Planar Clusters Research Articles

Plasmon excitations in sodium atomic planes: A time-dependent density functional theory study

The collective electronic excitation in planar sodium clusters is studied by time-dependent density functional theory calculations. The formation and development of the resonances in photoabsorption spectra are investigated in terms of the shape and size of the two-dimensional (2D) systems. The nature of these resonances is revealed by the frequency-resolved induced charge densities present on a real-space grid. For long double chains, the excitation is similar to that in long single atomic chains, showing longitudinal modes, end and central transverse modes. However, for 2D planes consisting of (n × n) atoms with n being up to 16, new 2D characteristic modes emerge regardless of the symmetries considered. For in-plane excitations, besides the equivalent end mode, mixed modes with contrary polarity occur. The relation between the frequency of the primary modes and the system size is similar to the case of a 2D electron gas but with a correction due to the realistic atomic structure. For excitations perpendicular to the plane there are corner, side center, bulk center, and circuit modes. Our calculation reveals the importance of dimensionality for plasmon excitation and how it evolves from 1D to 2D.

Probing the structures and chemical bonding of boron-boronyl clusters using photoelectron spectroscopy and computational chemistry: B4(BO)n−(n= 1–3)

The electronic and structural properties of a series of boron oxide clusters, B(5)O(-), B(6)O(2)(-), and B(7)O(3)(-), are studied using photoelectron spectroscopy and density functional calculations. Vibrationally resolved photoelectron spectra are obtained, yielding electron affinities of 3.45, 3.54, and 4.94 eV for the corresponding neutrals, B(5)O, B(6)O(2), and B(7)O(3), respectively. Structural optimizations show that these oxide clusters can be formulated as B(4)(BO)(n)(-) (n = 1-3), which involve boronyls coordinated to a planar rhombic B(4) cluster. Chemical bonding analyses indicate that the B(4)(BO)(n)(-) clusters are all aromatic species with two π electrons.

Three coordination polymers built from planar tetranuclear clusters and 5-sulfoisophthalic acid

Three coordination polymers built from planar tetranuclear clusters and H3sip ligands, Pb2Cl(sip)(bipy) (1), Pb2Br(sip)(H2O) (2), and Ni4(sip)2(pyz)2(H2O)8(OH)2·2H2O (3) (H3sip = 5-sulfoisophthalic acid, bipy = 2,2′-bipyridine, and pyz = pyrazine), have been hydrothermally synthesized and characterized by IR, TGA, and single-crystal X-ray diffraction. Compound 1 features a 2-D layer-like structure containing tetranuclear square [Pb4(SO3)2] clusters. Complex 2 has a 3-D open framework architecture constructed from tetranuclear cluster [Pb4Br2(SO3)2] inorganic building blocks. The tetranuclear units, [Ni4(OH)2(COO)4], in 3 are interlinked through carboxylates and µ2-pyz ligands to generate a 2-D layer structure. The connecting modes between tetranuclear clusters and organic ligands in the three compounds are discussed in this article. In the solid state at room temperature, yellow photoluminescence in 1 and 2 are observed.

Two-Dimensional 3d–4f Networks Containing Planar Co4Ln2 Clusters with Single-Molecule-Magnet Behaviors

Two novel two-dimensional 3d-4f networks based on planar Co(4)Ln(2) clusters supported by rigid 4'-(4-carboxyphenyl)-2,2':6',2"-terpyridine afford the first examples of high-dimensional networks with 3d-4f clusters behaving as single-molecule magnets.

CH3OH + 2H (2Sg) hydrogen abstraction reactions occurring in the presence of a copper tetramer: A DFT study

AbstractThe density functional approximation M05 with 6‐31G** and m‐6‐31G* basis sets were used to calculate the classical barrier heights, structures, reaction energies, and enthalpies of the hydrogen abstraction reaction paths of 2H + (CH3OH)·Cu4 → 2H2 + (COH2)·Cu4, which is a prototype system for dehydrogenation of methanol catalyzed by copper clusters, consisting of two sequential elementary reactions of the methanol combustion mechanism. Electronic structure and intermolecular/intramolecular bond energies were computed as well as the energy variations for the reaction both free and in the presence of the tetramer copper cluster. It was observed that the first dehydrogenation path, related to the abstraction from hydroxyl group of methanol, shows no classical barrier in this level of calculation. We have demonstrated that the planar rhombus cluster Cu4 has bonding properties which mimic quantitatively catalytic properties for some elementary reactions in the methanol combustion mechanism. © 2012 Wiley Periodicals, Inc.

