The microscopic properties that determine hygroscopic behavior are complex. The importance of hygroscopicity to many areas, and particularly atmospheric chemistry, in terms of aerosol growth and cloud nucleation, mandate the need for robust models to understand this behavior. Toward this end, we have employed molecular dynamics simulations to calculate hygroscopicity from atomistic models using free energy perturbation. We find that currently available force fields may not be well-suited to modeling the extreme environments of aerosol particles. Nonetheless, the results illuminate some shortcomings in our current understanding of hygroscopic growth and cloud nucleation. The most widely used model of hygroscopicity, κ-Köhler Theory (κKT), breaks down in the case of deviations from ideal solution behavior and empirical adjustments within the simplified framework cannot account for non-ideal behavior. A revised model that incorporates non-ideal mixing rescues the general framework of κKT and allows us to understand our simulation results as well as the behavior of atmospheric aerosols over the full range of humidity. The revised model shows that non-ideal mixing dominates hygroscopic growth at subsaturation humidity. Thus, a model based on ideal mixing will fail to predict subsaturation growth from cloud condensation nucleus (CCN) activation or vice versa; a single parameter model for hygroscopicity will generally be insufficient to extrapolate across wide ranges of humidity. We argue that in many cases, when data are limited to subsaturation humidity, an empirical model for non-ideal mixing may be more successful than one for ideal mixing.