Predicting H₂S solubility in ionic liquids by the quantitative structure–property relationship method using S_σ-profile molecular descriptors

Abstract

Predicting hydrogen sulfide (H₂S) solubility in ionic liquids (ILs) is vital for industrial gas desulphurization. In this work, the qualitative analysis of the influence of cations and anions on the H₂S solubility in ILs has been conducted. The results indicate that anions play an important role in determining the H₂S solubility in ILs. Subsequently, two novel quantitative structure–property relationship (QSPR) models are developed based on charge distribution area (S_σ-profile) descriptors and an extreme learning machine (ELM) algorithm. To develop the QSPR models, a total of 1282 pieces of data belonging to 27 ILs are employed to validate the models. The average absolute relative deviation (AARD%) and coefficient of determination (R²) of the two QSPR models of the entire data set are 3.73% and 0.998, as well as 3.80% and 0.997, respectively. These results suggest that the proposed QSPR models can be useful for the prediction of H₂S solubility in ILs.

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1. Introduction

Ionic liquids (ILs) are gaining more and more attention in the field of gas absorption and separation because of their unique properties, such as negligible vapour pressure, high solubility as well as separation capacity, tunable properties and so on.^1–7 Consequently, ILs have been extensively used in absorbing and separating gases e.g. CO₂,^8–11 NH₃,¹² SO₂ ¹³ and so on. Unlike CO₂ which has been widely studied using ILs as absorbents, using ILs to absorb hydrogen sulfide (H₂S) only started in 2007 to the best of our knowledge.^14,15 H₂S, as a kind of toxic and caustic gas, must be removed from natural gas, synthesis gas, refinery gas, and hydrodesulphurization processes of crude oils.¹⁶ Although alkanolamine absorbents (e.g. monoethanolamine, diethanolamine, and methyldiethanolamine) are the commercial absorbents at present, they have some disadvantages, for example, high economic cost, high energy consumption, and caustic byproducts.¹⁷ Therefore, to circumvent the above mentioned problems, ILs have been used as the solvents to absorb H₂S in the recent years. However, there are so many possible ILs can be synthesized in the lab due to their tunable property, and thus it is impossible to synthesize and measure the H₂S solubility in all possible ILs through experimental techniques.^18,19 Therefore, from the practical point of view, it is imperative to establish the predictive model for overcoming the shortcomings such as experimentally time consuming and expensive.

For the past few years, some models have been developed to predict the H₂S solubility in ILs using the conductor-like screening model for real solvents (COSMO-RS) method,²⁰ equation of state (EOS) and intelligence algorithms.^21–24 The COSMO-RS method was proposed by Klamt and co-workers,^25–28 which is a novel and an a priori predictive method. In contrast with other typical methods, the COSMO-RS only needs molecular structure as the input information and is independent of experimental data. However, from the quantitative point of view, this method often not sufficient to accurately predict the solubility of gases in ILs (summarized by Lei et al.²⁰). For example, the average absolute relative deviation (AARD%) of H₂S solubility in ILs is 38.64% and 38.14% for two different software versions (ADF combi2005 and ADF combi1998), respectively.²⁰ Recently, as described by Ahmadi et al.,²¹ a set of specific parameters of the EOS models need to be fitted with experimental data, and these parameters are exclusively valid for a special systems but not suitable for others. Therefore, they employed artificial neural network (ANN) using the back propagation (BP) and particle swarm optimization (PSO) to build the model. The mean squared error (MSE) of the models is 0.00335 and 0.00025, respectively. Ahmadi et al.^22,23 and Rahimpour et al.²⁴ also established some models using intelligence algorithms including least square support vector machine (LSSVM), gene-expression programming (GEP), and ANN, respectively. The results are all more accurate than the EOS models. However, there are two aspects of the above mentioned studies that need to be improved. The first one is the experimental input parameters should be replaced with molecular structure information, which makes the new model being independent of experimental data. The second one is that the intelligence algorithms such as ANN and SVM should be substituted with more effective algorithm. Extreme learning machine (ELM) is a relatively new intelligence algorithm and was proposed by Huang et al.^29–31 It can tend to reach a global optimum, and usually has faster speed than ANN and SVM. Therefore, the ELM algorithm is employed to predict the H₂S solubility in ILs in this work.

