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Original article
07 2022
:15;
103870
doi:
10.1016/j.arabjc.2022.103870

Computational insights into quinoxaline-based corrosion inhibitors of steel in HCl: Quantum chemical analysis and QSPR-ANN studies

, , , , , , , , ,
a Department of Chemistry, School of Chemical and Physical Sciences and Material Science Innovation & Modelling (MaSIM) Research Focus Area, Faculty of Natural and Agricultural Sciences, North-West University, Private Bag X2046, Mmabatho 2735, South Africa
b Department of Chemistry, Faculty of Science, Obafemi Awolowo University, Ile Ife 220005, Nigeria
c Department of Chemical Sciences, University of Johannesburg, P.O. Box 17011, Doornfontein Campus, Johannesburg 2028, South Africa
d Innovative Durable Building and Infrastructure Research Center, Center for Creative Convergence Education, Hanyang University-ERICA, 55 Hanyangdaehak-ro, Sangrok-gu, Ansan-si, Gyeonggi-do, 15588, Korea
e Institute for Nanotechnology and Water Sustainability, College of Science, Engineering and Technology, University of South Africa, Johannesburg 1710, South Africa
f Department of Mechanical Engineering, College of Engineering, King Saud University, P.O. Box 800, Al-Riyadh 11421, Saudi Arabia
g Chemistry Department, Umm Al-Qura University, Al-Qunfudah University College, Saudi Arabia
h Department of Architectural Engineering, Hanyang University-ERICA, 1271 Sa 3-dong, Sangrok-gu, Ansan 426791, Korea

⁎Corresponding authors. hlgaz@hanyang.ac.kr (Hassane Lgaz), ercleehs@hanyang.ac.kr (Han-Seung Lee), ebensee@unisa.ac.za (Eno E. Ebenso)

Received: , Accepted: ,
© The Author(s) 2022
Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

The inhibition of mild steel deterioration via organic substances has become popular nowadays. Among the myriads of organic substances applied as potential inhibitors, quinoxalines stand out as toxic-free, cheap and effective compounds in different electrolytes. This report investigates the computational aspects of selected quinoxaline compounds tested as suppressors of mild steel deterioration in HCl medium using quantum chemical method (Density Functional Theory, DFT) and quantitative structure property relationship (QSPR). Feature selection tool was utilized to choose five top molecular descriptors (constitutional indices) that were used to characterize the quinoxaline molecules. Linear (ordinary least squares regression) and nonlinear (artificial neural network) modelling were adopted to correlate the selected constitutional indices of the studied quinoxalines with their experimental inhibition performances. The nonlinear model showed better performance as shown by the obtained results; RMSE of 5.4160, MSE of 29.3336, MAD of 2.3816 and MAPE of 5.0389. The developed models were utilized to determine the inhibition performances of ten new quinoxaline-based corrosion inhibitors which showed excellent inhibition performances of 87.88 to 95.73%.

Keywords

Corrosion inhibitors
Quinoxalines
Molecular descriptors
Quantitative structure property relationship
Ordinary least squares regression
Artificial neural network
PubMed
1

1 Introduction

Metallic deterioration has received a lot of attention in the academic and research communities because of its socio-economic effects on the world at large (Saranya et al., 2021). The economic impact of corrosion has been reported to be 3–5% of the annual global gross domestic product (GDP) which amounts to nearly $2.5 trillion (Mishra et al., 2018). Corrosion has direct effect on materials that humans heavily depend upon for survival and convenience. More so, corrosion has resulted in the collapse of bridges and buildings as well as contamination of water bodies due to pipe bursts/explosions which affect human and aquatic life (Goni and Mazumder, 2019). Chemical inhibitors have been widely formulated by corrosion researchers to mitigate metallic corrosion. Quinoxalines belong to a group of organic inhibitors that have been widely assessed for their inhibitive properties in different corrosive media (Chauhan et al., 2020, Saranya et al., 2021). They have also been found to be environmentally friendly and suited for application in various chemical, mechanical, material and metallurgical industries. The high performance of quinoxaline-based corrosion inhibitors has been traced to the functional groups, conjugate multiple bonds and aromatic rings present in their molecular structures. Generally, researchers have employed theoretical tools such as quantum chemical studies and atomic simulations to identify relevant electronic and structural properties that relate to the inhibition performance. Moreover, several studies have applied results from theoretical calculations such as density functional theory (DFT) and molecular simulations to interpret the inhibition mechanism of investigated quinoxalines (Zarrouk et al., 2013, Zarrouk et al., 2014, Ouakki et al., 2021).

Quantitative structure property relationship (QSPR) is the one of the latest and reliable theoretical methods that has been widely used in designing drugs and developing new materials for different applications (Liu et al., 2017, Lin et al., 2020). This technique makes it possible to forecast the property of interest for a series of non-tested compounds based on the established relationship between the differences in their structural features and the targeted property (Al-Fakih et al., 2016, Rybińska-Fryca et al., 2020). QSPR has become a desirable approach for determining the inhibition performance of potential chemical compounds. The process of QSPR analysis begins with collection and preparation of inhibitor molecules and their experimental inhibition efficiencies (IE%). Thousands of molecular descriptors comprising electronic and structural descriptors derived from calculations performed using theoretical software packages are reduced to a relevant small number. Selection of relevant molecular descriptors utilized in model development is often done using feature selection tools. As a rule of thumb, Topliss and Costello proposed that the ratio of chemical compounds to molecular descriptors should be at least 5:1 for simple linear models to avoid overfitting (Topliss and Costello, 1972, Topliss and Edwards, 1979). The selected relevant molecular descriptors are utilized in developing correlation models via linear and/or nonlinear methods which are validated using statistical indicators and further employed in designing novel organic inhibitors (Quadri et al., 2021b). Molecular descriptors are the most significant and critical elements in obtaining a reliable QSPR model as they are employed in modelling several different chemical properties in scientific fields (Khan, 2016). The type of molecular descriptors employed and how best they encode the structural features of chemical compounds that are correlated to the activity are critical determinants of the reliability of any QSPR model. An ideal descriptor is expected to be related to a wide range of compounds, correlate with the structural characteristics for inhibition performance, show insignificant correlation with other descriptors and should be easily computed. Additionally, an ideal descriptor should yield different values for molecules with different structures and should possess physical interpretation (Puzyn et al., 2010, Roy et al., 2015a,b).

