Bound State of Electrons in a One-Dimensional Chain

1994 ◽  
Vol 182 (1) ◽  
pp. 89-96 ◽  
Author(s):  
L. S. Brizhik ◽  
A. A. Eremko
2016 ◽  
Vol 72 (6) ◽  
pp. 480-484 ◽  
Author(s):  
Qiu-Ying Huang ◽  
Xiao-Yi Lin ◽  
Xiang-Ru Meng

The N-heterocyclic ligand 2-[(1H-imidazol-1-yl)methyl]-1H-benzimidazole (imb) has a rich variety of coordination modes and can lead to polymers with intriguing structures and interesting properties. In the coordination polymercatena-poly[[cadmium(II)-bis[μ-benzene-1,2-dicarboxylato-κ4O1,O1′:O2,O2′]-cadmium(II)-bis{μ-2-[(1H-imidazol-1-yl)methyl]-1H-benzimidazole}-κ2N2:N3;κ2N3:N2] dimethylformamide disolvate], {[Cd(C8H4O4)(C11H10N4)]·C3H7NO}n, (I), each CdIIion exhibits an irregular octahedral CdO4N2coordination geometry and is coordinated by four O atoms from two symmetry-related benzene-1,2-dicarboxylate (1,2-bdic2−) ligands and two N atoms from two symmetry-related imb ligands. Two CdIIions are connected by two benzene-1,2-dicarboxylate ligands to generate a binuclear [Cd2(1,2-bdic)2] unit. The binuclear units are further connected into a one-dimensional chain by pairs of bridging imb ligands. These one-dimensional chains are further connected through N—H...O hydrogen bonds and π–π interactions, leading to a two-dimensional layered structure. The dimethylformamide solvent molecules are organized in dimeric pairsviaweak interactions. In addition, the title polymer exhibits good fluorescence properties in the solid state at room temperature.


2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.


Author(s):  
Dominic Vella ◽  
Emmanuel du Pontavice ◽  
Cameron L. Hall ◽  
Alain Goriely

Spherical neodymium–iron–boron magnets are permanent magnets that can be assembled into a variety of structures owing to their high magnetic strength. A one-dimensional chain of these magnets responds to mechanical loadings in a manner reminiscent of an elastic rod. We investigate the macroscopic mechanical properties of assemblies of ferromagnetic spheres by considering chains, rings and chiral cylinders of magnets. Based on energy estimates and simple experiments, we introduce an effective magnetic bending stiffness for a chain of magnets and show that, used in conjunction with classic results for elastic rods, it provides excellent estimates for the buckling and vibration dynamics of magnetic chains. We then use this estimate to understand the dynamic self-assembly of a cylinder from an initially straight chain of magnets.


Author(s):  
Dong Liu

Solvothermal reaction between Cd(NO3)2, 1,4-phenylenediacetate (1,4-PDA) and 1,3-bis(pyridin-4-yl)propane (bpp) afforded the title complex, [Cd(C10H8O4)(C13H14N2)]n. Adjacent carboxylate-bridged CdIIions are related by an inversion centre. The 1,4-PDA ligands adopt acisconformation and connect the CdIIions to form a one-dimensional chain extending along thecaxis. These chains are in turn linked into a two-dimensional network through bpp bridges. The bpp ligands adopt ananti–gaucheconformation. From a topological point of view, each bpp ligand and each pair of 1,4-PDA ligands can be considered as linkers, while the dinuclear CdIIunit can be regarded as a 6-connecting node. Thus, the structure can be simplified to a two-dimensional 6-connected network.


2009 ◽  
Vol 12 (11) ◽  
pp. 1164-1167 ◽  
Author(s):  
Yong-Tao Wang ◽  
Gui-Mei Tang ◽  
Yong-Qin Wei ◽  
Ting-Xiao Qin ◽  
Tian-Duo Li ◽  
...  

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