Artificial neural network-based estimation of interaction parameters between carbon dioxide and organic solvents using the Peng–Robinson equation of state with the van der Waals one-fluid mixing rule and quantum chemical data

The Peng–Robinson (PR)-van der Waals (vdW) model, which combines the PR equation of state with the vdW one-fluid mixing rule, is often used to estimate the physical properties of CO₂/organic solvent mixtures. Calculating these properties using the PR-vdW model requires interaction parameters k_ij; however, reports on these parameters are limited. This article introduces an artificial neural network (ANN) to predict k_ij between CO₂ and organic solvents, using pure-component parameters and molecular information as inputs. The molecular information is obtained through the general-purpose quantum chemical calculation software Gaussian. In addition, the ANN is optimized by varying the transfer function, number of neurons, and number of hidden layers. The optimized ANN employs a tanh function as the transfer function for the hidden layers, with two hidden layers containing 40 and 10 neurons. This model effectively predicts k_ij for a wide range of substances and temperature conditions. Furthermore, SHapley Additive exPlanations analysis of the optimized ANN reveals a significant contribution from the quadrupole moment, likely due to quadrupole interactions between CO₂ and the organic solvents. These results support the estimation of the physical properties of CO₂/organic solvent mixtures.