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Novel molecular descriptors for prediction of H2S solubility in ionic liquids
Accepted Manuscript Novel molecular descriptors for prediction of H2S solubility in ionic liquids
Xuejing Kang, Jianguo Qian, Jing Deng, Ullah Latif, Yongsheng Zhao PII: DOI: Reference:
S0167-7322(17)35098-5 doi:10.1016/j.molliq.2018.06.113 MOLLIQ 9311
To appear in:
Journal of Molecular Liquids
Received date: Revised date: Accepted date:
26 October 2017 3 May 2018 27 June 2018
Please cite this article as: Xuejing Kang, Jianguo Qian, Jing Deng, Ullah Latif, Yongsheng Zhao , Novel molecular descriptors for prediction of H2S solubility in ionic liquids. Molliq (2018), doi:10.1016/j.molliq.2018.06.113
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ACCEPTED MANUSCRIPT
Novel molecular descriptors for prediction of H2S solubility in ionic liquids Xuejing Kang a,b,1, Jianguo Qianc,1, Jing Dengd, Ullah Latifc, Yongsheng Zhaoa,e a
Key Laboratory for Thin Film and Microfabrication of Ministry of Education, Department of
College of Materials and Chemical Engineering, Zhengzhou University of light industry, Zhengzhou 450002, China
Department Beijing Key Laboratory of Ionic Liquids Clean Process, Key Laboratory of
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c
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b
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Micro/Nano-electronics, Shanghai Jiao Tong University, Shanghai 200240, China
Green Process and Engineering, State Key Laboratory of Multiphase Complex Systems,
d
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Institute of Process Engineering, Chinese Academy of Sciences, Beijing, 100190, China Department of Chemical Engineering, Norwegian University of Science and Technology,
e
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Trondheim 7491, Norway Department of Chemical Engineering, University of California, Santa Barbara, California
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93106-5080, USA
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Abstract: Molecular descriptors are very important input parameters for establishing properties prediction models of materials, such as ionic liquids (ILs). In this work, as a new class of
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molecular descriptors, namely, electrostatic potential surface (SEP) is proposed to predict one of the important representative properties of ILs, i.e. the H2S solubility in ILs. 1318 experimental
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data points of 28 ILs, including 7 cations and 12 anions covering diverse temperatures and pressures, have been gathered from 15 references. According to the qualitative analyses, it is found that anions play a more important role than cations for the H2S solubility in ILs, besides the anions with stronger hydrogen-bond basicity have higher capacities to absorb H2S. Combining the SEP descriptors with the extreme learning machine (ELM) algorithm, two new
Corresponding author. Fax: +1 805-837-4996 E-mail addresses: [email protected] 1 The authors contributed equally. 1
ACCEPTED MANUSCRIPT quantitative models (ELM1 based on the isolated ions and ELM2 based on the ion pairs) for predicting H2S solubility are established. The average absolute relative deviation (AARD%) for the total set of ELM1 and ELM2 models are 5.87% and 3.84%, respectively. The results indicate that the SEP descriptors can extensively be employed to predict properties of ILs due to
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their rich information at electron level.
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Keywords: Molecular descriptors; Ionic liquids; H2S; Extreme learning machine; Model
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ACCEPTED MANUSCRIPT 1. Introduction The electrostatic potential[1-3] 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)
r ' dr ' ZA rA r r ' r
A
(1)
r
represents the electronic density function for molecule. As
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between nucleus A and r,
rA r stands for the distance
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where ZA denotes the charge of the nuclear A, located at rA,
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V r
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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
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(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
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expected to use them as descriptors to precisely predict properties of materials under investigation.
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Benefiting from the excellent properties (e.g. high thermal stability, high solubility, low melting point, generally negligible flammability and almost null volatility)[4-7], ionic liquids
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(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 its nonvolatility and excellent capacity, ILs have also been employed to capture poisonous acid gases[13-20] 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 3
ACCEPTED MANUSCRIPT 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.
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Some predictive models have been established for calculating the H2S solubility in ILs by
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applying the intelligence algorithms[23-26], equation of state (EOS)[27, 28], and conductor-
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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.
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Ahmadi and his co-workers[23] employed temperature (T), pressure (P), critical temperature
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(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
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construct the gene-expression programming (GEP) and least-squares support vector machine
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(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
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the number of groups for each IL were used as input parameters to develop the predictive
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models by extreme learning machine (ELM) approach, however; the shortcomings of these models are that 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 prediction for H2S solubility in ILs. In the present study, at first, we optimized the structures of individual cations and anions 4
ACCEPTED MANUSCRIPT as well as their 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.
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2. Data and molecular descriptors
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2.1. Data preparation
In order to establish the models to calculate the H2S solubility in ILs, 1318 data points in
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28 various ILs, including 7 cations and 12 anions, were collected from 15 references. The type
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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
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model establishment was randomly divided into training subset including 1055 data points and
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test subset containing 263 data points. The data of training subset was utilized to train and build different models, while the test data subset was applied to identity the performance of the
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established models.
Table 1. Temperature, pressure, and H2S solubility range as well as AARD %* of the ILs used
No. of ILs
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in this study.