Instances of QSPR models developed to study the relationship between features of organic compounds and IE% include a study conducted by Zhao and coworkers (Zhao et al., 2014). They performed quantum chemical studies and molecular dynamic simulations on 19 amino acids tested as anticorrosive agents for mild steel degradation in hydrochloric acid. Subsequently, feature selection of obtained chemical descriptors was done using principal component analysis (PCA) before QSPR model building. The model was constructed using a nonlinear technique, support vector machine (SVM) and the model performance was determined by the root mean square error (RMSE) and correlation coefficient (R2) value. Individual quantum chemical indices were correlated with the IE% and showed low correlation which necessitated the demand for a nonlinear model. Reported statistical parameters for RMSE and R2 were 1.48 and 0.97 for the testing set which showed good performance. The authors theoretically designed 5 amino acids and the predicted IE% was in the range of 62 to 68%. In another study, this research group reported theoretical approaches of DFT calculations and molecular simulations to study the inhibitive properties of 20 benzimidazole-based inhibitors (Li et al., 2015). Correlation of molecular descriptors with IE% conducted with a linear model generally showed poor results, improved results were obtained when descriptors for protonated forms of the benzimidazoles were used. PCA was conducted to select appropriate quantum chemical parameters to be considered for modelling. Nonlinear SVM was adopted to develop the QSPR model for the studied benzimidazoles using six DFT-based indices of the protonated organic inhibitors including nuclear independent chemical shift (NICS). The reliability and predictive power of the model was demonstrated by the obtained results; low RMSE (6.79) and high R2 (0.96). The established model was adopted to calculate 6 newly designed benzimidazole molecules. Al-Fakih and coworkers built a QSPR model for 18 furan derivatives previously tested to impede metallic disintegration in HCl. Dragon 6 was used to calculate over 4,000 chemical descriptors that were reduced to 12 useful variables using the sure independence screening method (Al-Fakih et al., 2016). Two stage sparse multiple linear regression (MLR) was conducted, and the obtained results showed that the elastic net method yielded a better predictive capacity than the ridge penalty model judging by the two statistical criteria used (MSE and R2). In another study, seven DFT-based parameters were derived from 11 thiophene molecules used as chemical additives for metallic corrosion inhibition. The authors developed a neural network model to correlate the selected molecular variables with the experimental IE% and obtained an excellent correlation of 0.958 which indicated the predictive potential of the developed model (Khaled and Al-Mobarak, 2012).

The aim of the present report is to present computational insight into the inhibition mechanism of 40 quinoxalines using quantum chemical method and QSPR model with constitutional indices as input parameters. Quantum chemical parameters are commonly used as input variables for QSPR model construction but recently, some researchers have continued to challenge the simplistic correlation often reported between quantum chemical indices and inhibition performances (Kokalj, 2010, Winkler et al., 2014, Winkler et al., 2016, Kokalj, 2021, Kokalj et al., 2021). Constitutional indices derived from Dragon 7 software have been employed in this study to model the relationship between experimental inhibition performances and 40 quinoxaline molecules. Linear model using ordinary least squares regression (OLS) and nonlinear model via artificial neural network (ANN) was developed. Several studies have reported traditional linear regression tools in QSPR model development. On the other hand, ANN which offers a modern intelligent approach to solving regression and classification problems has been scarcely reported. ANN has gained wide acceptance and applications in several fields of study and is also suitable for QSPR studies in corrosion inhibition. Furthermore, the built models were used to forecast the inhibition performances of 10 non-synthesized, non-tested quinoxaline molecules as potential inhibitors of metallic deterioration in acidic solution.

2

2 Materials and methods

2.1

2.1 Selected quinoxaline compounds

A database of 40 quinoxaline-based corrosion inhibitors and their inhibition performances were retrieved from published reports (Adardour et al., 2010, Benbouya et al., 2012, Fu et al., 2012, Adardour et al., 2013, El-Hajjaji et al., 2014, Olasunkanmi et al., 2015, Lgaz et al., 2016a,b, Olasunkanmi et al., 2016a,b, Tazouti et al., 2016, Rbaa et al., 2018, Benhiba et al., 2020, Laabaissi et al., 2020, Olasunkanmi and Ebenso, 2020). Data curation and filtration were done to ensure the development of a reliable model. This includes ensuring collected data are from reliable sources, confirming the correctness of the molecular structures of collected compounds, and removing redundant and/or duplicate inhibitor molecules if any (Golbraikh et al., 2012). Important information on the collected series of quinoxalines used for QSPR model development are displayed in Table 1. From the table, it is clear that 4-(quinoxalin-2-yl)phenol (PHQX) offered the maximum protection of 98.30% to the steel substrate.

