Medium-sized Silicon Clusters Research Articles

New candidates for the global minimum of medium-sized silicon clusters: A hybrid DFTB/DFT genetic algorithm applied to Sin, n = 8-80

In this study, we perform a systematic search to find the possible lowest energy structure of silicon nanoclusters Sin (n = 8-80) by means of an evolutionary algorithm. The fitness function for this search is the total energy of density functional tight binding (DFTB). To be on firm ground, we take several low energy structures of DFTB and perform further geometrical optimization by density functional theory (DFT). Then we choose structures with the lowest DFT total energy and compare them with the reported lowest energy structures in the literature. In our search, we found several lowest energy structures that were previously unreported. We further observe a geometrical transition at n = 27 from elongated to globular structures. In addition, the optical gap of the lowest energy structures is investigated by time-dependent DFTB (TD-DFTB) and time-dependent DFT (TD-DFT). The results show the same trend in TD-DFTB and TD-DFT for the optical gap. We also find a sudden drop in the optical gap at n = 27, precisely where the geometrical transition occurs.

Revisit of Sin (n = 21–29) Clusters by Ab Initio Global Search

Using our improved genetic algorithm combined with density functional theory calculations, we perform unbiased global search for the most stable structures of Sin clusters with n = 21–29. A new principal direction crossover operation is introduced to search the prolate structures on the potential energy surface. We confirmed previous results for most sized Sin clusters and find more stable structure at n = 23 and 26. In particular, we find a new endohedral cage structure at Si23, which is 0.4 eV lower in energy than previously reported prolate structure and exhibit a distinct peak on the second order difference of total cluster energy. We discuss the competition between prolate and spherical motifs in the medium-sized Sin clusters in light of binding energy and HOMO–LUMO gap. The transition of structural motif from prolate to near spherical in Sin clusters occurs at n = 26. The outer cages are composed of pentagon, hexagon, quadrangle and heptagon, with one to three interior atoms filled inside the cage. These results establish a more complete picture for the structural evolution of the medium-sized silicon clusters. Average bond lengths and Mayer bond order are also discussed.

Using the small Si cluster as a building block

Assembly between Si4 clusters is calculated to search for the Si8 cluster with the lowest energy. Tetrahedral Si4 cluster leads to a larger binding energy of the assembled Si8, compared with the rhombus Si4 cluster, although the latter is confirmed as the configuration with the lowest energy among the isomers of Si4. So the prediction of larger silicon clusters should involve the building blocks with the lowest energy as well as those are meta-stable. The binding energy of silicon clusters versus the number of building blocks shows a unique curve. Thus, using the binding energy of the building blocks to predict the energy evolution of larger silicon clusters is suggested as a new feasible scheme for the medium-sized silicon clusters.

Reexamine structures and relative stability of medium-sized silicon clusters: Low-lying endohedral fullerene-like clusters Si 30–Si 38

We report improved results of lowest-lying silicon clusters Si 30–Si 38. A large population of low-energy clusters are collected from previous searches by several research groups and the binding energies of these clusters are computed using density-functional theory (DFT) methods. Best candidates (isomers with high binding energies) are identified from the screening calculations. Additional constrained search is then performed for the best candidates using the basin-hopping method combined with DFT geometry optimization. The obtained low-lying clusters are classified according to binding energies computed using either the Perdew–Burke–Ernzerhof (PBE) functional or the Becke exchange and Lee–Yang–Parr correlation (BLYP) functional. We propose to rank low-lying clusters according to the mean PBE/BLYP binding energies in view that the PBE functional tends to give greater binding energies for more compact clusters whereas the BLYP functional tends to give greater binding energies for less compact clusters or clusters composed of small-sized magic-number clusters. Except for Si 30, the new search confirms again that medium-size silicon clusters Si 31–Si 38 constructed with proper fullerene cage motifs are most promising to be the lowest-energy structures.

Structural features of silicon clusters ()

Abstract The structural transition in inner portions of medium-sized silicon clusters has been a puzzle over a decade. By performing extensive search of the “compressing-liquid-silicon” strategy we proposed together with the “stuffing-fullerene” approach, the low-lying structures of Si n ( n = 40 – 57 , 60 ) are achieved. We reveal that the surfaces of these low-lying isomers are endohedral silicon fullerenelike cages, and the inner portions evolve from loose patterns to aggregate structures as the cluster size increases. These findings not only imply that the stuffed-cage structures are the preferred growth pattern for n = 40 – 57 , 60 still, but also clue that before becoming a bulk pattern, the inner portions of clusters undergo transition states.

Identification of Silicon Clusters by Electron Diffraction Spectra

By simulating the electron diffraction spectra (EDS) of medium-sized silicon clusters, we find that the features in the EDS are sensitive to the atomic structures of the clusters. This enables us to differentiate the different isomers of Si clusters effectively. Moreover, our calculations reveal that for a gas-phase system consisting of different Si isomers, the total electron diffraction spectra can be approximately expressed as a linear combination of the electron diffraction spectra of the individual isomers. Thus, we propose a scheme to determine the atomic structures of the individual isomers in a gas-phase product of silicon clusters.

