QSPR Models Based on Multiple Linear Regression and Back-Propagation Artificial Neural Network for Predicting Electrical Conductivity of Ionic Liquids

Abstract

Electrical conductivity of ionic liquids (ILs), a crucial transfer property, has been investigated using various methods, including experimental measurements, semiempirical models, and molecular simulations. Among these methods, the quantitative structure−property relationship (QSPR) model is extensively utilized in diverse applications. However, constructing an effective QSPR model depends on the selection of the appropriate molecular descriptors. In this study, linear and nonlinear QSPR models were developed to predict the conductivity of the ILs. These models incorporated temperature as well as the molecular descriptors of cavity volume (V COSMO ) and charge-density-distribution area at specific intervals (S σi ) obtained from the conductor-like screening model for segment activity coefficient (COSMO-SAC). The evaluated data set comprised 254 ILs with 3102 data points; the ILs were considered to consist of "pure ions" or "ion pairs". Three distinct models were developed in this study: model I represented the pure ion model combined with multiple linear regression (MLR), model II referred to the ion pair model combined with MLR, and model III was constructed by considering ILs as ion pairs and using the back-propagation artificial neural network (BP-ANN). For the entire data set, models I and II exhibited coefficients of determination (R 2 ) of 0.9478 and 0.9642, respectively. Furthermore, the calculated average absolute relative deviations (AARDs) were 25.38 and 21.37% with root mean square errors (RMSEs) of 0.3291 and 0.2724, respectively. By contrast, model III demonstrated R 2 values of 0.9939, 0.9911, and 0.9887 for the training, validation, and testing sets, respectively. The corresponding AARD values were 6.96, 8.13, and 8.97%, while the RMSE values were 0.1132, 0.1214, and 0.1569, respectively. Application domain (AD) analysis revealed that 91.1% of the data points lie within the AD of model II and only 0.16% of the data showed response outliers. In contrast, 93.42% of the data were bound within the AD of model III, with no response outliers. These findings indicate that the QSPR model, which treats ILs as "ion pairs" and combines them with the BP-ANN, can predict the conductivity of diverse ILs at various temperatures with a high accuracy.