Competition between 2D and 3D structures of Na6

Based on the tight-binding molecular dynamics, the structural properties for the two lowest energy structures of Na6 isomers (the first one is 2D structure with D3h symmetry and the second one is 3D structure with C5v symmetry) are studied. The vibrational frequencies of these two structures are calculated by diagonalization of the Hessian matrix and by suing the Fourier transform of velocity auto-correlation function from the trajectories of the distance dependent tight-binding molecular dynamics. Although they have almost the same energy, they have very different eigen- frequencies which corresponds their different structures