MLR Data-Driven for the Prediction of Infinite Dilution Activity Coefficient of Water in Ionic Liquids (ILs) Using QSPR-Based COSMO Descriptors

Abstract

To predict the partial molar excess enthalpy, entropy at infinite dilution, and phase equilibria, the availability of an infinite dilution activity coefficient is vital. The “quantitative structure-activity/property relationship” (QSAR/QSPR) approach has been used for the prediction of infinite dilution activity coefficient of water in ionic liquids using an extensive data set. The data set comprised 380 data points including 68 unique ILs at a wide range of temperatures, which is more extensive than previously published data sets. Moreover, new predictive QSAR/QSPR models including novel molecular descriptors, called “COSMO-RS descriptors”, have been developed. Using two different techniques of external validation, the data set was divided to the training set for the development of models and to the validation set for external validation. Unlike former available models, internal validation using leave one/multi out-cross validations (LOO–CV/LMO–CV) and Y-scrambling methods were performed on the models using statistical parameters for further assessment. According to the obtained results of statistical parameters (R² = 0.99 and Q²_LOO–CV = 0.99), the predictive capability of the developed QSPR model was excellent for training set. Regarding the external validation, other statistical parameters such as AAD = 0.283 and AARD % = 30 were also satisfactory for the validation set. While the values of γ_H2^∞_O increase or decrease with increasing temperature, the QSAR/QSPR models based on the van’t Hoff equation takes into account the negative and positive effects of temperature on the γ_H2^∞_O in ILs well, depending on the nature of ILs. It was also shown that γ_H2^∞_O in some new ILs which had not been experimentally studied before can be predicted using the QSPR model.

1. Introduction

Simultaneous presence of water (H₂O) as one of the unavoidable associated compounds alongside natural gas streams may cause some serious issues such as freezing and hydrate formation.^1,2 Hence, many researchers have been looking for finding a proper solvent to remove the water in the dehydration processes.^1,2 Many conventional solvents such as ethylene glycol, diethylene glycol, and new solvents like ionic liquids (ILs) have been screened for the removal of water from natural gas streams.¹

Among the solvents screened, ILs have recently received significant attention. ILs consist of two separate parts called “organic or inorganic anion” and “organic cation”. Some intrinsic and outstanding features of ILs, such as minimal volatility, high degradation temperature, high selectivity, and low flammability, caused the ILs have gained the growing interest for use in different chemical processes.¹ When it comes to design and selection of appropriate ILs, the extensive combination of anion and cation imposes time-consuming and cost problems and restrictions for the engineers. Moreover, a molecular insight of their phase behavior and their interactions with other components like H₂O is still required.

Infinite dilution activity coefficient (γ^∞) is a key property for the prediction of phase equilibrium. γ^∞ is one of the significant thermodynamic properties which has been frequently studied in the binary mixture of IL and H₂O.^1,2 Since γ^∞ can provide helpful information on enthalpy and entropy changes and chemical potential, it can be considered as a good criteria and measure for finding the most suitable ILs with highest and lowest affinities into the H₂O.³ The ln (γ^∞) can be split into its respective entropic and enthalpic components.³ γ^∞ values also show the interaction between solvent and solute.⁴ In other words, the higher the solute–solvent interaction, the lower the activity coefficient and vice versa.⁴ There are many commonly used methods for determining infinite dilution activity coefficent of compounds, such as gas–liquid chromatography (GLC) and vapor–liquid equilibria (VLE) methods.⁵ Computational^1,2 and experimental [4,6–61] point of views, the influence of structural variations of ILs (anions and cations) on the infinite dilution activity coefficent of H₂O (γ_H2^∞_O), has been frequently studied by researchers.

Domanska and Laskowska.⁶ as one of most active research groups in this field measured the values of γ_H2^∞_O in many ILs. There are many experimental studies [6–61] including a large number of cation and anion structural variations. However, with an estimate of 10¹⁸ potential ILs,³ determining γ_H2^∞_O values for all systems is not practically possible. Hence, reliable white-box and predictive methods are of utmost importance. In the earlier computational studies, Gonfa et al.² figured out that the COSMO-RS model as a direct predictive tool overestimates the γ_H2^∞_O in ILs. For this reason, they¹ tried to apply and combine two computational methods which called “quantitative structure–property (or activity) relationship (QSPR/QSAR)” and “COSMO-RS”. Gonfa et al.¹ suggested the following linear regression technique for the prediction of γ_H2^∞_O in ILs using new molecular-inputs (descriptors) and temperature (eq 1)

