Vibration spectra of benzene-like models with Hooke’s law interactions

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 simila...

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Bibliographic Details
Published in:Low temperature physics (Woodbury, N.Y.) N.Y.), 2023-12, Vol.49 (12), p.1444-1457
Main Authors: Bogdan, M. M., Charkina, O. V., Holovashchenko, A. Y.
Format: Article
Language:English
Subjects:
Benzene
Cylindrical coordinates
Deuteration
Elastic properties
Euler-Lagrange equation
Frequency spectrum
Harmonic oscillation
Lattice vibration
Vibration mode
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Summary: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.
ISSN:1063-777X
1090-6517
DOI:10.1063/10.0022370