Electronic structure and stability of AlnPn (n = 2-4) clusters

The geometry, electronic configurations, harmonic vibrational frequencies, and stability of the structural isomers of aluminum phosphide clusters have been investigated using the density functional theory. For dimers and trimers, the lowest energy structures are cyclic (IIs, IIIs) with D(nh) symmetry. The caged structure with Td symmetry (Xs) lie lowest in energy among the tetramers. The Al--P bond dominates the structures for many isomers so that one preferred dissociation channel is loss of the AlP monomer. The hybridization and chemical bonding in the different structures are also discussed. Comparisons with silicon and boron nitride clusters, the ground state structures of Al(n)P(n) clusters are analogous to those of their corresponding Si(2n) counterparts. This similarity follows the isoelectronic principle.     

Structure and stability of oxygen adsorption on Si(n) (n = 5-10) clusters

The structures, binding energies, and electronic properties of one oxygen atom (O) and two oxygen atoms (2O) adsorption on silicon clusters Si(n) with n ranging from 5 to 10 are studied systematically by ab initio calculations. Twelve stable structures are obtained, two of which are in agreement with those reported in previous literature and the others are new structures that have not been proposed before. Further investigations on the fragmentations of Si(n)O and Si(n)O2 (n = 5-10) clusters indicate that the pathways Si(n)O --> Si(n-1) + SiO and Si(n)O2 --> Si(n-2) + Si2O2 are most favorable from thermodynamic viewpoint. Among the studied silicon oxide clusters, Si8O, Si9O, Si5O2 and Si8O2 correspond to large adsorption energies of silicon clusters with respect to O or 2O, while Si8O, with the smallest dissociation energy, has a tendency to separate into Si7 + SiO. Using the recently developed quasi-atomic minimal-basis-orbital method, we have also calculated the unsaturated valences of the neutral Si(n) clusters. Our calculation results show that the Si atoms which have the largest unsaturated valences are more attractive to O atom. Placing O atom right around the Si atoms with the largest unsaturated valences usually leads to stable structures of the silicon oxide clusters.     

多体展开势能函数在碳族元素原子簇研究中的应用(Ⅳ)──Si9─Si16原子簇的分子结构与稳定性

多体展开势能函数研究表明,Si₄-Si₁₆原子簇分子间的结构衍生关系为:依次增加一个二配位或三配位的表面原子,分子表面被四元蝶形环Si₄(D_2d)所覆盖;Si_n(n=5-16)结构中多含有Si₅(D_3h)、Si₆(D_2d)区域结构单元,笼状Si₁₀及Si₁₆的表面原子均为三配位或三配位以上,预计Si₅、Si₆、Si₁₀及Si₁₆是硅原子簇碎片化产物分布中丰度较高的序列;在这一范围内的分子结构呈与晶体硅结构(金刚石)无关的密堆积,最高配位数为5,在小于半球的立体角内形成六配位的硅中心,使该簇合物在能量上不稳定。     

Investigation of Size-Selective Zr(2)@Si(n) (n = 16-24) Caged Clusters

The size-selective Zr(2)Si(n) (n = 16-24) caged clusters have been investigated by density functional approach in detail. Their geometries, relative stabilities, electronic properties and ionization potentials have been discussed. The dominant structures of bimetallic Zr(2) doped silicon caged clusters gradually transform to Zr(2) totally encapsulated structures with increase of the clustered size from 16 to 24, which is good agreement with the recent experimental result (J. Phys. Chem. A. 2007, 111, 42). Two novel isomers, i.e., naphthalene-like and dodecahedral Zr(2)Si(20) clusters, are found as low-lying conformers. Furthermore, the novel quasi-1D naphthalene-like Zr(n)Si(m) nanotubes are first reported. The second-order energy differences reveal that magic numbers of the different sized neutral Zr(2)Si(n) clusters appear at n = 18, 20 and 22, which are attributed to the fullerene-like, dodecahedral and polyhedral structures, respectively. The HOMO-LUMO gaps (>1 eV) of all the size-selective Zr(2)Si(n) clusters suggest that encapsulation of the bimetallic zirconium atoms is favorable for increasing the stabilities of silicon cages.     