1

where a₁ to a₈ are the adjustable parameters of the effect of structural variations (i.e., cation and anion) and a₉ is the adjustable parameter of the effect of temperature (T) on the γ_H2^∞_O in the ILs. Equation 1 represents the relationship between the γ_H2^∞_O and independent inputs, which are the numerical values of the σ-profile descriptor and the temperature. They¹ divided the sigma profile of each cation and anion into four regions. In other words, the occupied areas of each region are considered as COSMO-RS numerical molecular descriptors, called “S₁^Cat, S₂^Cat, S₃^Cat, S^Cat₄” and “S^Ani₅, S₆^Ani, S₇^Ani, S₈^Ani”. They have taken into account the temperature effect on the γ_H2^∞_O in the ILs, according to the van’t Hoff equation. The proposed model by Gonfa et al.¹ never can consider the dependency of the temperature for all kinds of ILs. Because such model always has a constant adjustable parameter for “1/T” variable (i.e., a₉). Although the γ_H2^∞_O in majority of ILs decreases with an increase in temperature,⁶² there are also ILs where γ_H2^∞_O increases or stays almost constant. For this reason and to avoid the deficiency of the model, Gonfa et al.¹ presented separate linear QSAR models for each constant temperature. In the continuation of above study, Benimam et al.⁶³ attempted to enhance the prediction capability using the nonlinear method called “Dragonfly-Support Vector Machine”. In their studies, they used the same kind of molecular inputs and temperature to model the γ_H2^∞_O in imidazolium-based ILs. To the best of our knowledge, there are only three research studies^1,2,63 for the prediction of γ_H2^∞_O in ILs. However, there were some missing points in their studies which should be studied more. One same missing point in these studies was that all used limited amount of data points and limited variations of cation and anion. Another missing point which was quite obvious in a study by Gonfa et al.¹ is the misunderstanding of 1/T term in van’t Hoff equation. To avoid of such misunderstanding, Thangarajoo et al.³ improved the use of the van’t Hoff equation by the varied coefficient of “1/T” term which was rationally depended on the molecular inputs for the first time. According to the proposed model by Thangarajoo et al.³ which was developed for methanol and IL mixtures (not γ_H2^∞_O), the values of molecular descriptors of “1/T” vary with respect to the nature of ILs. Nevertheless, the molecular variables selection had been ignored in all three discussed studies.^1,3,63 Therefore, applying artificial intelligence (AI) methodology as a predictive tool is still required to not only precisely adjust the varied parameters of the “1/T” term in the van’t Hoff equation, with respect to the structure and nature of ILs, but also select the proper molecular variables, simultaneously.

The (QSPR/QSAR) approach as one of the robust methods is commonly used to make qualitative and quantitative correlation between ILs and their specific properties.⁶⁴⁻⁶⁷ Therefore, it is possible to design and/or develop new ILs using the QSPR method for different applications. Up to now, researchers have not applied the QSPR/QSAR approach, including variable selection for the prediction of γ_H2^∞_O in ILs, with a large space of cation and anion structural variations at a wide range of temperatures. This approach has been applied in the well-known software called “QSARINS”⁶⁸⁻⁷⁰ as the first time which features several methods such as molecular variables selection, internal, and external validations in its environment. However, Gonfa et al.¹ and Benimam et al.⁶³ used a somewhat similar approach with this work but with a major difference with the lack of molecular variables selection. In this work, molecular variable selection has been carried out from a descriptors pool. A comparison with the proposed models by Gonfa et al.¹ and Benimam et al.⁶³ was carried out to highlight the improvements and novelty made in this study. This work has the novel feature of examining the advantages of using the QSPR/QSAR approach-based new COSMO-RS descriptors for the prediction of γ_H2^∞_O in ILs. Gathering and using a comprehensive data set [a much larger data set (i.e., 380 total data points)] including additional structural variations of cation and anion is one of the biggest differences in comparison with former data sets. The use of this new data set enables the development of the predictive models for a wide range of ILs. The developed predictive and reliable QSPR/QSAR model aids the chemical engineering community to select the proper ILs for the specific applications. In this work, we report in addition to γ_H2^∞_O the two most important thermodynamic properties [i.e., the partial molar excess enthalpy (i.e., ΔH^E,∞_IL) and entropy (i.e., ΔS^E,∞_IL) at infinite dilution] for numerous systems including IL and H₂O to screen the ILs.

2. Methods

2.1. Basic Theory

In this study, the influence of temperature on the γ_H2^∞_O in ILs was included as an independent variable based on the van’t Hoff equation. Van’t Hoff equation expresses the relationship between γ_H2^∞_O in ILs and temperature as below (eq 2)

2

where “A” and “B” are adjustable parameters which depend on the molecular descriptors and their weights determined by the QSPR method.

The partial molar excess enthalpy (i.e., ΔH^E,∞_IL) and entropy (i.e., ΔS^E,∞_IL) at infinite dilution, which are shown in eq 3, can be calculated using “A” and “B” (see eq 2), respectively.

3

In this study, the most significant COSMO-RS descriptors (points of specific charge densities) were applied to distinguish the effect of cation and anion structural variations. In fact, these prominent descriptors are rationally and strongly related to the two most important thermodynamic properties (i.e., ΔH^E,∞ and ΔS^E,∞). As mentioned earlier, the influence of the temperature on γ_H2^∞_O in the ILs varies with the nature of the ILs. For a majority of ILs, the γ_H2^∞_O value decreases as the temperature increases, but for a limited amount of ILs, the opposite behavior has been observed. Therefore, the predictive QSPR/QSAR based-COSMO-RS model should be able to consider this complexity. Hence, the model should be able to change sign of “A” parameter according to the behavior of the solute in the ILs. It means that the sign of “A” parameter is often “+”, stating the values of γ_H2^∞_O in the majority of ILs decrease. Otherwise (contrarily), the sign of “A” parameter is rarely “–”, stating the values of γ_H2^∞_O in other ILs increase. In brief, the included ILs in this study belong to three different regions with increasing temperature: (1) the values of γ_H2^∞_O decrease, (2) the values of γ_H2^∞_O increase, and (3) the values of γ_H2^∞_O are almost constant (see Figure 1).

Figure 1.

