Heat capacity prediction of ionic liquids based on quantum chemistry

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Heat Capacity Prediction of Ionic Liquids Based on Quantum Chemistry Descriptors Xuejing Kang,†,‡ Xinyan Liu,§ Jianqing Li,∥ Yongsheng Zhao,*,⊥ and Hongzhong Zhang*,†,‡ †

School of Material and Chemical Engineering, Zhengzhou University of Light Industry, Zhengzhou 450001, China Collaborative Innovation Center of Environmental Pollution Control and Ecological Restoration, Henan Province Zhengzhou 450001, China § Department of Chemical & Biochemical Engineering, Technical University of Denmark, DK 2800 Kgs. Lyngby, Denmark ∥ Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China ⊥ Department of Chemical Engineering, University of California, Santa Barbara, California 93106-5080, United States

Ind. Eng. Chem. Res. Downloaded from pubs.acs.org by UNIV OF WINNIPEG on 11/30/18. For personal use only.

‡

S Supporting Information *

ABSTRACT: Heat capacity is an important and fundamental physicochemical property of ionic liquids (ILs). Here, a new class of quantum chemical descriptor, namely electrostatic potential surface area (SEP) descriptor, is employed to predict the heat capacity of ILs. In this study, 2416 experimental data points (254.0−1805.7 J mol−1 K−1) covering a wide temperature range (223.1−663 K) were employed. Multiple linear regression (MLR) and extreme learning machine (ELM) are applied to establish the linear and nonlinear models based on the SEP descriptors, respectively. The obtained six-parameter models show good predictive performance. The R2 of the linear MLR model is 0.988 for the entire set, while the ELM model has a higher value of R2 = 0.999, indicating the robustness of the nonlinear model. The results suggest that the SEP descriptors are closely related to the heat capacity of ILs and can be potentially used to predict the properties of ILs.

1. INTRODUCTION Ionic Liquids (ILs) have been the focus of intense attention as solvents, catalysts, materials, etc.,1−6 owing to their superior and unique properties, such as negligible vapor pressure, high thermal and chemical stability, wide liquidus, high ionic conductivity, and large electrochemical window.7−12ILs are also considered as designable liquids because their properties can be tailored by appropriate combinations of ions (cations and anions). However, it is impractical to experimentally screen the ILs with desired properties due to their potentially large number of combinations. This spurred interest in computational methods to predict properties of ILs including quantitative structure−property relationships (QSPR), group contribution (GC), and artificial intelligence (AI)algorithms, etc.13 Among them, AI algorithms such as artificial neural network (ANN), support vector machine (SVM), extreme learning machine (ELM), etc. are receiving increasing attention.14−16 The heat capacity at constant pressure (Cp) is a subject of interest in terms of understanding the fundamental chemical and physical processes and is of significance in engineering applications being required in calculations of energy transfer and thermodynamics.17−19 However, experimental data on the Cp of ILs are still insufficient at present. Therefore, using © XXXX American Chemical Society

computational methods to predict the Cp of ILs is necessary. Recently, some of the above-mentioned AI algorithms have been employed for predicting the Cp of ILs. Valderrama et al.20 predicted the Cp of ILs using ANN algorithm and some input descriptors including mass ratio of cation/anion, mass connectivity index, and temperature. 477 data points for 31 ILs were employed to train the network and 65 data points for nine ILs were used to test the network. The average absolute relative deviation (AARD%) for the training set was 0.10%, and for the test set was 0.22%, respectively, indicating the good performance of the established ANN model. Sattari et al.21 developed a model based on genetic function approximation (GFA) algorithm to predict the Cp of ILs at atmospheric pressure. The entire data set (including 3726 data points of 82 ILs) was split into two subsets, namely, training set (with 80% of the data) and test set (with 20% of the data). The established model included 13 input descriptors with an overall AARD% of 1.70%. Zhao et al.22 employed multiple linear regression (MLR) and ELM algorithm as well as charge Received: Revised: Accepted: Published: A

