Eur. Phys. J. B (2017) 90: 193
https://doi.org/10.1140/epjb/e2017-80277-2

Regular Article

Advanced computational method for studying molecular vibrations and spectra for symmetrical systems with many degrees of freedom, and its application to fullerene

Department of Theoretical Physics, Moldova State University, A. Mateevici Str. 60, Chisinau 2009, Republic of Moldova

^a e-mail: fpaladi@usm.md

Received: 16 May 2017
Received in final form: 23 July 2017
Published online: 16 October 2017

Abstract

A computational method for studying molecular vibrations and spectra for symmetrical systems with many degrees of freedom was developed. The algorithm allows overcoming difficulties on the automation of calculus related to the symmetry determination of such oscillations in complex systems with many degrees of freedom. One can find symmetrized displacements and, consequently, obtain and classify normal oscillations and their frequencies. The problem is therefore reduced to the determination of eigenvectors by common numerical methods, and the algorithm simplifies the procedure of symmetry determination for normal oscillations. The proposed method was applied to studying molecular vibrations and spectra of the fullerene molecule C₆₀, and the comparison of theoretical results with experimental data is drawn. The computational method can be further extended to other problems of group theory in physics with applications in clusters and nanostructured materials.