Examples of ILs from each region with different dependencies to temperature.^6,9,44,47,61

As can be seen in Figure 1, three distinct regions can be categorized for the values of γ_H2^∞_O in ILs, called “high”, “middle”, and “low” regions. In other words, the values of γ_H2^∞_O in the high region decrease significantly with increasing temperature, and the values are relatively high or much higher than 1. While the values of γ_H2^∞_O in middle and low regions are almost constant (with very slight reduction) and increase with increasing temperature, respectively. The values of γ_H2^∞_O in the middle region are scattered around 1, and the values of γ_H2^∞_O in the low region are relatively low or much lower than 1. Some representatives of ILs for each region can be found in the Supporting Information Excel file (see Sheet S1). As briefly shown in Figure 1, H₂O in [C3C1Pip][NTF2] belongs to the first region, where γ_H2^∞_O decreases remarkably with increasing temperature. H₂O in [C2C1Im][C(CN)3] and [C4C1Im][C(CN)3] belongs to the middle region, where γ_H2^∞_O is nearly temperature invariant with increasing temperature. H₂O in [C4C1Im][SCN] and [OHC3–C1Im][N(CN)2] is example of the third region, where γ_H2^∞_O increases with increasing temperature. Regarding the third region, it should be mentioned that the changes of values of γ_H2^∞_O in some ILs such as [C4C1Im][SCN] and [OHC3–C1Im][N(CN)2] are slight, while in other ILs like [C4C1Im][Br], changes can be tangible. These observed complexities of different behaviors of ILs make the modeling of such systems challenging, and novel sophisticated models are needed. Therefore, there is still a need to applying new methodologies on eq 2 (i.e., van’t Hoff equation), for further/future investigations.

2.2. Data Set

According to the collected experimental data [6–61], an extensive data set with very high structural variations of cations and anions has been created for QSPR/QSAR studies. The details of this data set can be found in Table 1 and Supporting Information Excel file (see Sheets S2 and S3). All in all, 380 data points including 68 unique ILs (34 cations and 15 anions) at a wide range of temperatures with the above-described features are listed in Table 1.

Table 1. Studied ILs in Different Binary Systems (i.e., IL + H₂O) with Their Ranges of Temperature and Experimental Values as Well as Statistical Parameters.

mixture IL/H2O	temperature range (K)	range of ln (γH2∞OExp)	AARD %b	refs
[C4C1Im][SCN]a	328–368	(−1.298) – (−1.269)	32.9	(6)
[C4–3-C1Py][CF3SO3]	318–358	(−0.116) – (−0.267)	73.4	(7)
[C4C1Pyrro][FAP]	318–368	(2.236) – (1.350)	8.4	(8)
[C3C1Pip][NTF2]	308–358	(1.488) – (0.896)	12.2	(9)
[HOC3Py][FAP]	308–358	(0.974) – (0.548)	26.3	(10)
[C4C1Im][TFA]	333–393	(−1.851) – (−1.639)	5.3	(11)
[C2C1Im][SCN]	328–368	(−1.298) – (−1.269)	30.5	(12)
[C4C1Pip][SCN]	328–368	(−1.105) – (−1.064)	25.6	(13)
[C4–4-C1Py][SCN]	328–368	(−1.187) – (−1.155)	24.7	(14)
[C4C1Pyrro][SCN]	328–368	(−1.335) – (−1.269)	37.1	(14)
[C6C1Im][SCN]	328–368	(−0.572) – (−0.623)	33.1	(15)
[C6-iqui][SCN]	328–368	(−0.913) – (−0.872)	17.1	(16)
[C4C1Mor][C(CN)3]	318–368	(0.029) – (−0.248)	315.9	(17)
[C4C1Pyrro][C(CN)3]	318–368	(−0.027) – (−0.261)	132	(18)
[C4C1Pyrro][B(CN)4]	318–368	(0.765) – (0.246)	6.9	(19)
[C10C1Im][B(CN)4]	328–378	(0.751) – (0.300)	4.6	(20)
[C2C1Im][B(CN)4]	298–358	(0.806) – (0.254)	1.6	(21)
[C6C1Im][B(CN)4]	318–368	(0.717) – (0.285)	3.4	(22)
[C4C1Pyrro][CF3SO3]	318–368	(−0.145) – (−0.339)	19	(23)
[C4C1Im][CF3SO3]	328–368	(−0.212) – (−0.362)	13.1	(24)
[C2C1Im][TFA]	348–368	(−1.944) – (−1.838)	10.0	(25)
[C6OC1C1Im][NTF2]	298–358	(1.474) – (0.712)	2.4	(26)
[(C6OCH2)2Im][NTF2]	298–368	(1.488) – (0.593)	6.7	(26)
[C4–4-C1Py][NTF2]	298–368	(1.581) – (0.717)	10.1	(4)
[N1112OH][NTF2]	318–368	(0.270) – (−0.069)	355.6	(27)
[C8iquin][NTF2]	328–368	(1.398) – (0.838)	5.7	(28)
[C4C1Pip][NTF2]	308–358	(1.566) – (0.879)	10.7	(29)
[S222][NTF2]	308–368	(1.363) – (0.631)	4.2	(30)
[C1C1Im][NTF2]	303–333	(1.050) – (0.698)	27.6	(31)
[C2C1Im][NTF2]	293–323	(1.302) – (0.932)	16.7	(31)
[C2Py][NTF2]	303–323	(1.022) – (0.693)	26.9	(32)
[HOC3Py][NTF2]	318–378	(0.425) – (0.029)	101.7	(33)
[COC2C1Pip][NTF2]	318–368	(1.208) – (0.625)	1.8	(34)
[COC2C1Mor][NTF2]	318–368	(0.912) – (0.343)	14.6	(35)
[COC2C1Pyrro][NTF2]	318–368	(1.147) – (0.615)	1.4	(36)
[C5C1Pip][NTF2]	308–358	(1.619) – (0.892)	10.3	(37)
[C6C1Pip][NTF2]	308–358	(1.669) – (0.896)	9.1	(37)
[C4–4-C1Py][N(CN)2]	338–368	(−1.224) – (−1.158)	33.2	(38)
[COC2C1Mor][FAP]	318–368	(1.547) – (1.101)	4.4	(39)
[COC2C1Pip][FAP]	318–368	(1.954) – (1.308)	4.4	(40)
[COC2C1Pyrro][FAP]	318–368	(2.086) – (1.371)	7.5	(41)
[HOC2C1Im][FAP]	318–368	(0.797) – (0.570)	16.5	(42)
[C1C1Im][DMP]	363–383	(−2.960) – (−2.856)	1.5	(32)
[C4C1Im][Br]	333–393	(−2.631) – (−2.017)	4.9	(11)
[C2C1Im][MeSO3]	318–358	(−2.645) – (−2.430)	6.7	(43)
[C2C1Im][C(CN)3]	318–368	(−0.080) – (−0.153)	41.7	(44)
[C2C1Im][FAP]	318–368	(1.906) – (1.425)	4.9	(45)
[HOC2C1Im][N(CN)2]	328–358	(−0.946) – (−0.991)	66.1	(46)
[C4C1Im][Ac]	298–393	(−4.342) – (−3.194)	1.2	(11)
[C4C1Im][C(CN)3]	318–368	(0.019) – (−0.164)	23.5	(47)
[C4C1Im][Cl]	333–428	(−3.324) – (−2.364)	3.6	(11,48)
[C4C1Im][N(CN)2]	318–368	(−1.171) – (−0.978)	25.2	(49)
[C4C1Im][NTF2]	293–363	(1.373) – (0.688)	6.7	(31,50)
[C4C1Im][DMP]	333–428	(−3.381) – (−2.292)	4.1	(11,48)
[C4C1Im][MeSO3]	333–428	(−2.120) – (−1.431)	8.2	(11,48)
[C6C1Im][CF3SO3]	303–333	(0.270) – (−0.446)	200.8	(51)
[B Cya Py][NTF2]	308–368	(1.196) – (0.693)	6.9	(52)
[C12C1Im][NTF2]	318–368	(1.501) – (1.022)	5.2	(53)
[C4C1Py][C(CN)3]	318–368	(−0.029) – (−0.228)	42.8	(47)
[4OHC3 4-C1Mor][NTF2]	318–368	(0.357) – (0.095)	48.1	(54)
[C8Quin][NTF2]	313–353	(1.071) – (0.350)	92.9	(55)
[C6Quin][NTF2]	313–353	(1.446) – (1.098)	6.9	(55)
[P4442][DEP]	328–368	(−2.292) – (−2.154)	9.1	(56)
[C8C1Im][NTF2]	303–333	(1.358) – (0.947)	13.3	(57)
[C2C1Im][C8SO4]	333–358	(−1.832) – (−1.897)	5.5	(58)
[C2C1Mor][N(CN)2]	318–368	(−1.127) – (−0.941)	0.95	(59)
[HOC3Py][N(CN)2]	328–358	(−0.918) – (−0.839)	74.6	(60)
[OHC3–C1Im][N(CN)2]	318–368	(−1.049) – (−0.891)	33.4	(61)