Table 1 Molecular structures and experimental IE% of the investigated quinoxaline-based corrosion inhibitors.
S/N Quinoxalines Chemical structures IE% Ref
1. 1-[3-(4-methylphenyl)-5-(quinoxalin-6-yl)-4,5-dihydropyrazol-1-yl]butan-1-one
(Me-4-PQPB)		 80.42
 Olasunkanmi et al. (2016a)
2. 1-[3-(4-methoxyphenyl)-5-(quinoxalin-6-yl)-4,5-dihydro-1H-pyrazol-1-yl]butan-1-one
(Mt-4-PQPB)
72.01 Olasunkanmi et al. (2016a)
3. 1-[3-(3-methoxylphenyl)-5-(quinoxalin-6-yl)-4,5-dihydropyrazol-1-yl]butan-1-one
(Mt-3-PQPB)		 69.66
 Olasunkanmi et al. (2016a)
4. 1-[3-(2H-1,3-benzodioxol-5-yl)-5-(quinoxalin-6-yl)-4,5-dihydropyrazol-1-yl]butan-1-one
(Oxo-PQPB)		 68.41
 Olasunkanmi et al. (2016a)
5. 1-[3-(phenyl-5-quinoxalin-6-yl)-4,5-dihydro-1H-pyrazol-1-yl]butan-1-one
(PQDPB)		 90.50
 Olasunkanmi et al. (2015)
6. 1-[3-(phenyl-5-quinoxalin-6-yl)-4,5-dihydro-1H-pyrazol-1-yl]propan-1-one
(PQDPP)		 93.65
 Olasunkanmi et al. (2015)
7. 2-phenyl-1-[3-phenyl-5-(quinoxalin-6-yl)-4,5-dihydro-1H-pyrazol-1-yl]ethanone
(PPQDPE)		 86.88
 Olasunkanmi et al. (2015)
8. N-{2-[1-propanoyl-5-(quinoxalin-6-yl)-4,5-dihydro-1H-pyrazol-3-yl]phenyl}methanesulfonamide
(MS-2-PQPP)
 91.54
 Olasunkanmi et al. (2016b)
9. N-{3-[1-propanoyl-5-(quinoxalin-6-yl)-4,5-dihydro-1H-pyrazol-3-yl]phenyl}methanesulfonamide
(MS-3-PQPP)		 93.88
 Olasunkanmi et al. (2016b)
10. N-{4-[1-propanoyl-5-(quinoxalin-6-yl)-4,5-dihydropyrazol-3-yl]phenyl}methanesulfonamide
(MS-4-PQPP)		 93.56
 Olasunkanmi et al. (2016b)
11. N-{2-[1-(methanesulfonyl)-5-(quinoxalin-6-yl)-4,5-dihydro-1H-pyrazol-3-yl]phenyl}methanesulfonamide
(MS-2-PQPMS)		 92.68
 Olasunkanmi et al. (2016b)
12. N-{3-[1-(methanesulfonyl)-5-(quinoxalin-6-yl)-4,5-dihydro-1H-pyrazol-3-yl]phenyl}methanesulfonamide
(MS-3-PQPMS)		 93.39 Olasunkanmi et al. (2016b)
13. N-{4-[1-(methanesulfonyl)-5-(quinoxalin-6-yl)-4,5-dihydro-1H-pyrazol-3-yl]phenyl}methanesulfonamide
(MS-4-PQPMS)		 94.00
 Olasunkanmi et al. (2016b)
14. 1-[3-(3-methoxyphenyl)-5-(quinoxalin-6-yl)-4,5-dihydropyrazol-1-yl]propan-1-one
(Mt-3-PQPP)		 93.69
 Olasunkanmi and Ebenso (2020)
15. 1-(3-(4-chlorophenyl)-5-(quinoxalin-6-yl)-4,5-dihydro-1H-pyrazol-1-yl)propan-1-one
(Cl-4-PQPP)		 92.27 Olasunkanmi and Ebenso (2020)
16. (E)-1-benzyl-3-(4-methoxystyryl)quinoxalin-2(1H)-one
(QN1)		 93.00
 Lgaz et al. (2016a)
17. (E)-3-(2-(furan-2-yl)vinyl)quinoxalin-2(1H)-one
(QN2)		 90.00
 Lgaz et al. (2016a)
18. (E)-3-(4-methoxystyryl)quinoxalin-2(1H)-one
(QN3)		 87.00
 Lgaz et al. (2016a)
19. (E)-3-styrylquinoxalin-2(1H)-one
(QN4)
 85.00
 Lgaz et al. (2016a)
20. 3-methyl-1-prop-2-ynylquinoxalin-2(1H)-one
(Pr-N-Q = O)		 88.80 El-Hajjaji et al. (2014)
21. 3-methyl-1-prop-2-ynylquinoxaline-2(1H)-thione
(Pr-N-Q = S)		 92.30
 El-Hajjaji et al. (2014)
22. Quinoxaline
(QX)		 84.20
 Fu et al. (2012)
23. 2-chloroquinoxaline
(CHQX)		 92.50
 Fu et al. (2012)
24. 2-quinoxalinethiol
(THQX)		 95.50 Fu et al. (2012)
25. 4-(quinoxalin-2-yl)phenol
(PHQX)		 98.30
 Fu et al. (2012)
26. 3-methylquinoxalin-2(1H)-one
(Q = O)		 66.60
 Benbouya et al. (2012)
27. 3-methylquinoxalin-2(1H)-thione
(Q = S)		 82.80
 Benbouya et al. (2012)
28. 7-chloro-3-methylquinoxalin-2(1H)-thione
(Cl-Q = S)		 75.00
 Benbouya et al. (2012)
29. 7-chloro-2-(4-methoxyphenyl)thieno[2,3-b]quinoxaline
(CMOPTQ)		 89.00
 Adardour et al. (2013)
30. 7-chloro-3-(4-methoxystyryl)quinoxalin-2-one
(CMOSQ)		 87.00
 Adardour et al. (2013)
31. (E)-3-(4-methoxystyryl)-7-methylquinoxalin-2(1H)-one
(MOSMQ)		 92.00
 Tazouti et al. (2016)
32. (E)-3-(2-(furan-2-yl)vinyl) quinoxalin2(1H)-one
(FVQ)		 94.98
 Lgaz et al. (2016b)
33. 3,7-dimethylquinoxalin-2 (1H)-one
(DMQ = O)		 88.07
 Adardour et al. (2010)
34. 3,7-dimethylquinoxalin-2 (1H)-thione
(DMQ = S)		 93.27
 Adardour et al. (2010)
35. 1,4-bis((8-hydroxyquinolin-5-yl)-methyl)-6-methylquinoxalin-2,3-(1H,4H)-dione
(Q-HNHyQ)		 89.40
 Rbaa et al. (2018)
36. 1,4-bis-((8-hydroxyquinolin-5-yl)-methyl)-quinoxalin-2,3-(1H,4H)-dione (QCH3NHyQ) 95.40 Rbaa et al. (2018)
37. 2-(2,4-dichlorophenyl)-1,4-dihydroquinoxaline
(HQ)		 91.00
 Benhiba et al., 2020
38. 2-(2,4-dichlorophenyl)-6-methyl-1,4-dihydroquinoxaline
(CQ)		 94.20
 Benhiba et al., 2020
39. (E)-3-(4-chlorostyryl)quinoxalin-2(1H)-one
(CSQN)		 92.80
 Laabaissi et al. (2020)
40. (E)-3-(4-(dimethylamino)styryl)quinoxalin-2(1H)-one
(NSQN)		 96.40
 Laabaissi et al. (2020)

2.2

2.2 Molecular descriptors calculation

The study considered molecular descriptors derived from quantum chemical calculations and Dragon 7 software. Quantum chemical descriptors were generated by carrying out DFT calculations using B3LYP functional with 6-31+(d,p) basis set on the neutral forms of the quinoxaline molecules in aqueous and gaseous phases.The chemical structures of the quinoxalines were modelled using ChemDraw Professional 15.0 software and viewed using Gaussview 5.0. Optimizations of the molecules to a local minimum were performed using Gaussian 09 software and full optimization was verified by the absence of imaginary vibrational frequencies. Total energy (TE), dipole moment (μ) and energies of the lowest unoccupied molecular orbital (ELUMO) and highest occupied molecular orbital (EHOMO) were obtained for all the studied molecules. Other molecular descriptors for the inhibitor molecules were calculated using the following equations (Yusuf et al., 2020, Quadri et al., 2021a).

