A data set of twenty-eight coumarin-based antioxidants (1-28, Figure 1(Fig. 1)) was retrieved from the literature (Khoobi et al., 2011[18]; Saeedi et al., 2014[42]), in which their antioxidant activities are presented in Table 1(Tab. 1). All tested compounds were evaluated by 1,1-diphenyl-2-picryhydrazyl (DPPH) assay (detailed methodology is provided in original literatures (Khoobi et al., 2011[18]; Saeedi et al., 2014[42])). The activity was denoted as an IC₅₀ value (mM) which indicates concentration of the compound which can inhibit 50 % of the generated DPPH radicals in experimental setting. As a part of data pre-processing, the unit of IC₅₀ values was converted from mM to M, and the IC₅₀ values were further transformed into pIC₅₀ (−log IC₅₀) by taking the negative logarithm to base 10 as shown in Table 1(Tab. 1). The compound with high pIC₅₀ (low IC₅₀) represented the high antioxidant activity. A schematic workflow of QSAR model development is provided in Figure 2(Fig. 2).

Molecular structures of the coumarin derivatives were constructed by GaussView (Dennington et al., 2003[7]), which were subjected to geometrical optimization by Gaussian 09 (Revision A.02) (Frisch et al., 2009[12]) at the semi-empirical level using Austin Model 1 (AM1) followed by density functional theory (DFT) calculation using Becke's three-parameter hybrid method and the Lee-Yang-Parr correlation functional (B3LYP) together with the 6-31 g(d) basis.

The physicochemical properties (i.e., quantum chemical and molecular descriptors) were generated by different calculating softwares including Gaussian 09, Dragon, version 5.5. (Talete, 2007[49]), PaDEL, version 2.20 (Yap, 2011[60]) and Mold², version 2.0 (Hong et al., 2008[15]) softwares. The calculated descriptors as numerical values could be used to represent properties of the compounds, and were further used as predictors (X variables) for QSAR model construction. List of calculated descriptors are shown as follows.

Quantum chemical descriptors calculation obtained by low energy conformers from the geometrical optimization using Gaussian 09 composed of the total energy (E_total) of the molecule, the highest occupied molecular orbital energy (E_HOMO), the lowest unoccupied molecular orbital energy (E_LUMO), the total dipole moment (μ) of the molecule, the electron affinity (EA), the ionization potential (IP), the energy difference of HOMO and LUMO (HOMO-LUMO_Gap), Mulliken electronegativity (χ), hardness (η), softness (S), electrophilicity (ω), electrophilic index (ω_i), and the mean absolute atomic charge (Q_m) (Worachartcheewan et al., 2014[57]). Furthermore, the output files from geometrical optimization of Gaussian 09 were used as the input data for calculating a set of 3,224 molecular descriptors using Dragon software. The calculated descriptors included 22 classes comprising 48 constitutional descriptors, 119 topological descriptors, 47 walk and path counts, 33 connectivity indices, 47 information indices, 96 2D autocorrelation, 107 edge adjacency indices, 64 burden eigenvalues, 21 topological charge indices, 44 eigenvalue based indices, 41 randic molecular profiles, 74 geometrical descriptors, 150 RDF descriptors, 160 3D-MoRSE descriptors, 99 WHIM descriptors, 197 GETAWAY descriptors, 154 functional group counts, 120 atom centered fragments, 14 charge descriptors, 29 molecular properties, 780 2D binary fingerprints, and 780 2D frequency fingerprints.

An additional set of molecular descriptors was calculated by PaDEL software to give 1,444 1D and 2D descriptors, and Mold² software to generate 777 descriptors by encoding the 2D chemical structure information. Before the calculation, the molecular structures were saved to *.smi and then converted to *.mol files using OpenBabel version 2.3.2 (The Open Babel Package 2015). The *.mol files were used as the input data for calculation by PaDEL and Mold² softwares.