^aBold means validation set.

^bUsing eq 16 [see Supporting Information Excel file (see Sheet S4)].

2.3. Former Available Models

There were multilinear-regression (MLR) and nonlinear models for the prediction of γ_H2^∞_O in the ILs which were proposed by Gonfa et al.¹ and Benimam et al.,⁶³ respectively. The quantitative and qualitative descriptors were sigma profile segments of cations and anions. Although they used the small data sets with low variations of cations and anions for training and validation models, the results of this study will be compared with their results. They evaluated the prediction capability of their predictive models using coefficient of determination (i.e., R²) and root-mean-square error (i.e., RMSE %) statistical parameters. For this reason, R² and RMSE % alongside other relevant statistical parameters will be reported in this study, for further comparisons.

2.4. QSPR Method

2.4.1. Calculation of COSMO-Based Molecular Descriptors

Molecular descriptors are from σ-profile which is calculated via COSMO-RS theory.⁷¹⁻⁷⁴ Sigma profiles are taken from database (COSMObase 2023) which is provided in COSMOtherm 2023⁷⁵ software, and the chosen sigma profiles were calculated by using TZVP-basis set. Descriptor values are taken from the lowest energy configuration of cation and anion molecules.

In a nutshell, sigma profile is 2D representation from 3D surface polarities of molecules, as shown in Figure 2, the x-axis tells you the strength of surface charge density (SCD) and the y-axis tells you the probability (amount) of finding this SCD. Sigma profile is calculated with 0.001 interval, and typically it varies from −0.03 to 0.03 e/Ų. An example of sigma profile descriptors for cations and anions is shown in Figure 2.

Figure 2.

Demonstration of some cationic and anionic descriptors [i.e., values of probability (amount) at some specific charge densities (SCD)] for [C4C1im] cation (or [BMIM]) and [DMP] anion (or [(Me)2PO4)].

2.4.2. Model Development

As can be seen in eq 2, ln (γ_H2^∞_O) is a function of cation and anion descriptors along with temperature. Since both cation and anion structures were changing in data set, “A” and “B” including cation and anion descriptors must distinguish the effect of cation and anion structures on ln (γ_H2^∞_O). For model construction, the suitable descriptors must be selected [i.e., the missing effort in the former studies^1,63 (i.e., variables selection)] from 61 sigma profile descriptors. There are well-known methods of variables selection such as genetic algorithm (GA) method,⁷⁶ artificial neural network (ANN),⁷⁷ and replacement method (RM).⁷⁸ In this study, GA was used to build MLR QSPR model-based COSMO descriptors. The details of the GA-MLR algorithm can be found elsewhere.^79,80 QSARINS software was applied to develop the GA-MLR models.

