The stable structures of cationic neon clusters containing up to 57 atoms have been located using a diatomic-in-molecules potential energy surface and basin-hopping hierarchical optimization. The effects of vibrational delocalization were included either in the harmonic approximation, or by performing Langevin molecular dynamics simulations coupled to a quantum thermal bath at T = 0. For most clusters, zero-point motion is sufficiently high to blur the picture of a single well-defined structure. However, structural diversity of the ground state wavefunction is found to be lower at sizes 14, 21, and 56, which correspond to special stabilities in experimental mass spectra. (C) 2012 Elsevier B.V. All rights reserved.