DOI: https://doi.org/10.30970/jps.01.564
TIME DEPENDENT VELOCITY AUTOCORRELATION FUNCTIONS OF CLUSTERS WITH CYCLIC BOUNDARY CONDITIONS
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Journal of Physical Studies 1(4), 564–569 (1997)
DOI: https://doi.org/10.30970/jps.01.564 TIME DEPENDENT VELOCITY AUTOCORRELATION FUNCTIONS OF CLUSTERS WITH CYCLIC BOUNDARY CONDITIONS |
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I. I. Talyansky, A. T. Maksymov
Lviv State University, Chair for Theoretical Physics
12 Drahomanov Str., Lviv, UA–290005, Ukraine
The possibility of molecular dynamics usage for the calculation of vibrational spectra of crystals has been studied. The basis of this approach is the fact that Fonrier transform of velocity autocorrelation function defines the density of vibrational states. In the proposed work an analytical expression of the autocorrelation function and its Fourier transform have been found in approach of a linear chain with the cyclic boundary conditions of two kinds of atoms (model of ionic crystal). The molecular dynamics simulation of this model has been performed. The curve of the Fourier transform includes a number of sharp peaks, whose positions define the frequency of the normal vibrational modes and their areas correspond to the masses that are vibrating with these modes. Vibrations of chains (clusters) with the number of atoms $N$ equal to 4 and 8 have been investigated. In the case of $N=4$ the results have been compared with the analytical expression. For $N=8$ the molecular dynamics results have been compared with the corresponding results obtained by the diagonalization of a dynamical matrix. A complete agreement of the results of comparison has been observed, which shows a possibility to use the molecular dynamics technique for the calculations of the vibrational spectra of crystals.