Model-based clustering of multivariate skew data with circular components and missing values

Motivated by classification issues that arise in marine studies, we propose a latent-class mixture model for the unsupervised classification of incomplete quadrivariate data with two linear and two circular components. The model integrates bivariate circular densities and bivariate skew normal densities to capture the association between toroidal clusters of bivariate circular observations and planar clusters of bivariate linear observations. Maximum-likelihood estimation of the model is facilitated by an expectation maximization (EM) algorithm that treats unknown class membership and missing values as different sources of incomplete information. The model is exploited on hourly observations of wind speed and direction and wave height and direction to identify a number of sea regimes, which represent specific distributional shapes that the data take under environmental latent conditions.

B12H n and B12F n : planar vs icosahedral structures

Using density functional theory and quantum Monte Carlo calculations, we show that B12Hn and B12Fn (n = 0 to 4) quasi-planar structures are energetically more favorable than the corresponding icosahedral clusters. Moreover, we show that the fully planar B12F6 cluster is more stable than the three-dimensional counterpart. These results open up the possibility of designing larger boron-based nanostructures starting from quasi-planar or fully planar building blocks.

Quality Assessment Of Geometric Façade Models Reconstructed From TLS Data

AbstractTerrestrial laser scanner (TLS) data plays an important role in 3D modelling of urban scenes. Much research is carried out in the fields of pre‐processing, segmentation and geometric reconstruction of laser data of building faÇades. However, the quality of 3D models obtained from this data is rarely assessed. This paper proposes a qualitative and quantitative assessment approach to evaluate the quality of 3D models of faÇades constructed with TLS data. Only segmentation and reconstruction operations are considered in this paper, because they cover the main steps in the 3D modelling process. Since every processing step produces an intermediate result, each one must be analysed and compared with an appropriate reference model. A new approach has been conceived to evaluate the precision of the segmentation results. It is based on the calculation of Boolean operators enabling the comparison of planar clusters produced by the segmentation. To evaluate the vector models resulting from the reconstruction step, a method based on quality indices is proposed. It is adapted not only for precision but also for accuracy calculations. The results show that the quality assessment approach is coherent and, moreover, easy to apply.

Imperfection of the clustered perovskite structure, phase transitions, and magnetoresistive properties of ceramic La0.6Sr0.2Mn1.2 − x Ni x O3 ± δ (x = 0–0.3)

Ceramic samples of lanthanum strontium manganite perovskites La0.6Sr0.2Mn1.2 − xNixO3 ± δ (0 ≤ x ≤ 0.3) have been investigated using the X-ray diffraction, magnetic (χac), 55Mn NMR, resistive, and magnetoresistive methods. The specific features of the influence of the composition on the structure and properties of nonstoichiometric manganite perovskites have been established. It has been found that the rhombohedrally (R\(\bar 3\)c) distorted perovskite structure contains cation and anion vacancies, as well as nanostructured clusters with Mn2+ ions in the A-positions. The substitution of Ni3+ ions (r = 0.74 A) for Mn3+ ions (r = 0.785 A) leads to a decrease in the lattice parameter a, the ferromagnetic-paramagnetic phase transition temperature TC, and the metal-semiconductor phase transition temperature Tms due to the disturbance of the superexchange interactions between heterovalent manganese ions Mn3+ and Mn4+. The observed anomalous magnetic hysteresis at 77 K has been explained by the antiferromagnetic effect of the unidirectional exchange anisotropy of the ferromagnetic matrix structure on the magnetic moments of the superstoichiometric manganese Mn2+ ions located in nanostructured planar clusters. An analysis of the asymmetrically broadened 55Mn NMR spectra of the compounds has revealed a high-frequency electronic superexchange of the ions Mn3+ ⟷ O2− ⟷ Mn4+; a local heterogeneity of their surrounding by other ions, vacancies, and clusters; and a partial localization of Mn4+ ions. The local hyperfine interaction fields on 55Mn nuclei have been determined. The concentration dependences of the activation energy and charge hopping frequency have confirmed that the Ni ions decrease the electrical conductivity due to the weakening of the electronic superexchange Mn3+ ⟷ O2− ⟷ Mn4+. Two types of magnetoresistive effects have been found: one effect, which is observed near the phase transition temperatures TC and Tms, is caused by scattering at intracrystalline nanostructured heterogeneities, and the other effect, which is observed in the low-temperature range, is induced by tunneling through intercrystalline mesostructured boundaries. The phase diagram has demonstrated that there is a strong correlation between magnetic and electrical properties in rare-earth manganites.

