{Prediction of osmotic coefficients for ionic liquids in various solvents with artificial neural network} J. Serb. Chem. Soc. 82 (4) 399–409 (2017) UDC 532.7:544.275–128+54–145.2:510.644 JSCS–4975 Original scientific paper 399 Prediction of osmotic coefficients for ionic liquids in various solvents with artificial neural network YU CAO1, SHUN YAO2, XIANLONG WANG3,4, TIAN YAO2 and HANG SONG2* 1College of Life Science & Biotechnology, Mianyang Normal University, Mianyang 621000, China, 2Department of Pharmaceutical and Biological Engineering, Sichuan University, Chengdu 610065, China, 3School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu 610054, China and 4Department of Chemistry, Bryn Mawr College, 101 N Merion Ave, Bryn Mawr, PA 19010, USA (Received 17 September, revised 23 December 2016, accepted 9 January 2017) Abstract: The relationship between the structural descriptions and osmotic coefficients of binary mixtures containing sixteen different ionic liquids and seven kinds of solvents has been investigated by back propagation artificial neural network (BP ANN). The influence of temperature on the osmotic coef- ficients was considered and the concentrations of ionic liquids were close to 1 mol kg-1, except in acetonitrile. Multi linear regression (MLR) was used to choose the variables for the artificial neural network (ANN) model. A three layer BP ANN with seven variables containing structural descriptions of the ionic liquids and the character of the solvent as input variables was developed. Compared with experimental data, the osmotic coefficients calculated using the ANN model had a high squared correlation coefficient (R2) and a low root mean squared error (RMSE). Keywords: binary mixture; back propagation; artificial neural network; multi linear regression. INTRODUCTION Ionic liquids (ILs), as a type of widely applied green solvents, have aroused popular interest of academic community. Their excellent properties, such as chemical stability, thermal stability, low vapor pressure, high electronic conduct- ivity, etc.1 determine the extensive application of ionic liquids in different fields.2 Currently, ILs have been successfully used in the extraction of bioactive components from natural products3 and extraction of biological substances, such as proteins, amino acids, DNA, etc.4 The use of an extraction solvent demands an understanding of its physical chemistry. In these properties, the osmotic coef- ficient is thought to be very important for the selection of an extraction solvent.5 * Corresponding author. E-mail: hangsong@scu.edu.cn doi: 10.2298/JSC160725013D 400 CAO et al. Moreover, ionic liquids are thought to be designable solvents because their syn- thesis is relatively simple. A model that could predict the osmotic coefficients of ionic liquids would aid in the design of new and excellent ionic liquids as ext- raction solvents. A prediction model that could guide the chemical synthesis of ionic liquids is required by chemists. Recently, the osmotic coefficients of ionic liquids in some ordinary solvents, such as water, alcohols, benzene, acetonitrile, etc., have been studied by experi- mental and theoretical methods.6–8 However, compared with other physico- chemical and related properties of ionic liquids (see Fig. 19–19), theoretical models for estimating the osmotic coefficients of ionic liquids are relatively little researched at present. Fig. 1. Reported calculation methods in the study of some properties of ionic liquids. For aqueous solutions, the osmotic coefficients could be calculated theor- etically by the Pitzer equations or by the three-characteristic parameter correl- ation (TCPC) model.20 In addition, the earlier and more popular Pitzer model was successfully used to correlate the osmotic coefficients of ionic liquid dis- solved in water and acetonitrile.5,21 