Using a combination of classical molecular dynamics and symmetry adapted intermolecular perturbation theory, we develop a high-accuracy computational method for examining the solubility energetics of nonelectrolytes. This approach is used to accurately compute the cohesive energy density and Hildebrand solubility parameters of 26 molecular liquids. The energy decomposition of symmetry adapted perturbation theory is then utilized to develop multicomponent Hansen-like solubility parameters. These parameters are shown to reproduce the solvent categorizations (nonpolar, polar aprotic, or polar protic) of all molecular liquids studied while lending quantitative rigor to these qualitative categorizations via the introduction of simple, easily computable parameters. Notably, we find that by monitoring the first-order exchange energy contribution to the total interaction energy, one can rigorously determine the hydrogen bonding character of a molecular liquid. Finally, this method is applied to compute explicitly the Flory interaction parameter and the free energy of mixing for two different small molecule mixtures, reproducing the known miscibilities. This methodology represents an important step toward the prediction of molecular solubility from first principles.