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.     

Fluxional and aromatic behavior in small magic silicon clusters: a full ab initio study of Si(n), Si(n) (1-), Si(n) (2-), and Si(n) (1+), n=6, 10 clusters

The structural, electronic, vibrational, optical, magnetic, and aromatic characteristics of Si(n), Si(n) (1-), Si(n) (2-), and Si(n) (1+), clusters have been calculated very accurately with a variety of high level ab initio techniques. These calculations have been performed with the aim to clarify existing ambiguities in the literature and to bring up the fluxional and aromatic characteristics of these species. The fluxional behavior, according to earlier conjecture of the present author, could be connected to the magic property. In addition such behavior could also explain the existence of conflicting results. The ab initio techniques include quadratic configuration interaction, coupled cluster, and multireference second order perturbation theory, together with density functional theory ("static" and time dependent) with the hybrid B3LYP functional. Various high quality correlation-consistent basis sets, ranging from 2Z up to 5Z quality, were employed. It is demonstrated that Si(6) is fluxional, fluctuating around a symmetric D(4h) structure. Si(10) is also fluxional but to a lesser degree, in contrast to Si(10) (1-) anion which is highly fluxional. For both clusters, in full agreement with Wade's and Lipscomb's rules for deltahedral boranes, the corresponding dianions have higher symmetry (O(h) and D(4d), respectively) and lower energy than the neutral clusters. The aromatic behavior of Si(6) fits better to a mixed conflicting aromaticity picture. This type of aromatic and fluxional behavior has also been observed in stable "magic" carbon clusters as C(6) and carbon fullerenes such as C(20). The present results, which support possible connection of fluxional and magic properties, are in excellent agreement with experimental measurements of ionization energies, electron affinities, and vibrationally resolved photoelectron spectra.     

Comparison of the growth patterns of Si(n) and Ge(n) clusters (n = 25-33)

We performed an unbiased search for low-energy structures of medium-sized neutral Si n and Ge n clusters ( n = 25-33) using a genetic algorithm (GA) coupled with tight-binding interatomic potentials. Structural candidates obtained from our GA search were further optimized by first-principles calculations using density functional theory (DFT). Our approach reproduces well the lowest-energy structures of Si n and Ge n clusters of n = 25-29 compared to previous studies, showing the accuracy and reliability of our approach. In the present study, we pay more attention to determine low-lying isomers of Si n and Ge n ( n = 29-33) and study the growth patterns of these clusters. The B3LYP calculations suggest that the growth pattern of Si n ( n = 25-33) clusters undergoes a transition from prolate to cage at n = 31, while this transition appears at n = 26 from the PBE-calculated results. In the size range of 25-33, the corresponding Ge n clusters hold the prolate growth pattern. The relative stabilities and different structural motifs of Si n and Ge n ( n = 25-33) clusters were studied, and the changes of small cluster structures, when acting as building blocks of large clusters, were also discussed.     

Structures and energetics of Be(n)Si(n) and Be(2n)Si(n) (n = 1-4) clusters

The structures and energies of Be(n)Si(n) and Be(2n)Si(n) (n = 1-4) clusters have been examined in ab initio theoretical electronic structure calculations. Cluster geometries have been established in B3LYP/6-31G(2df) calculations and accurate relative energies determined by the G3XMP2 method. The two atoms readily bond to each other and to other atoms of their own kind. The result is a great variety of low-energy clusters in a variety of structural types.     

Gold as hydrogen: structural and electronic properties and chemical bonding in Si3Au3(+0-) and comparisons to Si3H3(+0-)

A single Au atom has been shown to behave like H in its bonding to Si in several mono- and disilicon gold clusters. In the current work, we investigate the AuH analogy in trisilicon gold clusters, Si3Au3(+0-). Photoelectron spectroscopy and density functional calculations are combined to examine the geometric and electronic structure of Si3Au3-. We find that there are three isomers competing for the ground state of Si3Au3- as is the case for Si3H3-. Extensive structural searches show that the potential energy surfaces of the trisilicon gold clusters (Si3Au3-, Si3Au3, and Si3Au3+) are similar to those of the corresponding silicon hydrides. The lowest energy isomers for Si3Au3- and Si3Au3 are structurally similar to a Si3Au four-membered ring serving as a common structural motif. For Si3Au3+, the 2pi aromatic cyclotrisilenylium auride ion, analogous to the aromatic cyclotrisilenylium ion (Si3H3+), is the most stable species. Comparison of the structures and chemical bonding between Si3Au3(+0-) and the corresponding silicon hydrides further extends the isolobal analogy between Au and H.     

