**2. Materials and method**

#### **2.1 Materials**

The present work has utilized a theoretical approach to study the structure and properties of all compounds under consideration. The molecular forms of **1a** and **1b** were downloaded from the PubChem database in SDF file format and converted to GJF file format by Open Babel [24]. The structures of **1c**, **1d**, and **1e** were drawn using the Gaussview 5.0.8 graphical user interface [25]. All the computational works have been carried out through Gaussian 09 software package to get the output [26]. The spin density (SD) and electron delocalization (DI) analysis are explained with the help of the software Multiwfn 3.6 [27].

#### **2.2 Computational methodology**

The present work was carried out using density functional theory (DFT) because it is based on electron density, and antioxidant activity is mainly influenced by electron density [28–32]. In DFT calculation, 6–311+ G (d, p) basis set with B3LYP (Becke's exchange functional in conjunction [33] with Lee-Yang–Parr [34]) correlational functional has been used for geometry optimization, computation of harmonic vibrational frequencies, BDE, IP, PDE, PA and ETE calculations. To obtain antioxidant parameters BDE, IP, PDE, PA, and ETE, the geometry optimization of neutral, radicals, anions, and radical cation structures of all the studied molecules are conducted in the ground state both in the gas phase and aqueous phases. Solvent effects on the calculated systems were investigated with the self-consistent reaction field (SCRF) method via the integral equation formalism polarized continuum model (IEF-PCM).

#### *2.2.1 Frontier molecular orbital (FMO) analysis*

Frontier molecular orbital theory is an application of MO theory that explains HOMO/LUMO interactions. HOMO is the highest occupied molecular orbital, and LUMO is the lowest unoccupied molecular orbital. Frontier molecular orbital analysis is fundamental because HOMO or LUMO energies and bandgap energies are the key factors that drive the antiradical property of molecules. Since HOMO is in the highest energy state, so easier to remove an electron from this orbital. So in a chemical reaction or bond formation, HOMO is donating electrons, or it acts as a Lewis base or undergoes oxidation. LUMO is the lower-lying orbital; it is empty, so it is easier for LUMO to accept electrons into its orbital or acts as a Lewis acid or undergoes reduction. Reactivity becomes lower when the molecule has a higher bandgap. The distribution of HOMO orbitals and energies is calculated using the DFT-B3LYP/6–311 + G (d, p) level of theory from the optimized structures of **1a** and its derivatives.

#### *2.2.2 Radical scavenging activity*

Several mechanisms have theoretically explained the radical scavenging mechanism of phenolic compounds. The widely used mechanisms are hydrogen atom

transfer (HAT) mechanism (Eq. (1)), single-electron transfer followed by proton transfer (SET-PT) mechanism (Eqs. (2)–(4)), and sequential proton loss electron transfer (SPLET) mechanism (Eqs. (5) and (6)) [35–40]. These mechanisms have been briefly addressed here.

1.HAT (hydrogen atom transfer) mechanism

$$ArOH + X^{\bullet} \to ArO^{\bullet} + XH \tag{1}$$

By transferring the hydrogen atom of the –OH group to the radical species, the antioxidant (ArOH) scavenges the free radical (X**•** ) and transforms it into phenoxide radical. The descriptor associated with the HAT mechanism is bond dissociation enthalpy (BDE), and the lower value indicates good radical scavenging activity. The ArO∙ radical species'stabilizing features, like the resonance delocalization of the electron within the aromatic ring, are the basis of lowest energy and increased antiradical activity.

2. SET (single electron transfer) mechanism

$$ArOH + X^{\bullet} \to ArOH^{\bullet+} + X^{-} \tag{2}$$

Here, the reactive free radicals are neutralized by transferring electrons to them, resulting in anions. The most reactive hydroxyl group in antioxidant compounds provides these electrons and finally becomes a radical cation. The descriptor associated with this mechanism is AIP (adiabatic ionization potential).

3. SET-PT (single electron transfer followed by proton transfer) mechanism

$$ArOH + X^{\circ} \to ArOH^{\bullet+} + X^{-} \tag{3}$$

$$ArOH^{\bullet+} \rightarrow ArO^{\bullet} + H^{+} \tag{4}$$

The first process involves an electron transfer from the antioxidant (Eq. (2)), and the second step consists of a proton transfer from the radical cation (Eq. (4)) generated in the first step. Proton dissociation enthalpy is the descriptor connected with the second phase (PDE).

