Drugs solubility parameter prediction using modified Cubic Plus Chain equation of state

Accurate prediction of drug solubility parameter is essential for understanding drug-solvent interactions and guiding formulation design. Experimental determination is often limited by low solubility and measurement complexity; thus, reliable predictive methods are required. In this work, the main objective is to estimate drug solubility parameter using a modified Cubic-Plus-Chain (CPC) equation of state (EoS). This work emphasizes that a simple cubic-based EoS can effectively model complex pharmaceutical systems and can be readily implemented in commercial simulation software. Accordingly, the CPC EoS was coupled with the Two-State Theory (TST) to enhance the description of complex molecular interactions, such as association in drug systems. The primary motivation for employing the TST instead of Wertheim's theory lies in the difficulty of defining the number and types of association sites in large and complex drug molecules. In contrast to Wertheim's approach, TST does not require explicit specification of association sites, which greatly simplifies the modeling of associating components. Moreover, the proposed CPC-TST model retains analytical solvability comparable to conventional cubic EoS, further enhancing its practicality for implementation in commercial simulation tools. The model parameters were determined using available experimental solubility data for selected drug-solvent systems. The solubility of drugs in various pure and mixed solvents was then estimated with the CPC-TST model. The analysis shows that accounting for a binary interaction parameter that varies with temperature leads to a notable improvement in the model's capability, yielding the average RMSD of 0.034 and AAD% of 0.168. The CPC-TST model was employed to predict the solubility parameter of several drug compounds. The predicted values were compared with those obtained from regression-based, group-contribution methods, and PC-SAFT EoS. The CPC-TST model demonstrated good accuracy in predicting solubility parameter, particularly for strongly associating systems, while maintaining low computational complexity. These results highlight the potential of the CPC-TST model as a robust and efficient alternative for modeling solubility behavior in pharmaceutical systems.