(1)
Δ E = E LUMO - E HOMO
(2)
EA = - E LUMO
(3)
IP = - E HOMO
(4)
χ = - 1 2 ( E HOMO + E LUMO )
(5)
η = 1 2 ( E LUMO - E HOMO )
(6)
σ = η - 1
(7)
Δ N = χ Fe - χ inh 2 ( η Fe + η inh ) where ΔE, EA, IP, χ, η, σ and ΔN represent energy gap, electron affinity, ionization potential, absolute electronegativity, global hardness, global softness and change in the number of electrons transferred, respectively.

Using the optimized molecular structures, numerous molecular descriptors were obtained from Dragon 7 (Mauri et al., 2006). Dragon 7 is a software application that calculates above 5000 molecular descriptors (0D, 1D, 2D and 3D) divided into 30 categories which can be used for QSPR modelling. Optimized quinoxaline molecules were converted from .log to .mdl file format using Open Babel (O'Boyle et al., 2011) and were used as inputs into Dragon 7 to calculate a host of molecular descriptors. Preliminary eliminations of high dimensional descriptors were done using the Dragon 7 software to remove descriptors with missing entries, descriptors with zero values and those with constant and/or near constant values. In addition, multicollinear descriptors and descriptors having standard deviation (SD) lower than 0.0001 were removed. The filtered descriptors were combined with DFT-based descriptors and subjected to standardization with the aim of ranking the descriptors in order of relative significance to the experimental IE%. This process was performed using Minitab 7.

2.3

2.3 Statistical modelling

Ordinary least squares regression, a form of MLR, was utilized to model the linear correlation between the filtered chemical variables (X) and the inhibition performance (Y) where X denotes the independent variable and Y is the dependent variable. The OLS regression was carried out using Minitab 7 and characterized by correlation coefficient and standard deviation.

On the other hand, ANN was adopted to model the nonlinear relationship between the chosen chemical variables and the inhibition performances of the investigated 40 quinoxaline molecules. Using a supervised learning method and a feedforward backpropagation architecture, neural network modelling was performed using Matlab. Six input parameters comprising five selected constitutional indices and inhibitor concentration served as the inputs, while three hidden neurons governed by logsig activation function and five hidden neurons controlled by the softmax activation function were utilized to model the output inhibition efficiencies (Fig. 1). The Levenberg-Marquardt training algorithm was implemented because of its effectiveness and quick convergence. Several iterations (training and retraining) were carried out until a low statistical error value was obtained.

ANN architecture for the model.
Fig. 1
ANN architecture for the model.

2.4

2.4 Statistical criteria

The performance of the linear model was characterized using R2 and SD while the nonlinear model was characterized using several statistical criteria. Statistically robust and reliable models are demonstrated by low statistical error values. The main statistical parameters are obtained using the following relationships (Gramatica 2013, Eftekhari et al., 2018, Liu et al., 2019, Olatunji et al., 2019, Adedeji et al., 2020a,b):

Root mean square error,

(8)
RMSE = ∑ k = 1 N y k - y k ^ 2 N

Mean square error,

(9)
MSE = ∑ k = 1 N y k - y k ^ 2 N

Mean average deviation,

(10)
MAD = 1 N ∑ k = 1 N y k - y ¯

Mean average percentage error,

(11)
MAPE = 1 N ∑ k = 1 N y k - y k ^ y k × 100 %

Coefficient of variation,

(12)
CoV = m e d i a n y k ^ - y k _ m e d i a n ^ y k _ m e d i a n ^

Relative mean bias error,

(13)
rMBE = 1 N ∑ k = 1 N y k ^ - y k y k where N denotes the number of dataset for analyzing each ANN model, y k , represents the experimental IE%, y k ^ , represents the predicted IE%, y k _ m e d i a n ^ represents the median of the predicted IE% and y ¯ denotes the mean IE%.

3

3 Results and discussion

3.1

3.1 DFT studies of selected quinoxalines

Inhibition performances of organic corrosion inhibitors of metal are closely correlated with their chemical stability or reactivity. The chemical reactivity of a series of chemical compounds are predicted by the analysis of frontier molecular orbital (FMO) theory. The theory gives useful insight on the probable adsorption centres of the organic molecules under study. From the presented images in Table 2, it is clear that the LUMO and HOMO energy orbitals in aqueous phase are widely spread on the quinoxaline moiety with minimal extension to the different substituent groups in some cases. This indicates that these sites would be the sites of preference for adsorption onto the mild steel (Fu et al., 2012, Olasunkanmi and Ebenso 2020). It should also be noted that there are a few cases where the HOMO and LUMO are localized around the phenyl rings (MS-n-PQPP series) (Olasunkanmi et al., 2016) and a few other cases where nearly all the atoms in the quinoxaline molecule act as sites of adsorption.

Table 2 Molecular orbital electron density distribution for investigated quinoxalines in aqueous phase.

Generally, the adherence capacity of inhibitor compounds can be explained as a donor–acceptor interface between the investigated compounds and the metal of interest. EHOMO is proportional to the electron contributing potential of the studied inhibitor, while ELUMO is connected to the electron accepting potential of the investigated compound. Lesser values of energy gap, ΔE are reported to imply higher inhibition efficiencies as these molecules undergo ease of transfer of one or more electrons from the HOMO level to the metallic orbital (Olasunkanmi et al., 2015, Benhiba et al., 2020). Studies have also shown that a hard molecule possesses higher values of energy gap, while the reverse occurs for soft molecules. It is therefore expected that a compound with a greater value of softness and lesser value of hardness will be more reactive and consequently favour adsorption potential ((Lgaz et al., 2016a) (Olasunkanmi et al., 2016a)). Lower TE also indicates that the quinoxaline compound adsorbs favourably through the active adsorption sites (Benhiba et al., 2020). The calculated DFT variables shown in Table 3 for the investigated quinoxalines do not follow any particular trend with respect to the reported experimental IE% due to the complex nature of the reaction occurring at the mild steel/electrolyte interface. The factors affecting the IE% of the quinoxaline-based inhibitors are quite numerous (Li et al., 2015).