New input parameter, namely, charge distribution area (S_σ-profile) which is calculated by the conductor-like screening model (COSMO), has been proved to be an effective descriptor (input parameter) for the quantitative structure–activity relationship (QSPR) model. S_σ-profile is an a priori quantum chemical descriptor, which can represent rich information such as electronic structure and molecular size of ILs. Several studies have successfully used S_σ-profile descriptor for predicting different properties of ILs, such as toxicity,³² density,³³ viscosity,³⁴ and heat capacity.³⁵ Therefore, S_σ-profile will be employed as input parameter for establishing the QSPR model in this study.

This work aims to establish new QSPR models using the S_σ-profile descriptors and the ELM algorithm. Firstly, the qualitative analysis of the influence of the cations and anions on the H₂S solubility in ILs has been performed. Subsequently, the S_σ-profile descriptors of 27 kinds of ILs are calculated by the quantum chemistry method. Thirdly, two QSPR models have been developed using the ELM algorithm based on the S_σ-profile descriptors. At last, the comparison of the two established QSPR models and previous studies was conducted in detail.

2. Methodology

2.1. Data set and molecular structures

The data set including 1282 pieces of data points belonging to 27 ILs was obtained from open ref. 14–17 and 36–46. As depicted in Fig. 1, the 27 kinds of ILs mainly based on cations including 1-(2-hydroxyethyl)-3-methyl-imidazolium ([HEMIM]), methyldiethanolammonium (MEDAH), dimethylethanolammonium (DMEAH), 1-butyl-3-methyl-imidazolium ([BMIM]), 1-octyl-3-methyl-imidazolium ([OMIM]), 1-ethyl-3-methyl-imidazolium ([EMIM]), 1-hexyl-3-methyl-imidazolium ([HMIM]), and different anions including methylsulfate ([MeSO₄]), bis(trifluoromethylsulfonyl)amide ([Tf₂N]), acetate (OAc), propionate (Pro), tetrafluoroborate ([BF₄]), formate (For), hexafluorophosphate ([PF₆]), tris(pentafluoroethyl)trifluorophosphate (TPTP), ethylsulfate ([EtSO₄]), trifluoromethanesulfonate ([TfO]), bromide (Br) and lactate (Lac). Similar with open literature^21,22,47 and our previous work,^18,34,35,48 the whole data set are divided into the training set (1026 data points) and test set (256 data points) in proportion of 80% to 20%. The more detailed information of all the data points can be seen form Table 1 and ESI.†

Fig. 1 Optimized ILs structures with COSMO surfaces in this study. Red part represents positive COSMO charge density, and the blue part represents negative COSMO charge density.

Table 1 Temperature, pressure, and H₂S solubility range as well as AARD% of the used ILs in this study

