriphosphazene, which had been characterized by single-crystal X-ray diffraction and magnetic measurement. This compound consists of one-dimensional (1D) cobalt-hydroxyl chains based on planar nonanuclear clusters, which are located in the b-c plane to form the nearly two-dimensional cobalt layer. Magnetic measurements reveal that 1 shows spin-canted antiferromagnetism with spin-glass behavior. These results suggest that reasonable design and choice of large carboxylate ligand based on a specific scaffold could be effective for the construction of magnetic materials based on a novel 1D magnetic chain.

Quasi‐static slip patch growth to 20 m on a geological fault inferred from acoustic emissions in a South African gold mine

AbstractThree months of acoustic emission (AE) monitoring in a South African gold mine down to Mw −5 revealed a newly emergent planar cluster of 7557 events −3.9 ≤ Mw ≤ −1.8 (typical rupture radius of 6–70 cm) that expanded with time to reach a size of 20 m on a preexisting geological fault near an active mining front 1 km beneath the ground. It had a sharply defined, planar configuration, with hypocenters aggregated within a thickness of only several decimeters. We infer that the zone defines an aseismic slip patch on the fault, wherein the individual AEs represent failures of very small asperities being loaded by the aseismic slip. Additional support for the interpretation was obtained by analyzing composite focal mechanisms and repeating events. The patch expansion over 2 months was likely quasistatic because all individual AEs ruptured much smaller areas than the cluster size at the corresponding time. The b values dropped gradually from 2.6 to 1.4, consistent with a significant increase in shear stress expected of the mining style. Another cluster with similar characteristics emerged later on a neighboring part of the same fault and grew to a 10 m extent in the last weeks of the study period. The quasi‐static expansion of inferred localized slow‐slip patches to sizes of 10–20 m suggests that the critical crack length on natural faults can be at least as large, much exceeding the decimeter range derived from laboratory stick‐slip experiments on saw‐cut rocks.

The debut of all-boron fullerene

Boron is the fifth element and next to carbon in the periodic table of the elements, but boron has been researched less than its neighbor carbon. Borax sourced from a natural boronrich mine in Yamdrok Lake, Tibet, China, has been used as a fusion agent to make glass from ancient times. Elemental boron, however, was elusive until 1808 when it was prepared from electrolysis of melted boron trioxide or by reducing boric acid with potassium. Structures of elemental boron include an icosahedral (Ih) B12 motif connected in an ordered manner, as exemplified by α-rhombohedral boron (Fig. 1a). The dangling bonds in each Ih-B12 unit can be saturated by hydrogen to produce borane species. In stark contrast to the ubiquitous Ih-B12 unit in elemental boron allotropes and boranes, a different B12 all-boron clusterwith aC3v-symmetric planar structure that resembles a solid disk with three boron atoms in the center surrounded by a peripheral ring of boron atoms has also been observed (Fig. 1b) [1]. With six delocalized π electrons that exhibit ‘disk delocalization’, the planar B12 cluster is analogous to benzene with its wellknown cyclic delocalization. Bn clusters adopt 2D planar or quasi-planar structures even up to n = 36 [2]. Because of their diverse set of structural and bonding characteristics, scientists believe that boron and carbon form a set of complementary chemical systems and have long been fascinated with whether or not structures such as cage-like all-boron clusters are as prevalent as all-carbon fullerenes. A series of all-boron cage configurations stabilized by three-center Figure 1. The structures of all-boron clusters (B12 and B40). (a) Icosahedral B12 motifs bound by threecenter two-electronσ bonds (indicated by dashed lines) to form a B12 layer inα-rhombohedral boron; (b) Top and side views of a C3v-symmetric B12 cluster; (c) Top and side views of Cs-symmetric B40 with two adjacent hexagonal holes; (d) Top and side views of a neutral B40 cluster with two hexagonal and four heptagonal holes. This figure was redrawn according to the coordinates of a B40 cluster provided in the supplementary information of [5].

Fabrication of planar colloidal clusters with template-assisted interfacial assembly.

The synthesis of nanoparticle clusters, also referred to as colloidal clusters or colloidal molecules, is being studied intensively as a model system for small molecule interactions as well as for the directed self-assembly of advanced materials. This paper describes a technique for the interfacial assembly of planar colloidal clusters using a combination of top-down lithographic surface modification and bottom-up Langmuir-Blodgett deposition. Micrometer sized polystyrene latex particles were deposited onto a chemically modified substrate from a decane-water interface with Langmuir-Blodgett deposition. The surface of the substrate contained hydrophilic domains of various size, spacing, and shape, while the remainder of the substrate was hydrophobic. Particles selectively deposited onto hydrophilic regions from the decane-water interface. The number of deposited particles depended on the size of each patch, thereby demonstrating that tuning cluster size is possible by engineering patch geometry. Following deposition, the clusters were permanently bonded with temperature annealing and then removed from the substrate via sonication. The permanently bonded planar colloidal clusters were stable in an aqueous environment and at a decane-water interface laden with isotropic colloidal particles. The method is a simple and fast way to synthesize colloidal clusters with few limitations on particle chemistry, composition, and shape.