2.4.3. Statistical Parameters

The goodness-of-fit of the QSPR model should be carefully checked using the standard statistical parameters, including coefficient of determination (R²), leave-one-out cross-validated coefficient of determination (Q²_LOO-_CV), adjustable coefficient of determination (R²_Adj), average absolute relative deviation (%AARD), average absolute deviations (AAD), Fisher function (F), root-mean-square error (RMSE), standard residual (S), and maximum (or critical) leverage (h*). More detailed information regarding the statistical parameters used in this study can be found in Table 2 (eqs 4–12).

Table 2. Applied Statistical Parameters in This Study^a.

introduced parameters	introduced parameters equations
coefficient of determination	4
adjustable coefficient of determination	5
leave-one-out cross-validated coefficient of determination	6
Fisher function	7
standard residual	8
root-mean-square error (RMSE)	9
average absolute deviation	10
average absolute relative deviation %	11
maximum leverage	12

^aY_i^exp, Y_i^pre, , n, and p demonstrate experimental values (ln-Based), predicted values (ln-Based), average experimental values (ln-Based), the number of the experimental data set, and the number of employed descriptors, respectively.

Applicability domain (AD) analysis as a vital concept of the QSPR approach should be considered. It allows:⁸¹ (1) the uncertainty in prediction and (2) the extent of extrapolation of QSPR models.^82,83 In order to predict γ_H2^∞_O in new ILs, it is essential that new ILs lie within the same AD space. In other words, it means that new ILs are physicochemically, biologically, or structurally similar to molecules used for model development (i.e., training set). The more space of AD, the more reliable predictions of the new ILs. To carry out the external validation using validation set, it is essential to ensure that the validations set of molecules is inside of QSPR model’s AD.⁸⁴

The space of AD can be specified using two main parameters: (1) the leverage values (h_i) and (2) the standardized residual (SDR) and. SDR was defined as eq 13

13

where h_i represents a measure of a molecule’s distance from the center of the training set. It is needed to determine whether new ILs are within the applicability of the domain of the developed QSPR model or not. The parameter can be calculated with eq 14.

14

where z_i, Z are the descriptor row vector of point i and a n × p matrix of descriptors for compounds derived from the training set, respectively. AD of developed QSPR models can be obtained in QSARINS software for each model, and maximum leverage (i.e., h*) can be calculated using eq 12.

2.4.4. Internal and External Validations

After building of the QSAR/QSPR model, it is essential to conduct internal and external validations on the training (approximately 75% of main data set) and validation (approximately 25% of main data set) sets, respectively. Regarding the external validation, the prediction capability of developed QSAR/QSPR models was evaluated using two validation sets which are created in two different methods:⁸⁵ 1: leave random data points out-cross validation and 2: leave one ion out-cross validation (i.e., LOIO–CV). In the random method, some data points (not necessarily all) of ILs at some temperature may be set into the validation set, randomly. While, in the ion method, all data points of the specific cation and anion must be set into the validation set, completely. In the LOIO–CV method, neither the cation nor the anion of some ILs of the validation set can reappear in the training set. The LOIO–CV method enhances the stability of developed QSAR/QSPR models when predicting the properties of ILs with novel cations and anions, which is crucial for the data-driven design of new ILs.⁸⁵

Regarding the internal validation, Y-Scrambling, leave multiout-cross-validation (LMO-CV), and leave one-out-cross-validation (LOO-CV) methods should be conducted on the developed QSAR/QSPR model. In fact, these methods were performed on the training set (not the validation set).

3. Results and Discussion

3.1. Developed QSAR/QSPR Models

Before the development of the QSAR/QSPR models, some ILs were set intentionally aside in the validation set (see Table 1, bold ILs). The LOIO-CV method guarantees the presence of ILs with new structures for both cations and anions. In another words, all present data points of those ILs including anions ([SCN], [N(CN)2]), and [Cl] or cations ([C4–3-C1Py], [C3C1Pip], [C6-iqui], [C2C1Mor], and [OHC3–C1Im]) in the data set were deliberately set aside into validation set. Among specified ILs as the validation set, the involved structures for both cation and anion in [C6-iqui][SCN], [C2C1Mor][N(CN)2], and [OHC3–C1Im][N(CN)2] were absent in the training set. The details of the validation set for the LOIO–CV method can be found in Supporting Information Excel file (see Sheet S5). The main aim of this categorization is to investigate the QSAR/QSPR’s prediction capability for new structures of cation and anion.

After dividing an extensive data set into training and validation sets for performing internal and external validations, the QSAR/QSPR model eq 16 which was developed using training set with above features is indicated in Table 3. Moreover, another QSAR/QSPR model eq 17 using another training set, which was created using leave random data points out-cross method, was built for further investigations and comparisons. The details of the validation set for the random method can be found in Supporting Information Excel file (see Sheets S6 and S7).

Table 3. Developed QSAR/QSPR Models Using Two Different Methods of External Validations (i.e., LOIO–CV and Random).

external validations	number of data points in training set	modelsc
LOIO–CV	297a	ln (γH2O∞) = 16 + (W11.C0)+(W12.A0.010)+(W13.A0.017)+(W14)
random	285b	ln (γH2O∞) = 17 + (Q11.C0)+(Q12.A0.010)+(Q13.A0.017)+(Q14)

^a83 data points were set aside into validation set.

^b95 data points were set aside into validation set.