Descriptors selection was performed to filter a set of important informative descriptors from a whole set of descriptors. Feature selection was initially performed by stepwise multiple linear regression (MLR) using SPSS statistics 18.0 (SPSS Inc., USA) followed by determination of intercorrelation using Pearson's correlation coefficient using cutoff value of |r| ≥ 0.9. Any pairs of descriptors with |r| ≥ 0.9 were defined as highly correlated predictors, and one of them was excluded.

The data set of coumarin derivatives (1-28) was randomly selected, in which 85 % (~23 compounds) of the original data set was used as the training and the leave one-out cross-validation (LOO-CV) sets, and 15 % (~5 compounds) was used as the external set. The training set was employed to generate the QSAR models, whereas LOO-CV and external sets were used to evaluate the models. LOO-CV method was performed for internal validation by excluding one sample out from the whole data set to be used as the testing set while the remaining N−1 samples were used as the training set (Prachayasittikul et al., 2014[34]). This sampling process was repeated iteratively until every sample in the data set was used as the testing set. The external sets were used to validate the models.

QSAR models were generated using the MLR according to the equation 1.

where Y is the antioxidant activity (pIC₅₀), B₀ is the intercept, and B_n are the regression coefficients of the descriptors X_n. The MLR method was performed using Waikato Environment for Knowledge Analysis (Weka), version 3.4.5 (Witten et al., 2011[54]).

Statistical parameters were used to evaluate predictive performance of the constructed QSAR models. The calculated parameters included correlation coefficient (R²), root mean squared error (RMSE), predictivity (Q²), variance ratio (F ratio), adjusted correlation coefficient (R²_Adj), standard deviation (s) and predicted residual sum of squares (PRESS) (Saghaie et al., 2013[43]; Worachartcheewan et al., 2013[56]).

Chemical structures of the compounds and their antioxidant activities (Table 1(Tab. 1)) were used for construction of predictive models. The compounds were geometrically optimized with semi-empirical method AM1 followed by DFT/B3LYP/6-31 g(d) basis using Gaussian 09 to obtain lower-energy conformers. The optimized compounds were extracted to obtain 13 quantum chemical descriptors. These compounds were subsequently used as input files for calculating an additional set of 3,224 molecular descriptors (0D-3D) using Dragon software. The calculated descriptors with constant values and multi-collinearity were determined and removed to give a final set of 1,489 descriptors. In addition, original molecular structures of compounds were saved as *.smi file format and were converted into *.mol files using OpenBabel version 2.3.2. These *.mol files then were used as input files for descriptors calculation using Mold² and PaDEL softwares to obtain sets of 777 Mold² 2D descriptors and 1,444 PaDEL 0D-2D descriptors, respectively. Consequently, feature selection was performed to select a set of informative descriptors for the whole calculated set. Descriptors showing significant correlation with their bioactivities were selected using stepwise MLR. A set of 14 informative descriptors included 4 Dragon descriptors (i.e., nArNHR, ISH, B04[O-O] and G2p), 6 Mold² descriptors (i.e., D467, D278, D491, D384, D580 and D461), 4 PaDEL descriptors (i.e., SHBint4, SpMin2_Bhe, MATS8e and SssCH2) were obtained. Definition and numerical values of important descriptors are shown in Tables 2(Tab. 2) and 3(Tab. 3), respectively. Furthermore, the intercorrelation matrix between pair of molecular descriptors was performed using Pearson's correlation coefficient (r) (Supplementary Tables 1-3). Cutoff value of |r| ≥ 0.9 was used to determine the intercorrelation. The results showed that there was no intercorrelation within a set of selected descriptors as displayed by low |r| values ≤ 0.9, which suggested that each descriptor was independent from other descriptors. Finally, a set of 14 selected descriptors was further employed to construct 3 QSAR models (according to types of software used to calculate descriptor values) for predicting antioxidant activity of the coumarin derivatives.