No. of ILs	ILs	T range (K)	P range (bar)	H2S solubility range (mole fraction)	No. of data points	AARD^a%	AARD^b%	Ref.
a QSPR1 model.b QSPR2 model.
1	[BMIM][PF6]	298.15–403.15	0.69–96.30	0.016–0.875	39	2.88	4.78	14
		303.15–333.15	1.23–10.11	0.044–0.405	42	3.03	3.08	17
2	[BMIM][EtSO4]	303.15–353.15	1.14–12.70	0.012–0.118	36	3.26	3.53	37
3	[BMIM][MeSO4]	298.10	0.11–7.51	0.022–0.521	8	3.25	5.04	40
4	[BMIM][BF4]	303.15–343.15	0.61–8.36	0.03–0.354	42	2.64	1.97	17
5	[BMIM][Tf2N]	303.15–343.15	0.94–9.16	0.051–0.51	44	1.27	1.50	17
6	[EMIM][Tf2N]	303.15–353.15	1.08–16.86	0.049–0.609	42	0.64	1.04	38
7	[EMIM][PF6]	333.15–363.15	1.45–19.33	0.032–0.359	40	2.43	1.92	38
8	[OMIM][Tf2N]	303.15–353.15	0.94–19.12	0.063–0.7355	47	1.51	0.99	42
9	[OMIM][PF6]	303.15–353.15	0.85–19.58	0.0463–0.6972	48	1.32	1.19	45
10	[HMIM][Tf2N]	303.15–353.15	0.69–20.17	0.0368–0.7012	57	6.16	6.11	42
		303.15–343.15	0.97–10.50	0.029–0.533	30	17.51	17.58	16
11	[HMIM][BF4]	303.15–343.15	1.11–11.0	0.06–0.499	33	1.77	1.21	16
12	[HMIM][PF6]	303.15–343.15	1.38–10.9	0.05–0.441	34	1.24	1.15	16
13	[HEMIM][BF4]	303.15–353.15	1.21–10.66	0.02–0.247	51	1.36	2.80	41
14	[HEMIM][PF6]	303.15–353.15	1.34–16.85	0.0347–0.4627	47	2.15	1.36	39
15	[HEMIM][Tf2N]	303.15–353.15	1.56–18.32	0.0576–0.5724	41	1.33	1.69	39
16	[HEMIM][TfO]	303.15–353.15	1.06–18.39	0.0357–0.5483	41	1.94	1.52	39
17	[EMIM][OAc]	293.15–333.15	0.014–3.248	0.0917–0.5103	64	5.96	5.94	43
18	[EMIM][Pro]	293.15–333.15	0.011–3.239	0.1206–0.5897	62	7.27	7.67	43
19	[EMIM][Lac]	293.15–333.15	0.044–3.216	0.0759–0.4898	57	2.54	2.29	43
20	[BMIM][OAc]	293.15–333.15	0.001–3.415	0.0740–0.5790	69	11.06	10.98	43
21	[HMIM][OAc]	293.15–333.15	0.003–3.309	0.0900–0.6094	66	7.04	7.01	43
22	[EMIM][TPTP]	303.15–353.15	0.582–19.415	0.0220–0.5926	79	1.52	1.45	44
23	[BMIM][Br]	299.15	1	0.03	1	0	0	46
24	[MEDAH][OAc]	303.2–333.2	0.097–1.396	0.0095–0.1618	35	0.93	1.99	36
25	[MEDAH][For]	303.2–333.2	0.079–1.242	0.0061–0.0807	33	2.53	5.51	36
26	[DMEAH][OAc]	303.2–333.2	0.031–1.111	0.0104–0.2085	53	2.23	1.34	36
27	[DMEAH][For]	303.2–333.2	0.058–1.153	0.0065–0.1189	41	3.14	2.01	36

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All geometric optimizations of independent cations and anions of ILs were performed at the B3LYP/6-31++G** theoretical level in the ideal gas phase using the quantum-chemical Gaussian 09 B.01 version.⁴⁹ Vibrational frequencies were calculated for each structure to ensure no negative frequency and confirm the existence of an energy minimum.

2.2. Calculation of the S_σ-profile descriptors

The COSMO files of cations and anions of ILs were calculated by the Gaussian 03 ⁵⁰ package using the BVP86/TZVP/DGA1 level of theory. Optimized 27 ILs structures with COSMO surfaces were shown in Fig. 1. The red part represents positive COSMO charge density as well as the blue part represents negative charge density. Moreover, the darker the color (blue and red), means the stronger the polarity of the ILs. In order to obtain σ-profile, the 3D COSMO surfaces should be converted into a 2D surface composition function using the COSMOtherm program.⁵¹ After the σ-profile was obtained, one can quantify the relative number of surface P^x(σ) with polarity σ. In this study, considering the computational cost and simplicity, the ILs were treated in two forms. The first is in the form of independent counterions, and the second is in the form of single σ-profile (simply combined the cation and anion into one single IL). As shown in Fig. 2(a) and (b), the σ-profiles of independent counterions (cations and anions) were both divided into 5 different regions respectively (S_C/1–5 and S_A/1–5, subscripts C and A mean cations and anions respectively) by integrating those segments over the σ, and thus there are 10 descriptors altogether. As depicted in Fig. 2(c), there are 6 descriptors (S_1–6) of the single σ-profile of the combined ILs.

Fig. 2 Solvent theoretical descriptors defined by COSMO σ-profile areas (σ-profile of representative cation [DMEAH] (a) and anion (b) [Lac] and ionic liquid [DMEAH][Lac] (c) are used for illustration) in this study.

2.3. Extreme learning machine (ELM) algorithm

ELM algorithm is one of the most popular algorithms, which was first proposed by Huang et al.^29–31 The important features of ELM are that the weights and biases between input layer and hidden layer are randomly assigned and there is no bias between the hidden layer and output layer. These characteristics endow ELM with several excellent advantages: (1) the ELM is simpler than many algorithms such as ANN and SVM; (2) the learning speed is fairly fast; (3) the ELM has very good generalization ability; (4) the ELM works for all bounded nonconstant piecewise continuous activation functions; (5) the ELM can tend to reach the solutions straightforward compared traditional learning algorithms. Because the advantages mentioned above, the ELM has been extensively applied in many fields.²⁹ The more detailed introduction of ELM can be found elsewhere.^29–31

As can be seen from Fig. 3, the ELM structure in this study is made of three parts, which are the input, hidden, and output layers. The input parameters of input layer include temperature (T), pressure (P), and several S_σ-profile descriptors, and the output is the H₂S solubility in ILs (mole fraction). The functions of f₁ and f₂ are the activation function and linear function respectively. As mentioned above, the biases and weights (w) between input and output layers are randomly generated, and thus, the weights (β) between hidden and output layers are the only parameters need to be learned. At last, the ELM model boils down to solving a linear system.