^cModels’ parameters: W1 = −240.0077, W2 = −11.3664, W3 = −28.5232, W4 = −28.9690, W5 = 51.8990, W6 = −26.6256, W7 = 82.5691, W8 = −70.7223, W9 = −68.4551, W10 = −1816.7257, W11 = 0.0102, W12 = −0.1697, W13 = 0.1319, W14 = −0.4159 and Q1 = −166.4001, Q2 = −10.9408, Q3 = −42.8764, Q4 = −23.3850, Q5 = 53.5780, Q6 = −28.7002, Q7 = 88.2013, Q8 = −75.1182, Q9 = −72.4609, Q10 = −1709.8307, Q11 = 0.0108, Q12 = −0.2002, Q13 = 0.1463, and Q14 = −0.4453.

In both eqs 16 and 17 including the same descriptors, three points of specific charge density from the sigma profile (i.e., “C–0.018”, “C–0.011”, and “C0”) are the cationic descriptors, and nine points of specific charge density (i.e., “A–0.009”, “A0”, “A0.002”, “A0.003”, “A0.009”, “A0.010”, “A0.017′, “A0.020”, and “A0.029”) are the anionic descriptors. The values of probability at above points of specific charge density for each cation and anion are used for the prediction of γ_H2^∞_O in ILs. In these models, the effect of temperature on the γ_H2^∞_O in ILs has been computationally taken into account based on the van’t Hoff equation. Such considerations were lacking in the former studies (Gonfa et al.¹ and Benimam et al.⁶³). The values of the statistical parameters of each model are shown in Table 4.

Table 4. Values of Statistical Parameters of Selected QSPR Models for Both of Training and Validation Sets.

eqs. no	sets	number of data points	R2	R2-Adj	Q2-LOO	Q2-LMO	F	S	RMSE	AARD %	AAD
(16)	training	297	0.99	0.99	0.99	0.98	1937	0.1411	0.1378	33	0.099
	validation	83	0.85						0.3344	30	0.283
(17)	training	285	0.98	0.98	0.98	0.98	1062	0.1935	0.1887	29	0.142
	validation	95	0.98						0.1796	29	0.139

As indicated in Table 4, the obtained values of Q² (either LOO or LMO) for each developed model were extremely high which are confirming that each model has accurate capability for the prediction of γ_H2^∞_O in studied ILs in a wide range of temperatures (see Table 1). Also, the Y-scrambling technique has been carried out on the training set in QSARINS software for each selected QSAR/QSPR model, and results confirmed the validity of each model. As external validation, it is also shown that γ_H2^∞_O in ILs of validation set predicted with enough accuracy based on the obtained values of AAD and RMSE. In the LOIO–CV method (i.e., eq 16), the temperature dependency of many validation-set’s ILs has been predicted well at each triple-region. Such good consistency had not been observed in the literature.^1,63

First, it should be mentioned that the obtained values of statistical parameters of this study were much better than those values which were reported for the test set by Gonfa et al.¹ For example, the (R² and AARD %) parameters of this study (i.e., eq 16) for the same test set [see Supporting Information Excel file (see Sheet S8)] which was previously¹ specified, were obtained (0.97, 26). This enhancement can be attributed to two important points: (1) the selection of most important molecular descriptors and (2) diversity of cation and anion structures in the data set. It seemed that these two points were neglected by Gonfa et al.¹ Another advantage of the proposed models in this study in comparison with Gonfa’s model is the wider AD. The more structural variations of cation and anion in the training set, the more AD. In other words, the developed QSAR/QSPR models in this study are more reliable than former models for the screening of ILs for systems containing H₂O. Apart from the above advantages, the proposed QSAR/QSPR models in this study have completely solved the issue in the previous model (i.e., the positive coefficient of 1/T) in Gonfa’s study. As can be seen in eqs 16 and 17, the adjustable parameter of 1/T (in van’t Hoff equation) in each model varies with respect to the structure and nature of cations and anions and it is not a constant value. For this reason, the low region of γ_H2^∞_O was predicted excellent using eqs 16 and 17, unlike the Gonfa’s model. For instance, the values of γ_H2^∞_O in some ILs (i.e., [C4C1Im][TFA] and [C1C1Im][DMP]) in a wide range of temperatures have been increasingly predicted using eqs 16 and 17 with increasing temperature, while the proposed model by Gonfa et al.¹ has decreasingly predicted them which were completely inverse with experimental results.

In comparison with Benimam et al.,⁶³ it should be mentioned that they took advantage of some powerful nonlinear methods which are complicated for general use. In contrast, the developed MLR-QSPR models in our study are much easier. The model by Beniman et al.⁶³ was examined only for imidazolium-based ILs, while our developed models were examined for many kinds of ILs. This point varies the extensive AD of our predictive models.

Therefore, the proposed QSAR/QSPR models (i.e., eqs 16 and 17) could take into account the effect of temperature on the γ_H2^∞_O in more than 95% of ILs (the included ILs in Table 1) well and satisfactorily. However, for some limited ILs like [C6C1Im][SCN], the capability of models (i.e., eqs 16 and 17) was not satisfactory. For example, the temperature dependence of γ_H2^∞_O in this IL was not correct. Such conflict was observed also by Thangarajoo et al.³ For example, the values of γ^∞_MeOH in [HydEMIM][FAP] were experimentally increasing with increasing temperature, while the developed model using GCM by Thangarajoo et al.³ predicted the opposite.

The plots of predicted versus experimental values for both of training and validation sets, which were obtained using QSAR/QSPR models (i.e., eqs 16 and 17), are shown in Figure 3.

Figure 3.