ILs
H2S solubility T range (K)
P range (bar)
range (mole fraction)
No. of data points
AARD %
AARD %
(ELM1)
(ELM2)
Refs
1
[BMIM][MeSO4]
298.1
0.11-7.51
0.022-0.521
8
4.81
4.31
[31]
2
[BMIM][Br]
299.15
1
0.03
1
99.39
0
[32]
3
[EMIM][OAc]
293.15-333.15
0.014-3.248
0.0917-0.5103
64
5.94
6.09
[33]
4
[EMIM][Pro]
293.15-333.15
0.011-3.239
0.1206-0.5897
62
7.58
7.63
[33]
5
[EMIM][Lac]
293.15-333.15
0.044-3.216
0.0759-0.4898
57
2.4
2.39
[33]
6
[BMIM][OAc]
293.15-333.15
0.001-3.415
0.0740-0.5790
69
10.98
11.1
[33]
7
[HMIM][OAc]
293.15-333.15
0.003-3.309
0.0900-0.6094
66
7.03
7.04
[33]
5
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[BMIM][PF6]
298.15-403.15
0.69-96.30
0.016-0.875
39
3.66
3.22
[21]
303.15-333.15
1.23-10.11
0.044-0.405
42
4.84
3.42
[14]
[BMIM][BF4]
303.15-343.15
0.61-8.36
0.03-0.354
42
5.58
3.34
[34]
10
[BMIM][Tf2N]
303.15-343.15
0.94-9.16
0.051-0.51
44
1.88
1.84
[14]
11
[HMIM][Tf2N]
303.15-353.15
0.69-20.17
0.0368-0.7012
57
5.95
5.86
[35]
303.15-343.15
0.97-10.50
0.029-0.533
30
17.54
17.35
[36]
[HMIM][BF4]
303.15-343.15
1.11-11.0
0.06-0.499
33
12.46
2.2
[36]
13
[HMIM][PF6]
303.15-343.15
1.38-10.9
0.05-0.441
34
15.48
2.71
[36]
14
[BMIM][EtSO4]
303.15-353.15
1.14-12.70
0.012-0.118
36
4.86
5.6
[37]
15
[EMIM][Tf2N]
303.15-353.15
1.08-16.86
0.049-0.609
42
0.9
2.13
[38]
16
[OMIM][Tf2N]
303.15-353.15
0.94-19.12
0.063-0.7355
47
1.31
1.4
[35]
17
[OMIM][PF6]
303.15-353.15
0.85-19.58
0.0463-0.6972
48
1.31
1.2
[39]
18
[HEMIM][BF4]
303.15-353.15
1.21-10.66
0.02-0.247
51
15.54
1.56
[34]
19
[HEMIM][PF6]
303.15-353.15
1.34-16.85
0.0347-0.4627
47
12.24
1.17
[34]
20
[HEMIM][Tf2N]
303.15-353.15
1.56-18.32
0.0576-0.5724
41
2.41
1.44
[40]
21
[HEMIM][TfO]
303.15-353.15
1.06-18.39
0.0357-0.5483
41
2.38
1.35
[40]
22
[EMIM][TPTP]
303.15-353.15
0.582-19.415
0.0220-0.5926
79
1.33
0.94
[15]
23
[EMIM][TfO]
303.15-353.15
0.0643-24.553
0.0452-0.5672
36
3.15
2.25
[41]
24
[MEDAH][OAc]
303.2-333.2
0.097-1.396
0.0095-0.1618
35
2.2
1.87
[42]
25
[MEDAH][For]
303.2-333.2
0.079-1.242
0.0061-0.0807
33
4.81
4.3
[42]
26
[DMEAH][OAc]
303.2-333.2
0.031-1.111
0.0104-0.2085
53
5.27
2.55
[42]
27
[DMEAH][For]
303.2-333.2
0.058-1.153
0.0065-0.1189
41
5.54
2.55
[42]
28
[EMIM][PF6]
333.15-363.15
1.45-19.33
0.032-0.359
40
1.62
1.4
[38]
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*AARD: average absolute relative deviation
2.2. Determination of the molecular descriptors
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Since the anions and cations are the basic units of ILs, therefore the structures of 7 anions and 12 cations for the 28 ILs were pre-optimized by the Gaussian 09 software[43] at the
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B3LYP/6-31G* level, which was followed by full geometry optimization at the B3LYP/631++G** level. The vibration frequency and energy of those anions and cations were calculated to confirm the local minimal energy points without imaginary frequency. Since the individual cations and anions ignore the corresponding opposite charge during optimization, the ion-pairs of 28 ILs were optimized. On the basis of optimal configurations, the Multiwfn software[44] was used to calculate the SEP of the isolated ions and ion pairs of ILs, and the SEP values were presented by different colors on their surfaces. Figure 1 shows the SEP of 28 ILs (ion pairs) 6
ACCEPTED MANUSCRIPT employed in this work, and the SEP of anions and cations for 28 ILs can be found in supporting information. It should be noted that the molecular surface is generally van der Waals surface defined by Bader[3, 45], which is the surface at the electron density of 0.001 e/Bohr3. The ranges of calculated electrostatic potential are 0~200 kcal/mol for cations, -200~0 kcal/mol for
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anions and -60~60 kcal/mol for ion pairs, respectively, and the step size was set at 0.5 kcal/mol.
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For convenience, we used the intermediate value to stand for the SEP of each step. For instance,
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SEP0.25 represents the electrostatic potential surface areas in the range of 0~0.5 kcal/mol. Three representative SEP of [BMIM]+, [BF4]-, and [BMIM][BF4] are shown in Figure 2 (a), (b) and (c),
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respectively. As can be seen from Figure 2(a), the surface of [BMIM]+ is blue due to the
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electrostatic potentials upon it is over 40 kcal/mol. In contrast, the electrostatic potentials of [BF4]- are below -115kcal/mol leading to a red surface. It can also be observed that the
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cation and anion.
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electrostatic potentials of [BMIM][BF4] are relatively reduced owing to interaction between the
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Figure 1. Electrostatic potential surface mapped electron total density with an isovalue 0.001 e/Bohr3 of the 28 optimized ILs
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6 +
(a)
[BMIM] 5
2
Surface area(Å )
4
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3
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2
0 0
20
40
60
80
100
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1
120
140
160
180
200
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Electrostatic potential (kcal/mol) 10 -
8
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6
4
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2
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2
Surface area(Å )
(b)
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[BF4]
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0 -200
-180
-160
-140
-120
-100
-80
-60
Electrostatic potential (kcal/mol)
9
-40
-20
0
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[BMIM][BF4]
(c)
5
2
Surface area(Å )
4
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3
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2
0 -60
-40
-20
0
SC
1
20
40
60
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Electrostatic potential (kcal/mol)
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Figure 2 Electrostatic potentials versus corresponding surface areas of [BMIM]+, [BF4]- and [BMIM][BF4]
3. Methodology
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3.1. Extreme learning machine (ELM)
ELM, which is a single-hidden layer feedforward neural networks (SLFNs) learning
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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
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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 huge work, including adjusting the input weights and hidden biases of the network in the process of algorithm implementation, could be abandoned, while the optimal solution will be obtained. As a result, the time needed to develop an ELM model is significantly reduced without sacrificing the good generalization performance. Independent variables, hidden neurons, and dependent variables are the three units of the 10
ACCEPTED MANUSCRIPT ELM network structure used in this work (as shown in Figure 3). The independent variables, including temperature, pressure and the SEP of independent cation and anion or ion pairs, were selected by stepwise regression algorithm. The dependent variable is the H2S solubility in ILs. The activation function between the independent variables and hidden neurons is the sine
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function, and the function from hidden neurons to dependent variables is the linear function.
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The parameters ωij and bias between the input and hidden layers are generated at random, and
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the coefficients ωjk between the hidden and output layers are the only parameter needed to be
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learned.
