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Symmetry classification of electron and phonon states in TiO 2 ‐based nanowires and nanotubes
Author(s) -
Evarestov Robert A.,
Panin Andrej I.
Publication year - 2015
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.23875
Subject(s) - nanowire , anatase , hexagonal crystal system , code (set theory) , factorization , phonon , group (periodic table) , orbit (dynamics) , homogeneous space , line (geometry) , materials science , crystallography , pure mathematics , computational chemistry , physics , nanotechnology , condensed matter physics , mathematics , chemistry , geometry , quantum mechanics , computer science , algorithm , catalysis , biochemistry , set (abstract data type) , engineering , photocatalysis , aerospace engineering , programming language
Procedure for deriving Wyckoff positions for nanowires (NWs) and nanotubes (NTs) from Wyckoff positions of ambient space group is described. It is proposed how to use SITESYM code available on Bilbao Crystallographic Server to calculate representations induced from orbit stabilizers for 1‐periodic groups. This procedure is demonstrated on the example of TiO 2 rutile‐based NWs. General analytic expressions for Line group representations induced from irreps of their orbit stabilizers are obtained. This approach presupposes the use of the standard (crystallographic) factorization of Line groups. Computer construction of orbits and induced representations can be efficiently implemented and the corresponding computer code SITESYML, which can be considered as a certain elaboration of the existing code SITESYM is written. The application of the code is demonstrated on the example of TiO 2 anatase‐based NTs with the rectangular and hexagonal morphology. © 2015 Wiley Periodicals, Inc.