4. SPLET (sequential proton loss electron transfer) mechanism

$$ArOH \rightarrow ArO^- + H^+ \tag{5}$$

$$ArO^{-} + X^{\bullet} + H^{+} \rightarrow ArO^{\bullet} + XH \tag{6}$$

This is also a two-stage mechanism, with the dissociation of the antioxidant into phenoxide anion and proton as the first step (Eq. (5)). The first-step phenoxide anion then interacts with free radicals at a certain pH (Eq. (6)); the compounds generated are similar to those developed in the HAT mechanism. Proton affinity (PA) is the regulating descriptor for the first stage, and electron transfer enthalpy is the driving descriptor for the second stage (ETE).

The Eqs. (7)–(11) are used for analyzing the type of mechanism involved by the compound

*DFT Study of Structure and Radical Scavenging Activity of Natural Pigment Delphinidin… DOI: http://dx.doi.org/10.5772/intechopen.98647*

$$BDE = H(ArO^\*) + H(H^\*) - H(ArOH) \tag{7}$$

$$\text{AIP} = H(ArOH^{\bullet+}) + H(e^-) - H(ArOH) \tag{8}$$

$$\text{PDE} = H(\text{ArO}^{\bullet}) + H(\text{H}^{+}) - H(\text{ArOH}^{\bullet+}) \tag{9}$$

$$PA = H(ArO^-) + H(H^+) - H(ArOH) \tag{10}$$

$$ETE = H(ArO^\*) + H(e^-) - H(ArO^-) \tag{11}$$

Thus, in the present study, BDE, IP, PDE, PA, and ETE values were used as the primary molecular descriptors to elucidate the radical scavenging activity of the investigated compounds. The enthalpies of hydrogen radicals in the water and gas phase are calculated by G09 software using the DFT/B3LYP/6–311 + G (d, p) level of theory. The enthalpies of the electron (e�) and proton in the gas phase are taken from the commonly accepted values 0.00236 Hartree for proton and 0.00120 Hartree for electron. In contrast, for water, these corresponding values are calculated with the help of the DFT/B3LYP/6–311 + G(d, p) level of theory. The enthalpies of electron and proton in solvent water were computed using the same level of theory with methodology suggested by Markovic et al. (Eqs. (12) and (13)) [41, 42].

$$H\_{\text{gas}}^{+} + \text{S}\_{\text{sol}} \rightarrow (\text{S} - H)\_{\text{sol}}^{+} \tag{12}$$

$$\text{e}\_{gas}^{-} + \text{s}\_{sol} \rightarrow (\text{S} - \text{e})\_{sol}^{-\text{-}\text{}} \tag{13}$$

Where Ssol is the solvent molecule solvated by the same kind of molecule, ð Þ *S* � *H* <sup>þ</sup> *sol* and ð Þ *S* � *e* �� *sol* are the charged particles formed. The solvation enthalpies of proton and electron are calculated using the Eqs. (14) and (15), respectively, and that of *H*• by optimizing hydrogen atom using the same level of theory. The enthalpy of hydrogen radical taken for gas is �0.49764 Hartree and � 0.497466 Hartree for water. The enthalpies of proton and electron in water, respectively, are �0.37725431 Hartree and 0.093551 Hartree.

$$
\Delta H\_{sol}(H^+) = H(\text{S} - H)^+\_{sol} - H(\text{S}\_{sol}) - H\left(H^+\_{gas}\right) \tag{14}
$$

$$
\Delta H\_{sol}(e^{-}) = H(\text{S} - e)\_{sol}^{\cdots \text{ } \text{ }} - H(\text{S}\_{sol}) - H\left(e\_{gas}^{\cdots}\right) \tag{15}
$$

### **3. Results and discussion**

#### **3.1 Conformation analysis and geometry optimization**

To elucidate the reactivity of the compounds towards free radicals, the conformational and geometrical features of compounds are very significant. The structures of **1a** and **1b** are downloaded from the PubChem database and **1c**, **1d**, and **1e** are constructed from the optimized structure of **1a**. The potential energy surface of all five molecules is scanned by using the B3LYP/3-21G level of theory by varying the dihedral angles values in 12 steps of 30° from 0 to 360°. The dihedral angle between aromatic ring B and AC bicyclic in **1a** is performed on the dihedral Ф1 (C3, C2, C1ˈ, C2ˈ), and the five OH groups are also scanned as above mentioned procedure. All phenolic OH is in a position that forms hydrogen bonding with the nearest OH. The dihedral Ф1 about (C3, C2, C1ˈ, C2ˈ) of **1a** completely reveals the planar geometry of the molecule, whereas other molecules are slightly becoming nonplanar because of the steric cloud around flavylium cationic ring. The dihedral (C3, C2, C1ˈ, C2ˈ) of **1a**, **1b, 1c, 1d**, and **1e** respectively are �179.95499, �158.12940, �167.05569, �169.70713, and 171.29496 degrees.