Oxidation Effects on the Electronic Properties of Hydrogenated Silicon Clusters

The geometric and electronic properties of some hydrogenated silicon clusters in the presence of oxygen on the surface have been investigated.The density functional theory with generalized gradient approximation functional was applied in our calculations.By calculating the total energy,the double bond Si=O is shown to be more stable than the bridge bond Si-O-Si for large size oxidized clusters.The results of Mulliken population analysis indicate that a so-called passivation effect is enhanced by oxidization effects.From the energy band structures and density of states,we find that some localized states are induced by the p-orbital of O atom mainly and reduce the energy gaps substantially.     

Silicon clusters: chemistry and structure

The chemical reactions of size selected silicon cluster ions (containing up to 70 atoms) have been studied with a number of different reagents using injected ion drift tube techniques. Both kinetic and equilibrium measurements have been performed as a function of temperature, and the influence of cluster annealing on chemical reactivity explored. Unlike metal clusters, where bulk behavior appears to be approached with around 30 atoms, large silicon clusters (n up to 70) are much less reactive than bulk silicon surfaces. These results suggest that the clusters in the size range examined here are not small crystals of bulk silicon, but have compact, high coordination number structures with few dangling bonds.     

Excess electron and lithium atom solvation in water clusters at finite temperature: an ab initio molecular dynamics study of the structural, spectral, and dynamical behavior of (H2O)6- and Li(H2O)6

The roles of hydrogen bonds in the solvation of an excess electron and a lithium atom in water hexamer cluster at 150 K have been studied by means of ab initio molecular dynamics simulations. It is found that the hydrogen bonded structures of (H(2)O)(6)(-) and Li(H(2)O)(6) clusters are very different from each other and they dynamically evolve from one conformer to other along their simulation trajectories. The populations of the single acceptor, double acceptor, and free type water molecules are found to be significantly high unlike that in pure water clusters. Free hydrogens of these type of water molecules primarily capture the unbound electron density in these clusters. It is found that the binding motifs of the free electron evolve with time and the vertical detachment energy of (H(2)O)(6)(-) and vertical ionization energy of Li(H(2)O)(6) also change with time. Assignments of the observed peaks in vibrational power spectra are done, and we found direct correlations between the time-averaged population of water molecules in different hydrogen bonding states and the spectral features. The dynamical aspects of these clusters have also been studied through calculations of time correlations of instantaneous stretch frequencies of OH modes which are obtained from the simulation trajectories through a time series analysis.     

Optical properties of passivated silicon nanoclusters: the role of synthesis

The effect of preparation conditions on the structural and optical properties of silicon nanoparticles is investigated. Nanoscale reconstructions, unique to curved nanosurfaces, are presented for silicon nanocrystals and shown to have lower energy and larger optical gaps than bulk-derived structures. We find that high-temperature synthesis processes can produce metastable noncrystalline nanostructures with different core structures than bulk-derived crystalline clusters. The type of core structure that forms from a given synthesis process may depend on the passivation mechanism and time scale. The effect of oxygen on the optical of different types of silicon structures is calculated. In contrast to the behavior of bulklike nanostructures, for noncrystalline and reconstructed crystalline structures surface oxygen atoms do not decrease the gap. In some cases, the presence of oxygen atoms at the nanocluster surface can significantly increase the optical absorption gap, due to decreased angular distortion of the silicon bonds. The relationship between strain and the optical gap in silicon nanoclusters is discussed.     

Structures and relative stability of medium- and large-sized silicon clusters. VI. Fullerene cage motifs for low-lying clusters Si(39), Si(40), Si(50), Si(60), Si(70), and Si(80)

We performed a constrained search, combined with density-functional theory optimization, of low-energy geometric structures of silicon clusters Si(39), Si(40), Si(50), Si(60), Si(70), and Si(80). We used fullerene cages as structural motifs to construct initial configurations of endohedral fullerene structures. For Si(39), we examined six endohedral fullerene structures using all six homolog C(34) fullerene isomers as cage motifs. We found that the Si(39) constructed based on the C(34)(C(s):2) cage motif results in a new leading candidate for the lowest-energy structure whose energy is appreciably lower than that of the previously reported leading candidate obtained based on unbiased searches (combined with tight-binding optimization). The C(34)(C(s):2) cage motif also leads to a new candidate for the lowest-energy structure of Si(40) whose energy is notably lower than that of the previously reported leading candidate with outer cage homolog to the C(34)(C(1):1). Low-lying structures of larger silicon clusters Si(50) and Si(60) are also obtained on the basis of preconstructed endohedral fullerene structures. For Si(50), Si(60), and Si(80), the obtained low-energy structures are all notably lower in energy than the lowest-energy silicon structures obtained based on an unbiased search with the empirical Stillinger-Weber potential of silicon. Additionally, we found that the binding energy per atom (or cohesive energy) increases typically >10 meV with addition of every ten Si atoms. This result may be used as an empirical criterion (or the minimal requirement) to identify low-lying silicon clusters with size larger than Si(50).     

