Geometric stability and electronic structure of infinite and finite phosphorus atomic chains

One-dimensional mono- or few-atomic chains were successfully fabricated in a variety of two-dimensional materials, like graphene, BN, and transition metal dichalcogenides, which exhibit striking transport and mechanical properties. How- ever, atomic chains of black phosphorus （BP）, an emerging electronic and optoelectronic material, is yet to be investigated. Here, we comprehensively considered the geometry stability of six categories of infinite BP atomic chains, transitions among them, and their electronic structures. These categories include mono- and dual-atomic linear, armchair, and zigzag chains. Each zigzag chain was found to be the most stable in each category with the same chain width. The mono-atomic zigzag chain was predicted as a Dirac semi-metal. In addition, we proposed prototype structures of suspended and sup- ported finite atomic chains. It was found that the zigzag chain is, again, the most stable form and could be transferred from mono-atomic armchair chains. An orientation dependence was revealed for supported armchair chains that they prefer an angle of roughly 35°-37° perpendicular to the BP edge, corresponding to the [110] direction of the substrate BP sheet. These results may promote successive research on mono- or few-atomic chains of BP and other two-dimensional materials for unveiling their unexplored physical properties.

Matching Boundary Conditions for a Heterogeneous Atomic Chain

We propose accurate boundary treatments for a heterogeneous atomic chain, in terms of matching boundary conditions （MBCs）. The main challenge lies in reproducing the physical reflection across the boundary to a correct amount. With reflection coefficients we demonstrate that the accuracy is improved when more atoms are used under the boundary condition. The inclusion of an atom in the embedded sublattice B may considerably enhance the performance. Numerical testing illustrates the effectiveness of the proposed MBCs.

Energetics and electronic structure of a single copper atomic chain wrapped in a carbon nanotube:a first-principles study

In the generalized gradient approximation, the energy and electronic structure are investigated for a single copper atomic chain wrapped in （4, 4）, （5, 5） and （6, 6） armchair carbon nanotubes by using the first-principles projector-augmented wave potential within the framework of density functional theory. The results show that the （4, 4） and （5, 5） tubes are too narrow to wrap a Cu chain, but the （6, 6） tube is nearly ideal to wrap a Cu chain on its centre axis. Wider tubes are anticipated to wrap more than one Cu chain spontaneously with forces amounting to a fraction of a nanonewton. Although the tube-chain interaction decreases with the increase of the tube diameter of （4, 4）, （5, 5） and （6, 6） successively, the charge density of the Cu@（6, 6） combined system still does not show complete superposition of that of the pristine （6, 6） tube and Cu chain. Successively reducing the restrictions of （4, 4）, （5, 5） and （6, 6） tubes on the Cu chain leads to a reduction in shift of the highest peak of the Cu chain towards lower energies, that is from -0.5177 eV of the isolated Cu chain to -1.36785 eV, -0.668 eV and -0.588 eV for the Cu@（4, 4）, Cu@（5, 5） and Cu@（6, 6） systems, respectively. In reverse, the strong metallic character of the Cu chain also enhances the metallic character of the combined systems so that the broader pseudogaps of the pristine carbon nanotubes around the Fermi level change into the narrow pseudogaps of the combined systems.

A Defective Linear Pentachromium Complex for the Enhanced Catalysis of the Cycloaddition of CO2 with Propylene Oxide

Based on the ligand（2,7-bis（α-pyrimidylamino）-1,8-naphthyridine（H2 bpmany））, a linear pentachromium complex [Cr5（μ5-bpmany）4Cl2]PF6（1, μ5-bpmany = 2,7-bis（a-pyrimidylamino）-1,8-naphthyridine） was synthesized. The crystal structure of compound 1 has been characterized by X-ray crystallography. Interestingly, one metal atom in the center is missing in this linear chain, leading to the defective pentachromium metal string structure which is similar with the reported complex [Cr5（μ5-dpznda）4Cl2]（2, dpznda = N^2,N^7-di（pyrazin-2-yl）-1,8-naphthyridine-2,7-diamine）. The central Cr（Ⅲ） ion of 1 is eight-coordinated and is also rare in the chromium complex. The reaction of carbon dioxide with propylene oxide that generates propylene carbonate（PC） when catalyzed by [Cr5（μ5-bpmany）4Cl2]PF6 was investigated. Different reaction conditions including temperature and pressure were studied to optimize the reaction conditions.