benzene-like systems; branches of the dispersion law.; cyclic conditions; elastic mechanical hexagonal model; vibration frequency spectrum; Benzene-like system; Branch of the dispersion law.; Cyclic conditions; Cylindrical coordinates; Dispersion law; Elastic mechanical hexagonal model; Harmonic oscillation; Mechanical; Vibration frequency spectrum; Vibration spectra; Physics and Astronomy (miscellaneous)
Abstract :
[en] The harmonic oscillations of a spring-ball model of benzene-like nanosystems with Hooke’s law interactions between nearest, second, and third neighbors are explored. We show that in the cylindrical coordinates the dynamics of this cyclic hexagonal system is described by the Lagrange equations similar to those of the one-dimensional two-component crystal model. We demonstrate that the vibration frequencies of the hexagonal model lie on the branches of the dispersion law of the associated lattice model, and their positions are determined by the cyclic Born-Von Karman condition. The hexagonal model is generalized to one describing the benzene molecule and the fully deuterated and halogenated benzenes. The effect of hybridization of vibration modes and pushing apart of spectral branches in the crossover situation is revealed. All the discrete frequency spectrum and normal modes of oscillations and their explicit dependencies on all the constants of elastic interactions are exactly found.
Disciplines :
Physics
Author, co-author :
Bogdan, M.M. ✱; B. Verkin Institute for Low Temperature Physics and Engineering, the National Academy of Sciences of Ukraine, Kharkiv, Ukraine
CHARKINA, Oksana ✱; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS) ; B. Verkin Institute for Low Temperature Physics and Engineering, the National Academy of Sciences of Ukraine, Kharkiv, Ukraine
Holovashchenko, A.Y.; V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
✱ These authors have contributed equally to this work.
External co-authors :
yes
Language :
English
Title :
Vibration spectra of benzene-like models with Hooke’s law interactions
This research was funded in part by the Luxembourg National Research Fund (FNR) Grant No. 17568826 (ELEMENT). For the purpose of open access, O.C. has applied a Creative Commons Attribution 4.0 International (CC BY 4.0) license to any Author Accepted Manuscript version arising from this submission.
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