Predicted versus experimental values (ln-based) for both of training and validation sets using eqs 16 and 17.

The Williams plots for the training and validation sets which were obtained using QSAR/QSPR models (i.e., eqs 16 and 17) are shown in Figure 4. According to these plots, except of three data points which seem to be outliers, the values of SRD for some data points are higher than ±3, but their leverage values are lower than h* which mean no outliers are in the data set.

Figure 4.

Williams plots for training and validation sets using eqs 16 and 17.

As the temperature dependency of γ_H2^∞_O in ILs can be expressed by physicochemical properties (i.e., ΔH^E,∞_IL and ΔS^E,∞_IL), it may be interesting to look at these predicted properties separately. Although these values are determined indirectly from the temperature dependency of γ_H2^∞_O, they may reveal interesting further structure–property relationships. These two properties for each studied IL in Table 1 have been calculated using descriptors in “A” and “B” parameters and have been reported in Table 5. More details can be found in the Supporting Information Excel file (see Sheet S9).

Table 5. Calculated Partial Molar Excess Enthalpy (i.e., ΔH^E,∞_IL) and Entropy (i.e., ΔS^E,∞_IL) of Each IL at Infinite Dilution Using Molecular Descriptors in “A” and “B” Parameters of van’t Hoff Equation.

mixture IL/H2O	temperature range (K)	range of ln (γH2∞OExp)	ΔHE,∞IL(J·(mol)−1)	ΔSE,∞IL(J·(K·mol)−1)
[C4C1Im][SCN]	328–368	(−1.298) – (−1.269)	–638.42	5.32
[C4–3-C1Py][CF3SO3]	318–358	(−0.116) – (−0.267)	667.88	4.57
[C4C1Pyrro][FAP]	318–368	(2.236) – (1.350)	8130.46	10.05
[C3C1Pip][NTF2]	308–358	(1.488) – (0.896)	10460.40	22.69
[HOC3Py][FAP]	308–358	(0.974) – (0.548)	6046.38	10.44
[C4C1Im][TFA]	333–393	(−1.851) – (−1.639)	6046.38	10.44
[C2C1Im][SCN]	328–368	(−1.298) – (−1.269)	–6402.96	–4.02
[C4C1Pip][SCN]	328–368	(−1.105) – (−1.064)	–642.39	5.56
[C4–4-C1Py][SCN]	328–368	(−1.187) – (−1.155)	–481.46	5.31
[C4C1Pyrro][SCN]	328–368	(−1.335) – (−1.269)	–743.70	5.18
[C6C1Im][SCN]	328–368	(−0.572) – (−0.623)	–475.03	5.42
[C6-iqui][SCN]	328–368	(−0.913) – (−0.872)	–627.75	4.81
[C4C1Mor][C(CN)3]	318–368	(0.029) – (−0.248)	–657.04	4.26
[C4C1Pyrro][C(CN)3]	318–368	(−0.027) – (−0.261)	3780.99	13.47
[C4C1Pyrro][B(CN)4]	318–368	(0.765) – (0.246)	4460.35	13.33
[C10C1Im][B(CN)4]	328–378	(0.751) – (0.300)	8595.49	21.32
[C2C1Im][B(CN)4]	298–358	(0.806) – (0.254)	8443.44	19.56
[C6C1Im][B(CN)4]	318–368	(0.717) – (0.285)	8428.13	21.46
[C4C1Pyrro][CF3SO3]	318–368	(−0.145) – (−0.339)	8442.78	20.71
[C4C1Im][CF3SO3]	328–368	(−0.212) – (−0.362)	966.03	4.78
[C2C1Im][TFA]	348–368	(−1.944) – (−1.838)	802.64	4.68
[C6OC1C1Im][NTF2]	298–358	(1.474) – (0.712)	–6406.92	–3.77
[(C6OCH2)2Im][NTF2]	298–368	(1.488) – (0.593)	10058.68	21.84
[C4–4-C1Py][NTF2]	298–368	(1.581) – (0.717)	9763.95	20.66
[N1112OH][NTF2]	318–368	(0.270) – (−0.069)	10210.83	22.40
[C8iquin][NTF2]	328–368	(1.398) – (0.838)	7813.72	23.27
[C4C1Pip][NTF2]	308–358	(1.566) – (0.879)	10473.06	22.52
[S222][NTF2]	308–368	(1.363) – (0.631)	10178.70	22.46
[C1C1Im][NTF2]	303–333	(1.050) – (0.698)	10265.26	23.10
[C2C1Im][NTF2]	293–323	(1.302) – (0.932)	10312.13	22.78
[C2Py][NTF2]	303–323	(1.022) – (0.693)	9957.94	22.84
[HOC3Py][NTF2]	318–378	(0.425) – (0.029)	8395.42	23.03
[COC2C1Pip][NTF2]	318–368	(1.208) – (0.625)	10367.70	22.74
[COC2C1Mor][NTF2]	318–368	(0.912) – (0.343)	9832.35	23.01
[COC2C1Pyrro][NTF2]	318–368	(1.147) – (0.615)	10349.27	22.86
[C5C1Pip][NTF2]	308–358	(1.619) – (0.892)	10470.42	22.32
[C6C1Pip][NTF2]	308–358	(1.669) – (0.896)	10484.03	22.06
[C4–4-C1Py][N(CN)2]	338–368	(−1.224) – (−1.158)	–2762.59	–1.23
[COC2C1Mor][FAP]	318–368	(1.547) – (1.101)	7483.32	10.43
[COC2C1Pip][FAP]	318–368	(1.954) – (1.308)	8018.66	10.15
[COC2C1Pyrro][FAP]	318–368	(2.086) – (1.371)	8000.23	10.28
[HOC2C1Im][FAP]	318–368	(0.797) – (0.570)	5809.05	10.37
[C1C1Im][DMP]	363–383	(−2.960) – (−2.856)	–9679.53	–2.11
[C4C1Im][Br]	333–393	(−2.631) – (−2.017)	–17394.13	–28.59
[C2C1Im][MeSO3]	318–358	(−2.645) – (−2.430)	–10297.05	–10.80
[C2C1Im][C(CN)3]	318–368	(−0.080) – (−0.153)	4292.99	13.47
[C2C1Im][FAP]	318–368	(1.906) – (1.425)	7963.10	10.19
[HOC2C1Im][N(CN)2]	328–358	(−0.946) – (−0.991)	–4815.33	–0.67
[C4C1Im][Ac]	298–393	(−4.342) – (−3.194)	–10035.54	1.80
[C4C1Im][C(CN)3]	318–368	(0.019) – (−0.164)	4296.96	13.22
[C4C1Im][Cl]	333–428	(−3.324) – (−2.364)	–8171.56	1.73
[C4C1Im][N(CN)2]	318–368	(−1.171) – (−0.978)	–2657.32	–1.10
[C4C1Im][NTF2]	293–363	(1.373) – (0.688)	10316.10	22.53
[C4C1Im][DMP]	333–428	(−3.381) – (−2.292)	–9628.69	–2.68
[C4C1Im][MeSO3]	333–428	(−2.120) – (−1.431)	–10293.08	–11.05
[C6C1Im][CF3SO3]	303–333	(0.270) – (−0.446)	813.32	4.17
[B Cya Py][NTF2]	308–368	(1.196) – (0.693)	10172.84	22.71
[C12C1Im][NTF2]	318–368	(1.501) – (1.022)	10334.24	20.30
[C4C1Py][C(CN)3]	318–368	(−0.029) – (−0.228)	4191.69	13.09
[4OHC3 4-C1Mor][NTF2]	318–368	(0.357) – (0.095)	8397.84	23.15
[C8Quin][NTF2]	313–353	(1.071) – (0.350)	10634.38	21.47
[C6Quin][NTF2]	313–353	(1.446) – (1.098)	10627.95	22.04
[P4442][DEP]	328–368	(−2.292) – (−2.154)	–8271.31	–3.62
[C8C1Im][NTF2]	303–333	(1.358) – (0.947)	10302.30	21.46
[C2C1Im][C8SO4]	333–358	(−1.832) – (−1.897)	–6116.82	–2.60
[C2C1Mor][N(CN)2]	318–368	(−1.127) – (−0.941)	–3166.68	–0.59
[HOC3Py][N(CN)2]	328–358	(−0.918) – (−0.839)	–4578.00	–0.60
[OHC3–C1Im][N(CN)2]	318–368	(−1.049) – (−0.891)	–3928.65	–0.68

