In this dissertation, the diffusion Monte Carlo (DMC) method is applied to study the ground state of anionic hydrogen, neutral para-hydrogen, and Lennard Jones clusters. The nuclear quantum effects in anionic hydrogen and neutral para-hydrogen clusters are investigated based on previous claims related to the existence of “magic numbers”. In anionic hydrogen clusters H−(H2)n, the binding energies are found to be a smooth function of increasing cluster size, and their ground state wavefunctions are highly delocalized and do not resemble the structures of the potential energy surface minima. For their deuterated analogues, the wavefunctions are localized, yet their structures are still characterized as disordered. In the para-hydrogen clusters (pH2)N, the analysis of the ground state wavefunctions for N = 24 − 28 revealed that these clusters are structurally very similar to one another. Thus, no “magic number” clusters exist in this range. This lack of size sensitivity is the result of the strong quantum delocalization in these systems, which further suggests that clusters in a much wider size range are also structurally similar. Lastly, in the Lennard Jones clusters, the degree of delocalization of the ground state wavefunction is investigated by decreasing the de Boer quantum delocalization length from ⇤ ∼ 0.28 (⇤pH2)to⇤∼ 0.2 (⇤oD2).. As this parameter is gradually decreased, the completely delocalized ground state wavefunction undergoes a transition to the regime of “quantum glass”. In other words, the system gradually becomes localized, but remains disordered.