Table 3 DFT-based indices for neutral forms of quinoxaline molecules in gas and liquid phases, as well as experimental parameters*.
Quinoxalines Conc* (M) Temp* (K) Phase TE
(eV)		 EHOMO (eV) ELUMO (eV) ΔΕ (eV) µ
(D)		 IP
(eV)		 EA
(eV)		 Χ
(eV)		 η
(eV)		 σ
(eV−1)		 ΔΝ IE%*
Me-4-PQPB 0.000280 303 G −31182.23 −6.035 −2.269 3.766 4.738 6.035 2.269 4.152 1.883 0.531 0.756 80.42
A −31182.71 −6.143 −2.418 3.725 7.156 6.143 2.418 4.281 1.863 0.537 0.730
Mt-4-PQPB 0.000270 303 G −33228.80 −5.839 −2.249 3.590 5.114 5.839 2.249 4.044 1.795 0.557 0.823 72.01
A −32610.20 −6.160 4.946 11.106 2.632 6.160 −4.946 0.607 5.553 0.180 0.576
Mt-3-PQPB 0.000270 303 G −33228.78 −6.077 −2.258 3.819 5.462 6.077 2.258 4.168 1.909 0.524 0.742 69.66
A −32610.18 −6.523 4.949 11.471 3.332 6.523 −4.949 0.787 5.736 0.174 0.542
Oxo-PQPB 0.000260 303 G −34588.63 −6.211 4.910 11.121 2.353 6.211 −4.910 0.650 5.561 0.180 0.571 68.41
A −35243.16 −5.912 −2.417 3.495 7.146 5.912 2.417 4.165 1.747 0.572 0.811
PQPDB 0.000170 303 G −29550.99 −6.574 4.927 11.502 2.529 6.574 −4.927 0.824 5.751 0.174 0.537 90.50
A −30112.69 −6.256 −2.421 3.835 6.313 6.256 2.421 4.338 1.918 0.521 0.694
PQDPP 0.000180 303 G −28501.14 −6.580 4.925 11.505 2.546 6.580 −4.925 0.827 5.753 0.174 0.537 93.65
A −28501.14 −6.580 4.925 11.505 2.547 6.580 −4.925 0.827 5.753 0.174 0.537
PPQDPE 0.000150 303 G −34260.11 −6.202 −2.270 3.932 4.117 6.202 2.270 4.236 1.966 0.509 0.703 86.88
A −34260.62 −6.296 −2.422 3.874 6.546 6.296 2.422 4.359 1.937 0.516 0.682
MS-2-PQPP 0.000240 303 G −46546.65 −6.327 −2.403 3.925 6.173 6.327 2.403 4.365 1.962 0.510 0.671 91.54
A −46547.39 −6.325 −2.437 3.888 9.869 6.325 2.437 4.381 1.944 0.514 0.674
MS-3-PQPP 0.000240 303 G −45739.13 −6.739 4.869 11.608 5.577 6.739 −4.869 0.935 5.804 0.172 0.522 93.88
A −31560.33 −6.527 4.947 11.474 3.342 6.527 −4.947 0.790 5.737 0.174 0.541
MS-4-PQPP 0.000240 303 G −45739.16 −6.470 4.844 11.314 4.062 6.470 −4.844 0.813 5.657 0.177 0.547 93.56
A −46547.38 −6.118 −2.422 3.695 7.497 6.118 2.422 4.270 1.848 0.541 0.739
MS-2-PQPMS 0.000230 303 G −57319.91 −6.589 −2.420 4.169 9.081 6.589 2.420 4.505 2.085 0.480 0.598 92.68
A −57320.90 −6.471 −2.448 4.023 14.915 6.471 2.448 4.460 2.012 0.497 0.631
MS-3-PQPMS 0.000230 303 G −56372.15 −7.070 4.861 11.931 4.737 7.070 −4.861 1.105 5.966 0.168 0.494 93.39
A −45739.13 −6.739 4.869 11.608 5.577 6.739 −4.869 0.935 5.804 0.172 0.522
MS-4-PQPMS 0.000230 303 G −57319.87 −6.369 −2.369 4.000 5.952 6.369 2.369 4.369 2.000 0.500 0.658 94.00
A −57320.89 −6.373 −2.441 3.932 11.481 6.373 2.441 4.407 1.966 0.509 0.659
Mt-3-PQPP 0.000275 303 G −31560.33 −6.527 4.947 11.474 3.342 6.527 −4.947 0.790 5.737 0.174 0.541 93.69
A −31560.33 −6.527 4.947 11.474 3.342 6.527 −4.947 0.790 5.737 0.174 0.541
Cl-4-PQPP 0.000275 303 G −40855.49 −6.823 4.834 11.658 1.247 6.823 −4.834 0.995 5.829 0.172 0.515 92.27
A −40855.49 −6.823 4.834 11.658 1.247 6.823 −4.834 0.995 5.829 0.172 0.515
QN1 0.005000 303 G −32290.52 −5.591 −2.421 3.170 0.539 5.591 2.421 4.006 1.585 0.631 0.945 93.00
A −31687.93 −5.667 4.602 10.269 1.860 5.667 −4.602 0.533 5.135 0.195 0.630
QN2 0.005000 303 G −21756.03 −5.742 −2.606 3.136 2.513 5.742 2.606 4.174 1.568 0.638 0.901 90.00
A −21756.41 −5.845 −2.739 3.106 3.753 5.845 2.739 4.292 1.553 0.644 0.872
QN3 0.005000 303 G −24467.82 −5.714 4.585 10.299 1.733 5.714 −4.585 0.564 5.149 0.194 0.625 87.00
A −24467.82 −5.713 4.584 10.297 1.733 5.713 −4.584 0.565 5.149 0.194 0.625
QN4 0.005000 303 G −21408.61 −5.959 4.529 10.488 2.008 5.959 −4.529 0.715 5.244 0.191 0.599 85.00
A −21408.61 −5.959 4.530 10.489 2.008 5.959 −4.530 0.715 5.244 0.191 0.599
Pr-N-Q = O 0.001000 303 G −17304.46 −6.355 5.263 11.618 2.056 6.355 −5.263 0.546 5.809 0.172 0.555 88.80
A −17634.00 −6.593 −2.226 4.367 4.608 6.593 2.226 4.410 2.184 0.458 0.593
Pr-N-Q = S 0.001000 303 G −26421.81 −6.044 −2.555 3.488 4.015 6.044 2.555 4.299 1.744 0.573 0.774 92.30
A −26422.09 −6.292 −2.680 3.612 6.436 6.292 2.680 4.486 1.806 0.554 0.696
QX 0.001000 298 G −11374.34 −6.987 −2.299 4.688 0.596 6.987 2.299 4.643 2.344 0.427 0.503 84.20
A −11374.52 −7.031 −2.382 4.649 0.765 7.031 2.382 4.706 2.325 0.430 0.493
CHQX 0.001000 298 G −23880.88 −7.184 −2.533 4.651 2.399 7.184 2.533 4.859 2.325 0.430 0.460 92.50
A −23881.05 −7.144 −2.554 4.590 3.161 7.144 2.554 4.849 2.295 0.436 0.469
THQX 0.001000 298 G −22209.92 −6.620 −2.326 4.295 1.087 6.620 2.326 4.473 2.147 0.466 0.588 95.50
A −22210.15 −6.659 −2.386 4.273 1.422 6.659 2.386 4.522 2.136 0.468 0.580
PHQX 0.001000 298 G −19709.40 −6.187 −2.240 3.947 1.951 6.187 2.240 4.214 1.974 0.507 0.706 98.30
A −19709.72 −6.263 −2.386 3.877 2.435 6.263 2.386 4.325 1.938 0.516 0.690
Q = O 0.001000 308 G −14492.12 −6.538 −2.117 4.421 3.335 6.538 2.117 4.328 2.210 0.452 0.604 66.60
A −14492.44 −6.553 −2.168 4.384 4.846 6.553 2.168 4.360 2.192 0.456 0.602
Q = S 0.001000 308 G −23280.35 −6.115 −2.573 3.541 4.192 6.115 2.573 4.344 1.771 0.565 0.750 82.80
A −23280.66 −6.271 −2.649 3.622 6.751 6.271 2.649 4.460 1.811 0.552 0.701
Cl-Q = S 0.001000 308 G −35786.78 −6.275 −2.759 3.516 2.501 6.275 2.759 4.517 1.758 0.569 0.706 75.00
A −35787.08 −6.355 −2.747 3.609 4.469 6.355 2.747 4.551 1.804 0.554 0.679
CMOPTQ 0.010000 303 G −45481.52 −6.199 4.034 10.233 4.906 6.199 −4.034 1.082 5.116 0.195 0.578 89.00
A −45481.52 −6.199 4.034 10.233 4.906 6.199 −4.034 1.082 5.116 0.195 0.578
CMOSQ 0.010000 303 G −36822.14 −5.919 4.236 10.156 1.767 5.919 −4.236 0.842 5.078 0.197 0.606 87.00
A −37439.97 −5.805 −2.731 3.074 1.689 5.805 2.731 4.268 1.537 0.651 0.889
MOSMQ 0.000100 298 G −25517.79 −5.633 4.640 10.274 2.138 5.633 −4.640 0.496 5.137 0.195 0.633 92.00
A −25517.79 −5.633 4.640 10.274 2.138 5.633 −4.640 0.496 5.137 0.195 0.633
FVQ 0.000100 298 G −21756.03 −5.742 −2.606 3.136 2.513 5.742 2.606 4.174 1.568 0.638 0.901 94.00
A −21756.41 −5.845 −2.739 3.106 3.753 5.845 2.739 4.292 1.553 0.644 0.872
DMQ = O 0.000100 298 G −15271.34 −6.267 5.384 11.651 2.631 6.267 −5.384 0.441 5.825 0.172 0.563 88.07
A −15271.34 −6.267 5.384 11.651 2.631 6.267 −5.384 0.441 5.825 0.172 0.563
DMQ = S 0.010000 298 G −23960.66 −5.348 4.890 10.239 2.871 5.348 −4.890 0.229 5.119 0.195 0.661 93.27
A −23960.66 −5.348 4.890 10.238 2.871 5.348 −4.890 0.229 5.119 0.195 0.661
Q-HNHyQ 0.001000 298 G −42704.01 −6.235 5.150 11.384 3.496 6.235 −5.150 0.542 5.692 0.176 0.567 89.40
A −42704.01 −6.235 5.150 11.384 3.496 6.235 −5.150 0.542 5.692 0.176 0.567
Q-CH3NHyQ 0.001000 298 G −44583.73 −6.081 −2.033 4.047 6.401 6.081 2.033 4.057 2.024 0.494 0.727 95.40
A −43753.97 −6.172 5.158 11.329 3.774 6.172 −5.158 0.507 5.665 0.177 0.573
HQ 0.001000 303 G −42072.41 −5.323 5.519 10.842 1.961 5.323 −5.519 −0.098 5.421 0.184 0.655 91.00
A −42707.73 −4.741 −1.263 3.478 2.418 4.741 1.263 3.002 1.739 0.575 1.149
CQ 0.001000 303 G −43777.44 −4.566 −1.266 3.300 2.024 4.566 1.266 2.916 1.650 0.606 1.238 94.20
A −43122.36 −5.251 5.541 10.793 2.131 5.251 −5.541 −0.145 5.396 0.185 0.662
CSQN 0.001000 303 G −33762.98 −6.162 4.271 10.433 4.983 6.162 −4.271 0.946 5.217 0.192 0.580 92.80
A −33762.98 −6.162 4.271 10.433 4.984 6.162 −4.271 0.946 5.217 0.192 0.580
NSQN 0.001000 303 G −24986.21 −5.445 4.659 10.104 1.236 5.445 −4.659 0.393 5.052 0.198 0.654 96.40
A −24986.21 −5.445 4.659 10.104 1.236 5.445 −4.659 0.393 5.052 0.198 0.654
* Experimental parameters i.e temperature, concentration and experimental IE% were retrieved from published studies.