Electronic structures and thermochemical properties of the small silicon-doped boron clusters B(n)Si (n=1-7) and their anions

We perform a systematic investigation on small silicon-doped boron clusters B(n)Si (n=1-7) in both neutral and anionic states using density functional (DFT) and coupled-cluster (CCSD(T)) theories. The global minima of these B(n)Si(0/-) clusters are characterized together with their growth mechanisms. The planar structures are dominant for small B(n)Si clusters with n≤5. The B(6)Si molecule represents a geometrical transition with a quasi-planar geometry, and the first 3D global minimum is found for the B(7)Si cluster. The small neutral B(n)Si clusters can be formed by substituting the single boron atom of B(n+1) by silicon. The Si atom prefers the external position of the skeleton and tends to form bonds with its two neighboring B atoms. The larger B(7)Si cluster is constructed by doping Si-atoms on the symmetry axis of the B(n) host, which leads to the bonding of the silicon to the ring boron atoms through a number of hyper-coordination. Calculations of the thermochemical properties of B(n)Si(0/-) clusters, such as binding energies (BE), heats of formation at 0 K (ΔH(f)(0)) and 298 K (ΔH(f)([298])), adiabatic (ADE) and vertical (VDE) detachment energies, and dissociation energies (D(e)), are performed using the high accuracy G4 and complete basis-set extrapolation (CCSD(T)/CBS) approaches. The differences of heats of formation (at 0 K) between the G4 and CBS approaches for the B(n)Si clusters vary in the range of 0.0-4.6 kcal mol(-1). The largest difference between two approaches for ADE values is 0.15 eV. Our theoretical predictions also indicate that the species B(2)Si, B(4)Si, B(3)Si(-) and B(7)Si(-) are systems with enhanced stability, exhibiting each a double (σ and π) aromaticity. B(5)Si(-) and B(6)Si are doubly antiaromatic (σ and π) with lower stability.     

Structural and electronic properties of Si(n), Si(n)-, and PSi(n-1) clusters (2 < or = n < or = 13): Theoretical investigation based on ab initio molecular orbital theory

The geometric and electronic structures of Si(n), Si(n)-, and PSi(n-1) clusters (2 < or = n < or = 13) have been investigated using the ab initio molecular orbital theory formalism. The hybrid exchange-correlation energy functional (B3LYP) and a standard split-valence basis set with polarization functions (6-31+G(d)) were employed to optimize geometrical configurations. The total energies of the lowest energy isomers thus obtained were recalculated at the MP2/aug-cc-pVTZ level of theory. Unlike positively charged clusters, which showed similar structural behavior as that of neutral clusters [Nigam et al., J. Chem. Phys. 121, 7756 (2004)], significant geometrical changes were observed between Si(n) and Si(n)- clusters for n = 6, 8, 11, and 13. However, the geometries of P substituted silicon clusters show similar growth as that of negatively charged Si(n) clusters with small local distortions. The relative stability as a function of cluster size has been verified based on their binding energies, second difference in energy (Delta2 E), and fragmentation behavior. In general, the average binding energy of Si(n)- clusters is found to be higher than that of Si(n) clusters. For isoelectronic PSi(n-1) clusters, it is found that although for small clusters (n < 4) substitution of P atom improves the binding energy of Si(n) clusters, for larger clusters (n > or = 4) the effect is opposite. The fragmentation behavior of these clusters reveals that while small clusters prefer to evaporate monomer, the larger ones dissociate into two stable clusters of smaller size. The adiabatic electron affinities of Si(n) clusters and vertical detachment energies of Si(n)- clusters were calculated and compared with available experimental results. Finally, a good agreement between experimental and our theoretical results suggests good prediction of the lowest energy isomeric structures for all clusters calculated in the present study.     