The lowest energy conformer obtained after the last scan was then subjected to geometry optimization, and B3LYP/6–311 + G(d, p) level of theory with a correlation coefficient of 0.89281 are selected for the study. The crystal structure data of cyanidin are considered for experimental validation of results obtained from the computational analysis since these are not available for delphinidin molecules and tabulated in **Table 1** [43]. But the basic structural unit of **1a** is similar, except in cyanidin, one OH is missing from the 5<sup>0</sup> position. The optimized structures of the five compounds are shown in **Figure 2**. These optimized structures are considered for further calculations.

#### **3.2 Molecular orbital analysis**

Frontier molecular orbital analysis gives a detailed account of HOMO/LUMO interactions in the molecule. It is very useful in describing optical and electronic properties as well as the reactivity of a molecule. The HOMO value of the molecule is strongly influenced by radical scavenging activity. The higher the HOMO energy, the easier the electron is being excited and acts substantial donor of the electron. The chemical reactivity of the molecule can be described by knowing the HOMO– LUMO gap. Like that, the distribution of orbitals among the molecule reveals probable sites for the attack of free radicals. The HOMO distribution among molecule **1a** is completely distributed on each atom, whereas the LUMO orbitals have distributed all atoms except 3- OH, 3'- OH, and 5'-OH. For the molecules studied here, the distribution of the LUMO distributed among each atom other than 3- OH, 30 - OH, and 5'-OH. So these three bonds are involved in the HOMO-LUMO transition. In **1c** and **1e**, HOMO is present only on the gallate moiety, whereas the LUMO is distributed only in the flavylium ring. The HOMO of **1b** and **1d** occur throughout the flavylium ring though only negligible HOMO/LUMO contributions are present on glucoside moiety.


#### **Table 1.**

*Comparison of bond length with experimental values in different basis sets.*

*DFT Study of Structure and Radical Scavenging Activity of Natural Pigment Delphinidin… DOI: http://dx.doi.org/10.5772/intechopen.98647*

**Figure 2.**

*The obtained optimized structures of the compounds using B3LYP /6–311 + G(d, p) level of theory (delphinidin (1a), delphinidin-3-O-glucoside (1b), delphinidin-3-O-gallate (1c), delphinidin-4'-O-glucoside (1d), and delphinidin-4'-O-gallate (1e).)*

The increasing order of bandgap energies in the gas phase at **1e** < **1c** < **1d** < **1a** < **1b** reveals that the gallate-based compounds have the lowest bandgap energies and higher in activity. In the aqueous phase, the band gaps are higher compared to the gas phase, and the difference between the bandgap of water and gas is also represented in **Table 2**. One of the difficulties associated with anthocyanins as color pigments is their stability in polar solvents. When the medium changes from the gas phase to water, the only difference in the bandgap is 0.17 for **1a** and 0.20 for **1b**, but it is more significant for its gallates. So gallates are stable than others; hence expect higher reactivity in water (**Figure 3**).


**Table 2.**

*FMO analysis of studied compounds in gas and water media at B3LYP/6–311 + G(d, p) level of theory.*

**Figure 3.** *FMO of 1a, 1b, 1c, 1d, & 1e in the gas phase at B3LYP/6–311 + G(d, p) level of theory.*

#### **3.3 Radical scavenging activity**

The antioxidant activities of the compounds are studied using the antioxidant mechanism described in Section 2.2.2. The BDE, IP, PA, PDE, and ETE values obtained from the corresponding mechanism are used to analyze the activity of compounds. Among the five parameters, one with the lowest value and the corresponding mechanism is followed by the compound. The parameters of antioxidant activities are represented in the gas phase and aqueous phase, respectively, in **Tables 3** and **4**.

