The geometries and vibrational frequency of the most stable small AuN clusters with N = 3 to 20 are presented through global structure re-optimization Study. The finite-differentiation method has been implemented within the density-functional tight-binding (DFTB) approach. The desired set of system eigenfrequencies (3N-6) is obtained by a diagonalization of the symmetric positive semi definite Hessian matrix. We have observed the vibrational modes between 0.55 and 370.72 cm-1 in wavenumbers at T=0 for the small gold clusters. The effect of the range of interatomic forces was calculated, and even the very lower frequencies were occupied in some clusters.
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