Furthermore, Karimzadeh et al.19 used Monte Carlo simulations to compute the osmotic coefficient of aqueous solutions of ionic liquids and reviewed computational models in the investigation of binary mixtures containing ionic liquids. Within the methods concerning the investigation of ionic liquids, the quan- titative structure–property relationship (QSPR) model has been widely used in the study of the properties of ILs and was proved to be an ideal method to fit and predict related data.22 The artificial neural network (ANN) method that is good at predictions is a very important algorithm to develop a QSPR model and was suc- cessfully adopted to study the electronic conductivity of ionic liquids in a pre- vious work.18 In this context, a QSPR model based on the ANN method was set PREDICTION OF ILS OSMOTIC COEFFICIENTS 401 up to correlate the structural characteristics and osmotic coefficients of seven solvents containing sixteen different ionic liquids. COMPUTATIONAL DETAILS Dataset and descriptors 84 sets of osmotic coefficient data for 16 types of ionic liquids in 7 kinds of solvents (chemical names and acronyms for the ILs are provided as Table I) at different temperatures were collected from the Ionic Liquid Database23 and other references.6,8,24,25 TABLE I. Acronyms used for the studied ILs Name Acronym 1-Methyl-3-methylimidazolium methyl sulfate [Mmim] [MeSO4] 1-Butyl-3-methylimidazolium methyl sulfate [Bmim][MeSO4] 1-Ethyl-3-methylimidazolium ethyl sulfate [Emim] [EtSO4] 1-Ethyl-3-methylpyridinium ethyl sulfate [Empy][EtSO4] 1-Butyl-3-methylimidazolium octyl sulfate [Bmim][OctSO4] 1-Ethyl-3-methylimidazolium chloride [Emim][Cl] 1-Butyl-3-methylimidazolium chloride [Bmim][Cl] 1-Hexyl-3-methylimidazolium chloride [Hmim][Cl] 1-Ethyl-3-methylimidazolium bromide [Emim][Br] 1-Propyl-3-methylimidazolium bromide [Pmim][Br] 1-n-Butyl-3-methylimidazolium bromide [nBmim][Br] 1-Pentyl-3-methylimidazolium bromide [Pnmim][Br] 1-Hexyl-3-methylimidazolium bromide [Hmim][Br] 1-Butyl-3-methylimidazolium tetrafluoroborate [Bmim][BF4] 1-Octyl-3-methylimidazolium tetrafluoroborate [Omim][BF4] 1-Butyl-3-methylimidazolium hexafluorophosphate [Bmim][PF6] The 3D structural coordinates of ionic liquids were obtained from the Cambridge Struc- tural Database (CSD).26 To reflect the prediction capability of model, the data points of the same solvent containing the same ionic liquid were not divided into different datasets. The 84 sets of data were divided into three datasets, i.e., a training set, a validation set and a test set containing 46, 24 and 30 % of the total data, respectively (Table II). TABLE II. The solvents with ionic liquids and data sets; training set: entry 1–15, validation set: entry 16–24, test set: entry 25–36 Entry Solvent IL Concentration, mol kg-1 Temperature, K Osmotic coefficient 1 1-Propanol [Bmim][MeSO4] 1.0071 323.15 0.629 2 1-Propanol [Empy][EtSO4] 0.9272 323.15 0.605 3 2-Propanol [Mmim] [MeSO4] 0.9721 323.15 0.461 4 Ethanol [Bmim][Cl] 1.096 313.15 0.742 1.096 333.15 0.63 5 Water [Bmim][MeSO4] 0.9552 298.15 0.698 0.9552 308.15 0.716 0.9552 318.15 0.732 0.9552 328.15 0.76 402 CAO et al. TABLE II. Continued Entry Solvent IL Concentration, mol kg-1 Temperature, K Osmotic coefficient 6 Water [Emim][Cl] 1.0472 313.15 0.861 1.0472 333.15 0.812 7 Water [Bmim][BF4] 0.9322 298.15 0.523 7 Water [Bmim][BF4] 0.9322 308.15 0.545 0.9322 318.15 0.564 0.9322 328.15 0.589 8 Water [Empy][EtSO4] 1.0336 313.15 0.813 1.0336 333.15 0.784 9 Water [Pmim][Br] 1.0292 298.15 0.702 1.0292 308.15 0.714 1.0292 318.15 0.717 1.0292 328.15 0.724 10 Benzene [Bmim][OctSO4] 1.1483 298.15 0.018 1.1483 303.15 0.016 1.1483 308.15 0.027 1.1483 313.15 0.039 11 Methanol [Bmim][OctSO4] 1.1872 298.15 0.373 1.1872 303.15 0.466 1.1872 308.15 0.579 1.1872 313.15 0.71 12 1-Propanol [Omim][BF4] 1.0008 298.15 0.045 1.0008 303.15 0.097 1.0008 