Stability of hollow spheroidal silicon clusters Sin and SinHn

The structures of Si_n and Si_nH_n fullerenes with 20 ≶n ≶60 are calculated in the MINDO/3 approximation using the Monte Carlo technique for geometry optimization. The calculations show that spheroidal silicon clusters consisting of more than 36 atoms are stable and the bond energy increases with their size. This increase is not noticed for compact clusters calculated as an alternative. For n ≥40-50, the latter have lower bond energies compared to fullerenes. The geometry optimization of the tetrahedral cluster Si₄₅ results in a structure close to spheroidal, which gains in bond energy. The addition of hydrogen atoms to small deformed fullerenes and their geometry optimization make it possible to obtain stable spheroidal structures Si_nH_n whose bond energy is greater than that of alternative compact silicon hydride clusters. When the size of spheroidal clusters Si_nH_n increases, i. e., when n > 36, the hydrogen elimination barriers decrease abruptly; the Si_nH_n diamond structure of the cluster is more advantageous when n ≥50.     

Structure of hydrogenated silicon clusters. Small clusters

The ground state structures of silicon hydride clusters Si_nH_m containing up to 12 silicon atoms are obtained by numerical modeling. The cluster geometry is optimized for a wide set of initial structures using the MINDO/3 approximation for Monte Carlo simulation of interatomic interactions. The energy of the cluster depending on the content of hydrogen is studied, and it is shown that the Si-H and Si-Si bond energies depend little on the cluster size.     

Structure of hydrogenated silicon clusters. Medium-sized clusters

The structures of the Si_nH_m clusters containing 10 to 70 silicon atoms and different numbers of hydrogen atoms are calculated in the MINDO/3 approximation using the Monte Carlo technique. The geometry optimization of the clusters showed the existence of several structural varieties that determine the optimal geometry of the clusters differing in size and hydrogen content. Small clusters (n < 20) with various geometrical configurations often have a hollow structure if the number of silicon atoms in the cluster is more than 12. For 20 ≤ n < 60 and the hydrogen content m ≤ n, hollow spheroidal geometry is most favorable. Staring from n ≈ 56−60, diamond structures are more favorable. The ratio c = m/n < 1, at which the spheroidal structure remains optimal, decreases with further increase in n.     

Tetrasilatetrahedranide: a silicon cage anion

The first silicon cage anion, tris{bis[bis(trimethylsilyl)methyl](methyl)silyl}tetrasilatetrahedranide (6-), has been synthesized by the reaction of tetrakis{bis[bis(trimethylsilylmethyl](methyl)silyl}tetrasilatetrahedrane with potassium graphite in diethyl ether by reductive cleavage of exocyclic Si-Si bond. The structural characterization of K+(18-crown-6).6- has been achieved by X-ray crystallography, showing that 6- is a separated ion pair and the tetrasilatetrahedranide moiety has a significantly distorted tetrahedrane skeleton containing one inverted tetrahedral (umbrella type) silicon atom. The four silicon atoms in the Si4 skeleton are equivalent on the NMR time scale due to the migration of the Dis2MeSi substituent.     

Stability of alkali-atom clusters

A detailed study of the stability of alkali-atom clusters is presented and discussed. Free clusters are produced in an unseeded adiabatic expansion and ionized by a pulsed laser beam. A tandem time-of-flight system provides a size selection of ionized species and mass spectrometry of fragments. We have investigated for sodium and potassium clusters containing up to fifty atoms: the metastable decay following ionization, the photo-induced dissociation, the collisional induced dissociation and the collisional charge exchange. Experimental evidence is shown for dissociative process involving evaporation of monomers and dimers. This is explained by the statistical unimolecular theory and by the energetics of the systems.     

Electronic spectrum of small silicon clusters in silicon dioxide

Institute of Theoretical and Applied Mechanics, Siberian Branch, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 30, No. 4, pp. 23–26, July–August, 1989.     

Gas-phase structures of neutral silicon clusters

Vibrational spectra of neutral silicon clusters Si(n), in the size range of n = 6-10 and for n = 15, have been measured in the gas phase by two fundamentally different IR spectroscopic methods. Silicon clusters composed of 8, 9, and 15 atoms have been studied by IR multiple photon dissociation spectroscopy of a cluster-xenon complex, while clusters containing 6, 7, 9, and 10 atoms have been studied by a tunable IR-UV two-color ionization scheme. Comparison of both methods is possible for the Si(9) cluster. By using density functional theory, an identification of the experimentally observed neutral cluster structures is possible, and the effect of charge on the structure of neutrals and cations, which have been previously studied via IR multiple photon dissociation, can be investigated. Whereas the structures of small clusters are based on bipyramidal motifs, a trigonal prism as central unit is found in larger clusters. Bond weakening due to the loss of an electron leads to a major structural change between neutral and cationic Si(8).     