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Figure 3. ELM network structure in this study for the prediction of H2S solubility in ILs
3.2. Model validation and performance Following are the statistical parameters including absolute relative deviation (ARD %), the coefficient of determination (R2), average absolute relative deviation (AARD %), meansquare error (MSE) and root-mean-square error (RMSE), were employed to estimate the performance of the established ELM models. The equations of these statistical parameters are 11
ACCEPTED MANUSCRIPT formulated below:
ARD (%) 100( yical / yiexp 1.0)
ym yical yiexp
y NP
i 1
i 1
i
Np
AARD (%) = 100 i 1
NP
y
P
/N 2
NP
i 1
/N
cal
i
yi
exp
P
(4)
(5)
(6)
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RMSE
2
MSE yi yi i 1
(3)
yical yiexp / Np yiexp exp
cal
2
2
ym
exp
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i 1
i
NP
2
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R2
exp
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y NP
(2)
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where y represents the H2S solubility in ILs. The superscripts of “exp” and “cal” stand for the experimental values and calculated values, respectively.
ym denotes the average
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for the entire dataset.
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experimental values of the H2S solubility in ILs. Np is the number of experimental data points
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4. Result and discussion
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4.1 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 Equation 7: 12
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y 0.018P 0.003T 0.232SA-141.25 0.194SC81.75 0.308SA-52.25 0.056SA-62.75 0.53SA-103.25 0.091SC107.25 0.52SA-102.75 0.068SC108.25 1.210
(7)
(n=1318, R2=0.737, AARD %=130.87%) where y denotes the H2S solubility in ILs, P represents pressure, and T stands for temperature.
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Here, A and C represent anion and cation, respectively. The positive or negative constant in front of each parameter represents the positive or negative correlation between the parameter
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and the H2S solubility in ILs. In addition, the order of the parameters is descending in
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accordance with the t value which stands for the importance of the parameter for the H2S
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solubility in ILs. This means the first descriptor P has the most vital influence on the H2S solubility in ILs. The positive coefficient in front of it suggests that the H2S solubility in ILs
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increases with pressure. Thus the following T is the second important descriptor for the H2S solubility in ILs, which shows a negative correlation between them, i.e. H2S solubility in ILs
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decreases with increasing temperature. It can be observed that five SEP descriptors of anion, which are SA-141.25, SA-52.25, SA-62.75, SA-103.25, and SA-102.75, have important impact on the H2S
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solubility in ILs. Among them, the SA-141.25, SA-62.75, and SA-102.75 have positive correlations with H2S solubility in ILs, while SA-52.25 and SA-103.25 have negative correlations. Moreover, SC81.75,
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SC107.25 and SC108.25 belong to cations, which are the 4th, 8th, and 10th important descriptors, respectively. Therefore, it could be concluded that anions are more important than cations for the H2S solubility in ILs. It is worth mentioning that the most important SEP descriptor (SA-141.25) belongs to the anions of [OAc]-, [Pro]-, [Lac]-, [For]-, which are considered to have strong hydrogen-bond basicity. It could be speculated that the anions with strong hydrogen-bond basicity may have a stronger hydrogen-bonding with H2S, thus the corresponding IL will have higher H2S solubility. The results are in agreement with our previous work[47]. Although the 13
ACCEPTED MANUSCRIPT obtained model could be used to qualitatively analyze the factors of H2S solubility in ILs, the performance of the model is not good enough, and the reason may be that the interaction between H2S solubility and the input parameters is more complex than linear relationship. Therefore, it is necessary to develop non-linear models for more accurately modeling H2S
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4.2 ELM1 model based on the SEP of isolated ions
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solubility in ILs.
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In this part we utilized ten descriptors, with the same aforementioned linear model as
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independent variables and H2S solubility in ILs as dependent variables to build an ELM model. The test set and training set used in this work occupy 20% (263 data points) and 80% (1055
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data points) data points in datasheet, respectively. The activation function between the independent variables and hidden neurons is the sine function, and the function from hidden
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neurons to dependent variables is the linear function as mentioned above. Then it is required to achieve the optimal number of neurons between independent variables and hidden neurons. As
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can be seen from Figure 4, for the training set, the R2 values are almost steady, and AARD% decreases slightly with the rising number of neurons; however; for test set values the R2 reduces
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sharply and AARD% rises considerably when the number of neurons is over 400. As a result, the optimized number (400) of neurons is confirmed and the ELM model (here we call it ELM1 model) is obtained at the same time.
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20 1.0 18 16
2
training set R 2 test set R training set AARD% test set AARD%
0.6
14
R
2
12
PT
0.4
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0.2
250
300
SC
0.0
350
400
450
10
AARD (%)
0.8
8 6 4
500
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Number of neurons
Figure 4. R2 and AARD% of the ELM1 model versus the number of neurons for the training and test sets
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The calculated H2S solubility versus experimental data in ILs of the ELM1 model is shown in Figure 5. It can be seen that the calculated values agree well with the experimental values.
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The R2 and AARD% for the total set are 0.991 and 5.87%, respectively. The detailed information about ELM1 model has been listed in Table 2. This table shows that R2 and AARD%
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values are 0.994 and 5.68% for the training set, and 0.979 and 6.64% for the test set, respectively. The percent of the calculated values in different ARD% range for the ELM1 model are displayed
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in Figure 6. It can be seen that the ARD% of the predictive values distributed within 5% accounts for 69.43%, and the ARD% over 20% accounts for only 5.24%. These results indicate that this model provides good accuracy and dependence to estimate the H2S solubility values in ILs. In addition, the training time for the ELM1 model was 4.2716 seconds on an Intel 1.9GHz laptop computer with 4 GB of RAM.
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1.0 Exp. Cal. training set
Exp. Cal. test set
0.6
PT
0.4
0.2
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H2S solubility in ILs
0.8
0
200
400
600
SC
0.0
800
1000
1200
1400
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Data number
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Figure 5. Calculated versus experimental H2S solubility in ILs of the ELM1 model in this study
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Figure 6. Percent of value in different ARD% range of the ELM1 model
Data set Training set Test set Total set
Table 2. The statistical parameters for the ELM1 model. No. R2 AARD % MSE 1055 0.994 5.68 1.86 E-04 263 0.979 6.64 6.29 E-04 1318 0.991 5.87 2.74 E-04
RMSE 0.0136 0.0254 0.0166
4.3 ELM2 model based on the SEP of ILs (ion pairs) As mentioned above, the SEP descriptors of isolated cation and anion ignore the
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ACCEPTED MANUSCRIPT corresponding opposite charge thus the information provided is insufficient. Hence, we optimized the ion pair structure of each IL, and calculated the SEP descriptors of 28 ILs. Then the same approach with the linear model was employed to screen the descriptors and build the ELM2 model. As a result, eight descriptors as independent variables were extracted, which
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include: P, T and SA-47.75, SA-6.25, SA-15.25, SA-25.75, SC14.75, SC34.25 of ion pairs (the order of
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parameters also represents the importance for the H2S solubility in ILs). The employed
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functions in ELM2 model are the same with the ELM1 model. At last, the optimal number (400) of neurons was determined. Figure 7 shows the calculated H2S solubility versus experimental
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data in ILs of the training and test subsets for the ELM2 model. It illustrates that the calculated
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values have a good adaptation with experimental values during training and test procedures. Taking [HEMIM][Tf2N] as an example, a comparison between the estimated and experimental
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data points of H2S solubility in [HEMIM][Tf2N] is shown in Figure 8. The estimated and
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experimental values are in good agreement. The percentages of predictive values in different ARD% range of the ELM2 model are depicted in Figure 9. It can be seen that 82.5% of ELM2
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model predictions are in the ARD% range of 0-5%, and only 2.88% of model predictions have
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ARD% values exceeding 20%. Table 3 demonstrates a detailed summary of the statistical parameters for ELM2 model. For the total set, the R2 and AARD% values are 0.994 and 3.84%, respectively. They are 0.996 and 3.53% for the training set and 0.985 and 5.07% for the test set, respectively. These results illustrate that the ELM2 model has good performance and is feasible to estimate the H2S solubility in ILs. In addition, the training of the ELM2 model only costs 1.1553 seconds on the same laptop computer used for ELM1 model.