Planar dicyclic B6S6, B6S6(-), and B6S6(2-) clusters: boron sulfide analogues of naphthalene.

Inorganic analogues of hydrocarbons or polycyclic aromatic hydrocarbons (PAHs) are of current interest in chemistry. Based upon global structural searches and B3LYP and CCSD(T) calculations, we present herein the perfectly planar dicyclic boron sulfide clusters: D2h B6S6 (1, (1)Ag), D2h B6S6(-) (2, (2)B3u), and D2h B6S6(2-) (3, (1)Ag). These are the global minima of the systems, being at least 0.73, 0.81, and 0.53 eV lower in energy, respectively, than their alternative isomers at the CCSD(T) level. The D2h structures feature twin B3S2 five-membered rings, which are fused together via a B2 unit and terminated by two BS groups. Bonding analyses show that the closed-shell B6S6(2-) (3) cluster possesses 10 delocalized π electrons, closely analogous to the bonding pattern of the aromatic naphthalene C10H8. The B6S6(-) (2) and B6S6 (1) species are readily obtained upon removal of one or two π electrons from B6S6(2-) (3). The results build a new analogous relationship between boron sulfide clusters and their PAH counterparts. The B6S6(-) (2) monoanion and B6S6(2-) (3) dianion can be effectively stabilized in neutral LiB6S6 and Li2B6S6 salts, respectively.

B11(-): a moving subnanoscale tank tread.

We present a concept that an elongated, planar boron cluster can serve as a "tank tread" at the sub-nanometer scale, a novel propulsion system for potential nanomachines. Density functional calculations at the PBE0/6-311+G* level for the global-minimum B11(-)C2v ((1)A1) and B11C2v ((2)B2) structures along the soft in-plane rotational mode allow the identification of their corresponding B11(-)C2v and B11C2v transition states, with small rotational energy barriers of 0.42 and 0.55 kcal mol(-1), respectively. The energy barriers are refined to 0.35 and 0.60 kcal mol(-1) at the single-point CCSD(T) level, suggesting that the clusters are structurally fluxional at room temperature. Molecular dynamics simulations show that B11(-) and B11 behave exactly like a tank tread, in which the peripheral B9 ring rotates almost freely around the B2 core. A full turn of rotation may be accomplished in around 2 ps. In contrast to molecular wheels or Wankel motors, the peripheral boron atoms in the tank tread behave as a flexible chain gliding around, rather than as a rigid wheel rotation. This finding is beyond imagination, which expands the concepts of molecular wheels and Wankel motors.

Boronyl as a terminal ligand in boron oxide clusters: hexagonal ring C(2v) B6O4 and ethylene-like D(2h) B6O4(-/2-).

Considerable recent research effort has been devoted to the development of boronyl (BO) chemistry. Here we predict three perfectly planar boron boronyl clusters: C2v B6O4 (1, (1)A1), D2h B6O4(−) (2, (2)B3u), and D2h B6O4(2−) (3, (1)Ag). These are established as the global-minimum structures on the basis of the coalescence kick and basin hopping structural searches and electronic structure calculations at the B3LYP/aug-cc-pVTZ level, with complementary CCSD/6-311+G* and single-point CCSD(T)/6-311+G*//B3LYP/aug-cc-pVTZ calculations for 2. The C2v B6O4 neutral cluster features a hexagonal B4O2 ring with two terminal BO groups. The D2h B6O4(−/2−) clusters have ethylene-like structures and are readily formulated as B2(BO)4(−/2−), in which a B2 core with double bond character is bonded to four terminal BO groups. Chemical bonding analyses show that B6O4 (1) possesses an aromatic π bonding system with three delocalized, six-centered π bonds over the hexagonal ring, rendering it an inorganic analogue of benzene, whereas the B6O4(−/2−) (2 and 3) species closely resemble ethylene in terms of structures and bonding. This work provides new examples for the analogy between boron oxides and hydrocarbons.

Planar wheel-type M©BnHn2−/−/0 clusters (M = Cr, Mn and Fe for dianion, anion and neutral, respectively; n = 6 and 7)

A new “electronic” strategy that adds two electrons into the dz2 orbital of the central M atom to form a lone pair, in contrast to Hoffmann’s “electronic” strategy to turn the bowl-type MBnHn0/+ (M = Cr and Mn; n = 6 and 7) clusters into planar wheel-type clusters.

