In Silico Calculation of Infinite Dilution Activity Coefficients of Molecular Solutes in Ionic Liquids: Critical Review of Current Methods and New Models Based on Three Machine Learning Algorithms

Abstract

The aim of the paper is to address all the disadvantages of currently available models for calculating infinite dilution activity coefficients (γ(∞)) of molecular solutes in ionic liquids (ILs)-a relevant property from the point of view of many applications of ILs, particularly in separations. Three new models are proposed, each of them based on distinct machine learning algorithm: stepwise multiple linear regression (SWMLR), feed-forward artificial neural network (FFANN), and least-squares support vector machine (LSSVM). The models were established based on the most comprehensive γ(∞) data bank reported so far (>34 000 data points for 188 ILs and 128 solutes). Following the paper published previously [J. Chem. Inf. Model 2014, 54, 1311-1324], the ILs were treated in terms of group contributions, whereas the Abraham solvation parameters were used to quantify an impact of solute structure. Temperature is also included in the input data of the models so that they can be utilized to obtain temperature-dependent data and thus related thermodynamic functions. Both internal and external validation techniques were applied to assess the statistical significance and explanatory power of the final correlations. A comparative study of the overall performance of the investigated SWMLR/FFANN/LSSVM approaches is presented in terms of root-mean-square error and average absolute relative deviation between calculated and experimental γ(∞), evaluated for different families of ILs and solutes, as well as between calculated and experimental infinite dilution selectivity for separation problems benzene from n-hexane and thiophene from n-heptane. LSSVM is shown to be a method with the lowest values of both training and generalization errors. It is finally demonstrated that the established models exhibit an improved accuracy compared to the state-of-the-art model, namely, temperature-dependent group contribution linear solvation energy relationship, published in 2011 [J. Chem. Eng. Data 2011, 56, 3598-3606].

The solubility of gases in ionic liquids

“…Advanced neural networks and machine learning techniques have also been applied to develop more robust models for solubility in ILs . Paduszyński has reviewed much of this and previous QSPR work and then used three different machine learning algorithms to develop new QSPR models for infinite dilution activity coefficients in ILs . As neural network and machine learning techniques continue to advance, it is likely that they will play an increasingly important role in developing highly accurate solubility models.…”

Neural recommender system for the activity coefficient prediction andUNIFACmodel extension of ionicliquid‐solutesystems

“…In addition to the above methods, the machine learning (ML) technique and its implementation in cheminformatics have recently gained in popularity, which are promoting broad applications of data‐driven models in chemical engineering studies 22,23 . For predicting the physicochemical and thermodynamic properties of ILs, a number of ML‐based models have also been developed, taking advantage of databases, for example, the NIST Ionic Liquids Database (ILThermo) 24‐28 . For instance, (a) Nami and Deyhimi 26 reported a multi‐layer feed‐forward network for the prediction of infinite dilution activity coefficients ( γ ∞ ) of molecular solutes in ILs; however, this model is only based on 16 imidazolium ILs and 914 γ ∞ data points, suffering from a high overfitting risk and a narrow applicability range.…”

“…For instance, (a) Nami and Deyhimi 26 reported a multi‐layer feed‐forward network for the prediction of infinite dilution activity coefficients ( γ ∞ ) of molecular solutes in ILs; however, this model is only based on 16 imidazolium ILs and 914 γ ∞ data points, suffering from a high overfitting risk and a narrow applicability range. (b) In 2016, Paduszyński 27 proposed three models for solute‐in‐IL γ ∞ based on different ML algorithms: stepwise multiple linear regression (SWMLR), feed‐forward artificial neural network (FFANN), and least‐squares support vector machine (LSSVM). Over 34,000 data points covering 188 ILs and 128 solutes were used for the development of these models, which are demonstrated to be able to provide reasonable γ ∞ prediction, particularly for systems involving ILs similar to those in the development dataset.…”

Effect of Cation Structure in Quinolinium-Based Ionic Liquids on the Solubility in Aromatic Sulfur Compounds or Heptane: Thermodynamic Study on Phase Diagrams

“…Determining the efficiency of the IL as a solvent in the processes of EDS for fuels is mainly based on experimental measurements of activity coefficients at infinite dilution [8][9][10][11] and on the measurements of phase equilibria in binary-and ternary-systems composed of the IL and heptane, treated as model fuel or/and aromatic sulfur compounds (thiophene, benzothiophene, 2-methylthiophene) [12][13][14][15][16][17]. This is based on an extensive experimental database including the diversity of the cation and anion structure of the IL, which has created many computer simulation methods and the selection of interesting compounds for applications in EDS [7,11].…”