Based on the proposed QSAR/QSPR models, a large list including values of ln γ_H2^∞_O-Pseudo-Exp in large numbers of none-studied ILs at different temperatures has been provided in the Supporting Information Excel file (see Sheet S10). Also, to ease and facilitate the IL-screening for those systems including H₂O, separate heatmaps have been provided for two different temperatures, as shown in Figure 5. According to these heatmaps, the ILs with highest and lowest affinities to H₂O can be found. As can be seen in Figure 5, anions have a much larger effect than the cations. For example, when anion is constant, the color bands are very similar independent of the cation.

Figure 5.

Predicted ln γ_H2^∞_O values by the QSPR-model eq 16 at (a) 298 K and (b) 368 K.

4. Conclusions

The developed QSAR/QSPR models could successfully predict γ_H2^∞_O in ILs as a function of temperature. The versatility of the models is displayed by the ability to predict the effect of temperature both the increase and decrease of the γ_H2^∞_O which is determined by the structure of the IL. The present models succeed to predict the temperature dependency of γ_H2^∞_O for new ILs.

In this study, the γ_H2^∞_O in large data set of ILs has been predicted with a very good accuracy using QSPR-based COSMO-RS descriptors. The obtained values of statistical parameters (RMSE, AAD, R², and Q²_LOO–CV) of the developed QSPR model were acceptable for either training or validation set. The obtained values of the RMSE parameter were 0.1378 and 0.3344 for training and validation sets, respectively, expressing the high prediction capability of the QSPR model for the studied data set. The internal and LOIO–CV-external validations verified that the prediction of γ_H2^∞_O in a huge number of ILs which had not been experimentally studied can be practical with respect to the leverage value of ILs and AD of the QSPR model.

Data Availability Statement

The used experimental data for the training of the QSPR models can be found in the Supporting Information Excel file. In this study, the sigma-profile descriptors were taken from COSMO-RS software and model development has been performed in QSARINS free-software.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jcim.4c02095.

• Three regions, cation and anion matrix, data points of data set, results, training and validation sets, Gonfa’s test set, thermodynamic properties, pseudo-experimental data, and nomenclature of cations and anions and smile files (XLSX)

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. The authors contributions are given as follows: A.E.G.: writing—review and editing, writing—original draft, visualization, validation, software, methodology, investigation, formal analysis, data curation, and conceptualization. J.P.L.: writing—review, editing, and visualization. P.U.-K.: writing—review and editing, resources, and project administration. V.A.: writing—review and editing, supervision, resources, and project administration.

This work was finically supported by the Academy of Finland “In situ equilibrium shifting in CO₂ utilization reactions by novel absorbents (CO2Shift)” Project (351113).

The authors declare no competing financial interest.