Adsorption and Dissociation of H2 on B n and MgB n (n = 2–7) Clusters: A DFT Investigation

Density functional theory at the B3LYP/6-311++G(d,p) level was used to study the adsorption and dissociation property of a single H2 molecule on MgB n (n = 2–7) clusters. The hydrogenated structures with lowest-energy of different cluster sizes demonstrate that H atoms prefer to bind with the terminated B atoms with small coordination number by single bond. The structural and electronic stabilities of the hydrogenated clusters were investigated via analyzing the average binding energy, fragmentation energy, second-order energy difference, vertical ionization potential, vertical electron affinity and HOMO–LUMO gap energy. We also explored the feasibility of hydrogenation on B n and MgB n clusters from the viewpoints of thermodynamics and kinetics. The results demonstrate that the adsorption and dissociation of H2 on the MgB n clusters vary with cluster sizes. H2 tends to adsorb on the planar boron clusters rather than on three-dimensional boron clusters. Mg doping on B4 can improve the H2 storage both in the terms of thermodynamics and kinetic. Moreover, a new bonding way of H2 with boron clusters was found. Our work provided valuable information for the future boron-based H2 storage nano-materials.

Understanding Planar Ligand-Supported MAu5and MAu6Cores. Theoretical Survey of [MAu5(Mes)5] and [MAu6(Mes)6] (M = Cu, Ag, Au; Mes = 2,4,6-Me3C6H2) Under the Planar Superatom Model

The planar superatom model has been applied to the case of planar ligand-supported MAu5 and MAu6 cores, where M = Cu(I), Ag(I), and Au(I), in order to increase the understanding of the electronic structure and bonding properties of planar golden clusters. The study of [Au5(Mes)5], [Au6(Mes)6], [MAu5(Mes)5], and [MAu6(Mes)6] has been carried out by using relativistic DFT calculations, which describe the short d10–d10 contacts due to the bonding stabilization within the Aun core in addition to the respective aurophilic phenomena. The results under the planar superatom approach allow us to characterize the electronic structure in all the systems as formally 10 valence electron cores, depicting an overall 1s21px,y41dxy,x2–y24 configuration as a result of the ligand–metal interaction. The inclusion of the respective M(I) closed shell center increases the number of superatomic shells as 1s1p1d → 1s1p1d2s, denoting the interaction between each concentric section. Our results suggest that the MAun cores could be ...

Propene epoxidation with O2 or H2-O2 mixtures over silver catalysts: theoretical insights into the role of the particle size.

The adsorption and dissociation of molecular O2 over silver extended surfaces, nanoparticles and clusters of different size, as well as the reaction between adsorbed O2 and H2 to form less nucleophilic hydroperoxide groups have been investigated by means of periodic DFT calculations. Hydroperoxide formation from O2 and H2 is in all systems kinetically favoured over O2 dissociation, which becomes energetically forbidden on small planar clusters. The nature and reactivity towards propene of all oxygen species present on silver, including adsorbed molecular O2, atomic O, and hydroperoxide groups, have been theoretically explored. Formation of the oxametallacycle intermediate involved in propene epoxidation is energetically accessible on subnanometric three-dimensional silver nanoparticles, but competitive pathways leading to hydrogen abstraction and allyl formation always involve lower activation barriers. Theoretical findings have been experimentally confirmed by Raman spectroscopy of O2 adsorption and catalytic testing of planar and three dimensional silver clusters.

Structure of a low-lying isomer of BOSi2, as a free-space planar cluster, using the Hartree–Fock method plus second order perturbations

The Hartree–Fock (HF) method, supplemented by low-order Møller–Plesset (MP2) perturbation theory, has been utilized to predict the nuclear geometry, assuming planarity, of a low-lying isomer of the free space cluster BOSi2. The planar structure found at equilibrium geometry is shown to be stable against small amplitude molecular vibrations. Finally, some brief comments are made on the possible relevance of the above free-space cluster geometry to the known B–O defects which limit the improvement of minority carrier lifetime in a form of p-type silicon.

The boron conundrum: Bonding in the bowl B30 and B36, fullerene B40 and triple ring B42 clusters

Geometries and bonding of B30, B36, B40 and B42 clusters were studied using quantum chemical computations. The bowl B30 and B36 and planar B42 clusters exhibit disk aromaticity. Diatropic ring current is strong in B30 and weaker in B42. A fullerene-like B40 (D2d) having two hexagons and four heptagons was found as the lowest-lying isomer. Such a fullerene whose MOs closely mimic those of the buckyball B80, represents novel structural feature of boron clusters. The most stable B42 (C2h) isomer is a triple ring tube with consistent σ+π diatropic magnetic responses making it a tubular aromatic species.