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; Part 2, two-parameter m

• Neural networks predict interaction parameters for CO₂/organic solvent systems. • Quantum chemical data improve prediction accuracy. • The quadrupole moment was identified as a key interaction factor for k ij . • The volume of the mixture was identified as a key interaction factor for l ij . • New insights into interaction parameters are provided. The Peng–Robinson (PR)–van der Waals (vdW) model is a combination of the PR equation of state and the vdW mixing rule. In a previous study, we constructed a model that uses an artificial neural network (ANN) to predict the interaction parameters k ij in the vdW mixing rule, which is necessary for the wide application of this model. The vdW mixing rule includes a two-parameter mixing rule that combines l ij with k ij , and by using this rule, the range of application of the PR-vdW model can be expanded. In this study, an ANN model was constructed to predict k ij and l ij between CO 2 and organic solvents. The inputs used were the pure-component parameters and molecular information of the organic solvents, and the molecular information was obtained using the general-purpose quantum chemical calculation software Gaussian. In addition, the ANN was optimized by varying the transfer function, number of neurons, and number of hidden layers. The optimized ANN employed a tanh function as the transfer function for the hidden layers, with two hidden layers containing 40 and 20 neurons. This model could predict k ij effectively, but problems with predicting l ij remained. The results of the SHapley Addtive exPlanations analysis of the optimized ANN revealed that k ij was related to the interactions between different molecules and that l ij was related to the volume of the mixture. Thus, improving the accuracy of l ij prediction requires the addition of related parameters.