308.15 0.165 1.0008 313.15 0.201 13 Acetonitrile [Bmim][PF6] 0.1015 318.15 0.3139 14 Methanol [Omim][BF4] 1.2766 298.15 0.327 1.2766 303.15 0.401 1.2766 308.15 0.481 1.2766 313.15 0.543 15 Water [Emim][Br] 0.4422 298.15 0.85881 16 1-Propanol [Bmim][OctSO4] 1.0548 298.15 0.057 1.0548 303.15 0.202 1.0548 308.15 0.319 1.0548 313.15 0.417 17 2-Propanol [Emim] [EtSO4] 0.9702 323.15 0.575 18 Ethanol [Bmim][MeSO4] 0.9851 323.15 0.496 19 Ethanol [Empy][EtSO4] 0.982 323.15 0.498 20 Water [nBmim][Br] 0.9713 318.15 0.7125 21 Water [Mmim] [MeSO4] 0.9792 313.15 0.896 0.9792 333.15 0.87 22 Benzene [Omim][BF4] 1.4487 298.15 0.026 1.4487 303.15 0.036 1.4487 308.15 0.075 1.4487 313.15 0.173 PREDICTION OF ILS OSMOTIC COEFFICIENTS 403 TABLE II. Continued Entry Solvent IL Concentration, mol kg-1 Temperature, K Osmotic coefficient 23 Water [Hmim][Cl] 1.0049 313.15 0.765 1.0049 333.15 0.732 24 Water [Hmim][Br] 1.1189 298.15 0.384 1.1189 308.15 0.397 24 Water [Hmim][Br] 1.1189 318.15 0.413 1.1189 328.15 0.429 25 1-Propanol [Emim] [EtSO4] 0.9772 323.15 0.596 26 2-Propanol [Bmim][MeSO4] 0.9823 323.15 0.523 27 2-Propanol [Empy][EtSO4] 0.9707 323.15 0.594 28 Ethanol [Emim] [EtSO4] 0.9888 323.15 0.504 29 Ethanol [Mmim] [MeSO4] 0.9868 323.15 0.449 30 Ethanol [Hmim][Cl] 1.0138 313.15 0.677 1.0138 333.15 0.5679 31 Water [Pnmim][Br] 1.0258 298.15 0.618 1.0258 308.15 0.637 1.0258 318.15 0.632 1.0258 328.15 0.649 32 Water [Emim] [EtSO4] 0.8919 298.15 0.706 0.8919 308.15 0.721 0.8919 318.15 0.73 0.8919 328.15 0.747 33 Ethanol [Omim][BF4] 1.0646 298.15 0.107 1.0646 303.15 0.197 1.0646 308.15 0.255 1.0646 313.15 0.33 34 1-Propanol [Mmim] [MeSO4] 0.9815 323.15 0.454 35 Acetonitrile [Bmim][BF4] 0.1043 318.15 0.3139 36 Ethanol [Bmim][OctSO4] 0.7636 298.15 0.036 0.7636 303.15 0.061 0.7636 308.15 0.106 0.7636 313.15 0.137 The cations and anions of the ionic liquids were optimized using the B3LYP method27,28 with the 6-31G(d) basis set, respectively. The optimization calculations were performed with the Gaussian03 program29 and quantum mechanics descriptors, such as energy (E), volume (V), the highest occupied molecular orbital energy (EHOMO), the lowest unoccupied molecular orbital energy (ELUMO) of the cations and anions, were considered. The molecular connect- ivity index, which is thought to be helpful in the investigation of the physical properties,30 was considered and chi index of zero order (0X), first order (1X) and second order (2X) of the ions were also calculated. All descriptors of the ions are listed in Table III. The solvents were described by their dielectric constant. The osmotic coefficients of ionic liquids are influenced by temperature and their concentration in solvents. In this context, the concentration of ionic liquids was kept close to 1 mol kg-1, except for acetonitrile, because the osmotic coefficient is much larger in this solvent than in the other solvents and related experimental data are lacking. To predict the osmotic coefficients of ionic liquids at different 404 CAO et al. temperatures, temperature must be considered as a variable in the related models. To decrease the redundancy existing in the descriptor data matrix, the correlation among related des- criptors and their correlation with the osmotic coefficient of the ILs were examined and col- linear descriptors (i.e., |r| > 0.9) were detected.31 Among the collinear descriptors, those show- ing high correlation with the osmotic coefficient were retained and the others were removed from the data matrix. TABLE III. Data on the calculated descriptors of cations and anions Ion E / Ha V cm3 mol-1 EHOMO eV ELUMO eV 0X 1X 2X [Mmim]+ –305.2307599 79.190 –0.43626 –0.18467 4.5875126942.176597520 1.663519480 [Bmim]+ –423.1786802 131.637 –0.42798 –0.17697 6.1106756493.752718471 2.226796000 [Emim]+ –344.5497093 91.159 –0.43158 –0.1805 5.2946194752.752718471 1.828497838 [Empy]+ –366.6178078 106.616 –0.44336 –0.23357 5.9247560003.211203000 1.979076000 [Hmim]+ –501.8072113 176.128 –0.40700 –0.17572 7.5248892004.752718000 2.933903000 [Pmim]+ –383.8648154 98.590 –0.42903 –0.17839 5.4035690003.252718000 1.873243000 [nBmim]+ –423.1828425 122.342 –0.42344 –0.17091 7.0875130003.452991000 3.427070000 [Pnmim]+ –462.4932894 101.983 –0.42303 –0.17662 6.8177824304.252718471 2.580349390 [Omim]+ –580.4349008 166.481 –0.37963 –0.17545 8.9391028005.752718000 3.641010000 [MeSO4]- –738.9948944 72.761 –0.06002 0.25643 3.0802070001.090822000 0.495772000 [EtSO4]- –778.3139770 102.525 –0.06373 0.23851 3.7873135391.678356102 0.834257000 [OctSO4]- –1014.197168 149.131 –0.06399 0.14990 8.0299542304.678356102 3.549402980 [Cl]- –460.2522333 22.518 0.01479 0.64337 0.00 0.00 0.00 [Br]- –2571.7613390 35.840 0.21400 0.50035 0.00 0.00 0.00 [BF4]- –424.4990828 39.883 –0.11504 0.45846 2.2189646731.069044968 0.606092000 [PF6]- –940.6433857 60.874 –0.15668 0.28100 2.7677868381.133893419 1.071429000 Prediction models The retained descriptors, temperature and concentration were selected as input variables of the multilinear regression model (MLR) model. To decrease the number of input variables for an ANN model, the descriptors usually need to be selected. The MLR model was thought to be a simple selection method that was successfully used in other studies.18,32 All the 84 sets of data were used to study the MLR relationship between the descriptors and osmotic coefficients by statistical products and service solutions (SPSS) software. The descriptors contributing the most were selected according to the squared correlation coefficient (R2) of MLR model. The descriptors selected by MLR model were collected as input variables for the back propagation (BP) ANN model. A brief description of the ANN has already been given:33 “A computational neural network consists of simple processing units called neurons. The strength of the neurons is determined by the weights (adjusted) that are first summed (com- bined) and then passed through a transfer function to produce the output for that neuron.” The BP algorithm means that the determination of the weight change is based on the error of the output unit. The fundamental theory and formulas of BP ANN and transfer functions can be found elsewhere.33,34 The experimental data of the osmotic coefficients were the output variable. A three-layer BP ANN model usually used to deal with data was set up. All para- meters were first normalized to a scale of 0 to 1 before training, validation or testing to avoid numerical overflows during the ANN processing. The initial weights of the training network and momentum factor were random. Then different transfer functions, learning rates and num- PREDICTION OF ILS OSMOTIC COEFFICIENTS 405 ber of neurons were inputted to calculate the osmotic coefficient of the ILs in the training sets by the BP ANN method. The ANN algorithms were implemented in MATLAB programming language. RESULTS AND DISCUSSION Descriptor selected by MLR method The collected descriptors were the independent variables and the osmotic coefficient was the dependent variable. The good correlations with the experi- mental osmotic coefficient were selected based on the squared correlation coef- ficient (R2). After discarding the descriptors without effective influence on the squared correlation coefficient, the model with the least number of descriptors and a high R2 was developed. The correlation obtained for 84 data points of the osmotic coefficient of the ILs was presented by a seven-parameter equation as follows: 1 2 3 4 5 6 7 0.496 0.00459 0.00148 0.0440 0.00376 0.202 0.268 0.212 = + + − + + + − + Y X X X X X X X (1) R2 = 0.774, F = 37.199, adjusted R2 = 0.753 Standard error = 0.129 where Y is the predicted osmotic coefficient of the ionic liquids and X1 to X7 represent