3.2

3.2 Feature selection

Few highly informative descriptors from the numerous calculated quantum chemical and Dragon-based descriptors were obtained using feature selection. The MLR standardization method was adopted to carry out feature selection by ranking all the obtained molecular descriptors in order of their standardized coefficients or relative significance. Fig. 2 shows the significant features among the numerous molecular descriptors. The five topmost descriptors shown in Fig. 2 were utilized along with concentration in QSPR analysis using linear modelling (MLR) and nonlinear modelling (ANN) techniques. The selected descriptors (MW, nCsp2, nCsp3, nO and nN) have been described in Table 4. In addition, the plot of the Pearson’s correlation matrix of the selected chemical variables is presented in Table 5.

Significance of molecular descriptors to the inhibition efficiencies of quinoxalines.
Fig. 2
Significance of molecular descriptors to the inhibition efficiencies of quinoxalines.
Table 4 Definition of the selected descriptors for model building.
Descriptors Group name Description
MW Constitutional indices Molecular weight
nN Constitutional indices Number of nitrogen atoms
nO Constitutional indices Number of oxygen atoms
nCsp3 Constitutional indices Number of sp3 hybridized carbon atoms
nCsp2 Constitutional indices Number of sp2 hybridized carbon atoms
Table 5 Correlation matrix of selected features.
Conc MW nN nO nCsp3 nCsp2 IE%
Conc 1 −0.224 −0.473 −0.123 −0.427 −0.018 0.103
MW −0.224 1 0.845 0.819 0.697 0.818 0.108
nN −0.473 0.845 1 0.709 0.849 0.482 0.023
nO −0.123 0.819 0.709 1 0.504 0.629 0.079
nCsp3 −0.427 0.697 0.849 0.504 1 0.341 −0.246
nCsp2 −0.018 0.818 0.482 0.629 0.341 1 0.165
IE% 0.103 0.108 0.023 0.079 −0.246 0.165 1

