The present work reconsiders a classical and universally accepted concept of physical chemistry, the solubility parameter. Based on the insight derived from modern quantum chemical calculations, a new definition of solubility parameter is proposed, which overcomes some of the inherent restrictions of the original definition and expands its range of applications. The original single solubility parameter is replaced by four partial solvation parameters reflecting the dispersion, the polar, the acidic and the basic character of the chemical compounds as expressed either in their pure state or in mixtures. Simple rules are adopted for the definition and calculation of these four parameters and their values are tabulated for a variety of common substances. In contrast, however, to the well known Hansen solubility parameters, their design and evaluation does not rely exclusively on the basic rule of "similarity matching" for solubility but it makes also use of the other basic rule of compatibility, namely, the rule of "complementarity matching". This complementarity matching becomes particularly operational with the sound definition of the acidic and basic components of the solvation parameter based on the third σ-moments of the screening charge distributions of the quantum mechanics-based COSMO-RS theory. The new definitions are made in a simple and straightforward manner, thus, preserving the strength and appeal of solubility parameter stemming from its simplicity. The new predictive method has been applied to a variety of solubility data for systems of pharmaceuticals and polymers. The results from quantum mechanics calculations are critically compared with the results from Abraham's acid/base descriptors.