7 | ARTIFICIAL NEURAL NETWORK (ANN) APPLICATION IN PREDICTING THE DISSOCIATION CONSTANTS FOR AMINES
Although the dissociation constant values of amines can be experimentally measured, it is costly to purchase these chemicals, in addition to the cost for disposal of chemical waste and time used to generate the data. Furthermore, researchers are mostly interested in obtaining dissociation constants of new compounds which have not been synthesized yet. It is important to estimate the constant values in advance to save chemical costs and experimental efforts. Therefore, many studies have attempted and focused on improving pKa prediction accuracy.
In all prediction methods, computational chemistry is a common method for the development of pKa estimation. Khalili et al.12 predicted the pKa values of 17 amines using the Gaussian software with 0.68 pKa unit of accuracy. Later, Sumon et al.20 improved Khalili’s method (KHE method) to reduce the accuracy to 0.28 pKa unit. However, the computational chemistry method can be challenging to predict the dissociation constants for large molecule amines which consume longer time and computer memory for optimizing the structures.
Besides computational chemistry and quantitative structure-property relationship (QSPR) methods, artificial neural networks (ANN) can be applied to predict the dissociation constant values. In short, ANN is inspired by the human brain and aims to process information in a soft modeling way without forming a complicated mathematical model.22 Therefore, one of the advantages of ANN, compared to QSPR is its flexibility and ability to recognize the nonlinear relationship in complicated systems without prior knowledge of an existing model; as a result, ANN has become more popular in solving scientific as well as engineering problems.23,24Habibi-Yangjeh et al.24 have combined both ANN and QSPR to successfully estimate the dissociation constant values of different benzoic acids and phenol at 298.15K. The final squared correlation coefficients (R2) for training, validation and prediction were 0.9926, 0.9943 and 0.9939, respectively. However, the work was limited to a prediction at 298.15K. This work will focus on estimating the pKa of amines for CO2 capture at various temperatures by applying ANN.
Most researchers have combined ANN and QSPR for estimating pKa ; however, one of the challenges is to convert the chemical structures of the compounds to numerical information which are readable in ANN. In general, the researchers need to generate the descriptors by constructing and optimizing the molecular models using a software such as HyperChem or MOPAC.24 The descriptor process would consume much time and efforts. Furthermore, the ANN and QSPR combined model can only work at 298.15K.
For this work, 568 data points of 25 sets of amines which are relevant to CO2 capture were collected. The list of amines is provided in Table S7. The collected data were divided into three categories: (a) molecular weight, critical temperature and pressure as input data to identify the compounds; (b) temperature dependent properties such as density, viscosity, surface tension and refractive index to correlate the dissociation constant values; and (c) pKa values as output data. Table S8 reports the densities (g⸳mL-1) of the eight studied amines at the various temperatures while Table S9 lists the measured dynamic viscosities (mPa‧s) of the amines. Lastly, Table S10 and S11 report the refractive indices and surface tension (mN/m) of the amines, respectively.
For inputs, the critical properties (Tc and Pc) were used to identify the specific amines while the temperature dependent properties (density, dynamic viscosity, surface tension and refractive index) were chosen as variables of the ANN model. For the entire model, a default data set was applied for training, validating and testing. In particular, a random 70% of data was chosen for training the model while 15% of the data set was selected for validation and the remaining 15% for testing the model.
Optimization of ANN plays an important role in network training which include optimization of the hidden layer numbers and the number of neurons in each hidden layer. Theoretically, there are no methods for determining the optimal number of hidden layers and neuron numbers. As a result, the program was executed with one layer and several neurons varying from 5 to 15 firstly to compare their performance. Figure 4 shows the performance comparison in terms of R and mean squared error (MSE). Based on the Figure 4, the single hidden layer with number neurons of 5 had the best performance with Roverall = 0.97598, MSEtrain = 0.0062, MSEval = 0.0094 and MSEtest = 0.0244.
To improve the model, the ANN model with two hidden layers has been executed with five neurons for the first hidden layer while the second layer’s number of neurons varied from 4 to 15. Figure 5 shows the best performance when seven neurons were used in the second hidden layer with Roverall = 0.99424, MSEtrain = 2.2x10-5, MSEval = 0.0094 and MSEtest = 0.0078.