Ultrathin selenium nanorods from helical phases: a quantum chemical study using line group theory

Quantum chemical calculations of ultrathin nanorods cut from two bulk selenium phases were performed. Two sets of nanorods with trigonal and hexagonal geometric shapes described by the rod symmetry groups p3₁ and p3₁21, respectively, were constructed from the most stable Se-I (P3₁21) phase. The ultrathin nanorods generated by the Se-I phase were found to be unstable with respect to spontaneous torsion deformations, which slightly shift the helical axis order away from its crystallographic integer value of 3. In order to describe their correct atomic structure, one should use the line symmetry groups and determine the exact order of the helical axis for each nanorod. As the nanorod thickness increases, the true order quickly approaches the crystallographic value, but is never equal to it. Nanorods with a square geometric shape were constructed from the Se-II' (I4₁/acd) phase. Depending on their thickness, these nanorods are classified as either chiral or achiral, exhibiting p4₁22 or p4c2 symmetries, respectively. It was shown that square nanorods represent a unique class of nanostructures that alternately exhibit chiral and achiral properties as their thickness increases. Chiral square nanorods are unstable with respect to spontaneous torsion deformations, which shift the helical axis order from the crystallographic integer value of 4 (similar to nanorods cut from the Se-I phase). At the same time, achiral square nanorods are stable with respect to spontaneous torsion deformations.