A robust and efficient solution for COSMO-based activity coefficient models

COSMO-based activity coefficient models, such as COSMO-RS and COSMO-SAC, offer a powerful tool that bridges quantum chemical calculations with macroscopic phase equilibrium calculations. These models utilize a group contribution methodology similar to UNIFAC but require an expensive numerical solution of the self-consistency equation for interactions among all surface segments, representing a primary bottleneck in their application to analyses that involve extensive phase equilibrium calculations. This work demonstrates that the self-consistency equation can be derived by minimizing the system energy from all pairwise segment interactions. The derivation leads to an optimization-based second-order solution procedure that ensures convergence and enhances efficiency. We demonstrate the robustness and efficiency of the proposed solution using various examples, including a comparison with the classical successive substitution method, and illustrate that COSMO-based models can be coupled with modern second-order convergent algorithms for phase equilibrium calculations. Furthermore, this work reveals the similarity between COSMO-based models and the SAFT method.