The Occurrence of π Molecular Orbitals in Planar Boron Clusters

Abstract The energy of the lowest π molecular orbital in a planar boron cluster can be estimated from the connectivity of constituent boron atoms, or the mean valency of the boron atoms. Low-energy π molecular orbitals were then predicted to occur in all realistic planar polycyclic boron clusters. In fact, all such boron clusters studied have one or more π molecular orbitals with two or more π electrons. They are aromatic with positive topological resonance energies. π Conjugation and aromaticity must be totally or partially responsible for the planarity of low-energy boron clusters.

Disk Aromaticity of the Planar and Fluxional Anionic Boron Clusters B20−/2−

The presence of excess electrons modifies the structural landscape and tends to extend the planarity of boron clusters. While the neutral B(20) is tubular, both the anion and dianion B(20)(-/2-) become planar. Geometrical features of the stable anions suggest the existence of a new type of cluster that is planar and doubly cyclic with one atom located at the center (see figure), as well as being fluxional.

A Density Functional Theory Investigation for the Open-Shell Metal-Carbide Endofullerene Lu3C2@C88(D2:35) and Closed-Shell Metal-Nitride Endofullerene Lu3N@C88(D2:35)

By means of the density functional theory calculations, two C88(D2:35)-based endohedral fullerenes, Lu3C2@C88(D2:35) and Lu3N@C88(D2:35) which encapsulate tri-lutetium carbide and tri-lutetium nitride cluster were investigated. For the cores in Lu3C2@C88 and Lu3N@C88, the trivalent C2 and N respectively template a butterfly-shaped endohedral moiety and a planar tri-lutetium cluster within the same D2-symmetric C88 cage. Moreover, Lu3N@C88 - D2 has a closed-shell electronic structure but for LuC3C2@C88 - D2, it owns an unpaired electron mainly localized on the internal Lu3C2 cluster. These results clearly showed that the core unit C2(3) as well as N3- play an important role in constructing molecular structures and electronic features of metallofullerenes. Furthermore, the electrochemical redox potentials, and vibrational frequencies of the two endofullerenes agree well with our experimental results. The electronic structures, ionization energies, electron affinities, inner clusters' dynamic motions of them have been predicted to further disclose the characters of these two metallofullerenes.

INVESTIGATION ON THE MORPHOLOGY AND PROPERTIES OF AGGREGATE STRUCTURES OF NATURAL PHOSPHOLIPIDS IN AQUEOUS SYSTEM USING CRYO-TEM

Cryogenic transmission electron microscopy (Cryo-TEM) was used to investigate the aggregates morphology and properties of candle tree (Aleurites moluccana) endosperm, sesame (Sesamum indicum L. syn.) seeds, and coconut (Cocos nucifera) endosperm phospholipids in dilute aqueous system. The micrographs showed that candle tree phospholipids formed planar bilayer and cluster of vesicles with lipid droplets, while coconut and sesame phospholipids formed well-defined unilamellar vesicles. The vesicles size could be as small as 50 nm in diameter. Coconut phospholipids also showed a good bending ability. Formation of clusters of vesicles was also found in coconut phospholipids dispersion, but this cluster was easily broken by extrusion through a small pore membrane.

