Band Structures of Quasi-One-Dimensional Incommensurate Helical Systems: A Case Study of Infinite Chromium Extended Metal Atom Chain

Abstract

Extended metal atom chains (EMACs) are promising candidates for molecular wires but their band structures remain to be explored. As a quasi-one-dimensional (Q1D) system, the incommensurate helical nature of EMACs hinders such calculations. In this work, we resolved this issue via explicit implementation of helical symmetry. Moreover, the pattern of metal d bands was rationalized by a systematic investigation on a series of related Q1D helical systems. Two critical factors, helical ligand field and chemically asymmetric ligand field, are proposed and identified. We found that the symmetry and ligand fields of the system dominate the pattern of the metal d bands, instead of specific chemical composition of ligands. The presented method and rationale are applicable to not only EMACs but also related Q1D helical systems.

Revisit of trinickel metal string complexes [Ni3L4X2] (L = dipyridylamido, diazaphenoxazine; X = NCS, CN) for quantum transport

“…Metal string complexes (e.g., trinickel strings in Figure ) are a string of metal atoms supported by the coordination of four equatorial ligands, resembling miniaturized nanowires with the metal string shrouded by a relatively insulating layer . Reported metal string complexes include those with the metal atoms composed of the same element, defected atom chains where one of the metal centers is missing from the 1‐D coordination sites, and mixed elements in which the positions of the metal elements can be designated .…”

“…Metal string complexes (e.g., trinickel strings in Figure 1) are a string of metal atoms supported by the coordination of four equatorial ligands, resembling miniaturized nanowires with the metal string shrouded by a relatively insulating layer. [2,[37][38][39][40][41][42][43][44][45] Reported metal string complexes include those with the metal atoms composed of the same element, [25,27,[43][44][45][46][47][48][49] defected atom chains where one of the metal centers is missing from the 1-D coordination sites, [37,50] and mixed elements in which the positions of the metal elements can be designated. [39][40][41][51][52][53][54][55][56][57] A range of coordinating groups (e.g., amido, pyridyl, naphthyridyl, anthyridinyl, and thiophenyl) are formulated as the equatorial ligands.…”

Subperiodic groups, line groups and their applications

“…Examples include certain polymers like DNA double helix (Milos ˇevic ´et al, 1996), carbon (Damnjanovic ´et al, 1999) and transition metal dichalcogenide nanotubes (Milos ˇevic ´et al, 2000), ZnO nanosprings (Milos ˇevic ´et al, 2006), structural analogs of single-wall carbon nanotubes (De Las Pen ˜as et al, 2014;Loyola et al, 2012) etc. Line groups also describe the symmetry of systems having only helical periodicity: the vast majority of multi-wall (Damnjanovic ´et al, 2003) and helically coiled carbon nanotubes (Milos ˇevic ´et al, 2012), extended metal atom chains (Ou & Jin, 2018), nanohelicenes (Domnin et al, 2023), polytwistanes (Domnin et al, 2022), helical polyacetylenes , and incommensurately modulated crystals (Me ´sza ´ros et al, 2020).…”