Structure-dependent ferroelectricity of niobium clusters (Nb_N, N=2–52)

The ground-state structures and ferroelectric properties of Nb_N⁢⁢ (N=2–52) have been investigated by a combination of density-functional theory in the generalized gradient approximation and an unbiased global search with the guided simulated annealing. It is found that the electric dipole moment (EDM) exists in most of the Nb_N and varies considerably with their sizes. The larger Nb_N (N⩾25) prefer the amorphous packing. Most importantly, our numerical EDM values of Nb_N (N⩾38) exhibit an extraordinary even-odd oscillation, which is consistent with the experimental observation, showing a close relationship with the geometrical structures of Nb_N. Finally, an inverse coordination number function is proposed to account for the structural relation of the EDM values, especially their even-odd oscillations starting from Nb₃₈.