Stability of clusters of fullerenes

We have studied the formation and stability of pure and mixed clusters of C ₆₀ and C ₆₀/C ₇₀ produced in a gas aggregation source. The source yields very smooth abundance distributions indicating an efficient cooling. The stability of the clusters was probed by varying the degree of heating with a XeCl excimer laser (hv I.P.) followed by single photon ionisation with a F ₂ excimer laser. The stability patterns show features related to geometrical packing structures but much stronger than previously seen in cluster spectra. The fragmentation patterns for the mixed clusters indicate that C ₆₀ and C ₇₀ have similar binding energies in the clusters in contrast to what would be expected from vapour pressure data of macroscopic samples.     

Novel cage clusters of MoS2 in the gas phase

Laser evaporation of MoS(2) nanoflakes gives negatively charged magic number clusters of compositions Mo(13)S(25) and Mo(13)S(28), which are shown to have closed-cage structures. The clusters are stable and do not show fragmentation in the post-source decay analysis even at the highest laser powers. Computations suggest that Mo(13)S(25) has a central cavity with a diameter of 4.5 A. The nanosheets of MoS(2) could curl upon laser irradiation, explaining the cluster formation.     

Predicting structural models for silicon clusters

This article introduces an efficient method to generate structural models for medium-sized silicon clusters. Geometrical information obtained from previous investigations of small clusters is initially sorted and then introduced into our predictor algorithm in order to generate structural models for large clusters. The method predicts geometries whose binding energies are close (95%) to the corresponding value for the ground-state with very low computational cost. These predictions can be used as a very good initial guess for any global optimization algorithm. As a test case, information from clusters up to 14 atoms was used to predict good models for silicon clusters up to 20 atoms. We believe that the new algorithm may enhance the performance of most optimization methods whenever some previous information is available.     

Optical spectra of size-selected matrix-isolated silicon clusters

Size selected silicon clusters have been isolated in rare gas matrices and studied by optical absorption spectroscopy. The clusters were produced in a pulsed laser vaporization source, size selected with a quadrupole mass spectrometer and deposited at low energies into a cocondensed krypton matrix held at T<20 K. A comparison of the optical spectra of ten atom wide bands (Si₂₅-Si₃₅, Si₃₅-Si₄₅ and Si₄₅-Si₅₅) shows the general size evolution of the optical properties. Single cluster sizes have also been isolated and show somewhat sharper spectra than the bands. The measured spectra show similarities to spectra calculated using Mie theory and bulk optical constants. Cluster-cluster agglomeration was studied by evaporating the inert gas matrix. The results suggest that the clusters agglomerate into larger particles even under the mildest "soft landing" conditions.     

Triangle contraction in six-membered-ring silicon clusters

We propose the “triangle contraction” as an important reconstruction mechanism of six-membered-ring silicon clusters on the basis of the force and virial analysis for Si₆, Si₁₀, Si₁₄, Si₁₈, Si₂₂, and Si₂₆ clusters. Forces acting on atoms have been calculated using the local-density-functional scheme with linear-combination-of-atomic-orbitals-Xα method. Calculated forces show that most of the (111)-surface equilateral triangles have tendency to contract, indicating the generality of the triangle-contraction mechanism.     

Thermochemical property estimation of hydrogenated silicon clusters

The thermochemical properties for selected hydrogenated silicon clusters (Si(x)H(y), x = 3-13, y = 0-18) were calculated using quantum chemical calculations and statistical thermodynamics. Standard enthalpy of formation at 298 K and standard entropy and constant pressure heat capacity at various temperatures, i.e., 298-6000 K, were calculated for 162 hydrogenated silicon clusters using G3//B3LYP. The hydrogenated silicon clusters contained ten to twenty fused Si-Si bonds, i.e., bonds participating in more than one three- to six-membered ring. The hydrogenated silicon clusters in this study involved different degrees of hydrogenation, i.e., the ratio of hydrogen to silicon atoms varied widely depending on the size of the cluster and/or degree of multifunctionality. A group additivity database composed of atom-centered groups and ring corrections, as well as bond-centered groups, was created to predict thermochemical properties most accurately. For the training set molecules, the average absolute deviation (AAD) comparing the G3//B3LYP values to the values obtained from the revised group additivity database for standard enthalpy of formation and entropy at 298 K and constant pressure heat capacity at 500, 1000, and 1500 K were 3.2%, 1.9%, 0.40%, 0.43%, and 0.53%, respectively. Sensitivity analysis of the revised group additivity parameter database revealed that the group parameters were able to predict the thermochemical properties of molecules that were not used in the training set within an AAD of 3.8% for standard enthalpy of formation at 298 K.     