Descriptors obtained from these softwares have been demonstrated for their successful QSAR modeling such as antioxidant (Alisi et al., 2018[1]; Rastija et al., 2018[39]), antimicrobial (Alyar et al., 2009[2]; Basic et al., 2014[4]; Podunavac-Kuzmanović et al., 2009[29]), anticancer (Sławiński et al., 2017[45]; Suvannang et al., 2018[48]) and antiviral (Duchowicz et al., 2018[8]; Saavedra et al., 2018[41]; Worachartcheewan et al., 2019[59]) activities. Herein, three models were separately constructed based on the types of key descriptors (i.e., model 1 Dragon descriptors, model 2 Mold² descriptors, and model 3 PaDEL descriptors). A set of 14 selected informative descriptors (as independent variables, Table 2(Tab. 2)) and antioxidant activities (pIC₅₀ values as dependent variables) of the studied compounds were included in the data sets for construction of QSAR models using Eq. (1). Before building the models, the data set of coumarin derivatives (1-28) was split into training, LOO-CV, and external sets. The training set was used to construct the model using MLR algorithm whereas both LOO-CV and external sets were utilized for validating the constructed models. Compounds 1, 6, 15, 21 and 27 were randomly selected to be used as external sets, while the remaining 23 compounds in the data sets (i.e., 2-5, 7-14, 16-20, 22-26 and 28) were employed as training set. As a result, three QSAR models (models 1-3) were successfully constructed for predicting antioxidant activities (pIC₅₀ values) of the studied coumarin analogs.

Model 1 (Dragon descriptors)

where N_Tr, N_LOO-CV and N_Ext are the number of compounds of training, LOO-CV and external sets. R²_Adj is the adjusted R².

Four molecular descriptors calculated from Dragon software were used as predictors to construct QSAR model 1 as shown in Eq. (2). Statistical parameters indicating predictive performance of the model are summarized in Table 4(Tab. 4). Training set showed R²_Tr = 0.901, RMSE_Tr = 0.154, while the LOO-CV set displayed the Q²_LOO-CV = 0.813, RMSE_LOO-CV = 0.210, and the external set with Q²_Ext = 0.952, RMSE_Ext = 0.104. Comparative plot of experimental versus predicted antioxidant activities (pIC₅₀) is shown in Figure 3a(Fig. 3). Residual values were calculated as a difference between experimental and predicted pIC₅₀ values. Small residual values indicated the precision of model prediction. Plot of the residual values is shown in Figure 3b(Fig. 3).

Model 2 (Mold² descriptors)

Six important descriptors obtained from the Mold² software were used to generate the model 2 as shown in Eq. (3). Statistical analysis of the model is given in Table 4(Tab. 4). It was observed that the model provided statistical R²_Tr = 0.958, RMSE_Tr = 0.099 for the training set, Q²_LOO-CV = 0.888, RMSE_LOO-CV = 0.169 for the LOO-CV set, and Q²_Ext = 0.875, RMSE_Ext = 0.170 for the external set. The experimental versus the predicted antioxidant activities of the model 2 were graphically plotted (Figure 3c(Fig. 3)), while Figure 3d(Fig. 3) was the plot of residual values.

Model 3 (PaDEL descriptors)

Model 3 of Eq. (4) was built using 4 significant descriptors generated by PaDEL software. Statistical evaluation of the model is shown in Table 4(Tab. 4). The results showed that the QSAR model displayed R²_Tr = 0.950, RMSE_Tr = 0.109 for the training set, Q²_LOO-CV = 0.908, RMSE_LOO-CV = 0.150 for the LOO-CV set, and Q²_Ext = 0.885, RMSE_Ext = 0.166 for the external set. Comparison of experimental and the predicted antioxidant activities of model 3 are outlined in Figure 3e(Fig. 3), while residual values were displayed in Figure 3f(Fig. 3).