Gold as hydrogen. An experimental and theoretical study of the structures and bonding in disilicon gold clusters Si2Au(n)- and Si2Au(n) (n = 2 and 4) and comparisons to Si2H2 and Si2H4

In a previous communication, we showed that a single Au atom behaves like H in its bonding to Si in a series of Si-Au clusters, SiAu(n) (n = 2-4) (Kiran et al. Angew. Chem., Int. Ed. 2004, 43, 2125). In this article, we show that the H analogy of Au is more general. We find that the chemical bonding and potential energy surfaces of two disilicon Au clusters, Si(2)Au(2) and Si(2)Au(4), are analogous to Si(2)H(2) and Si(2)H(4), respectively. Photoelectron spectroscopy and ab initio calculations are used to investigate the geometrical and electronic structures of Si(2)Au(2)(-), Si(2)Au(4)(-), and their neutral species. The most stable structures for both Si(2)Au(2) and Si(2)Au(2)(-) are found to be C(2)(v), in which each Au bridges the two Si atoms. For Si(2)Au(4)(-), two nearly degenerate dibridged structures in a cis (C(2)(h)) and a trans (C(2)(v)) configuration are found to be the most stable isomers. However, in the neural potential energy surface of Si(2)Au(4), a monobridged isomer is the global minimum. The ground-state structures of Si(2)Au(2)(-) and Si(2)Au(4)(-) are confirmed by comparing the computed vertical detachment energies with the experimental data. The various stable isomers found for Si(2)Au(2) and Si(2)Au(4) are similar to those known for Si(2)H(2) and Si(2)H(4), respectively. Geometrical and electronic structure comparisons with the corresponding silicon hydrides are made to further establish the isolobal analogy between a gold atom and a hydrogen atom.     

Density-functional study of structural and electronic properties of Si(n)C(n) (n=1-10) clusters

Density-functional theory with generalized gradient approximation for the exchange-correlation potential has been used to calculate the structural and electronic structure of Si(n)C(n) (n=1-10) clusters. The geometries are found to undergo a structural change from two dimensional to three dimensional when the cluster size n equals 4. Cagelike structures are favored as the cluster size increases. A distinct segregation between the silicon and carbon atoms is observed for these clusters. It is found that the C atoms favor to form five-membered rings as the cluster size n increases. However, the growth motif for Si atoms is not observed. The Si(n)C(n) clusters at n=2, 6, and 9 are found to possess relatively higher stability. On the basis of the lowest-energy geometries obtained, the size dependence of cluster properties such as binding energy, HOMO-LUMO gap, Mulliken charge, vibrational spectrum, and ionization potential has been computed and analyzed. The bonding characteristics of the clusters are discussed.     

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.     

Ab initio study of lithiathion of the Si4(-) cluster

The potential energy surfaces of the Li(n)Si(4)(-) (n = 0-5) clusters were explored using the Kick Coalescence method. We found that, for those systems with n ≤ 2, the butterfly and parallelogram Si(4)(2-) kernels prevail as building blocks; however, when n ≥ 3, the Si(4)(4-) tetrahedral kernel, which is commonly found in heavier alkali monosilicides, MSi (M = Na, K, Rb, Cs), arises as the prevailing building block. In addition, by a natural population analysis (NPA) we found that the maximum charge transfer -4 from Li atoms to Si atoms is attained when n = 3. The addition of more Li atoms to the Si(4)(4-) system does not increase the charge transfer, but keeps it almost constant at the maximum value. We also calculated theoretical vertical electron detachment energies (VDEs) for low-lying isomers of the Li(n)Si(4)(-) (n = 0-4) clusters in order to facilitate their experimental identification.     

Theoretical study of mixed silicon-lithium clusters Si(n)Li(p)(+) (n=1-6, p=1-2)

Theoretical study on the structures of neutral and singly charged Si(n)Li(p)((+)) (n=1-6, p=1-2) clusters have been carried out in the framework of the density functional theory (DFT) with the B3LYP functional. The structures of the neutral Si(n)Li(p) and cationic Si(n)Li(p)(+) clusters are found to keep the frame of the corresponding Si(n), Li species being adsorbed at the surface. The localization of the lithium cation is not the same one as that of the neutral atom. The Li(+) ion is preferentially located on a Si atom, while the Li atom is preferentially attached at a bridge site. A clear parallelism between the structures of Si(n)Na(p) and those of Si(n)Li(p) appears. The population analysis show that the electronic structure of Si(n)Li(p) can be described as Si(n)(p)(-)+pLi(+) for the small sizes considered. Vertical and adiabatic ionization potentials, adsorption energies, as well as electric dipole moments and static dipolar polarizabilities, are calculated for each considered isomer of neutral species.     

