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.