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1.0 Exp. Cal. test set
Exp. Cal. training set
0.6
PT
0.4
0.2
0.0 200
400
600
800
SC
0
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H2S solubility in ILs
0.8
1000
1200
1400
Data number
ELM2 model, 303.15K
Exp, T=313.15K
ELM2 model, 313.15K
Exp, T=323.15K
ELM2 model, 323.15K
Exp, T=333.15K
ELM2 model, 333.15K
Exp, T=343.15K
ELM2 model, 343.15K
Exp, T=353.15K
ELM2 model, 353.15K
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0.5
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0.4
0.3
0.2
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H2S Mole Fraction
0.6
Exp, T=303.15K
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0.7
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Figure 7. Calculated versus experimental the H2S solubility in ILs of the ELM2 model in this study
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0.1
0.0
0
2
4
6
8
10
12
14
16
18
Pressure (bar)
Figure 8. Comparison between experimental solubility data (given as mole fractions) versus pressure and those predicted by the ELM2 model for [HEMIM][Tf2N] at different temperatures.
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Table 3. The statistical parameters for the ELM2 model. No. R2 AARD % MSE 1055 263 1318
0.996 0.985 0.994
3.53 5.07 3.84
1.07 E-04 4.23 E-04 1.70 E-04
RMSE 0.0103 0.0208 0.0130
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Training set Test set Total set
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Data set
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Figure 9. Percent of value in different ARD% range of the ELM2 model
4.4 Comparison between this work and the previous publications
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As shown in Tables 2 and 3, the statistical parameters (R2, AARD%, MSE, and RMSE)
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indicate that the ELM2 model is more robust and efficient than the ELM1 model. To assess the final results of the two evolved models for estimating the H2S solubility in ILs, a broad
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comparison of different models including EOS, COSMO-RS and intelligence algorithms has
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been summarized in Table 4. In contrast to other models, the predictive models established by intelligence algorithms (such as ANN, LSSVM, and ELM) have better performances, and the ANN (MLP) models established by Barati-Harooni et al. has the best accuracy till the compilation of this work[48]. It is worth mentioning that in the current established intelligent algorithm models by other authors[23-26, 48, 49], experimental properties are needed as input parameters/descriptors (such as Tc, Pc, and ω), but in many cases, these critical properties of ILs are difficult to be measured directly[50]. Although our previous work[30] used chemical 19
ACCEPTED MANUSCRIPT groups as input descriptors, eliminating the need for experimental data as input parameters, it suffers from the bottleneck of not identifying isomers. However, compared with the models mentioned above, the main advantage of this study is that there is no need for experimental data as input descriptors, and the SEP descriptors proposed in this study are calculated from quantum
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chemistry having rich information at the electronic level. Due to the different data points, ILs
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and descriptors, it is reasonless to directly compare the ELM, ANN and LSSVM models, but it
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also can be concluded that models developed by ELM algorithm are established based on a larger number of experimental data points and kinds of ILs, hence they could be more general
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and practical to estimate the H2S solubility in ILs.
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Table 4. The comparison of different models for H2S solubility in ILs. Method Np NIL AARD % Reference PR EOSa
465
11
38.95
[24, 25]
465 465 465 664 664 664 722 722
11 11 11 14 14 14 16 16
36.43 4.90 4.87 196.76 8.35 5.03 38.64 38.14
[24, 25] [24, 25] [24, 25] [26] [26] [26] [29] [29]
GEP
465
11
4.38
[25]
ANN
465
11
4.58
[23]
ANN
664
14
2.07
[26]
LSSVM
465
11
2.28
[24]
ANN (GA-RBF)
465
11
1.90
[48]
ANN (MLP)
465
11
1.16
[48]
ANN
496
12
1.94
[49]
ELM
465
11
1.26
[30]
QSPR1(ELM)
1282
27
3.73
[47]
QSPR2(ELM) ELM1
1282 1318
27 28
3.80 5.87
[47] this work
ELM2
1318
28
3.84
this work
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SRK EOS PR EOSb SRK EOSb PR EOSa PR EOSb Empirical model COSMO-RS (ADF 2005) COSMO-RS (ADF 1998)
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a
NP: the number of experimental data points; NIL: the number of ILs a : that the interaction parameters (ki,j) is not considered; b : that the ki,j is considered. 20
ACCEPTED MANUSCRIPT 5. 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
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several SEP descriptors were screened via stepwise linear algorithm approach. Two novel ELM
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models (ELM1 and ELM2) were built based on screened parameters and both exhibited
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excellent accuracy and stability to precisely predict the H2S solubility in ILs. Notably, the ELM2 model with lower AARD% and RMSE has a better prediction ability. The models developed in
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this study were also compared with other models, and the comparative results illustrated that
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the established ELM models have relatively better accuracy for modeling the H2S solubility in ILs. This work implies that the SEP descriptors can be extensively used to predict the gas
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solubility properties of ILs and other materials.
Acknowledgement
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We are grateful for the financial support provided by the China Postdoctoral Science
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Foundation (2017M621477, 2017M621476).
21
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ACCEPTED MANUSCRIPT Highlights Electrostatic potential surface (SEP) quantum chemistry descriptors were proposed.
1318 experimental data points for 28 ILs were collected from 15 references.
Extreme learning machine algorithm was employed to develop predictive models.
The AARD% for the ELM1 and ELM2 models were 5.87% and 3.84%, respectively.
The SEP descriptors could be extensively employed to predict properties of ILs.