August 2, 2018 November 13, 2018 November 16, 2018 November 16, 2018 DOI: 10.1021/acs.iecr.8b03668 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

defined by Bader.27,28 The representative SEP of methylsulfate anion and 1-octyl-3-methylimidazolium cation are shown in Figure 1. As can be seen from Figure 1, the darker colors, red

distribution area (Sσ‑profiles) molecular descriptors to predict the Cp of ILs. The AARD% of the whole data set (including 2416 data points) was 2.72% for MLR and 0.60% for ELM, and the R2 was 0.985 for MLR and 0.998 for ELM, respectively. The results indicated the established 6-parameter ELM model has better performance. These above studies have demonstrated the reliability of AI algorithms that can be successfully used to predict the Cp of ILs. Furthermore, compared with AI algorithms, many studies have shown that molecular descriptors have a more important influence on establishing model.23,24 The electrostatic potential consists of two components: the atomic charge and the electron density contribution. Molecular electrostatic potential surface (SEP) refers to the molecular surface areas in the different intervals of electrostatic potential, which has the ability to display abundant information at the electron level. Therefore, it can be potentially used to predict the Cp of ILs. In this study, we develop two novel models by employing MLR and ELM algorithms to predict the Cp of ILs based on the quantum chemistry descriptors: SEP. The characteristic descriptors which have an important impact on Cp of the cations and anions have been screened and selected. Also, the predicted qualities of the two established models have been compared with the previous work, which used the same data set, number of input parameters, and AI algorithm.

Figure 1. SEP of a representative cation and anion of ILs used in this study.

and blue represent the stronger polarity for anion and cation, respectively. The SEP descriptors for isolated ions are with the ranges of −150−0 kcal/mol for anions and 0−150 kcal/mol for cations (the step size is 0.5 kcal/mol), respectively. 2.3. Prediction Model. With respect to the predicted model, it is generally assumed that there is a linear relationship between the target value and the input molecular descriptors, and thus the MLR algorithm is widely used to predict the properties of compounds.29−31 However, the above assumption cannot apply well to complex nonlinear systems.21 Therefore, complex nonlinear AI tools such as ANN,32−34 SVM,35−37 etc. are used to solve the above problems, and almost all of them can be well solved. However, ANN and SVM algorithms have some disadvantages, such as long training time. Therefore, the ELM algorithm38−40 was first employed by Zhao et al. to predict the properties of ILs due to its high training efficiency.22,24,41 In this work, MLR and ELM algorithms were applied as tools to establish predictive models. As shown in Figure 2, the temperature (T), molecular weight (M), and SEP descriptors are the input parameters for the linear (MLR) and nonlinear (ELM) models, and the heat capacity was the target/output value.

2. MATERIALS AND METHODS 2.1. Materials. In this work, the Cp values of 46 ILs are collected from the previous work.22 A total of 2416 experimental data points (254.0−1805.7 J mol−1 K−1) covering a wide temperature range (223.1−663 K) were finally obtained as shown in Table 1. Consistent with the published study,22 Table 1. Temperature and Heat Capacity Data Points for Different Families of ILs22 no.

family

temperaturerange (K)

heat capacity (J mol−1 K−1)

data points

1 2 3 4

imidazolium pyridinium pyrrolidinium phosphonium

223.1−663 290−425.15 283.15−358.15 293−513.15

254.0−743.7 343−665 544.2−661.22 660.8−1805.7

2203 62 29 122

the entire data set was divided into two subsets: a training set including 80% of the data to train the model/network and a test set containing 20% of the data to verify the predictive power of the established model/network. The anion, cation, and IL names, Cp and temperature values for each data point, as well as the data set and literature to which the data point belongs, are provided in the Supporting Information (SI). 2.2. Molecular Descriptors. The SEP descriptors for molecules mean the surface areas in the interval of different electrostatic potential and have abundant information at electron level. Hence, they can be expected to be used as input parameters to predict the Cp of ILs. Before calculating the SEP descriptors, the structures of isolated cations and anions are optimized based on Gaussian 03 package25 using the DFT theory at the B3LYP/6-31++G** level. The energy and vibration frequency of isolated cations and anions were calculated to ensure that the local minimum energy points were obtained without imaginary frequency. Then, SEP descriptors are calculated using Multiwfn package26 based on van der Waals surface at the electron density of 0.001 e/Bohr3

