**4. SET (***single electron transfer***) mechanism**

It takes place through two steps. Initially, a free radical cation is formed by the transfer of anelectron from a neutral species.

$$\rm{ArOH} + \rm{X^{\cdot}} \rightarrow \rm{ArOH^{\cdot +}} + \rm{X^{\cdot}} \tag{16}$$

Neumerical parameter associated to this step is AIP.

$$\text{IP} = \text{H}(\text{ArOH}^+) + \text{H}(\text{e}^-) \text{-H}(\text{ArOH}) \tag{17}$$

In the next step, phenolic radical cation decomposes into phenolic radical and proton.

$$\text{ArOH}^+ \rightarrow \text{ArO}^\cdot + \text{H}^+ \tag{18}$$

PDE is the neumerical parameter related to this step.

$$\text{PDE} = \text{H}(\text{ArO}) + \text{H}(\text{H}^+) \text{-H}(\text{ArOH}^+) \tag{19}$$

## **5. SPLET (***sequential proton loss electron transfer***)**

In SPLET mechanism, The phenolic antioxidant dissociates into an anionic form and proton in the first step, and then ions formed in the first reaction react with the free radical.

$$\text{ArOH} \rightarrow \text{ArO}^- + \text{H}^+ \tag{20}$$

$$\text{ArO}^{-} + \text{X}^{\cdot} + \text{H}^{+} \rightarrow \text{ArO}^{\cdot} + \text{XH} \tag{21}$$

The first step corresponds to the PA and it can be calculated using Eq. (15):

$$\text{PA} = \text{H}(\text{ArO}) + \text{H}(\text{H}^+) \text{-H}(\text{ArOH}) \tag{22}$$

The numerical parameter for the second step ETE can be calculated by the equation,

$$\text{ETE} = \text{H}(\text{ArO}) \text{-H}(\text{ArO}^{-}) \tag{23}$$

#### **6. Results and discussion**

#### **6.1 Optimisation of structures**

Coumestrol is a polycyclic aromatic compound containing a coumestan moiety, which consists of a benzoxole fused to a chromen-2-one to form 1-Benzoxolo[3, 2-c] chromen-6-one. The lowest energy conformer of coumestrol is obtained through potential energy scanning and is used for further analysis. The derivatives were drawn by substituting 16th position of coumestrol with electron donating groups like -OH, -NH2, -OCH3, -CH3, -Ph, -CHCR2, -OCOR and -NHCOR and electron withdrawing groups like -F, -CL, -BR, -CN, -NO2, -SO3H, -CHO, -COR, -COCL, -COOR and -COOH (where 'R' is a methyl group). All the structures were optimised through DFT-B3LYP/6–31 + G(2d,2p). The optimised structure of coumestrol is shown in **Figure 3**.

*Theoretical Studies on Anti-Oxidant Activity of the Phytochemical, Coumestrol and Its… DOI: http://dx.doi.org/10.5772/intechopen.96967*

**Figure 3.**

*Optimised lowest energy conformer of coumestrol.*


**Table 1.**

*The global descriptive parameters of coumestrol.*

## **6.2 Global descriptive parameters**

Global descriptive parameters were calculated for comparing the chemical reactivity of coumestrol derivatives with parent molecule.

The global descriptive parameters of coumestrol are shown in **Table 1**. It can be calculated in two different methods, energy vertical method (single point energy calculations) and Koopman's theorem.

**Table 2** indicates the global descriptive values for coumestrol substituted at the C-16th position according to koopman's theorem. Generally, derivatives of coumestrol substituted with an electron withdrawing group showed a common trend; Ionisation potential, electron affinity, electronegativity, softness and electrophilic index increases with increase in electron withdrawing power. Hardness and chemical potential decreases with increase in electron withdrawing power. The trend followed by derivatives of coumestrol substituted with electron donating group is given by; ionisation potential, electron affinity, hardness and electronegativity decreases with increase in electron donating power. And softness, chemical potential and electrophilic index increases with increase in electron donating power. As the electro negativity increases reactivity increases.

**Table 3** indicates the global descriptive values for coumestrol substituted at C-16th position calculated by vertical energy method. The derivatives substituted with electron withdrawing groups showed the same trend as in Koopman's, i.e. Ionisation potential, electron affinity, electro negativity, softness and electrophilic index like parameters generally increases with increase in the electron withdrawing power. Hardness and chemical potential decreases with increase in electron withdrawing power. The general trend followed by derivatives of coumestrol substituted with electron donating group was given by; ionisation potential, electron affinity, hardness and electronegativity decreases with increase in electron donating power. And softness, chemical potential and electrophilic index increases with increase in electron donating power. Derivatives substituted with electron donating groups also showed same trend as in Koopman's.


#### **Table 2.**

*Global descriptive parameters of coumestrol substituted at C-16th position according to Koopman's method.*

Analysing the reactivity based on ionisation potential, electronegativity and electron affinity; reactivity increases with increase in electron affinity and electron negativity and decrease in ionisation potential. According to this relation, the derivatives with more reactivity are 16-NO2 Coumestrol, 16-OH Coumestrol, 16-OCOR Coumestrol, and 16-NHCOR Coumestrol.

#### **6.3 Dam plot**

The **Figure 4** shown the DAM plot of coumestrol substituted at C-16th positions. The derivatives like 16-F Coumestrol, 16-Cl Coumestrol, 16-Br Coumestrol, 16-CN Coumestrol, 16-NO2 Coumestrol, 16-SO3H Coumestrol, 16-CHO Coumestrol, 16-COR Coumestrol, 16-COCl Coumestrol, 16-COOR Coumestrol, 16-COOH Coumestrol, 16-OH Coumestrol, 16-OCOR Coumestrol, and 16-NHCOR Coumestrol were good anti-reductants with large size and they were good acceptors. Most of the derivatives substituted with electron withdrawing groups were anti-reductants and bad donors. The derivatives substituted with electron donating groups like 16-NH2, 16-OCH3 Coumestrol and 16-CH3 Coumestrol showed good antioxidant capacity through their electron donating power and they were of small size. 16-OH Coumestrol, 16-OCOR Coumestrol, and 16-NHCOR Coumestrol were exceptional derivatives with electron donating substitution and anti-reductant capacity. Therefore, all the derivatives were good anti-radicals.


*Theoretical Studies on Anti-Oxidant Activity of the Phytochemical, Coumestrol and Its… DOI: http://dx.doi.org/10.5772/intechopen.96967*

#### **Table 3.**

*Global descriptive parameters of coumestrol substituted at C-16th position according to energy vertical method.*

**Figure 4.** *DAM plot of coumestrol substituted at C-16th position.*