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Xuejing Kang, Jianguo Qian, Jing Deng, Ullah Latif, Yongsheng Zhao PII: DOI: Reference:
S0167-7322(17)35098-5 doi:10.1016/j.molliq.2018.06.113 MOLLIQ 9311
To appear in:
Journal of Molecular Liquids
Received date: Revised date: Accepted date:
26 October 2017 3 May 2018 27 June 2018
Please cite this article as: Xuejing Kang, Jianguo Qian, Jing Deng, Ullah Latif, Yongsheng Zhao , Novel molecular descriptors for prediction of H2S solubility in ionic liquids. Molliq (2018), doi:10.1016/j.molliq.2018.06.113
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ACCEPTED MANUSCRIPT
Novel molecular descriptors for prediction of H2S solubility in ionic liquids Xuejing Kang a,b,1, Jianguo Qianc,1, Jing Dengd, Ullah Latifc, Yongsheng Zhaoa,e a
Key Laboratory for Thin Film and Microfabrication of Ministry of Education, Department of
College of Materials and Chemical Engineering, Zhengzhou University of light industry, Zhengzhou 450002, China
Department Beijing Key Laboratory of Ionic Liquids Clean Process, Key Laboratory of
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c
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b
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Micro/Nano-electronics, Shanghai Jiao Tong University, Shanghai 200240, China
Green Process and Engineering, State Key Laboratory of Multiphase Complex Systems,
d
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Institute of Process Engineering, Chinese Academy of Sciences, Beijing, 100190, China Department of Chemical Engineering, Norwegian University of Science and Technology,
e
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Trondheim 7491, Norway Department of Chemical Engineering, University of California, Santa Barbara, California
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93106-5080, USA
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Abstract: Molecular descriptors are very important input parameters for establishing properties prediction models of materials, such as ionic liquids (ILs). In this work, as a new class of
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molecular descriptors, namely, electrostatic potential surface (SEP) is proposed to predict one of the important representative properties of ILs, i.e. the H2S solubility in ILs. 1318 experimental
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data points of 28 ILs, including 7 cations and 12 anions covering diverse temperatures and pressures, have been gathered from 15 references. According to the qualitative analyses, it is found that anions play a more important role than cations for the H2S solubility in ILs, besides the anions with stronger hydrogen-bond basicity have higher capacities to absorb H2S. Combining the SEP descriptors with the extreme learning machine (ELM) algorithm, two new
Corresponding author. Fax: +1 805-837-4996 E-mail addresses: [email protected] 1 The authors contributed equally. 1
ACCEPTED MANUSCRIPT quantitative models (ELM1 based on the isolated ions and ELM2 based on the ion pairs) for predicting H2S solubility are established. The average absolute relative deviation (AARD%) for the total set of ELM1 and ELM2 models are 5.87% and 3.84%, respectively. The results indicate that the SEP descriptors can extensively be employed to predict properties of ILs due to
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their rich information at electron level.
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Keywords: Molecular descriptors; Ionic liquids; H2S; Extreme learning machine; Model
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ACCEPTED MANUSCRIPT 1. Introduction The electrostatic potential[1-3] 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)
r ' dr ' ZA rA r r ' r
A
(1)
r
represents the electronic density function for molecule. As
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between nucleus A and r,
rA r stands for the distance
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where ZA denotes the charge of the nuclear A, located at rA,
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V r
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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
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(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
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expected to use them as descriptors to precisely predict properties of materials under investigation.
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Benefiting from the excellent properties (e.g. high thermal stability, high solubility, low melting point, generally negligible flammability and almost null volatility)[4-7], ionic liquids
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(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 its nonvolatility and excellent capacity, ILs have also been employed to capture poisonous acid gases[13-20] 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 3
ACCEPTED MANUSCRIPT 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.
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Some predictive models have been established for calculating the H2S solubility in ILs by
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applying the intelligence algorithms[23-26], equation of state (EOS)[27, 28], and conductor-
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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.
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Ahmadi and his co-workers[23] employed temperature (T), pressure (P), critical temperature
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(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
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construct the gene-expression programming (GEP) and least-squares support vector machine
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(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
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the number of groups for each IL were used as input parameters to develop the predictive
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models by extreme learning machine (ELM) approach, however; the shortcomings of these models are that 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 prediction for H2S solubility in ILs. In the present study, at first, we optimized the structures of individual cations and anions 4
ACCEPTED MANUSCRIPT as well as their 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.
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2. Data and molecular descriptors
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2.1. Data preparation
In order to establish the models to calculate the H2S solubility in ILs, 1318 data points in
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28 various ILs, including 7 cations and 12 anions, were collected from 15 references. The type
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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
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model establishment was randomly divided into training subset including 1055 data points and
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test subset containing 263 data points. The data of training subset was utilized to train and build different models, while the test data subset was applied to identity the performance of the
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established models.
Table 1. Temperature, pressure, and H2S solubility range as well as AARD %* of the ILs used
No. of ILs
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in this study.
