Modern nano-synthesis methods make it possible to create atomic chains. Helical chains of sulfur [1], selenium [2] and tellurium [3] atoms placed in carbon nanotubes have recently been synthesized. Such objects have unique electronic and optical properties. As is known, crystalline tellurium and selenium can be considered as an ensemble of atomic helices of symmetry 31, interconnected by van der Waals forces. However, the free atomic helix of chalcogens in the general case has a symmetry different from the crystallographic one. Moreover, for such objects a more natural description is based on line symmetry groups [4]. Accordingly, the description of the electronic or phonon states of helical nanoobjects is carried out within the framework of the helical Brillouin zone [5]. The classification of states in translational and helical Brillouin zones is different as the corresponding intervals of wave vector change are (-π/a, π/a] and (-π/f, π/f] respectively (here f is partial translation). This makes it possible to consider the continuous evolution of states under both axial and torsional deformations [6]. [1] - T.Fujimori, at al Conducting linear chains of sulphur inside carbon nanotubes. Nature Comm. 4 (2013) 2162. [2] - T.Fujimori, at al. Formation and Properties of Selenium Double-Helices inside Double-Wall Carbon nanotubes: Experiment and Theory. ACS Nano 6 (2013) 5607 [3] - P.V.C.Medeiros, at al. Single-Atom Scale Structural Selectivity in Te Nanowires Encapsulated Inside Ultranarrow, Single-Walled Carbon Nanotubes. ACS Nano 11 (2017) 6178. [4] - M.Damnjanović, I.Milošević. // Line Groups in Physics. Lecture Notes in Physics, Volume 801; Springer: Berlin/Heidelberg, Germany, 2010. [5] - V.V.Porsev, R.A.Evarestov. Quantum mechanical calculation of electronic band structure of helically periodic systems: a case of nanotubes and nanohelicenes. Phys. Solid State 64 (2022) 1807. [6] - V.V.Porsev, et al. Line group approach for quantum chemical study of intrinsic helical twist of ultrathin tellurium nanorods. CrystEngComm (2024) DOI: 10.1039/D4CE00352G. Авторы выражают благодарность Вычислительному центру Санкт-Петербургского университета за предоставление компъютерных ресурсов. 1 Работа выполнена при финансовой поддержке Российского Научного Фонда, проект № 24-23-00207