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In this article, an interesting phenomenon has described the geometries and vibrational frequency of the stable AuN clusters with N=36, 37, 39 and 40. We have found all 4 clusters are having the very same C1 point symmetry group. For the re-optimization process, the finite-differentiation method has been implemented within the Density Functional Tight Binding (DFTB) approach. The effects of the range of interatomic forces were calculated and the desired set of system Eigen frequencies (3N-6) are obtained by diagonalization of the symmetric positive semidefinite Hessian matrix. More than anything else, we have observed the vibrational spectra, which occur between 0.98 cm-1 and 304.48 cm-1 at ∆E =0. Most significantly, all the clusters had come across the double and the triple state degeneracies, which are due to the stretching and the bending mode of the vibrations through the atoms. Nevertheless, the vibrational spectrum is strongly dependent upon size, shape, and structure.
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