3.3

3.3 MLR model

The obtained mathematical relation representing the QSPR model of investigated quinoxalines using the OLS method is as follows:

(14)
I E % = 74.84 + 270 C o n c + 0.0440 M W + 4.92 n N - 1.89 n O - 4.00 n C s p 3 - 0.170 n C s p 2

R2 = 0.3009, SD = 7.24607 where MW, nN, nO, nCsp2 and nCsp3 are the screened descriptors of interest and Conc denotes the concentration of quinoxalines. The developed OLS model clearly showed that the IE% of studied quinoxalines are influenced by increase in Conc, MW, nN and decrease in nO, nCsp3 and nCsp2. The screened descriptors are constitutional indices, which are known to affect the adherence ability of quinoxalines on mild steel surface. Numerous corrosion scientists have investigated the adsorption ability of organic molecules such as quinoxalines with oxygen and nitrogen atoms. These heteroatoms serve as active sites of adsorption thereby offering effective protection for the metal from corrosive ions. In addition, molecules having high molecular weight and sp2 and sp3 hybridized carbon atoms have been established to be effective corrosion inhibitors as they serve as anchoring sites for molecular adherence on the metallic substrate ((Lgaz et al., 2016a; Olasunkanmi et al., 2016a) Benhiba et al., 2020, Olasunkanmi and Ebenso, 2020).

Table 6 presents the ANOVA and regression coefficients table, which shows a p-value slightly higher than expected. It is clear that the model lacks the capability to accurately explain the inhibition mechanism of quinoxalines on the account of its low R2, high SD and high sum of squares error (SSE). Thus, it is mandatory to employ a nonlinear model to further investigate the relationship between the screened variables and the IE% of quinoxaline-based corrosion inhibitors.

Table 6 Analysis of variance and regression coefficients for the OLS model.
Source DF Adj SS Adj MS F-value p-value
Regression 6 745.92 124.320 2.37 0.052
Conc 1 15.58 15.578 0.30 0.590
MW 1 37.94 37.942 0.72 0.401
nN 1 127.18 127.180 2.42 0.129
nO 1 67.97 67.969 1.29 0.263
nCsp3 1 649.92 649.924 12.38 0.001
nCsp2 1 4.06 4.056 0.08 0.783
Error 33 1732.68 52.506
Lack-of-Fit 28 1725.83 61.637 44.97 0.000
Pure Error 5 6.85 1.371
Total 39 2478.60
Term Coeff SE Coeff T-value p-value
Constant 74.84 5.860 12.77 0.000
Conc 270.00 496.000 0.54 0.590
MW 0.04 0.052 0.85 0.401
nN 4.92 3.160 1.56 0.129
nO −1.89 1.660 −1.14 0.263
nCsp3 −4.00 1.140 −3.52 0.001
nCsp2 −0.17 0.613 −0.28 0.783

3.4

3.4 ANN model: internal validation

The inadequacy of the proposed linear model mandated the development of a nonlinear model to better comprehend the relationship between the descriptors and the IE% for quinoxaline compounds studied as anticorrosive agents. The neural network models were established to model the connection between the experimental IE% and the predicted IE%. The internal validation was carried out using k-fold validation technique. A k-fold of 5 was used which implies that the quinoxaline dataset was randomly divided into five equal groups and four groups (i.e., 32 compounds) were used to train the model in each case and one group (i.e., 8 compounds) was utilized to check the accuracy of the established model.

The results of the training and validation phase of the ANN built models for quinoxaline inhibitors are displayed in Fig. 3. The plots show instances of the calculated IE% diverging from the measured IE%. These divergences are observed both at the training and validation phases of the model development process. At the training phase, models 1 and 2 showed clear cases of underprediction while model 5 was clearly overpredicting the measured IE%. Models 3 and 4 revealed fair cases of divergence. At the validation stage, models 2, 4 and 5 clearly underpredict the checking dataset, while model 3 is a case of overprediction. These observed discrepancies between the experimental and calculated IE% are attributed to the misfiring of the neural network node (Adedeji et al., 2019).

Experimental IE% and predicted IE% at the model training and validation phase for quinoxaline derivatives (models 1–5).
Fig. 3
Experimental IE% and predicted IE% at the model training and validation phase for quinoxaline derivatives (models 1–5).
Experimental IE% and predicted IE% at the model training and validation phase for quinoxaline derivatives (models 1–5).
Fig. 3
Experimental IE% and predicted IE% at the model training and validation phase for quinoxaline derivatives (models 1–5).

ANN architecture used for model development was reported on Table 7 as 6-3-5-1. This implies that six molecular variables were used as input variables with 3 and 5 neurons at the hidden layers and an output of IE%. The error estimates between the measured and the predicted IE% have been established to be a reliable means of assessing the ability of the proposed models. Several statistical performance indices have been employed in this work to appraise the reliability and predictive power of the developed models. These include error functions such as MSE, RMSE, MAD and MAPE. These have been reported in other fields as excellent metrics to evaluate neural network models (Aouidate et al., 2016, Abdel-Ilah et al., 2017, Eftekhari et al., 2018). The selection of the best model is achieved by considering the model that yields the lowest values of these error functions and also shows minor variance between the training and validation phase (Gramatica, 2013). On this basis, the five proposed models with their respective error functions have been displayed in Table 7.

Table 7 ANN predictive model performance at the training and validation phase.
Metric Model 1 Model 2 Model 3 Model 4 Model 5 Average
Train Validation Train Validation Train Validation Train Validation Train Validation Train Validation
MSE 27.7813 57.9311 32.1215 1304.0 21.2783 29.3336 8.9254 140.9121 30.7511 338.9934 24.1715 380.4940
RMSE 5.2708 7.6112 5.6676 36.5421 4.6128 5.4160 2.9875 11.8706 5.5454 18.4118 4.8168 15.9703
MAD 3.3810 6.3525 2.7213 26.0772 2.8527 2.3816 2.0521 6.5330 3.6843 11.9122 2.9383 10.6513
MAPE 4.0055 7.9444 2.8803 22.1418 3.3460 5.0389 2.3188 11.7086 4.4810 10.5053 3.4063 11.4678
rMBE 0.5134 −0.8351 −1.1694 −22.1535 −0.8127 4.9120 0.6472 10.3818 0.3852 −9.7155 −2.1074 −3.4821
CoV 0.0171 0.0174 0.0440 0.0091 0.0296 0.0112 0.27 0.0098 0.0138 0.0357 0.1503 0.0166
Iterations 141 245 64 620 471 –
Topology 6-3-5-1 6-3-5-1 6-3-5-1 6-3-5-1 6-3-5-1 6-3-5-1

A careful comparison of the presented data in the table shows that model 3 could be adjudged to be the least biased to the selected dataset, based on statistical error analyses tools. This is because model 3 is characterized by consistent lower values of MSE, RMSE, MAD and MAPE when compared to the other developed models. Models 1 and 4 showed some promising error functions at some levels but were inconsistent with large variance between the training and validation phase.