ILs
H2S solubility T range (K)
P range (bar)
range (mole fraction)
No. of data points
AARD %
AARD %
(ELM1)
(ELM2)
Refs
1
[BMIM][MeSO4]
298.1
0.11-7.51
0.022-0.521
8
4.81
4.31
[31]
2
[BMIM][Br]
299.15
1
0.03
1
99.39
0
[32]
3
[EMIM][OAc]
293.15-333.15
0.014-3.248
0.0917-0.5103
64
5.94
6.09
[33]
4
[EMIM][Pro]
293.15-333.15
0.011-3.239
0.1206-0.5897
62
7.58
7.63
[33]
5
[EMIM][Lac]
293.15-333.15
0.044-3.216
0.0759-0.4898
57
2.4
2.39
[33]
6
[BMIM][OAc]
293.15-333.15
0.001-3.415
0.0740-0.5790
69
10.98
11.1
[33]
7
[HMIM][OAc]
293.15-333.15
0.003-3.309
0.0900-0.6094
66
7.03
7.04
[33]
5
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[BMIM][PF6]
298.15-403.15
0.69-96.30
0.016-0.875
39
3.66
3.22
[21]
303.15-333.15
1.23-10.11
0.044-0.405
42
4.84
3.42
[14]
[BMIM][BF4]
303.15-343.15
0.61-8.36
0.03-0.354
42
5.58
3.34
[34]
10
[BMIM][Tf2N]
303.15-343.15
0.94-9.16
0.051-0.51
44
1.88
1.84
[14]
11
[HMIM][Tf2N]
303.15-353.15
0.69-20.17
0.0368-0.7012
57
5.95
5.86
[35]
303.15-343.15
0.97-10.50
0.029-0.533
30
17.54
17.35
[36]
[HMIM][BF4]
303.15-343.15
1.11-11.0
0.06-0.499
33
12.46
2.2
[36]
13
[HMIM][PF6]
303.15-343.15
1.38-10.9
0.05-0.441
34
15.48
2.71
[36]
14
[BMIM][EtSO4]
303.15-353.15
1.14-12.70
0.012-0.118
36
4.86
5.6
[37]
15
[EMIM][Tf2N]
303.15-353.15
1.08-16.86
0.049-0.609
42
0.9
2.13
[38]
16
[OMIM][Tf2N]
303.15-353.15
0.94-19.12
0.063-0.7355
47
1.31
1.4
[35]
17
[OMIM][PF6]
303.15-353.15
0.85-19.58
0.0463-0.6972
48
1.31
1.2
[39]
18
[HEMIM][BF4]
303.15-353.15
1.21-10.66
0.02-0.247
51
15.54
1.56
[34]
19
[HEMIM][PF6]
303.15-353.15
1.34-16.85
0.0347-0.4627
47
12.24
1.17
[34]
20
[HEMIM][Tf2N]
303.15-353.15
1.56-18.32
0.0576-0.5724
41
2.41
1.44
[40]
21
[HEMIM][TfO]
303.15-353.15
1.06-18.39
0.0357-0.5483
41
2.38
1.35
[40]
22
[EMIM][TPTP]
303.15-353.15
0.582-19.415
0.0220-0.5926
79
1.33
0.94
[15]
23
[EMIM][TfO]
303.15-353.15
0.0643-24.553
0.0452-0.5672
36
3.15
2.25
[41]
24
[MEDAH][OAc]
303.2-333.2
0.097-1.396
0.0095-0.1618
35
2.2
1.87
[42]
25
[MEDAH][For]
303.2-333.2
0.079-1.242
0.0061-0.0807
33
4.81
4.3
[42]
26
[DMEAH][OAc]
303.2-333.2
0.031-1.111
0.0104-0.2085
53
5.27
2.55
[42]
27
[DMEAH][For]
303.2-333.2
0.058-1.153
0.0065-0.1189
41
5.54
2.55
[42]
28
[EMIM][PF6]
333.15-363.15
1.45-19.33
0.032-0.359
40
1.62
1.4
[38]
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12
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9
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*AARD: average absolute relative deviation
2.2. Determination of the molecular descriptors
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Since the anions and cations are the basic units of ILs, therefore the structures of 7 anions and 12 cations for the 28 ILs were pre-optimized by the Gaussian 09 software[43] at the
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B3LYP/6-31G* level, which was followed by full geometry optimization at the B3LYP/631++G** level. The vibration frequency and energy of those anions and cations were calculated to confirm the local minimal energy points without imaginary frequency. Since the individual cations and anions ignore the corresponding opposite charge during optimization, the ion-pairs of 28 ILs were optimized. On the basis of optimal configurations, the Multiwfn software[44] was used to calculate the SEP of the isolated ions and ion pairs of ILs, and the SEP values were presented by different colors on their surfaces. Figure 1 shows the SEP of 28 ILs (ion pairs) 6
ACCEPTED MANUSCRIPT employed in this work, and the SEP of anions and cations for 28 ILs can be found in supporting information. It should be noted that the molecular surface is generally van der Waals surface defined by Bader[3, 45], which is the surface at the electron density of 0.001 e/Bohr3. The ranges of calculated electrostatic potential are 0~200 kcal/mol for cations, -200~0 kcal/mol for
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anions and -60~60 kcal/mol for ion pairs, respectively, and the step size was set at 0.5 kcal/mol.
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For convenience, we used the intermediate value to stand for the SEP of each step. For instance,
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SEP0.25 represents the electrostatic potential surface areas in the range of 0~0.5 kcal/mol. Three representative SEP of [BMIM]+, [BF4]-, and [BMIM][BF4] are shown in Figure 2 (a), (b) and (c),
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respectively. As can be seen from Figure 2(a), the surface of [BMIM]+ is blue due to the
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electrostatic potentials upon it is over 40 kcal/mol. In contrast, the electrostatic potentials of [BF4]- are below -115kcal/mol leading to a red surface. It can also be observed that the
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cation and anion.
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electrostatic potentials of [BMIM][BF4] are relatively reduced owing to interaction between the
7
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ACCEPTED MANUSCRIPT
Figure 1. Electrostatic potential surface mapped electron total density with an isovalue 0.001 e/Bohr3 of the 28 optimized ILs
8
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6 +
(a)
[BMIM] 5
2
Surface area(Å )
4
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3
RI
2
0 0
20
40
60
80
100
SC
1
120
140
160
180
200
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Electrostatic potential (kcal/mol) 10 -
8
D
6
4
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2
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2
Surface area(Å )
(b)
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[BF4]
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0 -200
-180
-160
-140
-120
-100
-80
-60
Electrostatic potential (kcal/mol)
9
-40
-20
0
ACCEPTED MANUSCRIPT
6
[BMIM][BF4]
(c)
5
2
Surface area(Å )
4
PT
3
RI
2
0 -60
-40
-20
0
SC
1
20
40
60
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Electrostatic potential (kcal/mol)
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Figure 2 Electrostatic potentials versus corresponding surface areas of [BMIM]+, [BF4]- and [BMIM][BF4]
3. Methodology
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3.1. Extreme learning machine (ELM)
ELM, which is a single-hidden layer feedforward neural networks (SLFNs) learning
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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
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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 huge work, including adjusting the input weights and hidden biases of the network in the process of algorithm implementation, could be abandoned, while the optimal solution will be obtained. As a result, the time needed to develop an ELM model is significantly reduced without sacrificing the good generalization performance. Independent variables, hidden neurons, and dependent variables are the three units of the 10
ACCEPTED MANUSCRIPT ELM network structure used in this work (as shown in Figure 3). The independent variables, including temperature, pressure and the SEP of independent cation and anion or ion pairs, were selected by stepwise regression algorithm. The dependent variable is the H2S solubility in ILs. The activation function between the independent variables and hidden neurons is the sine
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function, and the function from hidden neurons to dependent variables is the linear function.
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The parameters ωij and bias between the input and hidden layers are generated at random, and
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the coefficients ωjk between the hidden and output layers are the only parameter needed to be
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learned.
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Figure 3. ELM network structure in this study for the prediction of H2S solubility in ILs
3.2. Model validation and performance Following are the statistical parameters including absolute relative deviation (ARD %), the coefficient of determination (R2), average absolute relative deviation (AARD %), meansquare error (MSE) and root-mean-square error (RMSE), were employed to estimate the performance of the established ELM models. The equations of these statistical parameters are 11
ACCEPTED MANUSCRIPT formulated below:
ARD (%) 100( yical / yiexp 1.0)
ym yical yiexp
y NP
i 1
i 1
i
Np
AARD (%) = 100 i 1
NP
y
P
/N 2
NP
i 1
/N
cal
i
yi
exp
P
(4)
(5)
(6)
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RMSE
2
MSE yi yi i 1
(3)
yical yiexp / Np yiexp exp
cal
2
2
ym
exp
PT
i 1
i
NP
2
RI
R2
exp
SC
y NP
(2)
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where y represents the H2S solubility in ILs. The superscripts of “exp” and “cal” stand for the experimental values and calculated values, respectively.
ym denotes the average
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for the entire dataset.