Modified genetic algorithms to model cluster structures in medium-sized silicon clusters:Si18−Si60

This paper presents the results obtained using a genetic algorithm (GA) to search for stable structures of medium-size silicon clusters. This is the third report in which a GA coupled with the MSINDO semiempirical molecular orbital program is used to find stable atomic cluster structures. The structures selected by the GA-MSINDO method were further optimized using the density functional theory (DFT). This combination of GA-MSINDO global optimization followed by DFT local optimization proves to be very effective for searching the structures of medium-size Si clusters. For most of the clusters studied here we report different structures with significant lower energy than those previously found using limited search approaches on common structural motifs. This demonstrates the need for global optimization schemes when searching for stable structures of medium-size silicon clusters.

Structures and relative stability of medium-sized silicon clusters. V. Low-lying endohedral fullerenelike clusters Si31–Si40 and Si45

We have performed unconstrained search for low-lying structures of medium-sized silicon clusters Si(31)-Si(40) and Si(45), by means of the minimum-hopping global optimization method coupled with a density-functional based tight-binding model of silicon. Subsequent geometric optimization by using density-functional theory with the PBE, BLYP, and B3LYP functionals was carried out to determine the relative stability of various candidate low-lying silicon clusters obtained from the unconstrained search. The low-lying characteristics of these clusters can be affirmed by comparing the binding energies per atom of these clusters with previously determined lowest-energy clusters(Si(n)) in the size range of 21</=n</=30. In view of the fact that there exist numerous low-lying "endohedral fullerenelike" isomers for each size in the range 30</=n</=40, we used the homologue carbon-fullerene cage to classify different families of isomers. This structural classification allows us to focus on generic features of various isomers and to group many apparently different isomers into a single family. In addition, we report a new family of low-lying clusters which have "Y-shaped three-arm" structures. Isomers in this "handmade" family can be energetically competitive as the endohedral fullerene isomers when the total energies are calculated with the BLYP or B3LYP functional.

Structures and relative stability of medium-sized silicon clusters. IV. Motif-based low-lying clusters Si21–Si30

Structures and relative stability of four families of low-lying silicon clusters in the size range of Sin(n=21-30) are studied, wherein two families of the clusters show prolate structures while the third one shows near-spherical structures. The prolate clusters in the first family can be assembled by connecting two small-sized magic clusters Sin (n=6, 7, 9, or 10) via a fused-puckered-hexagonal-ring Si9 unit (a fragment of bulk diamond silicon), while those in the second family can be constructed on the basis of a structural motif consisting of a puckered-hexagonal-ring Si6 unit (also a fragment of bulk diamond silicon) and a small-sized magic cluster Sin (n=6, 7, 9, or 10). For Si21-Si29, the predicted lowest-energy clusters (except Si27) exhibit prolate structures. For clusters larger than Si25, the third family of near-spherical clusters becomes energetically competitive. These near-spherical clusters all exhibit endohedral cagedlike structures, and the cages are mostly homologue to the carbon-fullerene cages which consist of pentagons and hexagons exclusively. In addition, for Si26-Si30, we construct a new (fourth) family of low-lying clusters which have "Y-shaped" three-arm structures, where each arm is a small-sized magic cluster (Si6, Si7, or Si10). Density-functional calculation with the B3LYP functional shows that this new family of clusters is also energetically competitive, compared to the two prolate and one near-spherical low-lying families.

Structure and electronic property of medium-sized silicon clusters

The lowest energy structures of Si n ( n = 10 – 20 ) clusters are obtained using the first principles pseudopotential simulated annealing within the local density functional approximation (LDA) implemented in SIESTA method. New low-energy structures are obtained for each cluster size. The Si n clusters generally follow a prolate structures for n < 16 and, like spherical structures, with the appearance of an endohedral atom with highly co-ordination starting at n ⩾ 17 . The size dependence of clusters binding energies, and highest-occupied and lowest-unoccupied molecular orbital (HOMO–LUMO) gap are discussed.

Structures and stability of medium-sized silicon clusters. III. Reexamination of motif transition in growth pattern from Si15 to Si20

It has been established from experiments that stable medium-sized ionic clusters Si15-Si20 are prolate in shape. Density-functional theories (DFTs) also predict that nearly all low-lying neutral clusters in this size range are prolate in shape. Moreover, most of them are built onto two generic structural motifs, either the tricapped-trigonal-prism (TTP) Si9 motif or the six/six Si6Si6 (sixfold-puckered hexagonal ring Si6 plus six-atom tetragonal bipyramid Si6) motif. However, it appears that the exact location of the TTP-to-six/six motif transition is dependent on the functional (e.g., PBE or BLYP) used in the DFT calculations. Here, we present total-energy calculations for two series of clusters (one series containing six/six motif and the other containing the TTP motif) in the size range of Si16-Si20. The calculations were based on all-electron DFT methods with a medium [6-311G (2d)] and a large (cc-pVTZ) basis sets, as well as coupled-cluster single and double substitutions (including triple excitations) [CCSD(T)] method with a modest (cc-pVDZ) basis set. In the DFT calculations, two popular hybrid density functionals, the B3LYP and PBE1PBE, were selected. It is found that the B3LYP total-energy calculations slightly favor the six/six motif, whereas the PBE1PBE calculations slightly favor the TTP motif. The CCSD(T) total-energy calculations, however, show that isomers based on the six/six motif are energetically slightly favorable in the size range of Si16-Si20. Hence, the TTP-to-six/six motif transition is more likely to occur at Si16.