3.5

3.5 ANN model: external validation

From the above findings and using the variants of molecules that yielded the highest inhibition efficiencies from experimental assessments, ten new quinoxaline compounds were theoretically designed. The inhibition performances of these novel quinoxalines were assessed using the QSPR models developed from MLR and ANN techniques. The calculated descriptors of the novel quinoxalines obtained from Dragon 7.0 software are displayed in Table 8.

Table 8 Descriptors for novel quinoxaline molecules.
Compounds Conc MW nN nO nCsp3 nCsp2
A 0.001 256.32 2 0 0 18
B 0.001 206.26 2 0 0 14
C 0.001 222.26 2 1 0 14
D 0.001 220.29 2 0 1 14
E 0.001 251.26 3 2 0 14
F 0.001 264.30 2 2 0 16
G 0.001 262.33 2 1 1 16
H 0.001 293.30 3 3 0 16
I 0.001 282.74 2 1 0 16
J 0.001 286.35 2 1 1 18

The chemical names and structures of the novel quinoxalines proposed as efficient anticorrosive agents for mild steel deterioration in HCl at 0.001 M are presented on Table 9. The predicted inhibition performances ranged from 87.88 to 94.77% for MLR model and 94.59 to 95.73% for the ANN model. The predicted IE% from the developed MLR and ANN models show that the novel quinoxalines are excellent inhibitors of acidic corrosion. The effect of the presence of substituents on the IE% of the newly designed quinoxaline molecules are also observed as is often reported in literature (Fu et al., 2012, Lgaz et al., 2016b, Tazouti et al., 2016, Benhiba et al., 2020).

Table 9 Inhibition efficiencies of novel quinoxaline molecules from MLR and ANN models.
Quinoxalines IUPAC nomenclature Molecular structure MLR predicted IE% ANN predicted IE%
A. 2-phenylquinoxaline 93.17 94.80
B. 2-(naphthalen-2-yl)quinoxaline 91.65 95.65
C. 3-(quinoxalin-2-yl)phenol 90.46 95.60
D. 2-(p-tolyl)quinoxaline 88.26 95.21
E. 2-(4-nitrophenyl)quinoxaline 94.77 95.73
F. (E)-3-(4-hydroxystyryl)quinoxalin-2(1H)-one 90.08 95.60
G. (E)-3-(4-methylstyryl)quinoxalin-2(1H)-one 87.88 95.27
H. (E)-3-(4-nitrostyryl)quinoxalin-2(1H)-one 94.39 95.66
I. (E)-7-chloro-3-styrylquinoxalin-2(1H)-one 92.78 95.46
J. (E)-3-(2-(1H-inden-7-yl)vinyl)quinoxalin-2(1H)-one 88.60 94.59

Fig. 4 showed a graphical representation of the predicted IE% from MLR and ANN models. It is obvious from the plot that the best ANN model showed a better surface coverage of the novel quinoxaline-based inhibitors on the mild steel surface in molar HCl than the linear model.

Comparison of predicted IE% of novel quinoxalines obtained with MLR and ANN models.
Fig. 4
Comparison of predicted IE% of novel quinoxalines obtained with MLR and ANN models.

A statistical analysis to ascertain whether the difference between the MLR and ANN models for the inhibition performance of the novel quinoxalines is statistically significant was conducted and the outcome is presented in Table 10. At a confidence level of 0.05, F (26.31093) > Fcrit (4.413873) which shows that there is a statistically significant variance between the MLR and ANN models for the test dataset.

Table 10 Analysis of variance between the MLR and ANN predicted test results.
Source of variation SS df MS F p-value Fcrit
Between Groups 86.22407 1 86.22407 26.31093 7.02E-05 4.413873
Within Groups 58.98817 18 3.27712
Total 145.2122 19

4

4 Conclusions

  1. Quantum chemical studies of 40 quinoxalines was performed and the orbital density distribution images provided information on the probable sites of adsorption. Molecular descriptors were calculated using DFT method and Dragon 7 software.

  2. Linear model showed poor correlation with the experimental IE% and high statistical error values which portends that corrosion inhibition mechanism is a complex nonlinear process that is affected by many factors. Nonlinear neural network presented a more reliable and robust alternative to modelling inhibition data to gain insight into inhibition mechanism.

  3. The established models suggest that the considered constitutional indices comprising molecular weight, number of oxygen atoms, number of nitrogen atoms and number of hybridized carbon atoms form an efficient group of molecular descriptors for QSPR modelling of quinoxaline inhibitors. Thus, constitutional indices are crucial for determining the inhibition efficiencies of quinoxaline molecules.

  4. Excellent inhibition performances of the 10 novel quinoxaline-based inhibitors obtained from the forecast using the developed QSPR models suggest that the non-synthesized compounds are potential organic compounds that can be explored experimentally as safe and effective inhibitors of metallic deterioration in molar HCl.

CRediT authorship contribution statement

Taiwo W. Quadri: Investigation, Data curation, Writing-Original draft. Lukman O. Olasunkanmi: Investigation, Data curation, Writing-Original draft. Omolola E. Fayemi: Investigation, Data curation, Writing-Original draft. Hassane Lgaz: Methodology, Validation, Formal analysis, Writing - Review & Editing, Supervision, Funding acquisition. Omar Dagdag: Investigation, Data Curation, Software, Writing - Review & Editing. El-Sayed M. Sherif: Investigation, Data Curation, Software, Writing - Review & Editing. Awad A. Alrashdi: Methodology, Validation, Formal analysis, Writing - Review & Editing, Supervision, Funding acquisition. Ekemini D. Akpan: Investigation, Data Curation, Software, Writing - Review & Editing. Han-Seung Lee: Methodology, Validation, Formal analysis, Writing - Review & Editing, Supervision, Funding acquisition. Eno E. Ebenso: Methodology, Validation, Formal analysis, Writing - Review & Editing, Supervision, Funding acquisition.

Acknowledgements

The authors acknowledge the Centre for High Performance Computing (CHPC), CSIR, South Africa for providing access to computational resources for this study. The authors would also like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: (22UQU4331100DSR01). This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2018R1A5A1025137).

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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