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experimental values of the H2S solubility in ILs. Np is the number of experimental data points
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4. Result and discussion
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4.1 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 Equation 7: 12
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y 0.018P 0.003T 0.232SA-141.25 0.194SC81.75 0.308SA-52.25 0.056SA-62.75 0.53SA-103.25 0.091SC107.25 0.52SA-102.75 0.068SC108.25 1.210
(7)
(n=1318, R2=0.737, AARD %=130.87%) where y denotes the H2S solubility in ILs, P represents pressure, and T stands for temperature.
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Here, A and C represent anion and cation, respectively. The positive or negative constant in front of each parameter represents the positive or negative correlation between the parameter
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and the H2S solubility in ILs. In addition, the order of the parameters is descending in
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accordance with the t value which stands for the importance of the parameter for the H2S
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solubility in ILs. This means the first descriptor P has the most vital influence on the H2S solubility in ILs. The positive coefficient in front of it suggests that the H2S solubility in ILs
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increases with pressure. Thus the following T is the second important descriptor for the H2S solubility in ILs, which shows a negative correlation between them, i.e. H2S solubility in ILs
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decreases with increasing temperature. It can be observed that five SEP descriptors of anion, which are SA-141.25, SA-52.25, SA-62.75, SA-103.25, and SA-102.75, have important impact on the H2S
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solubility in ILs. Among them, the SA-141.25, SA-62.75, and SA-102.75 have positive correlations with H2S solubility in ILs, while SA-52.25 and SA-103.25 have negative correlations. Moreover, SC81.75,
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SC107.25 and SC108.25 belong to cations, which are the 4th, 8th, and 10th important descriptors, respectively. Therefore, it could be concluded that anions are more important than cations for the H2S solubility in ILs. It is worth mentioning that the most important SEP descriptor (SA-141.25) belongs to the anions of [OAc]-, [Pro]-, [Lac]-, [For]-, which are considered to have strong hydrogen-bond basicity. It could be speculated that the anions with strong hydrogen-bond basicity may have a stronger hydrogen-bonding with H2S, thus the corresponding IL will have higher H2S solubility. The results are in agreement with our previous work[47]. Although the 13
ACCEPTED MANUSCRIPT obtained model could be used to qualitatively analyze the factors of H2S solubility in ILs, the performance of the model is not good enough, and the reason may be that the interaction between H2S solubility and the input parameters is more complex than linear relationship. Therefore, it is necessary to develop non-linear models for more accurately modeling H2S
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4.2 ELM1 model based on the SEP of isolated ions
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solubility in ILs.
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In this part we utilized ten descriptors, with the same aforementioned linear model as
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independent variables and H2S solubility in ILs as dependent variables to build an ELM model. The test set and training set used in this work occupy 20% (263 data points) and 80% (1055
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data points) data points in datasheet, respectively. The activation function between the independent variables and hidden neurons is the sine function, and the function from hidden
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neurons to dependent variables is the linear function as mentioned above. Then it is required to achieve the optimal number of neurons between independent variables and hidden neurons. As
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can be seen from Figure 4, for the training set, the R2 values are almost steady, and AARD% decreases slightly with the rising number of neurons; however; for test set values the R2 reduces
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sharply and AARD% rises considerably when the number of neurons is over 400. As a result, the optimized number (400) of neurons is confirmed and the ELM model (here we call it ELM1 model) is obtained at the same time.
14
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20 1.0 18 16
2
training set R 2 test set R training set AARD% test set AARD%
0.6
14
R
2
12
PT
0.4
RI
0.2
250
300
SC
0.0
350
400
450
10
AARD (%)
0.8
8 6 4
500
NU
Number of neurons
Figure 4. R2 and AARD% of the ELM1 model versus the number of neurons for the training and test sets
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The calculated H2S solubility versus experimental data in ILs of the ELM1 model is shown in Figure 5. It can be seen that the calculated values agree well with the experimental values.
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The R2 and AARD% for the total set are 0.991 and 5.87%, respectively. The detailed information about ELM1 model has been listed in Table 2. This table shows that R2 and AARD%
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values are 0.994 and 5.68% for the training set, and 0.979 and 6.64% for the test set, respectively. The percent of the calculated values in different ARD% range for the ELM1 model are displayed
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in Figure 6. It can be seen that the ARD% of the predictive values distributed within 5% accounts for 69.43%, and the ARD% over 20% accounts for only 5.24%. These results indicate that this model provides good accuracy and dependence to estimate the H2S solubility values in ILs. In addition, the training time for the ELM1 model was 4.2716 seconds on an Intel 1.9GHz laptop computer with 4 GB of RAM.
15
ACCEPTED MANUSCRIPT
1.0 Exp. Cal. training set
Exp. Cal. test set
0.6
PT
0.4
0.2
RI
H2S solubility in ILs
0.8
0
200
400
600
SC
0.0
800
1000
1200
1400
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Data number
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Figure 5. Calculated versus experimental H2S solubility in ILs of the ELM1 model in this study
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Figure 6. Percent of value in different ARD% range of the ELM1 model
Data set Training set Test set Total set
Table 2. The statistical parameters for the ELM1 model. No. R2 AARD % MSE 1055 0.994 5.68 1.86 E-04 263 0.979 6.64 6.29 E-04 1318 0.991 5.87 2.74 E-04
RMSE 0.0136 0.0254 0.0166
4.3 ELM2 model based on the SEP of ILs (ion pairs) As mentioned above, the SEP descriptors of isolated cation and anion ignore the
16
ACCEPTED MANUSCRIPT corresponding opposite charge thus the information provided is insufficient. Hence, we optimized the ion pair structure of each IL, and calculated the SEP descriptors of 28 ILs. Then the same approach with the linear model was employed to screen the descriptors and build the ELM2 model. As a result, eight descriptors as independent variables were extracted, which
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include: P, T and SA-47.75, SA-6.25, SA-15.25, SA-25.75, SC14.75, SC34.25 of ion pairs (the order of
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parameters also represents the importance for the H2S solubility in ILs). The employed
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functions in ELM2 model are the same with the ELM1 model. At last, the optimal number (400) of neurons was determined. Figure 7 shows the calculated H2S solubility versus experimental
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data in ILs of the training and test subsets for the ELM2 model. It illustrates that the calculated
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values have a good adaptation with experimental values during training and test procedures. Taking [HEMIM][Tf2N] as an example, a comparison between the estimated and experimental
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data points of H2S solubility in [HEMIM][Tf2N] is shown in Figure 8. The estimated and
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experimental values are in good agreement. The percentages of predictive values in different ARD% range of the ELM2 model are depicted in Figure 9. It can be seen that 82.5% of ELM2
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model predictions are in the ARD% range of 0-5%, and only 2.88% of model predictions have
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ARD% values exceeding 20%. Table 3 demonstrates a detailed summary of the statistical parameters for ELM2 model. For the total set, the R2 and AARD% values are 0.994 and 3.84%, respectively. They are 0.996 and 3.53% for the training set and 0.985 and 5.07% for the test set, respectively. These results illustrate that the ELM2 model has good performance and is feasible to estimate the H2S solubility in ILs. In addition, the training of the ELM2 model only costs 1.1553 seconds on the same laptop computer used for ELM1 model.