Disparate effects of Cu and V on structures of exohedral transition metal-doped silicon clusters: a combined far-infrared spectroscopic and computational study

The growth mechanisms of small cationic silicon clusters containing up to 11 Si atoms, exohedrally doped by V and Cu atoms, are described. We find that as dopants, V and Cu follow two different paths: while V prefers substitution of a silicon atom in a highly coordinated position of the cationic bare silicon clusters, Cu favors adsorption to the neutral or cationic bare clusters in a lower coordination site. The different behavior of the two transition metals becomes evident in the structures of Si(n)M(+) (n = 4-11 for M = V, and n = 6-11 for M = Cu), which are investigated by density functional theory and, for several sizes, confirmed by comparison with their experimental vibrational spectra. The spectra are measured on the corresponding Si(n)M(+)·Ar complexes, which can be formed for the exohedrally doped silicon clusters. The comparison between experimental and calculated spectra indicates that the BP86 functional is suitable to predict far-infrared spectra of these clusters. In most cases, the calculated infrared spectrum of the lowest-lying isomer fits well with the experiment, even when various isomers and different electronic states are close in energy. However, in a few cases, namely Si(9)Cu(+), Si(11)Cu(+), and Si(10)V(+), the experimentally verified isomers are not the lowest in energy according to the density functional theory calculations, but their structures still follow the described growth mechanism. The different growth patterns of the two series of doped Si clusters reflect the role of the transition metal's 3d orbitals in the binding of the dopant atoms.     

The Geometric Structure of Silver‐Doped Silicon Clusters

Cationic silver‐doped silicon clusters, Si_nAg⁺ (n=6–15), are studied using infrared multiple photon dissociation in combination with density functional theory computations. Candidate structures are identified using a basin‐hopping global optimizations method. Based on the comparison of experimental and calculated IR spectra for the identified low‐energy isomers, structures are assigned. It is found that all investigated clusters have exohedral structures, that is, the Ag atom is located at the surface. This is a surprising result because many transition‐metal dopant atoms have been shown to induce the formation of endohedral silicon clusters. The silicon framework of Si_nAg⁺ (n=7–9) has a pentagonal bipyramidal building block, whereas the larger Si_nAg⁺ (n=10–12, 14, 15) clusters have trigonal prism‐based structures. On comparing the structures of Si_nAg⁺ with those of Si_nCu⁺ (for n=6–11) it is found that both Cu and Ag adsorb on a surface site of bare Si_n⁺ clusters. However, the Ag dopant atom takes a lower coordinated site and is more weakly bound to the Si_n⁺ framework than the Cu dopant atom.     

Oxidation pattern of small silicon oxide clusters: structures and stability of Si6On (n = 1-12)

We have performed systematic ab initio calculations to study the structures and stability of Si(6)O(n)() clusters (n = 1-12) in order to understand the oxidation process in silicon systems. Our calculation results show that oxidation pattern of the small silicon cluster, with continuous addition of O atoms, extends from one side to the entire Si cluster. Si atoms are found to be separated from the pure Si cluster one-by-one by insertion of oxygen into the Si-O bonds. From fragmentation energy analyses, it is found that the Si-rich clusters usually dissociate into a smaller pure Si clusters (Si(5), Si(4), Si(3), or Si(2)), plus oxide fragments such as SiO, Si(2)O(2), Si(3)O(3), Si(3)O(4), and Si(4)O(5). We have also studied the structures of the ionic Si(6)O(n)(+/-) (n = 1-12) clusters and found that most of ionic clusters have different lowest-energy structures in comparison with the neutral clusters. Our calculation results suggest that transformation Si(6)O(n)+(a) + O --> Si(6)O(n+1)+(a) should be easier.     