In overview, three constructed models provided satisfactory results as indicated by their statistical parameters such as R², Q², RMSE, F ratio and PRESS values. The R² and Q² of the obtained QSAR models were considered as acceptable values when R²>0.6 and Q²>0.5 (Golbraikh and Tropsha, 2002[14]; Nantasenamat et al., 2010[26]). These parameters of all constructed models were in acceptable range (model 1: R²_Tr = 0.901, Q²_LOO-CV = 0.813 and Q²_Ext = 0.952, model 2: R²_Tr = 0.958, Q²_LOO-CV = 0.888 and Q²_Ext = 0.875, model 3: R²_Tr = 0.945, Q²_LOO-CV = 0.908 and Q²_Ext = 0.885. In addition, low values of RMSE, s and PRESS, but high value of F ratio indicated that the models were significant (RMSE_Tr = 0.154, RMSE_LOO-CV = 0.210, RMSE_Ext = 0.104, s = 0.238, PRESS = 1.019 and F ratio = 13.043 in model 1, RMSE_Tr = 0.099, RMSE_LOO-CV = 0.169, RMSE_Ext = 0.170, s = 0.203, PRESS = 0.659 and F ratio = 21.122 in model 2, and RMSE_Tr = 0.109, RMSE_LOO-CV = 0.151, RMSE_Ext = 0.164, s = 0.170, PRESS = 0.518 and F ratio = 44.52 and in model 3) (Frimayanti et al., 2011[11]; Rastija et al., 2018[39]). The statistical (Table 4(Tab. 4)) and graphical (Figure 3(Fig. 3)) results showed that the QSAR models (models 1-3) gave a reliable agreement of the experimental and the predicted antioxidant values. Furthermore, the plots of experimental activity and residual values (Figures 3b, 3d and 3f(Fig. 3)) displayed the distribution of residuals on both sides of the zero values indicating that there are no systemic error in the models (Jalali-Heravi and Kyani, 2004[16]). Therefore, the QSAR models 1-3 could be possibly used and reliable for predicting the antioxidant activity of coumarin derivatives. Considering the correlation coefficient (Q²) of external set, it was shown that the Dragon descriptors gave the highest quality of the prediction for external test set (model 1: Q²_Ext = 0.952) followed by the PaDEL descriptors (model 3: Q²_Ext = 0.885) and the Mold² descriptors (model 2: Q²_Ext = 0.875).

Regression coefficient values of the key descriptors (as independent variables) in QSAR models define the degree or weight of their influence on dependent variables (antioxidant activity: pIC₅₀ values). According to the linear QSAR equations, high values of descriptors with positive regression coefficient and low values of descriptors with negative regression coefficient are required for potent antioxidant activity (high pIC₅₀ values).

The descriptors in model 1 including nArNHR, B04[O-O] and G2p displayed positive values of regression coefficient involved in the increased antioxidant activity as a positive effect, while ISH descriptor having negative value of regression coefficient involved in the decreased activity as a negative effect. The important descriptors are ranked according to their regression coefficient values as G2p>nArNHR>B04[O-O]>ISH with corresponding values of 8.1471, 1.2245, 0.3944, and -4.3187, respectively. The descriptors in model 2 including D467 and D278 with positive regression coefficient values displayed the positive effect, whereas D491, D384, D580 and D461 descriptors exerted the negative effect on the bioactivity. The order of descriptors are D278>D467>D384>D461> D580>D491 with corresponding values of 7.1429, 1.4575, -0.1328, -0.5180, -2.0251, and -2.6745, respectively. For model 3, SHBint4, SpMin2_Bhe and SssCH2 descriptors showed the positive effect on activity, but MATS8e descriptor displayed the negative effect. The order of important descriptors are SpMin2_Bhe>SssCH2> SHBint >MATS8e with values of 6.9792, 0.3238, 0.2638 and -0.9768, respectively.