Figure 2. Scheme of linear and nonlinear models programming methodology B

DOI: 10.1021/acs.iecr.8b03668 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

3. RESULTS AND DISCUSSION 3.1. Results of Linear Model. To establish the MLR model, stepwise regression method is employed to determine the optimal input descriptors for multilinear correlations (the “stepping criteria” F = 3.84 for input and F = 2.71 for removing is used). As shown in Figure 3, when the number of descriptors

Figure 4. Calculated versus experimental toxicity values of ILs by MLR in this study. Figure 3. R2 versus parameter number for training data set

model for both training and test sets. The relative deviations versus experimental data for the MLR model are represented in Figure 5. According to these figures, it can be concluded that

2

is greater than 8, theR of the model has no obvious improvement, and the error does not change significantly. The final 6-parameter model is presented in eq 1, where a, b, Ci, are the coefficients and P0 is the intercept of the model. The specific coefficients and descriptors of the model are provided in Table 2. 4

Cp = P0 + aM + bT +

∑ CiSEP − i

(1)

i=1

Table 2. Coefficients and the t Values for eq 1 parameter M T SEP‑C 56.75 SEP‑A−119.75 SEP‑A‑138.25 SEP‑C 58.75

coefficient a b C1 C2 C3 C4 P0

1.426 0.466 127.767 16.761 −2.157 −75.376 −191.222

t 212.210 61.368 40.358 31.295 −31.245 22.061

Figure 5. Relative deviations of the linear model in this study

As shown in Table 2, “t” value is a reference criterion for determining the importance of a parameter. The larger the absolute value of “t” indicates that the parameter is more important, and vice versa. Therefore, the most important descriptor is M, which is consistent with the previous work.22 A positive coefficient value of the descriptor indicates a positive correlation between the descriptor and the Cp, and vice versa. The positive coefficient of the M indicates that as the M value increases, the Cp of the IL increases. In addition, the coefficient value of M is 1.426 which is close to the previously reported value of 1.454,22 indicating the reliability of this work. Totally there are four SEP parameters selected in eq 1, where subscript C represents cation, A represents anion, and numbers represent corresponding electrostatic potential value. Figure 4 shows the plot of the experimental data for Cp values against the predicted values obtained by the MLR

the calculated values by the MLR model are acceptably consistent with the experimental value, but some predictive values show large deviations, which means the established MLR model cannot predict these data points of ILs, and thus the ELM nonlinear model is introduced as the preferred model in this work. 3.2. Results of Nonlinear Model and Comparison. After developing the linear model, the nonlinear ELM model is established using the same input descriptors and same data set of the MLR model. The network of ELM model includes three layers (see Figure 2): input, hidden, and output layers. The input parameters are mapped randomly to the hidden layer and converted based on the triangular basis transfer function (tribas). The tribas transfer function can be defined in the following equation: C

DOI: 10.1021/acs.iecr.8b03668 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

l o o = 1 − abs(x), if − 1 ≤ x ≤ 1 y = tribas(x)m o o otherwise (2) n = 0, where y is the output value and x is the input value. Based on the output from the hidden layer, the coefficients between the hidden and the output layers can be obtained by a simple linear regression. In order to obtain the best ELM network, we need to train the network fordeterming the best number of neurons. The optimal ELM structure can be determined based on large R2 and small AARD% values for both training set and test set. The changing of R2 and AARD% with respect to the number of neurons is depicted in Figure 6. As shown in this

Figure 8. Relative deviations of the ELM model in this study.

and the validity of the SEP descriptors. In addition, the training time for building the ELM model is 1.8368 s using an Intel 1.9 GHz laptop including 4GB of RAM. A detailed comparison of the MLR and ELM models is depicted in Figure 9. As shown in this figure, for the MLR

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

figure, when the number of neurons exceeds 150, both the R2 and AARD% of the training set slightly change, whereas the R2 of the test set starts to decrease and the AARD% begins to increase, so the optimal number of neurons is 150. Figures 7 and 8 represent the predicted Cp value and relative deviation of the ELM model versus the experimental value, respectively. As can be seen from these figures, the predicted values are in good agreement with the experimental values, and the relative deviations of most data points are within ±5%, indicating good performance of the established ELM model