Ligand-free deltahedral clusters of silicon in solution: synthesis, structure, and electrochemistry of Si9(2-)

Deltahedral nine-atom clusters of silicon, Si(9)(2-), were synthesized by mild oxidation of a liquid ammonia solution of K(12)Si(17) with Ph(3)GeCl in the presence of 18-crown-6 (1,4,7,10,13,16-hexaoxacyclooctadecane) or 2,2,2-crypt (4,7,13,16,21,24-hexaoxa-1,10-diazabicyclo[8.8.8]hexacosane). The clusters were structurally characterized in [K(18-crown-6)](2)Si(9).C(5)H(5)N (yellow; orthorhombic, Pnma; a = 14.013(1), b = 18.108 (1), c = 18.320 (1) A; Z = 4) crystallized from a pyridine solution of the product of the aforementioned reaction in liquid ammonia. Si(9)(2-) is the first unequivocally characterized nine-atom cluster of group 14 with a charge of 2-. In addition to pyridine, the product from the reaction in liquid ammonia is also soluble in DMF, and the Si(9)(2-) clusters were characterized by mass spectrometry in such a solution. The more reduced clusters Si(9)(3-) have also been crystallized from pyridine solution. Cyclic voltammetry in both pyridine and DMF solutions clearly shows the Si(9)(2-)/Si(9)(3-) redox couple as one-electron reversible process. The structural similarities and differences between Si(9)(3-) and Si(9)(2-) are discussed herein.     

Silicon monohydride clusters Si(n)H (n = 4-10) and their anions: structures, thermochemistry, and electron affinities

The molecular structures, electron affinities, and dissociation energies of the Si(n)H/Si(n)H- (n = 4-10) species have been examined via five hybrid and pure density functional theory (DFT) methods. The basis set used in this work is of double-zeta plus polarization quality with additional diffuse s- and p-type functions, denoted DZP++. The geometries are fully optimized with each DFT method independently. The three different types of neutral-anion energy separations presented in this work are the adiabatic electron affinity (EA(ad)), the vertical electron affinity (EA(vert)), and the vertical detachment energy (VDE). The first Si-H dissociation energies, D(e)(Si(n)H --> Si(n) + H) for neutral Si(n)H and D(e)(Si(n)H- --> Si(n)- + H) for anionic Si(n)H- species, have also been reported. The structures of the ground states of these clusters are traditional H-Si single-bond forms. The ground-state geometries of Si5H, Si6H, Si8H, and Si9H predicted by the DFT methods are different from previous calculations, such as those obtained by Car-Parrinello molecular dynamics and nonorthogonal tight-binding molecular dynamics schemes. The most reliable EA(ad) values obtained at the B3LYP level of theory are 2.59 (Si4H), 2.84 (Si5H), 2.86 (Si6H), 3.19 (Si7H), 3.14 (Si8H), 3.36 (Si9H), and 3.56 (Si10H) eV. The first dissociation energies (Si(n)H --> Si(n) + H) predicted by all of these methods are 2.20-2.29 (Si4H), 2.30-2.83 (Si5H), 2.12-2.41 (Si6H), 1.75-2.03 (Si7H), 2.41-2.72 (Si8H), 1.86-2.11 (Si9H), and 1.92-2.27 (Si10H) eV. For the negatively charged ion clusters (Si(n)H- --> Si(n)- + H), the dissociation energies predicted are 2.56-2.69 (Si4H-), 2.80-3.01 (Si5H-), 2.86-3.06 (Si6H-), 2.80-3.03 (Si7H-), 2.69-2.92 (Si8H-), 2.92-3.18 (Si9H-), and 2.89-3.25 (Si10H-) eV.     

Geometries and stabilities of Ag-doped Si n (n=1-13) clusters: a first-principles study

The structures of AgSi(n) (n=1-13) clusters are investigated using first-principles calculations. Our studies suggest that AgSi(n) clusters with n=7 and 10 are relatively stable isomers and that these clusters prefer to be exohedral rather than endohedral. Moreover, doping leaves the inner core structure of the clusters largely intact. Additionally, the plot of fragmentation energies as a function of silicon atoms shows that the AgSi(n) are favored to dissociate into one Ag atom and Si(n) clusters. Alternative pathways exist for n>7 (except n=11) in which the Ag-Si cluster dissociates into a stable Si(7) and a smaller fragment AgSi(n-7). The AgSi(11) cluster dissociates into a stable Si(10) and a small fragment AgSi. Lastly, our analysis indicates that doping of Ag atom significantly decreases the gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital for n>7.     