To gain insights into SAR, coumarin derivatives (1-28, Figure 1(Fig. 1)) are categorized into 3 groups according to their core structures (i.e., thiazole group I (1-9 and 18), sulfonamides group II (10-17) and amides group III (19-28) for effective SAR analysis. Thiazoles group I (1-9 and 18) showed antioxidant activity (Table 1(Tab. 1)) with pIC₅₀ range of 2.539-4.612. The most potent and the least potent compounds of benzothiazoles group I were 5 (pIC₅₀ = 4.612) and 6 (pIC₅₀ = 2.539), respectively. Among group II compounds (10-17), compound 11 was the most active (pIC₅₀ = 3.180), and 14 was the least active compound. For group III of amides 19-28, compound 21 displayed the most potent activity (pIC₅₀ = 3.027) and compound 19 exhibited the lowest activity with pIC₅₀ of 2.640.

It should be noted that coumarins substituted by thiazole at 3-position displayed better activity when compared with those substituted by sulfonamides and amides at 7- or 4- or 6- position (group II and III). The antioxidant activity (Table 1(Tab. 1)) is shown as the following trend: group I 5>3>4>1>2>18>8>7>9>6; group II 11>16>13>17>15>12>10>14; group III 21>28>22>20>23>26>27>24>25>19.

According to the significant descriptors in models 1-3, secondary (sec-) amine, polarizability, electronegativity and H-bond displayed positive effect in the antioxidant activity. This is noted in the most potent coumarin 5 bearing sec-amine (part of aromatic thiazole), and 7-OH group (on the coumarin ring) with H-bond and polarizability properties. On the other hand, tertiary (tert-) amine 6 without 7-OH group exerted the lowest activity among the coumarin derivatives 1-28. This could be implied that the sec-amine (-NH-) and OH as H-bond and polarizing group are important for the better activity.

In a series of compounds 1-28, only the sec-amines (1-5) had nArNHR = 1. The most potent compound 5 had higher values of nArNHR = 1, SHBint4 = 7.5875, G2p = 0.193, D467 = 0.805, but lower values of van der Waals volume (D491 = 0.471 and D461 = 0.186) when compared with the least potent compound 6 (nArNHR = 0, SHBint4 = 0.000, G2p = 0.169, D467 = 0.646, van der Waals volume: D491 = 0.805 and D461 = 0.520). Apparently, the tert-amines (6-8) and other amides, sulfonamides (10-28) as well as non-aromatic sec-amine 9 had nArNHR = 0.

Because each descriptor represents certain characteristic/property of the compound, QSAR equations are useful to guide effective rational molecular design of novel bioactive compounds with preferable activity (De et al., 2017[6]; Mitra et al., 2011[25]; Prachayasittikul et al., 2017[35]; Pratiwi et al., 2019[38]). To improve the antioxidant activity of these derivatives (1-28), 8 compounds (i.e., 2, 3, 4, 5, 11, 13, 18 and 21) were selected as parent compounds for structural modification. A series of novel analogs were rationally designed based on key influencing properties (which were revealed by descriptors presented in models 1-3). The modification was conducted by substitution of diverse types of functional groups with electronegativity, polarizability and H-bond properties (i.e., electron donating and electron withdrawing groups such as OH, NH₂, SH, OCH₃, CN, CF₃ and halogen) on various positions of the coumarin ring. The new structurally modified compounds are shown in Supplementary Table 4). Values of molecular descriptors of these compounds are provided in Supplementary Tables 5-7). The prediction showed that the most potent compounds (pIC₅₀) of each modified series were 2b, 2e (4.503, 4.502), 3n (6.340), 4g (6.445), 5h (7.016), 11a (4.526), 13d (4.356), 18c (4.197) and 21d (5.634) as shown in Figure 4(Fig. 4). All highly potent modified compounds were ranked as 5h>4g>3n>21d>11a>2b= 2e>13d>18c. The top three modified compounds (ranked as 5h>4g>3n) shared a common feature of 4-amino coumarin moiety (Figure 4(Fig. 4)). This moiety involves in H-bonding, polarizability, and electronegativity properties of the compounds which are essential for potent predicted activity. Apparently, these most potent compounds displayed the highest SHBint4 values of 16.903, 13.660, and 13.064 for 5h, 4g, and 3n, respectively.

