Magic numbers, quantum delocalization, and orientational disordering in anionic hydrogen and deuterium clusters

The Diffusion Monte Carlo (DMC) method was applied to anionic hydrogen clusters H^-(H₂)_n (n = 1-16, 32) and their deuterated analogs using a polarizable all-atom potential energy surface (PES) developed by Calvo and Yurtsever. For the hydrogen clusters, the binding energy ΔE_n appears to be a smooth function of the cluster size n, thus contradicting the previous claim that n = 12 is a "magic number" cluster. The structures of the low energy minima of the PES for these clusters belong to the icosahedral motif with the H₂ molecules aligned toward the central H^- ion. However, their ground state wavefunctions are highly delocalized and resemble neither the structures of the global nor local minima. Moreover, the strong nuclear quantum effects result in a nearly complete orientational disordering of the H₂ molecules. For the deuterium clusters, the ground state wavefunctions are localized and the D₂ molecules are aligned toward the central D^- ion. However, their structures are still characterized as disordered and, as such, do not display size sensitivity. In addition, DMC simulations were performed on the mixed H^-(H₂)_n(D₂)_p clusters with (n, p) = (6, 6) and (16, 16). Again, in contradiction to the previous claim, we found that the "more quantum" H₂ molecules prefer to reside farther from the central H^- ion than the D₂ molecules.