Fig. 3 ELM network structure in this study for the prediction of H₂S solubility in ILs.

2.4. Model validation and performance

To evaluate the effectiveness of the established ELM models, different statistical parameters were employed, namely, coefficient of determination (R²), relative deviation (RD%), AARD%, MSE, and root-mean-square error (RMSE). These statistical parameters are given as below:

RD (%) = 100 × (y^cal_i/y^exp_i − 1.0) (2)

In which N_P is the total number of the whole data set, y and ȳ_m denote the experimental H₂S solubility in ILs and the average of the experimental data, and superscript “exp” and “cal” represent the experimental value and predicted value, respectively.

3. Results and discussion

3.1. Qualitative analysis of the H₂S solubility in ILs

As shown in Fig. 4, when the cation is same (e.g. [Bmim]), the anions embodied the following order, [EtSO₄]⁻ < [PF₆]⁻ < [BF₄]⁻ < [Tf₂N]⁻ < [OAc]⁻.^14,17,37,43 It is obvious that the [OAc]⁻ shows higher H₂S solubility than other anions. The reason maybe that the [OAc]⁻ has strong hydrogen-bond basicity,⁵² and thus can act as hydrogen-bond acceptor and form hydrogen-bond with H₂S. As shown in Fig. 5, when the anion of ILs is kept as [OAc]⁻, the longer the alkyl chain the larger the H₂S solubility in ILs ([HMIM]⁺ > [BMIM]⁺ > [EMIM]⁺).⁴³ This situation may be explained that the ILs with long alkyl chain may have large free volume and strong van der Waals interaction compared with the ILs with short alkyl chain.

Fig. 4 H₂S solubility in ILs with different anions at 313.15 K.

Fig. 5 H₂S solubility in ILs with different cations at 313.15 K.

In order to inspect the importance of the descriptors, multiple linear regression (MLR) was used to build a simple linear model using the enter method (eqn (6)).

y = 0.017P − 0.003T + 14.463S_A5 + 1.335S_A3 − 341.251S_C1 + 32.644S_C4 + 2.452S_A4 − 19.744S_C3 + 2931.616S_A1 − 66.287S_C2 − 2.146S_A2 + 5.576 (6)

(n = 1026, R² = 0.716, AARD% = 123.1%)

where y is the H₂S solubility in ILs, P is pressure, T is temperature, S is charge distribution area, and subscripts C and A mean cations and anions respectively. In eqn (6), the plus and minus before the descriptors represents positive and negative correlation, respectively. Moreover, the important of descriptors sort in descending order according to the t value, and thus, the most important descriptors is the headmost one. Hereby, two of the most important descriptors are P and T, and the plus and minus sign in front of them indicate that the H₂S solubility in ILs increases with the increase of the P and the decrease of the T. Besides of the P and T, two of the most important molecular structure descriptors are the S_A5 and S_A3 which belong to anions. This indicates that anions play more important role than cations, and the H₂S solubility in ILs will increase with the increase of the S_A5 and S_A3. In addition, the descriptor S_A5 belongs to the strong hydrogen-bond basicity anions, namely, [OAc]⁻, [Pro]⁻, [For]⁻, and [Lac]⁻. These results are consistent with the aforementioned speculation, that is, strong hydrogen-bond basicity anions will form strong hydrogen-bond, and thus, will have high H₂S solubility. Although eqn (6) can give qualitative rules, the predictive results are poor from the quantitative point of view. The AARD% of the training set and whole data set are 123.1% and 122.4% respectively, which indicates that the H₂S solubility in ILs not only just follows a simple linear rule. Therefore, a nonlinear model is required to obtain accurate quantitative results.