Uranyl peroxide pyrophosphate cage clusters with oxalate and nitrate bridges

Two complex cage clusters built from uranyl hexagonal bipyramids and multiple types of bridges between uranyl ions, U(30)Py(10)Ox(5) and U(38)Py(10)Nt(4), were crystallized from aqueous solution under ambient conditions. These are built from 30 uranyl hexagonal bipyramids, 10 pyrophosphate groups, and five oxalate bridges in one case, and 38 uranyl hexagonal bipyramids, 10 pyrophosphate groups, and four nitrate groups in the other. The crystal compositions are (H(3)O)(10)Li(18)K(22)[(UO(2))(30)(O(2))(30)(P(2)O(7))(10)(C(2)O(4))(5)](H(2)O)(22) and Li(24)K(36)[(UO(2))(38)(O(2))(40)(OH)(8)(P(2)O(7))(10)(NO(3))(4)](NO(3))(4)(H(2)O)(n) for U(30)Py(10)Ox(5) and U(38)Py(10)Nt(4), respectively. Cluster U(30)Py(10)Ox(5) crystallizes over a narrow range of solution pH that encourages incorporation of both oxalate and pyrophosphate, with incorporation of oxalate only being favored under more acidic conditions, and pyrophosphate only under more alkaline conditions. Cluster U(38)Py(10)Nt(4) contains two identical lobes consisting of uranyl polyhedra and pyrophosphate groups, with these lobes linked into the larger cluster through four nitrate groups. The synthesis conditions appear to have prevented closure of these lobes, and a relatively high nitrate concentration in solution favored formation of the larger cluster.     

Stability of multiply charged silver clusters

Using the gasaggregation technique it is possible to generate metal clusters in narrow size distributions and to vary their mean size by adjusting the cell parameters. The high intensity of this source allows to detect besides singly charged clusters also multiply charged ones. Ag _n ²⁺ and Ag _n ³⁺ are observed forn≧9 andn≧31, respectively; i.e. at values well below the critical sizes reported for spheres.     

Stability of isomeric Na n clusters

A method which combines density functional theory and the use of pseudopotentials is applied to obtain ground state and low-lying metastable geometries of Na _n clusters (7≤n≤40). The large variation in the magnitude of energy gaps between isomers suggests that the melting temperature is not a simple monotonous function of size. A detailed study of the differences between electronically stabilized (n=8, 20, 40) and structurally stabilized (n=13) clusters suggests some clues to understand the intriguing behaviour of Na₁₃.     

Large silicon clusters: Confirmation of Phillips'' conjecture

This paper attempts to verify the hypothesis put forward by Phillips that large silicon clusters are arranged in a cylindrical shape, as stacked quasigraphitic rings. It is shown that the periodic variations in reactivity can probably be explained by this hypothesis. A tight-binding calculation is employed, and the geometry and charge distribution of clusters ranging in size from 30 to 45 atoms is explored.     

Complex nanoscale cage clusters built from uranyl polyhedra and phosphate tetrahedra

Five cage clusters that self-assemble in alkaline aqueous solution have been isolated and characterized. Each is built from uranyl hexagonal bipyramids with two or three equatorial edges occupied by peroxide, and three also contain phosphate tetrahedra. These clusters contain 30 uranyl polyhedra; 30 uranyl polyhedra and six pyrophosphate groups; 30 uranyl polyhedra, 12 pyrophosphate groups, and one phosphate tetrahedron; 42 uranyl polyhedra; and 40 uranyl polyhedra and three pyrophosphate groups. These clusters present complex topologies as well as a range of compositions, sizes, and charges. Two adopt fullerene topologies, and the others contain combinations of topological squares, pentagons, and hexagons. An analysis of possible topologies further indicates that higher-symmetry topologies are favored.