Torsion and Axial Deformations of Chalcogen Helical Chains (S, Se, Te): First Principles Calculations Using Line Symmetry Groups.

The atomic structure, electronic, phonon, and optical properties of chalcogen helical chains (S, Se, Te) were studied using line symmetry groups and DFT calculations. The whole possible range of torsion deformations (from 0° to 180°), as well as the range of axial deformations (from 0.6 to 1.6) were considered. For the studied chains, the atomic and electronic structures at the energy minima were found. It was shown that for the considered chalcogen chains, the minimum of electronic energy is in the region of rotation angles ~103-107°. The electronic structure of all chains was considered in the helical Brillouin zone, which made it possible to trace its evolution up to the extreme torsional deformations: 0° (linear chain) and 180° (zigzag chain). A method for obtaining the dispersion of phonon states in the helical Brillouin zone has been developed based on the results of calculations by the CRYSTAL17 program. This allowed us to trace the evolution of phonon dispersion curves under torsion deformations up to their extreme values. Based on the known selection rules for helical polymers, the energies of optical, IR, and Raman transitions were obtained. This allows one to predict the optical properties of atomic chalcogen chains-both in a free state and inside carbon nanotubes.