the descriptors of ionic liquids and solvents. The MLR model was developed to predict the osmotic coefficient of the ILs as follows: X1 is the dielectric constant of the solvents; X2 is the energy of the cations; X3 is the anion chi index of second order; X4 is the temperature; X5 is the concentration of the ILs in solution; X6 and X7 are the energies of the HOMO and LUMO of the anion, respectively. The root mean squared error (RMSE), which is calculated as below, was used to measure the difference between the actual and the estimated values. ( )2exp calc 1 n i i i y y RMSE n = − =  (2) where i represents the i-th sample, yiexp is an experimental value, yicalc is the cor- responding value predicted by the model and n is the number of samples in the dataset.35 The RMSE of the above MLR model was 1.0014, which showed that the calculated osmotic coefficient of the ionic liquids had large deviations from the experimental data. The MLR model to predict the osmotic coefficient of the ionic liquids did not have enough precision to guide in the design of new ionic liquids. However, the descriptors that enabled the MLR model to have high R2 values in Eq. (1) may be major factors influencing the osmotic coefficient. 406 CAO et al. To avoid chance correlations, the y-randomization test was applied to the MLR model. The calculation procedure was repeated twenty-five times after shuffling the y vector randomly. The y-randomization results were that the high- est R2 within 25 time-calculations was 0.151, and the average R2 of 25 time- -calculations was 0.077. The low R2 values suggest minor risk of chance correl- ations. BP ANN model The descriptors selected by the MLR model were used as input variables for the BP ANN model, and the osmotic coefficient was the output variable. A three- layer ANN, which was usually used in QSPR models because of the good pre- diction capability, was chosen in this study. After optimization for the model several times, the number of neurons in the hidden layers was 7 and the learning rate was 0.06. A tan-sigmoid transfer function within the hidden layer and a linear transfer function within the output layer were selected for the ANN model. Multiple calculations were performed in order to obtain the global best results. Finally, the developed ANN model that achieved the goal of the training set and had good performance for the validation set was selected as the prediction model for the osmotic coefficient of ILs. The test set without contribution in model dev- elopment steps was calculated to test the prediction capability of the ANN model. The osmotic coefficients calculated by the ANN model are displayed in Fig. 2. Fig. 2. The plots of the osmotic coefficient calculated by the ANN model versus the experimental values. The dotted line presents y = x. PREDICTION OF ILS OSMOTIC COEFFICIENTS 407 The R2 of the training set, the validation set and the test set were 0.9733, 0.9478 and 0.9102, respectively. The RMSE of the training set, the validation set and the test set were 0.0428, 0.0658 and 0.0726, respectively. The results in Fig. 2 suggest that the osmotic coefficient calculated by the ANN model were similar to the experiment data. The training set was used to construct the ANN model, the high R2 and small RMSE suggested that the ANN model was able to fit the osmotic coefficient of ionic liquids. The validation set was used to determine the parameters of the ANN model. The data of test set did not appear in training and validation sets and did not participate in the construction of the ANN model. Thus, the test set could examine the prediction ability of the ANN model. The small RMSE of the test set suggested that the ANN model could be used to predict the osmotic coefficient of ionic liquids. Variable analysis The value of the variation inflation factor (VIF), which is thought