Nickel and copper doped palladium clusters from a first-principles perspective

A complete study on the evolution of structures and the variation of the energy properties of MPd_n−1 (M = Ni and Cu; n = 2-13) clusters is presented. The study was performed employing auxiliary density functional theory. The obtained results were compared with the results of Pd_n clusters studied with the same methodology. For each cluster size, several structures were studied to determine the lowest energy structures. The initial structures for the geometry optimization were taken along ab initio Born-Oppenheimer molecular dynamics trajectories. Different potentials energy surfaces were studied. All cluster structures were fully optimized without any symmetry restriction. Stable structures, frequencies, spin multiplicities, averaged bond lengths, spin density plots, different energy properties, dipole and magnetic moments as well as charge transfers are reported. This investigation indicates that the palladium clusters doped with a Ni atom are the most stable and potentially the most chemical active ones.     

Sequential reactions of silicon clusters with SiD4: constrained heterogeneous nucleation of deuterated silicon particles

The sequential clustering reactions of gas phase silicon cluster ions are ideally suited for studying heterogeneous nucleation of silicon particles. Stepwise reactions of silicon cluster ions with silane have been observed which lead to growth of larger deuterated silicon clusters. Extensive information is obtained about their exothermic gas phase reaction rates and product distributions as a function of cluster size and degree of hydrogenation. What is found is that each size of silicon cluster exhibits a unique pattern of growth. Furthermore, nearly all of the silicon clusters encounter chemical constraints to rapid nucleation. These constraints are a consequence of specific electronic and structural requirements in the chemical reactions. The nature of these requirements are deduced using experimental results in concert with ab initio electronic structure theoretical calculations of the energetics and structures of various species.     

Theoretical studies on carbon and silicon clusters: comparison of the structures and stabilities of neutral and ionic forms

Optimized molecular geometries and electronic structures are determined for neutral, positively charged, and negatively charged carbon and silicon clusters containing up to ten atoms. The effects of polarization functions and electron correlation are included in these claculations. Carbon clusters have linear or monocyclic ground state geometries whereas silicon clusters containing five or more atoms have three-dimensional ground state structures. Neutral C₄, C₆ and C₈ all have linear and monocyclic isomers of comparable stability whereas the ionic forms appear to be generally more stable as linear geometrical arrangements. In the case of neutral and positively charged carbon clusters, the odd-numbered clusters are significantly more stable than the adjacent even-numbered clusters whereas the opposite order of stability occurs for the negative ions. This is due to the large values of the electron affinities of the linear forms of even-numbered clusters such as C₄ and C₆. The relative stabilities of silicon clusters does not change with the charge state of the clusters.     

Order-<Emphasis Type="Italic">N</Emphasis> and embedded-cluster first-principles DFT calculations using SIESTA/Mosaico

Order-N and embedded-cluster first-principles DFT calculations have been performed with the Mosaico method for energy optimization (Seijo and Barandiarán in J Chem Phys 121:6698, 2004) for the first time. The Hamiltonian matrix elements have been computed with the SIESTA code. The order-N behavior of the method in DFT calculations was shown in total energy calculations performed on bulk silicon using supercells up to Si₈₀₀₀. The sizes of the orbital-specific-basis-sets needed for precise calculations have been explored in demanding (bulk silicon) and favorable (water clusters) cases for a method based on the calculation of localized molecular orbitals. Embedded-cluster calculations, which are much faster than full-system calculations, have been performed on an Si-vacancy of bulk silicon and on a water cluster with a displacing water molecule. The feasiability of calculations of this type with Mosaico has been demonstrated. The sizes of the variationally free, active clusters which are needed for an agreement with full-system calculations have been explored and result to be reasonably small. Contribution to the Serafin Fraga Memorial Issue.     

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.     

Quantum-mechanical simulation of the interaction of aluminum- and boron-containing zeolite clusters with molecules of water and ammonia

Quantum-mechanical computations of zeolite clusters with molecules of water and ammonia have been carried out. The clusters consisted of ten atoms of silicon and aluminum, where one atom of aluminum was also replaced with an atom of boron. Values of the bond length and bond angles have been obtained; the geometry of adsorption complexes and the bond energy for molecules of water and ammonia with atoms of aluminum and boron of a zeolite fragment have been determined. The computed values of bond energy for molecule probes yield the quantitative strength characteristic of zeolite aprotic acid centers.     

Exponentially divergent trajectories and RRKM behaviour of Ar3 clusters

The rate of exponential divergence of two initially adjacent trajectories has been studied for Ar₂ clusters at low and high energies. It is found that at the dissociation limit energy randomization occurs during two typical vibrational periods. Lifetime distributions for energies not far above the dissociation limit have a random lifetime pattern but highly energized clusters show non-RRKM behaviour