#### *3.3.1 Analysis of HAT mechanism*

In the gas phase, all studied molecules follow the HAT mechanism because of its lower BDE values. Hence, all compounds tending to form radicals by donating hydrogen atoms in respective positions are higher in the gas phase. In the case of **1a**, the positions 3-OH (81.56 kcal/mol), 4'-OH (83.19 kcal/mol), and 5'-OH (84.51 kcal/mol) have the lowest values of BDE, and hence these positions are involved in radical scavenging activity in the gas phase. For a compound possessing more than one phenolic hydroxyl group, its radical scavenging activity is determined by the one with the lowest value of BDE. Hence, in this case, 3-OH is the most active site, followed by 4'-OH and 5'-OH.


*DFT Study of Structure and Radical Scavenging Activity of Natural Pigment Delphinidin… DOI: http://dx.doi.org/10.5772/intechopen.98647*

#### **Table 3.**

*The antioxidant mechanism study of compounds 1a, 1b, 1c, 1d, and 1e in gas using B3LYP/6–311 + G(d, p) level of theory. All values are represented in kcal/Mol.*


#### **Table 4.**

*The antioxidant mechanism study of compounds 1a, 1b, 1c, 1d, and 1e in water using B3LYP/6–311 + G(d, p) level of theory. All values are represented in kcal/Mol.*

### *DFT Study of Structure and Radical Scavenging Activity of Natural Pigment Delphinidin… DOI: http://dx.doi.org/10.5772/intechopen.98647*

The glucose substituted derivatives of **1a**, **1b**, and **1d** in the gas phase also follow the HAT mechanism due to its lowest value of BDEs comparing with other parameters. In **1b**, 4'-OH has a higher tendency to participate in radical scavenging mechanism due to its lowest BDE value (82.15 kcal/mol) compared to other phenolic OH groups in the compound. When 4'-OH is substituted with glucose moiety or **1d**, 3-OH is contributing to the radical mechanism. So in **1b** and **1d** radical scavenging activity is mainly through B-ring (4'-OH) and C-ring (3-OH).

As from **Table 3** the antioxidant activity of compound **1c** are through its phenolic hydroxyl group at 4' OH (83.12 kcal/mol), 5' OH (84.18 kcal/mol), 6"OH (83.09 kcal/mol), and 7" OH (83.60 kcal/mol) positions with an increasing order of 6"OH < 4' OH < 7" OH < 5' OH. The phenolic hydroxyl groups at 4' OH and 5' OH situates on the B-ring of **1a**, whereas 6"OH and 7" OH at gallic acid moiety. Here, both rings, the gallate ring, and delphinidin ring moieties, contribute to the radical scavenging activity through the hydroxyl groups. Since an ester relation connects gallate and delphinidin moieties, the radicals produced in one ring do not delocalize much to another ring and acts as separate contributors to radical scavenging activity. Like that, **1e** also shows antioxidant activity through 3' OH (83.90 kcal/mol), 6" OH (82.80 kcal/mol) and 7" OH (83.22 kcal/mol). The 6" OH has a slightly lower value of BDE than the other two OH groups because the radical formed at para OH is highly stabilized through the aromatic system of gallate moiety. Similar to 1c, compound **1e** also possesses radical scavenging activity through B-ring and gallic acid moiety. When comparing **1c** and **1e** with other molecules, when gallic acid is substituted, the number of hydroxyl groups under lower BDE values increases. Hence, the chance of enhancing activity is clear.


To explain the differences in BDE and consequently the differences in the reactivity of OH sites, the spin density distribution of radicals was calculated and presented in **Table 5**. The stability of radicals formed can be explained with the help

#### **Table 5.**

*The SD distribution for the O-radical and delocalization index (DI) of C-O bond computed for 1a, 1b, 1c, 1d, & 1e in the gas-phase at B3LYP/6–311 + G (d, p) level of theory.*

of SD values; more delocalized SD means to be more stable is the radical formed. Moreover, the delocalization index is also a supporting parameter for explaining the stability of radicals created. The more stable the radical formed from an -OH bond, the more the corresponding C-O bond will be the delocalization index. The DI of

#### **Figure 4.**

*Electronic spin density distributions and optimized structures of 1c radicals in the gas-phase at B3LYP/6– 311 + G (d, p) level of theory.*

C-O bonds in each radical site are calculated using Fuzzy atomic space analysis [44–46]. The SD contours of **1c** are represented in **Figure 4**.