Stuffed fullerene structures for medium-sized silicon clusters

The structural properties of medium-sized silicon clusters (Si40, Si45 and Si50) have been studied using an unbiased global genetic algorithm search incorporated with a tight-binding model, followed by gradient-corrected density functional calculations. Stuffed fullerene cages are obtained as energetically favorite structures. The stuffing/cage ratio (m/n for Sim@Sin) can be understood by a space filling picture. The present results, along with our recent works on SiN (N=27-39) clusters [20], suggest that stuffed fullerene cages are the preferred structural growth pattern of medium-sized silicon clusters.

Endohedral Silicon Fullerenes SiN (27 ≤ N ≤ 39)

AbstractFor Abstract see ChemInform Abstract in Full Text.

Density functional theory studies of correlations between structure, binding energy, and dipole polarizability in Si 9 and Si 12

Two medium-size silicon clusters, namely, Si 9 and Si 12, have been used as model systems to investigate the correlations between structure, stability, and the static dipole polarizability by theoretical methods. Results show that polarizability correlates with the standard deviation of the atomic distances, and that the binding energy correlates with both the averaged atomic distance and the number of Si–Si bonds formed in the particular cluster. These correlations are significant, since they allow predictions of certain physical properties, i.e., dipole polarizability and stability, based solely on the structural information of the cluster.

Endohedral Silicon Fullerenes SiN (27 ≤ N ≤ 39)

We have performed an unbiased search for the lowest-energy geometric structures of medium-sized silicon clusters SiN (27 < or = N < or = 39) using a genetic algorithm and nonorthogonal-tight-binding method, followed by a refining and biased search using basin-hopping method coupled with density-functional theory. We show that the carbon fullerene cages are most likely generic cage motifs ("magic cages") to form low-lying stuffed-cage silicon clusters (beyond the size N > 27). An empirical rule that provides optimal "stuffing/cage" combinations for constructing low-energy endohedral silicon fullerenes is suggested, with a hope that it can provide guidance to future synthesis of "bucky" silicon.

Modified genetic algorithms to model cluster structures in medium-size silicon clusters

This paper presents the results obtained using a genetic algorithm (GA) to search for stable structures of medium size silicon clusters. In this work the GA uses a semiempirical energy function to find the best cluster structures, which are further optimized using density-functional theory. For small clusters our results agree well with previously reported structures, but for larger ones different structures appear. This is the case of Si 36 where we report a different structure, with significant lower energy than those previously found using limited search approaches on common structural motifs. This demonstrates the need for global optimization schemes when searching for stable structures of medium-size silicon clusters. DOI: 10.1103/PhysRevA.69.053202 PACS number(s): 36.40.2c I. INTRODUCTION The study of the structure and physical properties of atomic and molecular clusters is an extremely active area of research due to their importance, both in fundamental science and in applied technology [1]. Existing experimental methods for structural determination seldom can obtain the structure of atomic clusters directly. Therefore the calculation, using theoretical structures and comparison with experimental values of their physical and optical properties, is the most common way to obtain structural information of atomic clusters. While the prediction of the structures of clusters with a small number of atoms is well understood, the prediction of the structures and properties of medium-size (10‐ 100 atoms) clusters is much less developed in spite of their critical importance in understanding the transition from microscopic to macroscopic behavior of nanomaterials and their possible technological applications.

Structure and growth pattern of Si cluster (n=11—32): a tight-binding molecular dynamics simulation

By using the tight-binding molecular dynamics (TBMD) method, the structures and energies of the medium-sized silicon clusters (Si11—Si32) have been simulated, and the radial distribution function and bond-angle distribution for different size of clusters have been described in this paper. The structural transform from prolate to near-spherical configurations has been observed at the cluster size n=27 in silicon clusters.

Global geometry optimization of small silicon clusters with empirical potentials and at the DFT level

We have performed global parameter optimization of selected empirical potentials for silicon, resulting in improved performance for small to medium-sized silicon clusters, as judged by a comparison of globally optimized cluster structures to the structures accepted in the literature for the size range up to n = 10. Using global cluster structure optimizations with the resulting optimized model potential and ensuing local optimizations at the DFT level, we could find improved proposals for global minimum structures in the size region n = 10–16. This study confirms the applicability of our general global cluster optimization strategy for still larger silicon clusters.

Medium-sized silicon oxide clusters by Si 3O 3-ring assembly

Using Si 2O 2 rhombuses and Si 3O 3 rings as building blocks, we have investigated the structures of medium-sized silicon oxide clusters. Total energies of a series of Si 8O n and Si 12O n clusters with different growth motifs have been studied using first-principles calculations. Our studies discover a new motif for medium-sized silicon oxide clusters in a form of wheel-like structure composed of Si 3O 3 rings.

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.