3.2. Results of the ELM model based on independent counterions σ-profile

In this part, the training set and test set are in proportion of 80% to 20%. The input descriptors were the T, P, S_C1–5 of cations and S_A1–5 of anions, respectively. As mentioned above, the weights and biases between input and hidden layers were randomly assigned, and thus, we only need to confirm the f₁ function as well as the weights (β) between hidden and output layers. The f₁ function employed in this study was the sine function. After the f₁ function was confirmed, the only thing we need to do is to optimize the number of neurons between input and hidden layers and regress the β at the same time. As shown in Fig. 6, when the neurons exceeded 400, the AARD% of the test set began to increase and the R² of the test set began to decrease. Therefore, 400 were determined as the best number of neurons for the model (here called QSPR₁) in the hidden layer. As can be seen from Fig. 7, the calculated H₂S solubility values (dotted line) were close to the experimental H₂S solubility values (solid line), which indicates the QSPR₁ model has a satisfying results. As demonstrated in Fig. 8, 83.6% data points of the QSPR₁ model were estimated within 5% AARD%, and only 3.1% data points exceeded 20% AARD%. The detailed information for each of the ILs and data points can be found in Table 1 and ESI respectively.† As shown in Table 1, although most kinds of the ILs have good predictive results, [HMIM][Tf₂N] and [BMIM][OAc] have relative large deviations. The reason may be that the absorption mechanism of [BMIM][OAc] (chemical absorption) differs from most of other kinds of ILs (physical absorption). As for the [HMIM][Tf₂N], although the experimental data were collected from the same group' work, still there existed some errors between the two different references, which can be seen from Fig. 9. The experimental data of [HMIM][Tf₂N] in ref. 16 (large predictive deviations) obviously has lower H₂S solubility at a certain pressure such as ≈8 bar at 303.15 K and higher H₂S solubility at pressure > 8 bar than the ref. 42. Therefore, we can reasonably assume that the experimental data of [HMIM][Tf₂N] in ref. 16 perhaps not so accurate, and thus should be carefully treated. A summary of the statistical parameters for QSPR₁ was presented in Table 2, it was shown that the QSPR₁ model could predict the H₂S solubility in ILs with high accuracy and wide applicability by taking into account of the R², AARD%, MSE and RMSE. Moreover, the required time of QSPR₁ model having 400 neurons was only 1.5057 seconds on an Intel 2.93 GHz desktop computer with 2 GB of RAM.

Fig. 6 AARD% and R² of the QSPR₁ model versus the number of neurons for the training and test sets.

Fig. 7 Calculated versus experimental H₂S solubility in ILs of the QSPR₁ model.

Fig. 8 Percent of value in different deviation range of the QSPR₁ model. 44.1% of the H₂S solubilities in ILs are estimated within 0–1% (relative deviation range%); 39.5% within 1–5%, 8.4% within 5–10%, 3.2% within 10–15%, 1.7% within 15–20%, and 3.1% over 20%.

Fig. 9 H₂S solubility in [HMIM][Tf₂N] with different references.

Table 2 The statistical parameters for QSPR₁

Data set	No.	R^2	AARD%	MSE	RMSE
Training set	1026	0.999	3.32	1.03 × 10^−4	0.0101
Test set	256	0.996	5.35	3.91 × 10^−4	0.0198
Total set	1282	0.998	3.73	1.61 × 10^−4	0.0075

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3.3. Results of the ELM model based on single σ-profile

Based on the training set and test set used above, a new model (here called QSPR₂) was established using the S_1–6 (six descriptors), T and P as the input descriptors. The optimum number of neurons was 400, which was also obtained on the basis of R² and AARD%. As demonstrated in Fig. 10, the calculated values (dot line) overlay the experimental values (solid line) and close to each other very well. This means that, the QSPR₂ model using six structure descriptors can also estimate the H₂S solubility in various ILs at high precision. The detailed information for each of the ILs and data points can be found in Table 1 and ESI respectively.† From the Table 1, it can be seen that as with the QSPR₁ model, the two largest relative deviations of QSPR₂ model also belonged to the [HMIM][Tf₂N] and [BMIM][OAc] (17.58% and 10.98% respectively). The AARD% of the entire data set was shown in Fig. 11. It can be seen that, 83.9% data pints of the whole dataset were in the range of 5% deviations (AARD%), 7.6% were in the range of 5–10%, and only 3.3% were over than 20%. The statistical parameters for QSPR₂ including R², AARD%, MSE, and RMSE were listed in Table 3. In light of these results, the QSPR₂ model established in this study showed good ability to predict the H₂S solubility in ILs over wide temperature and pressure ranges. Moreover, the required time of QSPR₂ model having 400 neurons was only 1.3363 seconds on an Intel 2.93 GHz desktop computer with 2 GB of RAM.