Electronic properties of Si and Ge atoms doped in clusters: In(n)Si(m) and In(n)Ge(m)

Electronic properties of silicon and germanium atom doped indium clusters, In(n)Si(m) and In(n)Ge(m), were investigated by photoionization spectroscopy of the neutrals and photoelectron spectroscopy of the anions. Size dependence of ionization energy and electron affinity for In(n)Si(1) and In(n)Ge(1) exhibit pronounced even-odd alternation at cluster sizes of n = 10-16, as compared to those for pure In(n) clusters. This result shows that symmetry lowering with the doped atom of Si or Ge results in undegeneration of electronic states in the 1d shell formed by monovalent In atoms.     

Efficiency of random search procedures along the silicon cluster series: Si(n) (n=5-10, 15, and 20)

The efficiency of the simplest isomeric search procedure consisting in random generation of sets of atomic coordinates followed by density functional theory geometry optimization is tested on the silicon cluster series (Si(5-10, 15, 20)). Criteria such as yield, isomer distributions and recurrences are used to clearly establish the performance of the approach with respect to increasing cluster size. The elimination of unphysical candidate structures and the use of distinct box shapes and theoretical levels are also investigated. For the smaller Si(n) (n=5-10) clusters, the generation of random coordinates within a spherical box is found to offer a reasonable alternative to more complex algorithms by allowing straightforward identification of every known low-lying local minima. The simple stochastic search of larger clusters (i.e. Si(15) and Si(20)) is however complicated by the exponentially increasing number of both low- and high-lying minima leading to rather arbitrary and non-comprehensive results.     

Geometries and electronic properties of the neutral and charged rare earth Yb-doped Si(n) (n = 1-6) clusters: a relativistic density functional investigation

The neutral and charged YbSi(n) (n = 1-6) clusters considering different spin configurations have been systematically investigated by using the relativistic density functional theory with generalized gradient approximation. The total bonding energies, equilibrium geometries, Mulliken populations (MP), Hirshfeld charges (HC), fragmentation energies, and highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps are calculated and discussed. The optimized geometries indicate that the most stable YbSi(n) (n = 1-6) clusters keep basically the analogous frameworks as the low-lying Si(n)(+1) clusters, while the charged species deviate from their neutral counterparts, and that the doped Yb tends to occupy the substitutional site of the neutral and charged YbSi(n) isomers. The relative stabilities are investigated in terms of the calculated fragmentation energies, exhibiting enhanced stabilities for the remarkably stable neutral and charged YbSi2 and YbSi5 clusters. Furthermore, the calculated MP and HC values show that the charges of the neutral and charged YbSi(n) clusters transfer from the Yb atom to Si(n) atoms and the Yb atom acts as an electron donor, and that the f orbitals of the Yb atom in the neutral and charged YbSi(n) clusters behave as core without involvement in chemical bonding. The calculated HOMO-LUMO gaps indicate that the YbSi2 and YbSi4+ clusters have stronger chemical stabilities. Comparisons of the Yb-doped Si(n) (n = 1-6) with available theoretical results of transition-metal-doped silicon clusters are made. The growth pattern is investigated also.     

A Gaussian-3 theoretical study of small silicon-lithium clusters: electronic structures and electron affinities of SinLi(-) (n = 2-8)

The molecular structures of neutral Si n Li ( n = 2-8) species and their anions have been studied by means of the higher level of the Gaussian-3 (G3) techniques. The lowest energy structures of these clusters have been reported. The ground-state structures of neutral clusters are "attaching structures", in which the Li atom is bound to Si n clusters. The ground-state geometries of anions, however, are "substitutional structures", which is derived from Si n+1 by replacing a Si atom with a Li (-). The electron affinities of Si n Li and Si n have been presented. The theoretical electron affinities of Si n are in good agreement with the experiment data. The reliable electron affinities of Si n Li are predicted to be 1.87 eV for Si 2Li, 2.06 eV for Si 3Li, 2.01 eV for Si 4Li, 2.61 eV for Si 5Li, 2.36 eV for Si 6Li, 2.21 eV for Si 7Li, and 3.18 eV for Si 8Li. The dissociation energies of Li atom from the lowest energy structures of Si n Li and Si atom from Si n clusters have also been estimated respectively to examine relative stabilities.