Figure 9. Percent of value in different deviation ranges of the different models.

model, 54.47% of the calculated Cp values show an AARD range between 0 and 1%, 33.11% between 1 and 5%, 8.82% between 5 and 10%, and 3.60% between 10 and 20%. However, for the ELM model, the predicted Cp values show that 89.90% of the data points are within an AARD range of 0−1%, 9.44% within 1−5%, 0.62 within 5−10%, and 0.04% over 10%. The detailed information about the predicted value and deviation on each data point can be found in the SI. The comparison of the statistical parameters including R2 and AARD% between the MLR model, the ELM model and the results from previous work is summarized in Table 3. The R2 and AARD% of the entire set for the ELM model are 0.999 and 0.44% which are better than 0.988 and 2.29% of the MLR model, which shows that the statistical parameters for the ELM model developed in this work based on SEP descriptors are better than those of MLR mode. It illustrates that the nonlinear algorithm (ELM) is more reliable to calculate the heat capacity of ILs than the linear algorithm (MLR). The main reason for this should be that the heat capacity of ILs is not directly linear with the SEP of ILs. Besides, the ELM model is a suitable

Figure 7. Calculated versus experimental heat capacity values of ILs by ELM in this study. D

DOI: 10.1021/acs.iecr.8b03668 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research Table 3. Comparison of the Statistical Parameters of Different QSAR Models

Data points of ILs used in this study; literature of the data points; comparison between this study and previous work (XLSX)

model

data set

no.

R2

AARD%

MLR (Sσ‑profiles)

train test total

1933 483 2416

0.985 0.984 0.985

2.58 2.88 2.72

22 22 22

train test total

1933 483 2416

0.998 0.998 0.998

0.56 0.74 0.60

22 22 22

MLR (SEP)

train test total

1933 483 2416

0.988 0.987 0.988

2.24 2.51 2.29

this work this work this work

Notes

ELM (SEP)

train test total

1933 483 2416

0.999 0.999 0.999

0.41 0.57 0.44

this work this work this work

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ELM (Sσ‑profiles)

ref

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*(Y.Z.) E-mail: [email protected]. *(H.Z.) E-mail: [email protected]. ORCID

Yongsheng Zhao: 0000-0003-1224-1787 The authors declare no competing financial interest.

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choice for calculating the heat capacity of ILs also due to its good advantages, such as easy to use, time-saving and excellent generalization performance.42 In addition, compared to the models based on Sσ‑profiles molecular descriptors in ref.,22 the MLR and ELM models based on SEP descriptors have relatively good results (higher R2 and lower AARD%), indicating the reliability of the SEP descriptors. As shown in SI Table S1, we also compare the ELM model with the group contribution model in the previous literature.18 The literature18 used more ILs and data points to establish model, and thus it has a wider application range advantage, but our proposed ELM model (based on four families of ILs) has fewer input parameters and overall higher prediction accuracy in the temperature range presented in SI Table S1. In addition, as shown in SI Table S2, a more detailed comparison is also provided. It can be seen that most of the AARD% values for different ILs in this study are lower than that in the literature using group contribution method.18 The reasons may be that the effectiveness of the intelligent ELM algorithm and our model is developed based on the descriptors calculated by quantum chemistry.

4. CONCLUSION In this study, linear and nonlinear (MLR and ELM) models are developed based on a data set of 46 ILs including 2416 data points using SEP quantum chemistry descriptors. Six parameters are finally selected by stepwise regression method to establish the MLR and ELM models. The detailed statistical parameters demonstrate by the robustness of the models MLR model (R2 = 0.988, AARD = 2.29%) and ELM model (R2 = 0.999, AARD = 0.44%). It is proved that the ELM model gives better results than those of the linear MLR model for prediction of the heat capacity of ILs. Thus, we conclude that the SEP descriptors have rich information at the electron level and can be successfully employed to predict the heat capacity of ILs. It can also identify and shed some light on what microstructure features are responsible for the heat capacity of ILs.

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AUTHOR INFORMATION

Corresponding Authors

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.8b03668. E

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DOI: 10.1021/acs.iecr.8b03668 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.iecr.8b03668 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX