## 2 Materials and Methods
### Computation of Antioxidant Descriptors  
The ideal mechanism of free radical scavenging for the target molecules **1**-**14** was determined by computing the antioxidant descriptors as follows:  
The BDE was computed with Equation (1) under normal parameters, standard atmospheric pressure and 298.15 K. For instance, when a chemical bond is broken under standard conditions, BDE indicates the standard reaction enthalpy change at a specific temperature [40]. The O-H bond is less stable at lower BDE values [41].  
\[\text{BDE}=\text{H}_{\text{radical}}\,+\,\text{H}_{\text{electron}}\,-\,\text{H }_{\text{neutral}}. \tag{1}\]  
The adiabatic ionization potential (AIP) was calculated in Equation (2). The capability of the antioxidant compound is inversely proportional to the AIP value.  
\[\text{AIP}=\text{H}_{\text{cation radical}}\,+\,\text{H}_{\text{electron}}\,-\, \text{H}_{\text{neutral}}. \tag{2}\]  
The PDE was determined according to Equation (3) and compounds with lower PDE values are more exposed to proton abstraction [42].  
\[\text{PDE}=\text{H}_{\text{radical}}\,+\,\text{H}_{\text{H}^{+}}\,-\,\text{H }_{\text{cation radical}}. \tag{3}\]  
The PA and ETE were calculated by Equations (4) and (5).  
\[\text{PA}=\text{H}_{\text{anion}}\,+\,\text{H}_{\text{H}^{+}}-\,\text{H}_{ \text{neutral}}, \tag{4}\]  
\[\text{BDE}=\text{H}_{\text{radical}}\,+\,\text{H}_{\text{electron}}\,-\,\text{H }_{\text{anion}}\, \tag{5}\]  
where \(\text{H}_{\text{radical}}\) is the phenoxy radical total enthalpy, \(\text{H}_{\text{H}}\) is the hydrogen atom total enthalpy, \(\text{H}_{\text{neutral}}\) is the neutral compound enthalpy, \(\text{H}_{\text{H}^{+}}\) is the proton total enthalpy, \(\text{H}_{\text{cation radical}}\) is the cation radical total enthalpy, \(\text{H}_{\text{electron}}\) is the electron total enthalpy, \(\text{H}_{\text{anion}}\) is total enthalpy of the anion.  
The total species enthalpies were calculated as the sum of total electronic energy, zero-point energy and the translational, rotational, and vibrational contributions to the total enthalpy as presented in Equation (6). In order to convert the energy to enthalpy, the RT (PV-work) term was added [43].  
\[\text{H}=\text{E}_{0}+\text{ZPE}+\text{H}_{\text{trans}}\,+\,\text{H}_{\text{ rot}}\,+\,\text{H}_{\text{vib}}+\text{RT}. \tag{6}\]  
The translational, rotational, and vibrational contributions to enthalpy are \(\text{H}_{\text{trans}}\), \(\text{H}_{\text{rot}}\), and \(\text{H}_{\text{vib}}\). \(\text{E}_{0}\) represents the total energy at zero K, whereas ZPE represents the zero-point vibrational energy. When computing the antioxidant descriptors listed above, the following values were utilized to carry out the calculations: In the case of H(H\({}^{\bullet}\))vacuum, the value is \(-1312.479673\) kcal.mol\({}^{-1}\); in the case of H(H\({}^{+}\))vacuum, the value is \(6.1961805\) kcal.mol\({}^{-1}\); in the case of H(e\({}^{-}\))vacuum, the value is \(3.1454\) kcal.mol\({}^{-1}\); in the case of H(H\({}^{\bullet}\))vacuum, the value is \(3.1454\) kcal.mol\({}^{-1}\); in the case of H(H\({}^{\bullet}\))water, the value is \(-3.9908\) kJ/mol; in the case of \(H(H^{+})_{\text{water}}\) the value is \(-1090.0027\) kcal.mol\({}^{-1}\); in the case of H(e\({}^{-}\))hydr, the value is \(-105\) kcal.mol\({}^{-1}\)[44; 45; 46; 47].  
The geometry optimization was done on all molecular structures in the gas phase at the DFT/B3 LYP/6-311\({}^{++}\)G(d,p) level of theoretical. This study used methanol as the physiological medium in vitro and the self-consistent reaction field approach using a polarized continuum model (PCM) [47]. According to the reported literature [48] allchemical descriptors such as softness hardness, chemical potential, and electrophilicity were calculated. Using the Gaussian 09 program package, all calculations were carried out.