Abstract
The geometries and vibrational frequency of the stable AuN clusters with N = 21 to 25 are presented through the global structure re-optimization study. The finite-differentiation method has been implemented within the density-functionaltight-binding (DFTB) approach. The effect of the range of interatomic forces was calculated and the desired set of system eigenfrequencies (3N-6) is obtained by diagonalization of the symmetric positive semidefinite Hessian matrix. We have observed the vibrational spectral ranges of between 2.88 and 328.25 cm-1 Δ E=0, and even the minute details of the very lower frequencies were occupied in some clusters at the beginning of NVM itself which comes even below the scale of Far Infrared FIR, IR-C 200-10 cm-1. Significantly, some of the clusters spectrums are with double state degeneracy and the rest of them are having single state degeneracy. Nevertheless, our investigation has revealed that the vibrational spectrum strongly depends upon the size, shape, and structure, as well as, stretching and bending vibrations of the atoms.
Mathematics of the Spinning-Top:1
