The geometry and electronic properties of Bn (n=2—15) clusters with different growth pattern were calculated and analyzed by using the density functional theory at B3LYP level. The energy gap, first ionization potential and binding energy per atom of boron clusters were also discussed. The results show that linear structures are unstable and are strongly metallic, especially for n=8, which has an energy gap as low as 0.061 eV, indicating the metallic characteristic. Planar and quasi-planar structures are most stable and weak in metallicity. The stability and metallicity of tree-dimensional structures are intermediate between those of the linear and the planar or quasi-planar structures. Furthermore, we also analyzed the electronic properties of ground-state clusters, including the binding energy per atom, second difference in energy, energy gap and the first ionization potential. The results show that B12 and B14 are magic-number clusters.
The geometric structures, stabilities, and electronic properties of InnAsn tubelike clusters at up to n=90 and single-walled InAs nanotubes (InAsNTs) were studied by density functional theory (DFT) calculations. The lowest-energy structures and electronic properties of the small InnAsn (n=1-3) clusters are consistent with those found in earlier studies. A family of stable tubelike structures with In-As alternating arrangement was observed when n≥4 and their structural units (four-membered rings and sixmembered rings) obey the general developing formula. The average binding energies of the clusters show that the tubelike cluster with eight atoms in the cross section is the most stable cluster. The sizedependent properties of the frontier molecular orbital surfaces explain why we can successfully obtain long and stable tubelike clusters. They also illustrate the reason why InAsNTs can be synthesized experimentally. We also found that the single-walled InAsNTs can be prepared by the proper assembly of tubelike clusters to form semiconductors with large bandgap.
It is well known that carbon nanotubes (CNTs) have received much attention since they were discovered. With the rapid development of carbon-based electronics and quantum computers, CNTs are required to have their unique physical and chemical properties in many fields. However, due to their uncertain mechanism of growth, it is difficult to achieve high production of CNTs with certain controlled structures. In this paper, we construct the nuclei of specific single- and double-walled zigzag CNTs and study their structural derivatives and electronic properties by using the density functional theory. According to the study of carbon clusters, we find some stable cage-like clusters containing zigzag structure which can be used as the nucleus of the corresponding single-walled CNTs. The nucleus of the double-walled CNTs is composed of the corresponding nucleus of single-walled CNTs. It is possible to obtain a tubular cluster by optimizing the structure of the nucleus with accumulating carbon atoms at one end. The results show that the pentagonal structure plays a key role in the growing of tubular clusters. We find that the tubular clusters are grown in the form of global reconstruction when the clusters are short, but grown by local reconstruction when the clusters are longer. It can provide a theoretical reference to realize numerous CNTs with certain structures. Furthermore, the average binding energy (Eb) of tubular clusters is studied, and we find that their Eb is more and more stable and then close to the corresponding CNTs. At the same time, the study of the thermodynamic quantities of tubular clusters shows that their structures are thermodynamically stable. In addition, the infinite zigzag CNTs can be obtained by using the periodic boundary conditions. Furthermore, the energy bands and density of states are calculated to study their electronic properties. The results show that the energy band structures of zigzag CNTs are closely related to the chiral index n. For zigzag CNTs (n, 0) and (n, 0)@(2n, 0), they show a metal property or narrow band gap semiconductor when n=3q (q is an integer); when n3q, they show a wide band gap semiconductor, and the band gap decreases with the diameter increasing. It is interesting that the two metallic single-walled CNTs (SWCNTs) are nested to obtain metallic double-walled (CNTs) DWCNTs, while the two semiconducting SWCNTs are nested to obtain semiconducting DWCNTs. However, due to the obvious curvature effect, small-diameter CNTs (4, 0), (4, 0)@(8, 0) and (5, 0)@(10, 0) show the metal properties but CNT (6, 0)@(12, 0) shows the obvious semiconductor property.
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