The following discussed compounds are shown in Supplementary Table 4. Compound 2 (pIC₅₀ = 3.332) was modified by substitution of R1 (6-position) and R2 (5-position) groups (H, F, Cl, CF₃, CN, NO₂) on the core structure to give a new series of compounds 2a-2h with improved activity (pIC₅₀ = 3.167-4.503), except for compounds 2f and 2h. Compounds 2b (5-CF₃, 6-H) and 2e (5-CF₃, 6-NO₂) were the most potent compounds with comparable pIC₅₀ values of 4.503 and 4.502, respectively. These could be due to the enhancing effect of 5-CF₃ (R2) and 6-NO₂ (R1) groups that provided high polarizability (G2p: 2b = 0.1820, 2e = 0.1730), electronegativity (SpMin2_Bhe: 2b = 1.847, 2e = 1.847), and potential H-bond (SHBint4: 2b = 5.150, 2e =5.480), thus, improved antioxidant activity of the modified compounds comparing with their parent 2 (G2p = 0.164, SpMin2_Bhe = 1.8175, SHBint4 = 4.0816).

Similarly, modified compounds 3a-3p were obtained by substitution of R1, R2, R3 at positions 7, 6, and 4 of the parent compound 3 (R1 = H, OH, OCH₃, NH₂, N(CH₃)₂, SH, SC₆H₅; R2 = F, Cl, Br, CF₃; R3 = H, OH, OCH₃, NH₂, N(CH₃)₂). Compound 3n (R1 = H, R2 = Br, R3 = NH₂) was predicted as the most potent one with pIC₅₀ value of 6.340. Compounds 3f-3p (pIC₅₀ = 4.129-6.340) were mostly active than the parent compound 3 (pIC₅₀ = 4.003). It should be noted that these compounds (3f-3p) contained the same type of substituted R2 (Br) group as their parent 3 (6-Br). Therefore, higher H-bonding potential (SHBint4 = 13.064) and electronegativity (D467 = 0.736) play an important role in improving the activity of compound 3n when compared with its parent compound (3: SHBint4 = 4.2075, D467 = 0.722). The higher SHBint4 and D467 of 3n may result from the property of the substituted NH₂ group in forming H-bond with the interacting species. In addition, the substitution with high electronegativity Br group (R2) at position 6 is required for improving activity of the compounds as noted for compound 3f-3p and the parent compound 3.

Structural modification improved activity of most of the compounds in series 4 (4a-4i: pIC₅₀ = 4.033-6.445), except for compounds 4d and 4h.The results showed that 4g (R1 = 7-H, R2 = 4-NH₂) was the most potent compound (pIC₅₀ = 6.445). Comparing with the parent compound 4 (pIC₅₀ = 3.973, SHBint4 = 4.442, G2p = 0.174), the most potent derivative 4g displayed higher potential H-bond (SHBint4 = 13.660) and higher polarizability (G2p = 1.960). It is reasonable to explain that 4-NH₂ (R2) of 4g participates in H-bond forming and polarization through a keto group of the coumarin ring as shown by the resonant ionic form (4A) in Figure 5(Fig. 5). On the other hand, compound 4c (R1 = 7-NH₂, R2 = 4-H) exerted lower activity with lower descriptors values (pIC₅₀ = 0.4772, SHBint4 = 7.432, G2p = 0.1830) comparing with the most potent compound 4g.

