Electronic Cylindrical Waves in Nanotubes


Pavel D'yachkov


Kurnakov Institute of General and Inorganic Chemistry, RAS



Abstract:

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