Ion diffusion in semiconductor nanocrystals, or quantum dots (QDs), has gained recognition in recent years as a crucial process for advancing both energy storage and, more generally, the postsynthetic p-type doping chemistry of these materials. In this report, we present first an energetic analysis of group I cations (H+, Li+, and Na+) diffusion in (MX)84 – QDs, with M = Zn, Cd and X = S, Se. The bound solutions to the corresponding one-dimensional nuclear Schrödinger equation were solved for these systems, relying on the discrete variable representation method. From this vantage, the quantum nature of the intercalating ion can be revealed. Evidence for the importance of including quantum effects in the treatment of these diffusion processes is presented, both with the density of energy eigenstates of the intercalating ion and from a comparison of the standard deviation in the population distribution of the intercalating ion to the lattice spacings of its host material. Results suggest that the use of classical mechanics for simulations of the ion diffusion processes in these and other related materials can be a questionable practice for the smallest group I cations. Trends devised herein can be useful to help guide the development of new experimental approaches to postsynthetic doping of semiconductor nanocrystals, and in designing electrode materials for next generation electrochemical energy storage devices.