17
ACCEPTED MANUSCRIPT
1.0 Exp. Cal. test set
Exp. Cal. training set
0.6
PT
0.4
0.2
0.0 200
400
600
800
SC
0
RI
H2S solubility in ILs
0.8
1000
1200
1400
Data number
ELM2 model, 303.15K
Exp, T=313.15K
ELM2 model, 313.15K
Exp, T=323.15K
ELM2 model, 323.15K
Exp, T=333.15K
ELM2 model, 333.15K
Exp, T=343.15K
ELM2 model, 343.15K
Exp, T=353.15K
ELM2 model, 353.15K
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0.5
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0.4
0.3
0.2
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H2S Mole Fraction
0.6
Exp, T=303.15K
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0.7
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Figure 7. Calculated versus experimental the H2S solubility in ILs of the ELM2 model in this study
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0.1
0.0
0
2
4
6
8
10
12
14
16
18
Pressure (bar)
Figure 8. Comparison between experimental solubility data (given as mole fractions) versus pressure and those predicted by the ELM2 model for [HEMIM][Tf2N] at different temperatures.
18
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ACCEPTED MANUSCRIPT
Table 3. The statistical parameters for the ELM2 model. No. R2 AARD % MSE 1055 263 1318
0.996 0.985 0.994
3.53 5.07 3.84
1.07 E-04 4.23 E-04 1.70 E-04
RMSE 0.0103 0.0208 0.0130
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Training set Test set Total set
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Data set
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Figure 9. Percent of value in different ARD% range of the ELM2 model
4.4 Comparison between this work and the previous publications
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As shown in Tables 2 and 3, the statistical parameters (R2, AARD%, MSE, and RMSE)
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indicate that the ELM2 model is more robust and efficient than the ELM1 model. To assess the final results of the two evolved models for estimating the H2S solubility in ILs, a broad
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comparison of different models including EOS, COSMO-RS and intelligence algorithms has
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been summarized in Table 4. In contrast to other models, the predictive models established by intelligence algorithms (such as ANN, LSSVM, and ELM) have better performances, and the ANN (MLP) models established by Barati-Harooni et al. has the best accuracy till the compilation of this work[48]. It is worth mentioning that in the current established intelligent algorithm models by other authors[23-26, 48, 49], experimental properties are needed as input parameters/descriptors (such as Tc, Pc, and ω), but in many cases, these critical properties of ILs are difficult to be measured directly[50]. Although our previous work[30] used chemical 19
ACCEPTED MANUSCRIPT groups as input descriptors, eliminating the need for experimental data as input parameters, it suffers from the bottleneck of not identifying isomers. However, compared with the models mentioned above, the main advantage of this study is that there is no need for experimental data as input descriptors, and the SEP descriptors proposed in this study are calculated from quantum
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chemistry having rich information at the electronic level. Due to the different data points, ILs
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and descriptors, it is reasonless to directly compare the ELM, ANN and LSSVM models, but it
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also can be concluded that models developed by ELM algorithm are established based on a larger number of experimental data points and kinds of ILs, hence they could be more general
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and practical to estimate the H2S solubility in ILs.
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Table 4. The comparison of different models for H2S solubility in ILs. Method Np NIL AARD % Reference PR EOSa
465
11
38.95
[24, 25]
465 465 465 664 664 664 722 722
11 11 11 14 14 14 16 16
36.43 4.90 4.87 196.76 8.35 5.03 38.64 38.14
[24, 25] [24, 25] [24, 25] [26] [26] [26] [29] [29]
GEP
465
11
4.38
[25]
ANN
465
11
4.58
[23]
ANN
664
14
2.07
[26]
LSSVM
465
11
2.28
[24]
ANN (GA-RBF)
465
11
1.90
[48]
ANN (MLP)
465
11
1.16
[48]
ANN
496
12
1.94
[49]
ELM
465
11
1.26
[30]
QSPR1(ELM)
1282
27
3.73
[47]
QSPR2(ELM) ELM1
1282 1318
27 28
3.80 5.87
[47] this work
ELM2
1318
28
3.84
this work
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SRK EOS PR EOSb SRK EOSb PR EOSa PR EOSb Empirical model COSMO-RS (ADF 2005) COSMO-RS (ADF 1998)
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a
NP: the number of experimental data points; NIL: the number of ILs a : that the interaction parameters (ki,j) is not considered; b : that the ki,j is considered. 20
ACCEPTED MANUSCRIPT 5. 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
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several SEP descriptors were screened via stepwise linear algorithm approach. Two novel ELM
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models (ELM1 and ELM2) were built based on screened parameters and both exhibited
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excellent accuracy and stability to precisely predict the H2S solubility in ILs. Notably, the ELM2 model with lower AARD% and RMSE has a better prediction ability. The models developed in
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this study were also compared with other models, and the comparative results illustrated that
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the established ELM models have relatively better accuracy for modeling the H2S solubility in ILs. This work implies that the SEP descriptors can be extensively used to predict the gas
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solubility properties of ILs and other materials.
Acknowledgement
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We are grateful for the financial support provided by the China Postdoctoral Science
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Foundation (2017M621477, 2017M621476).
21
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[17] K. Kurnia, F. Harris, C. Wilfred, M.A. Mutalib, T. Murugesan, Thermodynamic properties of CO2 absorption in hydroxyl ammonium ionic liquids at pressures of (100–
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ACCEPTED MANUSCRIPT Highlights Electrostatic potential surface (SEP) quantum chemistry descriptors were proposed.
1318 experimental data points for 28 ILs were collected from 15 references.
Extreme learning machine algorithm was employed to develop predictive models.
The AARD% for the ELM1 and ELM2 models were 5.87% and 3.84%, respectively.
The SEP descriptors could be extensively employed to predict properties of ILs.
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