TY - JOUR

T1 - Symmetry Classification of Electron and Phonon States in TiO2-Based Nanowires and Nanotubes

AU - Evarestov, R.A.

AU - Panin, A.I.

PY - 2015

Y1 - 2015

N2 - Procedure for deriving Wyckoff positions for nanowires and nanotubes from Wyckoff positions of ambient space group is described. It is demonstrated 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 nanowires. 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 nanotubes with the rectangular and hexagonal morphology.

AB - Procedure for deriving Wyckoff positions for nanowires and nanotubes from Wyckoff positions of ambient space group is described. It is demonstrated 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 nanowires. 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 nanotubes with the rectangular and hexagonal morphology.

KW - Nanowires and nanotubes

KW - Line and Rod groups

KW - orbits

KW - induced representations

KW - DFT calculations

U2 - 10.1002/jcc.23875

DO - 10.1002/jcc.23875

M3 - Article

VL - 36

SP - 957

EP - 969

JO - Journal of Computational Chemistry

JF - Journal of Computational Chemistry

SN - 0192-8651

IS - 13

ER -