Electronic Cylindrical Waves in Nanotubes

Pavel D'yachkov

Kurnakov Institute of General and Inorganic Chemistry, RAS


Quantum chemistry is the quantum mechanics of atoms, molecules, and solids. Until recently, the quantum chemistry of crystals regarded as part of a solid-state physics was a theoretical foundation of materials sciences. Now at the times of nanotechnology, when individual molecules become the elements of electronic devices, the molecular quantum chemistry is a very important part of the fundamental materials sciences too. The nanotubes lie halfway from the molecules to crystals and they are at a center of nanoelectronics progress. The quantum chemistry of nanotubes is being developed by efforts of the molecular and solid-state theorists. At first, the electronic structure of carbon nanotubes was predicted using the simplest quantum chemical Hückel molecular orbital theory elaborated for π-conjugated organic compounds. The obtained qualitatively correct predictions of the relationships between the geometry and band structure of carbon nanotubes caused a huge stream of experimental studies of their electronic properties and a design of nanoelectronics elements up to a computer on carbon tubules. There was a need for more accurate calculations of nanotubes, and an alternative and somewhat theoretically more substantiated and detailed description of the nanotube’s electron states came from the solid-state quantum chemistry when Slater's augmented plane wave method was taken as a starting point for tubules studies. However, the cylindrical (tubular) geometry of nanotubes determines the formation of cylindrical electron waves in tubules, rather than plane waves as in crystals. We provide a detailed exposition of nonrelativistic and relativistic linearized augmented cylindrical wave technique and demonstrate its applications to the various carbon and non-carbon, achiral and chiral, pure, intercalated and doped single-walled, double-walled, and embedded nanotubes and nanowires. The use of cylindrical waves for the nanotubes offers the great advantages in the studies of their properties. Bibliography P.N. D’yachkov. Quantum Chemistry of Nanotubes: Electronic Cylindrical Waves. CRC Press. Taylor and Francis. London and New York. 2019, 212 p