Theoretical studies on the bonding and thermodynamic properties of Ge n Si m (m+n=5) clusters: the precursors of germanium/silicon nanomaterials

Theoretical studies on the Ge n Si m clusters have been carried out using advanced ab initio approaches. The lowest energy isomers were determined for the clusters with compositions n+m=2-5. All possible isomers arising due to permutations of Ge and Si atoms were investigated. The L-shaped structure for the trimers, tetragonal with diagonal bond for tetramers, and a trigonal bipyramid for pentamers represent the energy optimized ground state geometries. The bonding analyses revealed that the trimers and tetramers are stabilized through multicenter pi bonding. In pentamers, this stabilizing factor is eliminated due to the further cluster growth. The ionization of clusters does not change their geometrical characteristics. The agreement of the calculated ionization and atomization energies with those obtained from the mass spectrometric studies (through estimated appearance potential) validated the reported structures of the clusters. The bonding properties of these species are discussed using their molecular orbital characteristics and analysis of natural bond orbital population data.     

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.     

Charge-transfer processes in the assembly of Si(n)O(m) neutral clusters

The chemical bond formation in oxygen-rich Si(n)O(m) clusters was investigated by sampling the potential energy surface of the model systems SiO + SiO(2) → Si(2)O(3) and (SiO)(2) + SiO(2) → Si(3)O(4) along a two-dimensional reaction coordinate, by density functional theory calculations. Evidence for crossing between the weakly bound neutral-neutral (SiO)(n) + SiO(2) and the highly attractive ion-pair (SiO)(n)(+) + SiO(2)(-) surfaces was found. Analysis of frontier molecular orbitals and charge distribution showed that surface crossing involves transfer of valence electron charge from (SiO)(2) to SiO(2). The sum of the natural atomic charges over the (SiO)(n) and (SiO(2)) groups of the Si(n)O(m) cluster products, gave a net positive charge on the (SiO)(n) "core" and a net negative charge on the (SiO(2)) groups. This is interpreted as the "ion-pair memory" left on the Si(n)O(m) products by the charge-transfer mechanism and may provide a way to assess the role of charge-transfer processes in the assembly of larger Si(n)O(m) neutral clusters.     

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.     

Size-dependent properties of Zn(m)S(n) clusters: a density-functional tight-binding study

We present the results of our theoretical calculations on structural and electronic properties of ligand-free Zn(n)S(n) [with n ranging from 4 to 104 (0.8-2.0-nm diameter)] clusters as a function of size of the clusters. We have optimized the structure whereby our initial structures are spherical parts of either zinc-blende or wurtzite structure. We have also considered some hollow bubblelike structures. The calculations are performed by using a parametrized linear combination of atomic orbitals-density-functional theory-local-density approximation-tight-binding method. We have focused on the variation of radial distribution function, Mulliken populations, electronic energy levels, band gap, and stability as a function of size for both zinc-blende and wurtzite-derived ZnS clusters. We have also reported the results of some nonstoichiometric Zn(m)S(n) (with m+n=47, 99, 177) clusters of zinc-blende modification.     

Reactions of germanium atoms and small clusters with CO: experimental and theoretical characterization of Ge(n)CO (n = 1-5) and Ge2(CO)2 in solid argon

Reactions of germanium atoms and small clusters with carbon monoxide molecules in solid argon have been studied using matrix isolation infrared absorption spectroscopy. Besides the previously reported GeCO monocarbonyl, the Ge2(CO)2 and Ge(n)CO (n = 2-5) carbonyl molecules are formed spontaneously on annealing and are characterized on the basis of isotopic substitution and theoretical calculations. It is found that Ge2CO, Ge3CO, and Ge5CO are bridge-bonded carbonyl compounds, whereas Ge2(CO)2 and Ge4CO are terminal-bonded carbonyl molecules.     

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.     

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.     

First-principles study of electronic and magnetic properties of Co(n)Mn(m) and Co(n)V(m) (m + n < or = 6) clusters

The electronic and magnetic properties of small Co(n)Mn(m) and Co(n)V(m) (m + n < or = 6) clusters are systematically studied using density functional theory. The results show that Co and V atoms prefer to aggregate in Co-Mn and Co-V clusters, respectively. Significant magnetic moment enhancement in Co-Mn clusters with Mn doping and reduction in Co-V clusters with V doping are found, consistent with experiment results for larger clusters [Phys. Rev. Lett. 2007, 98, 113401]. The results are discussed by analyzing the magnetic coupling type and local magnetic moment on each atoms. Density of states and vertical ionization potentials are calculated and show cluster size dependent behavior.     

Low-lying isomers of Si(n)(+) and Si(n)(-) (n=31-50) clusters

We carry out a systematic search for the atomic structures of silicon cluster cations and anions in the size range n=31-50 using density functional theory in the generalized-gradient approximation. The obtained lowest-energy candidates feature cagelike structures. We find that the computed binding energies and the dissociation pathways as well as the mobilities of our lowest-energy isomers of the cations are all in good agreement with the measured data from experiments. Furthermore, based on these isomers, we reveal that the steplike feature appearing in the measured high-resolution mobilities can be correlated with the corresponding fullerenes explicitly, which strongly support the notion that endohedral silicon fullerenelike structures are the most favored growth pattern for silicon clusters in the range n=31-50. Our calculation and analysis suggest that the proposed isomers are probably very close to the major-abundance isomers observed in experiments.     

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.     