Structure of boron clusters revisited, Bn with n = 14–20

We reinvestigate the structures of neutral boron clusters Bn, with n=14–20. G3B3 calculations confirm that a transition between 2D and 3D shape occurs at B20, which has a tubular form. In disagreement with Boustani et al. (Phys. Rev. B, 83 (2011) 193405), we find a planar B19 cluster. Standard heats of formation are obtained and used to evaluate the clusters stability. The average binding energy tends to increase with increasing size toward a limit. Higher stability is found B14, B16, B18 and B20. All Bn have negative NICS-values. The bonding nature and electron delocalization of B20 are re-examined using CMO and LOL.

Phase Separation in Random Cluster Models I: Uniform Upper Bounds on Local Deviation

This is the first in a series of three papers that addresses the behaviour of the droplet that results, in the percolating phase, from conditioning the planar Fortuin-Kasteleyn random cluster model on the presence of an open dual circuit Γ0 encircling the origin and enclosing an area of at least (or exactly) n2. (By the Fortuin-Kasteleyn representation, the model is a close relative of the droplet formed by conditioning the Potts model on an excess of spins of a given type.) We consider local deviation of the droplet boundary, measured in a radial sense by the maximum local roughness, MLR(Γ0), this being the maximum distance from a point in the circuit Γ0 to the boundary ∂ of the circuit’s convex hull; and in a longitudinal sense by what we term maximum facet length, MLF(Γ0), namely, the length of the longest line segment of which the polygon ∂ is formed. The principal conclusion of the series of papers is the following uniform control on local deviation: that there are constants 0 < c < C < ∞ such that the conditional probability that the normalized quantity n−1/3(log n )−2/3MLR lies in the interval [c, C] tends to 1 in the high n-limit; and that the same statement holds for n−2/3 (log n )−1/3 MLF. In this way, we confirm the anticipated n1/3 scaling of maximum local roughness, and provide a sharp logarithmic power-law correction. This local deviation behaviour occurs by means of locally Gaussian effects constrained globally by curvature, and we believe that it arises in many radially defined stochastic interface models, including growth models belonging to the Kardar-Parisi-Zhang universality class.

Water monomer interaction with gold nanoclusters from van der Waals density functional theory

We investigate the interaction between water molecules and gold nanoclusters Au(n) through a systematic density functional theory study within both the generalized gradient approximation and the nonlocal van der Waals (vdW) density functional theory. Both planar (n = 6-12) and three-dimensional (3D) clusters (n = 17-20) are studied. We find that applying vdW density functional theory leads to an increase in the Au-Au bond length and a decrease in the cohesive energy for all clusters studied. We classify water adsorption on nanoclusters according to the corner, edge, and surface adsorption geometries. In both corner and edge adsorptions, water molecule approaches the cluster through the O atom. For planar clusters, surface adsorption occurs in a O-up/H-down geometry with water plane oriented nearly perpendicular to the cluster. For 3D clusters, water instead favors a near-flat surface adsorption geometry with the water O atom sitting nearly atop a surface Au atom, in agreement with previous study on bulk surfaces. Including vdW interaction increases the adsorption energy for the weak surface adsorption but reduces the adsorption energy for the strong corner adsorption due to increased water-cluster bond length. By analyzing the adsorption induced charge rearrangement through Bader's charge partitioning and electron density difference and the orbital interaction through the projected density of states, we conclude that the bonding between water and gold nanocluster is determined by an interplay between electrostatic interaction and covalent interaction involving both the water lone-pair and in-plane orbitals and the gold 5d and 6s orbitals. Including vdW interaction does not change qualitatively the physical picture but does change quantitatively the adsorption structure due to the fluxionality of gold nanoclusters.

