%0 Journal Article %T Symmetry of Gold Neutral Clusters Au3-20 and Normal Modes of Vibrations by using the Numerical Finite Difference Method with Density-Functional Tight-Binding(DFTB) Approach %J - %D 2018 %R 10.21767/2572-4657.100017 %X 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 %K Vishwanathan K %K Gold Atomic Clusters %K Density-Functional Tight-Binding (DFTB) approach %K Finite-Difference Method %K Force Constants (FCs) %K Normal Modes of Vibrations %U https://www.imedpub.com/abstract/symmetry-of-gold-neutral-clusters-au320-and-normal-modes-of-vibrations-by-usingrnthe-numerical-finite-difference-method-with-densityfunctional-tightbindingdftb-approach-21781.html