Novel molecular descriptors for prediction of H2S solubility in ionic liquids
Introduction
The electrostatic potential [[1], [2], [3]] V(r) is produced at the point r around a molecule, via its nuclear and electrons, i.e. it is calculated by the static distribution of a molecule. The molecular electrostatic potential is rigorously expressed by Eq. (1).where ZA denotes the charge of the nuclear A, located at rA, |rA − r| stands for the distance between nucleus A and r, ρ(r) represents the electronic density function for molecule. As can be seen from Eq. (1), the electrostatic potential is composed of two parts, the contributions of the nuclei (positive) and electrons (negative), respectively. The electrostatic potential surface (SEP) of molecules, which means the molecular surface areas in the interval of different electrostatic potential, can show the rich information at electron level and therefore it could be expected to use them as descriptors to precisely predict properties of materials under investigation.
Benefiting from the excellent properties (e.g. high thermal stability, high solubility, low melting point, generally negligible flammability and almost null volatility) [[4], [5], [6], [7]], ionic liquids (ILs) have gained great attentions due to their versatile applications, ranging from chemical industries [8, 9], such as reaction media in organic synthesis, catalysis, controlled processing of polymer materials [10], extraction processes [11], and broad range of electrolytes in electrochemical sector [12]. Owning to their nonvolatility and excellent capacity, ILs have also been employed to capture poisonous acid gases [[13], [14], [15], [16], [17], [18], [19], [20]] as an environment-friendly absorptive solvents by many researchers. Particularly, ILs have been successfully used to absorb toxic hydrogen sulfide (H2S) gas since early 2007 [21, 22]. However, due to the tremendous number of existing and potential ILs (vastly numerous combinations of existing cations and anions), the time-consuming and hazardous during experimental measurements is out of question, and there is a very urgent need to construct efficiently predictive models to predict the H2S solubility in ILs.
Some predictive models have been established for calculating the H2S solubility in ILs by applying the intelligence algorithms [[23], [24], [25], [26]], equation of state (EOS) [27, 28], and conductor-like screening model for real solvents (COSMO-RS) method [29]. Among them, the predictive models using the intelligent algorithm show stronger capabilities to offer better precision. Ahmadi and his co-workers [23] employed temperature (T), pressure (P), critical temperature (Tc), critical pressure (Pc), and acentric factor (ω) of ILs as input parameters to build artificial neural network (ANN) models, meanwhile, they also utilized the same input parameters to construct the gene-expression programming (GEP) and least-squares support vector machine (LSSVM) models [24, 25] for predicting the H2S solubility in ILs, and obtained comparatively better outcomes. In our previous study [30], temperature (T) and pressure (P) combining with the number of groups for each IL were used as input parameters to develop the predictive models by extreme learning machine (ELM) approach, however; the shortcomings of these models are that groups are not sufficiently rich in molecular information and their isomeric molecules cannot be effectively identified. Compared with the algorithm, molecular descriptors have greater influence on the precision of the model. Therefore, we intend to propose new kinds of molecular descriptors (SEP) which have abundant information at electron level to build models for the prediction of H2S solubility in ILs.
In the present study, at first, we optimized the structures of individual cations, anions and ion pairs, which was followed by calculation of their SEP values. Based on the obtained molecular descriptors, two novel predictive models for the H2S solubility in ILs were developed using the SEP, temperature, and pressure as the input parameters. At last, the proposed models were compared with the previous models obtained from the literature.
Section snippets
Data preparation
In order to establish the models to calculate the H2S solubility in ILs, 1318 data points in 28 various ILs, including 7 cations and 12 anions, were collected from 15 references. The type of ILs used, number of data points, H2S solubility values, as well as pressure and temperature range and the corresponding references, are listed in Table 1. The experimental dataset for the model establishment was randomly divided into training subset including 1055 data points and test subset containing 263
Extreme learning machine (ELM)
ELM, which is a single-hidden layer feedforward neural networks (SLFNs) learning algorithm, was firstly proposed by Huang et al. in 2004 [46] aiming to make the calculations valid, simple and efficient. Traditional neural network learning algorithms (such as BP algorithm) have to set manually a large number of network training parameters and easily produce local optimal solutions. In contrast, the ELM only needs the number of hidden nodes in the network to obtain the optimal solution. Thus, the
Qualitative analysis of the H2S solubility in ILs
To qualitatively analyze the effect of isolated anions and cations of ILs, a simple model was established based on the collected 1318 data points of 28 ILs including 7 cations and 12 anions. The vital descriptors for the H2S solubility in ILs were screened from SEP parameters of isolated cations and anions combined with temperature and pressure by using stepwise regression linear algorithm. Finally, 10 parameters were selected as the linear model input parameters, as shown in Eq. (7):
Conclusion
In this study, the SEP descriptors were proposed to predict the H2S solubility in ILs. 1318 data points of H2S solubility in 28 ILs with different ranges of temperature and pressure were collected from literature. The crucial parameters involving the pressure, temperature as well as several SEP descriptors were screened via stepwise regression approach. Two novel ELM models (ELM1 and ELM2) were built based on screened parameters and both exhibited excellent accuracy and stability to precisely
Acknowledgement
We are grateful for the financial support provided by the China Postdoctoral Science Foundation (2017M621477, 2017M621476).
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The authors contributed equally.