Electronic structure and thermochemical properties of silicon-doped lithium clusters Li(n)Si0/+, n = 1-8: new insights on their stability

A theoretical investigation on small silicon-doped lithium clusters Li(n)Si with n = 1-8, in both neutral and cationic states is performed using the high accuracy CCSD(T)/complete basis set (CBS) method. Location of the global minima is carried out using a stochastic search method and the growth pattern of the clusters emerges as follows: (i) the species Li(n)Si with n ≤ 6 are formed by directly binding one Li to a Si of the smaller cluster Li(n-1)Si, (ii) the structures tend to have an as high as possible symmetry and to maximize the coordination number of silicon. The first three-dimensional global minimum is found for Li(4)Si, and (iii) for Li(7)Si and Li(8)Si, the global minima are formed by capping Li atoms on triangular faces of Li(6)Si (O(h)). A maximum coordination number of silicon is found to be 6 for the global minima, and structures with higher coordination of silicon exist but are less stable. Heats of formation at 0 K (Δ(f)H(0)) and 298 K (Δ(f)H(298)), average binding energies (E(b)), adiabatic (AIE) and vertical (VIE) ionization energies, dissociation energies (D(e)), and second-order difference in total energy (Δ(2)E) of the clusters in both neutral and cationic states are calculated from the CCSD(T)/CBS energies and used to evaluate the relative stability of clusters. The species Li(4)Si, Li(6)Si, and Li(5)Si(+) are the more stable systems with large HOMO-LUMO gaps, E(b), and Δ(2)E. Their enhanced stability can be rationalized using a modified phenomenological shell model, which includes the effects of additional factors such as geometrical symmetry and coordination number of the dopant. The new model is subsequently applied with consistency to other impure clusters Li(n)X with X = B, Al, C, Si, Ge, and Sn.     

The structural and electronic properties of In(n)N(n = 1-13) clusters

The structural and electronic properties of In(n)N(n=1-13) clusters have been investigated by density-functional theory with the generalized gradient approximation. The results indicate that the equilibrium structures of In(n)N are linear for n=1,2, planar for n=3-5, and three dimensional for n=6-13. Maximum peaks were observed for In(n)N clusters at n=3,7,9 on the size dependence for second-order energy difference. These imply that these clusters possess relatively higher stability, which is consistent with the case of binding energy per atom. Moreover, the results show that the bonding in small In(n)N clusters has a little ionic character by Mulliken population analysis. The energy gap between the highest occupied and lowest unoccupied molecular orbitals, the vertical ionization potential and electron vertical affinity (VIP and VEA) form an even-odd alternating pattern with increasing cluster size. In general, the VIP tends to lower as the cluster size increases, while the VEA tends to increase as the cluster size increases.     

Electronic and structural investigations of gold clusters doped with copper: Aun-1Cu- (n=13-19)

We have obtained the ground state and the equilibrium geometries of Au(n) (-) and Au(n-1)Cu(-) in the size range of n=13-19. We have used first principles density functional theory within plane wave and Gaussian basis set methods. For each of the cluster we have obtained at least 100 distinct isomers. The anions of gold clusters undergo two structural transformations, the first one from flat cage to hollow cage and the second one from hollow cage to pyramidal structure. The Cu doped clusters do not show any flat cage structures as the ground state. The copper doped systems evolve from a general 3D structure to hollow cage with Cu trapped inside the cage at n=16 and then to pyramidal structure at n=19. The introduction of copper atom enhances the binding energy per atom as compared to gold cluster anions.     

Structure and stability of (TiO2)n, (SiO2)n, and mixed Ti(m)Si(n-m)O(2n) [n = 2-5, m = 1 to (n - 1)] clusters

Structures, energetics, and vibrational spectra are investigated for small pure (TiO(2))(n), (SiO(2))(n), and mixed Ti(m)Si(n-m)O(2n) [n = 2-5, m = 1 to (n - 1)] oxide clusters by density functional theory (DFT). The BP86/ATZP level of theory is employed to obtain constitutional isomers of the oxide clusters. In accordance with previous studies, our calculations show three-dimensional compact structures are preferred for pure (TiO(2))(n) with oxo-stabilized higher hexavalent states, and linear chain structures are favored for pure (SiO(2))(n) with tetravalent states. However, the herein theoretically first reported mixed Ti(m)Si(n-m)O(2n) oxide clusters prefer either three-dimensional compact or linear chain structures depending upon the stoichiometry of the compound. Vibrational analysis of the important modes of some highly stable structures is provided. Coupled-cluster single and double excitation (with triples) [CCSD(T)] computed energy gaps for the TiO(2) dimers compare well with results from previous study. Excitation energies are computed by use of time-dependent (TD) DFT and equation-of-motion coupled-cluster calculations with singles and doubles (EOM-CCSD) for the most stable isomers.     

Tight-Binding Molecular Dynamics Study of Heteronuclear Systems: Application to Si m Ge n Clusters

The structural properties of Si _m Ge _n clusters are investigated using both the tight-binding molecular dynamics (TBMD) and the ab initio simple and triple-coupled clusters [CCSD(T)] as well as the MP2/6–311G* methods. The TBMD scheme uses a minimal parameter basis and is formulated for heteroatomic systems. Excellent agreement is obtained between these methods, indicating transferability for the TBMD formulation.     

Competition between supercluster and stuffed cage structures in medium-sized Ge(n) (n=30-39) clusters

We have performed an unbiased global search for the geometries of low-lying Ge(n) clusters in the size range of 30相似文献