Endohedral metallofullerene Sc3NC@C84: a theoretical prediction

Very recently, two novel Sc(3)NC-based cluster fullerenes Sc(3)NC@C(80) (Wang et. al. J. Am. Chem. Soc. 2010, 132, 16362) and Sc(3)NC@C(78) (Wu et. al. J. Phys. Chem. C 2011, 115, 23755) were prepared and characterized, respectively. Inspired by these findings, the possibility of encapsulating Sc(3)NC cluster in the C(84) fullerene is performed using density functional theory (DFT). Firstly, the isolated pentagon rule (IPR) D(2d) (23) C(84) fullerene is employed to encase the Sc(3)NC cluster: four possible endohedral metallofullerene isomers a-d are designed. The large binding energies (ranging from 163.7 to 210.0 kcal mol(-1)) indicate that the planar quinary cluster Sc(3)NC can be stably encapsulated in the C(84) (isomer 23) cage. Further, we consider the incorporation of Sc(3)NC into the non-IPR C(s) (51365) C(84) cage leading to isomer e and show the high stability of isomer e, which has a larger binding energy, larger HOMO-LUMO gap, higher adiabatic (vertical) ionization potential, and lower adiabatic (vertical) electron affinity than the former four Sc(3)NC@C(84) (isomer 23). Significantly, the predicted binding energy (294.2 kcal mol(-1)) of isomer e is even larger than that (289.2 and 277.7 kcal mol(-1), respectively) of the synthesized Sc(3)NC@C(80) and Sc(3)NC@C(78,) suggesting a considerable possibility for experimental realization. The (13)C NMR chemical shifts and Raman spectra of this a new endofullerene have been explored to assist future experimental characterization.

Collectivity of plasmon excitations in small sodium clusters with planar structure

The collectivity of the electronic motion in small sodium clusters with planar structure is studied by the time-dependent density functional theory (TDDFT). The formation and development of collective resonances in the absorption spectra were obtained as the function of the size and shape of the plane. We find the symmetry plays an important role in the collective excitation. Resonance peaks increase with the reduction of the symmetries and, on the contrary, resonance peaks decrease with the increase of the symmetries. In the planar cluster, there are two main excitation modes: the higher-energy mode and the competitive mode, which is due to the coupling and competition of the quasi-lower-energy effect and the quasi-higher-energy effect. With the increase of the interatomic distance, peaks of the absorption spectra are all red-shifted and the evolutionary trend is also discussed.

Intramolecular Metal–Metal Bond Rearrangement in a Pt2PdHg Heterometallic Cluster Forming a HgI–PdI Covalent Bond

Reaction of the linear trinuclear complex [Pt2M(μ-dpmp)2(XylNC)2](PF6)2 (M = Pd (1b)) with HgX2 afforded the Pt2PdHg mixed-metal complexes [Pt2PdHgX2(μ-dpmp)2(XylNC)2](PF6)2 (X = Cl (2), Br (3), I (4)), which included an unprecedented HgI–PdI covalent bond formed via intramolecular metal–metal bond rearrangement. In contrast, reaction of 1a (M = Pt) with HgCl2 afforded the novel pentagonal-shaped Pt3Hg3 planar cluster [Pt3Hg3Cl4(μ-dpmp)2(XylNC)2]Cl2(PF6)2 (5).

Experimental Studies and Observations of Clusters of Rydberg Matter and Its Extreme Forms

A review is given of experimental studies of clusters of Rydberg matter (RM) with applications. This is a metallic type of matter with angular momentum l ≥ 1 for the conduction band electrons. The atoms in RM can be one-electron atoms like K, H and D which are most used in the laboratory, or two-electron atoms like He. Mixed clusters of one-electron atoms are easily studied. This material is stable in a vacuum both in the laboratory and in interstellar space. The large stability is valid for the lowest excitation level for each atom type, at l = 1 for H(1) which is the lowest energy state for protium. Typical clusters of RM are planar with magic numbers 7, 19, 37, 61 and 91. Small planar cluster can form stacks of clusters. Close-packed clusters exist for H(1) with magic numbers 4, 6, and 12, and chain clusters mainly formed by D–D “beads” are common for D(1). Several methods to study RM clusters are reviewed. Stimulated spectroscopy methods like stimulated emission and stimulated Raman are emphasized. Cluster properties like large polarizability and giant magnetic dipoles are described. Results on rotational levels, vibrational levels and electronic levels are reviewed. The observational evidence for RM clusters in space is discussed in relation to the fundamental experimental studies of the specific cluster properties.