The most potent coumarin 5 was modified to give derivatives 5a-5l, in which compounds 5f-5i displayed the improved antioxidant activity (pIC₅₀ = 4.745-7.016). Compound 5h was the most potent one (pIC₅₀ = 7.016) with higher H-bond potential (SHBint4 = 16.903), but lower electronegativity (MATS8e = 0.063) when compared with its parent 5 (pIC₅₀ = 4.612, SHBint4 = 7.5875, MATS8e = 0.0848).

The amides 11, 13, and 21 were structurally modified by removing oxyketo group from the parent core structures to give sec-amines. The amine derivatives 11a-11f with improved activity (pIC₅₀ = 3.402-4.526) were achieved from compound 11 (pIC₅₀ = 3.180). When compared with its parent (amide 11: nArNHR = 0, D467 = 0.479, SHBint4 = 0.000, D491 = 0.688, D461 = 0.544 and MATS8e = 0.1872), improved activity of the most potent amine 11a (pIC₅₀ = 4.526) was governed by its higher nArNHR = 1, electronegativity (D467 = 0.690), and H-bond (SHBint4 = 2.048), but lower van der Waals volume (D491 = 0.342 and D461 = 0.022) and electronegativity (MATS8e = -0.058). This could suggest that the improved activity of compounds requires a smaller size sec-amine (11a) with lower van der Waals volume but higher potential H-bonding. Similarly, a series of sec-amines 13a-13d (R1 = CH₃, OH, OCH₃, R2 = CH₃, OCH₃) were obtained (pIC₅₀ = 3.341-4.356) from the amide 13 (pIC₅₀ = 3.022). Compound 13d (pIC₅₀ = 4.356) was the most potent amine with higher nArNHR = 1, D467 = 0.640, SHBint4 = 4.368, but lower van der Waals volume D461 = 0.455 and MATS8e = -0.125 comparing to its parent compound 13 (nArNHR = 0, D467 = 0.503, SHBint4 = 0.000, D461 = 0.515 and MATS8e = 0.1400). The amide 21 (pIC₅₀ = 3.027) was modified to give analogs with improved antioxidant effect i.e., sec-amines analogs 21a-21h (pIC₅₀ = 3.549-5.634). The most potent modified amine 21d (pIC₅₀ = 5.634) displayed higher nArNHR = 1, electronegativity D467 = 0.657, H-bond SHBint4 = 9.823, electronegativity SpMn2-Bhe = 1.843 and SssCH₂ = 0, but lower ISH = 0.869, van der Waals volume D491 = 0.350 and D461 = 0.436, and MATS8e = -0.219 when compared with the parent 21 (nArNHR = 0, D467 = 0.489, SHBint4 = 0.000, SpMin2-Bhe = 1.8395, SssCH₂ = -0.1139, ISH = 0.923, van der Waals volume D491 = 0.82 and D461 = 0.612, and MATS8e = -0.0511).

Benzothiazole coumarin 18 was structurally modified to provide compounds 18a-18f (R1 = OH, OCH₃, NH₂, N(CH₃)₂, SH, SC₆H₅ at position 7). Comparing with the parent compound 18 (pIC₅₀ = 3.260), compounds 18b-18e were more potent antioxidants (pIC₅₀ = 3.758-4.197). Improved activity of the most potent compound 18c (pIC₅₀ = 4.197) was governed by higher electronegativity (D467 = 0.595), total information content (D278 = 0.473) and H-bond (SHBint4 = 2.894), but lower van der Waals volume (D491 = 0.377and D461 = 0.299) when compared to parent compound 18 (D467 = 0.501, D278 = 0.413, SHBint4 = 0.000, D491 = 0.472 and D461 = 0.471).

It should be noted that the most potent modified compounds had higher values of H-bonding descriptor (SHBint4 = 2.048-16.903, Supplementary Table 7) when compared with their parent compounds (SHBint4 = 0.000-7.5875, Table 3(Tab. 3)). Thus, SHBint4 might be the important descriptor in governing the potent antioxidant activity.