to reflect the statistic significance of a model,35 was calculated using the following equation: 2 1 1 = − VIF r (3) where, r is the correlation coefficient of the multiple regression equation between one descriptor and the others. The VIF value of the seven variables employed in the MLR and ANN models were 2.025, 2.532, 3.257, 1.453, 1.748, 4.000 and 1.261, respectively. For each descriptor, its VIF value was less than five, which indicated the model had obvious statistical significance. In the seven variables, except temperature and concentration, the other five variables were dielectric constant of solvents, the energy of cations, the anion chi index of second order, and the energy of the HOMO and LUMO of the anion, respectively. There were three descriptors related with the anion: the chi index belonging to molecular topology information, which affects the combination of atoms in a molecule, and the energies of the HOMO and LUMO, which is related to the reaction activity of molecule. There was only one descriptor of the cation, which affects the stability of ions in the model. CONCLUSIONS In this study, an ANN model was established based on MLR analysis to fit and predict the osmotic coefficient of seven solvents containing various ILs at different temperatures. The ANN model with R2 = 0.9733 and RMSE = 0.0428 for the training set showed its good fitting capability. The predictive capability of the ANN model was proven by R2 = 0.9102 and RMSE = 0.0726. The selection of the descriptors by the MLR method were investigated and proved by good results. The analysis of the descriptors reflected the model had obvious statistical significance. 408 CAO et al. Acknowledgments. Preparation of this paper was supported by the Educational Com- mission of Sichuan Province, China (No. 16ZB0319) and the Scientific Research Foundation of Mianyang Normal University (No. QD2014A008). И З В О Д ПРЕДВИЂАЊЕ ОСМОТСКИХ КОЕФИЦИЈЕНАТА ЗА ЈОНСКЕ ТЕЧНОСТИ У РАЗЛИЧИТИМ РАСТВАРАЧИМА ПОМОЋУ ВЕШТАЧКИХ НЕУРОНСКИХ МРЕЖА YU CAO1, SHUN YAO2, XIANLONG WANG3,4, TIAN YAO2 и HANG SONG2 1College of Life Science & Biotechnology, Mianyang Normal University, Mianyang 621000, China, 2Department of Pharmaceutical and Biological Engineering, Sichuan University, Chengdu 610065, China, 3School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu 610054, China и 4Department of Chemistry, Bryn Mawr College, 101 N Merion Ave, Bryn Mawr, PA 19010, USA Релација узмеђу структурних описника и осмотских коефицијената бинарних смеша које садрже шеснаест различитих јонских течности и седам врста растварача истраживана је са унатраг напредујућим вештачким неуронским мрежама (BP ANN). Узет је у обзир утицај температуре на осмотске коефицијенте а концентрација јонских течности је била близу 1 mol kg-1 изузев у ацетонитрилу. Мултилинеарна регресија (MLR) коришћена је за избор варијабли за модел вештачке неуронске мреже (ANN). Развијен је трослојни BP ANN са седам варијабли које садрже структурне описнике јонских течности и карактера растварача као улазне варијабле. Поређењем са експе- рименталним подацима, осмотски коефицијенти израчунати са ANN моделом имају висок корелациони коефицијент (R2) и малу просечну квадратну грешку (RMSE). (Примљено 17. септембра, ревидирано 23. децембра 2016, прихваћено 9. јануара 2017) REFERENCES 1. J. Lu, F. Yan, J. Texter, Prog. Polym. Sci. 34 (2009) 431 2. R. F. Alamdari, F. G. Zamani, N. Zekri, J. Serb. Chem. Soc. 79 (2014) 1337 3. Y. Fukaya, R. Asai, S. Kadotani, T. Nokami, T. Itoh, Chem. Lett. 89 (2016) 879 4. Y. Cao, S. Yao, X. M. Wang, Q. Peng, H. Song, in Handbook of Ionic Liquids: Pro- perties, Applications and Hazards, J. Mun, H. Sim, Eds., Nova Publishers, Hauppauge, NY, 2012, p. 162 5. H Shekaari, M. T. Zafarani-Moattar, Fluid Phase Equilib. 254 (2007) 198 6. N. 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