Fig. 10 Calculated versus experimental H₂S solubility in ILs of the QSPR₂ model.

Fig. 11 Percent of value in different deviation range of the QSPR₂ model. 44.9% of the H₂S solubilities in ILs are estimated within 0–1% (relative deviation range%); 39.0% within 1–5%, 7.6% within 5–10%, 3.4% within 10–15%, 1.8% within 15–20%, and 3.3% over 20%.

Table 3 The statistical parameters for QSPR₂ model

Data set	No.	R^2	AARD%	MSE	RMSE
Training set	1026	0.999	3.37	1.04 × 10^−4	0.0102
Test set	256	0.989	5.55	1.00 × 10^−3	0.0316
Total set	1282	0.997	3.80	2.84 × 10^−4	0.0169

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3.4. Comparison between this work and previous studies

The above discussions have demonstrated the performance of the QSPR₁ and QSPR₂ models. For the sake of comparison, a comprehensive statistics of different models including the COSMO-RS (ADF combi2005 and ADF combi1998 versions), EOS (PR and SRK), intelligence algorithms (ANN, GEP and LSSVM) and QSPR was summarized in Table 4. In generally, the models developed by intelligence algorithms have higher accuracy (low AARD%) than the EOS and COSMO-RS, and the models established by ELM algorithm have better performance. The results indicated that the ELM algorithm can more comprehensively represent the nonlinear structure of this work (H₂S solubility in ILs) than other algorithms. Therefore, the QSPR models established in this study based on ELM algorithm and S_σ-profile descriptors could be suitable for predicting H₂S solubility in ILs over wide temperature and pressure ranges. The detailed deviation information for each of the ILs and data points can be found in Table 1 and ESI respectively.†

Table 4 The comparison of different models for H₂S solubility in ILs^a

Method	NP	NIL	AARD%	Reference
a NP is the number of parameters, NIL is the number of ILs.b Is that the interaction parameters (ki,j) is not considered.c Means that the ki,j is considered.d Means that the number should be 16.
ANN	465	11	4.58	21
PR EOS^b	465	11	38.95	22 and 23
SRK EOS^b	465	11	36.43	22 and 23
PR EOS^c	465	11	4.90	22 and 23
SRK EOS^c	465	11	4.87	22 and 23
LSSVM	465	11	2.28	22
GEP	465	11	4.38	23
PR EOS^b	664	14	196.76	24
PR EOS^c	664	14	8.35	24
Empirical model	664	14	5.03	24
ANN	664	14	2.07	24
COSMO-RS (ADF 2005)	722	15^d	38.64	20
COSMO-RS (ADF 1998)	722	15^d	38.14	20
QSPR1	1282	27	3.73	This work
QSPR2	1282	27	3.80	This work

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4. Conclusions

In this study, firstly, the qualitative analysis of the influence of cations and anions on the H₂S solubility in ILs has been made. In general, anions play more important role than cations, and strong hydrogen-bond basicity anions (such as [OAc]⁻) may form strong hydrogen-bond with H₂S and thus have higher H₂S solubility. Then, two new QSPR models were proposed to predict the H₂S solubility in ILs using the S_σ-profile descriptors and ELM algorithm. The two QSPR models (QSPR₁ and QSPR₂) both have high coefficient of determination (R² = 0.998 and 0.997 respectively) as well as low average absolute relative deviation (AARD% = 3.73% and 3.80% respectively). The statistics indicate that the two QSPR models both have good predictive performance and could be used for predicting H₂S solubility in ILs. Finally, the two QSPR models have been compared with other previous models, and the two QSPR models have better results. In the two QSPR models, the S_σ-profile descriptors can present more molecular microstructure information and also can be independent of experimental descriptors (used by other works). In addition, the required time of the two QSPR models was only 1.5057 and 1.3363 seconds on an Intel 2.93 GHz desktop computer with 2 GB of RAM. Therefore, the proposed two QSPR models could be suitable for predicting the H₂S solubility in ILs.

Acknowledgements

This work was financially supported by the National Basic Research Program of China (No. 2015CB251403), the National Natural Science Fund for Distinguished Young Scholars (No. 21425625), the key program of Beijing Municipal Natural Science Foundation (No. 2141003) and the National Natural Science Foundation of China (No. 21506219).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra15429h

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