Introduction

It is well established that certain free radicals known as reactive oxygen species (ROS) and reactive nitrogen oxide species (RNOS) react with biomolecules (e.g., nucleic acid bases, lipids, and proteins) and damage them [1–4]. In biological systems, these radicals can form through both enzymatic and nonenzymatic processes, and may be initiated by various factors, such as environmental pollution, excess consumption of packaged food, smoking, and stressful living [5–9]. An excess of free radicals in biological systems, as caused by an imbalance between radical formation and radical removal or modification, leads to oxidative or nitrative stress [4, 5]. The main ROS include the hydroxyl radical (OH·), the peroxyl radical (OOR·), the methoxy radical (CH3O·), and the carbonate radical anion (CO3 −·) [10], while the main RNOS include NO·, NO2 ·, and ONOO− (peroxynitrite). OH· radicals can form due to homolytic fission of the O–O bond of H2O2 in the presence of ionizing radiation or certain metal cations, such as Fe++ or Cu+ (Fenton reaction) [11]. Methoxy radicals can be produced by the photolysis of methyl acetate, the pyrolysis of dimethyl peroxide, or the radiolysis of liquid methanol [12]. Peroxynitrite is both an ROS and an RNOS, as it can cause both oxidative and nitrative damage to biological systems [13–16]. The NO2 · radical is produced through either the homolysis of the conjugate acid of peroxynitrite (ONOOH) to OH· and NO2 · radicals [17–19] or the dissociation of the nitrosoperoxycarbonate anion (ONOOCO2 −), formed by the reaction of peroxynitrite and CO2 [19]. ROS and RNOS react with DNA bases, producing several mutagenic products [19–28] that can cause mutations and various diseases such as cancer and cardiovascular, Alzheimer’s, and Parkinson’s diseases [1–4].

Certain chemical species called antioxidants are present in biological systems that scavenge ROS and RNOS by converting them into nonreactive forms. Among these endogenous antioxidants are both enzymes and nonenzymes, such as superoxide dismutase, melatonin, glutathione, and bilirubin [29, 30]. Antioxidants that may be obtained from external sources include ascorbic acid (vitamin C), α-tocopherol (vitamin E), curcumin, β-carotene, and N-acetylcysteine [6, 31]. However, the concentrations of endogenous antioxidants may become inadequate to scavenge free radicals during disease states. In such a situation, the use of external antioxidants becomes very important [32]. Many natural antioxidants are obtained from plants [33]. For example, ellagic acid is a plant phenolic compound that can provide a significant part of our daily external anti-oxidant dose [34, 35]. Ellagic acid is obtained from ellagitannins, which are the main components of plant cell walls [35]. Ellagitannins contain high molecular weight proteins and alkaloids and are soluble in water. Ellagic acid is also found in berries, other fruits and different types of food items, such as strawberries, raspberries, cranberries, grapes, blackcurrants, walnuts, pecans, and distilled beverages [36–43]. The commonly occurring methyl derivatives of ellagic acid are 3′-O-methyl ellagic acid, 3,3′-di-O-methyl ellagic acid and 3′,4′-di-O-methyl ellagic acid [44]. In previous studies, it has been shown that ellagic acid and its methyl derivatives possess anticarcinogenic [45, 46], antimutagenic, and anti-inflammatory properties [47]. It has been also shown that ellagic acid is a more efficient radical scavenger than vitamin C and vitamin E [48]. Using pulse radiolysis, it has been found that ellagic acid scavenges hydroxyl and nitrogen dioxide radicals very efficiently [49].

Different parts of the ellagic acid molecule play various biological roles. For example, its lactone groups are involved in reducing the formation of O 6-methylguanine by participating in reactions involving certain carcinogens [50], while its four hydroxyl groups reduce CYPlAl-dependent benzo[a]pyrene hydroxylase activity [50]. It has been shown that ellagic acid binds with DNA due to its planar geometry and stacks between the DNA helical stands at orientations of 66–90° with respect to the DNA helix axis [48]. Due to this binding, ellagic acid prevents the mutagenesis of DNA caused by carcinogens [48]. Ellagic acid and its methyl derivatives inhibit the toxin PLA2, which occurs in a deadly snake poison [37]. Ellagic acid has also been used for blood clotting because it is a natural hemostatic agent [44]. Further, it has been found that ellagic acid acts as an antiglycating agent, and this means that it inhibits AGEs (advanced glycation end-products), thereby reducing the risk of diabetes [51].

Thus, ellagic acid and its methyl derivatives play several important roles in biological systems. In view of this, in the work reported in the present paper, we investigated the reaction mechanisms involved in the scavenging of hydroxyl (OH·), nitrogen dioxide (NO2 ·), and methoxy radicals (OCH3·) by ellagic acid and its three methyl derivatives using a reliable theoretical approach.

Computational details

The geometries of the three conformers of ellagic acid were optimized using the B3LYP and B3PW91 functionals of density functional theory (DFT) along with the 6-31G(d,p) basis set in the gas phase [52–58]. Subsequently, to study the relative stabilities of the three conformers of ellagic acid, single-point energy calculations were performed using the abovementioned two density functionals along with the AUG-cc-pVDZ basis set in the gas phase. Transition state theory was employed to study the reaction mechanisms involved in the scavenging of OH·, NO2 ·, and OCH3 · by ellagic acid and its three methyl derivatives [59]. The geometries of all reactant complexes (RCs), transition states (TSs), and product complexes (PCs) involving ellagic acid and its mono- and dimethyl derivatives were optimized at the B3LYP/6-31G(d,p) level of theory. This was followed by single-point energy calculations employing the B3LYP and B3PW91 functionals along with the AUG-cc-pVDZ basis set in the gas phase for all the RCs, TSs, and PCs. <S2> at all the optimized RCs, TSs, and PCs was found to be close to 0.75 (doublet multiplicity), so spin contamination was negligible. Vibrational frequency analyses were carried out and the necessary thermal energy corrections to the total energy made so as to obtain Gibbs barrier energies at 298.15 K in the gas phase. The validity of the transition states was ensured by performing a visual inspection of vibrational modes corresponding to the imaginary frequencies at the transition states. These vibrational motions connected the reactants and products convincingly, and intrinsic reaction coordinate (IRC) calculations were not needed in any case. The gas-phase optimized RCs, TSs, and PCs involved in the calculations were solvated in aqueous media at the level of single-point energy calculations employing the polarizable continuum model (PCM) [54, 55]. The thermal energy corrections obtained in the gas phase were also considered to be valid for aqueous media. Rate constants were calculated, employing transition state theory [59]. The Windows version of the Gaussian G09 suite of programs (G09W) was used for all of the calculations, while the GaussView 5.0 suite of programs was used to visualize the molecular structures and vibrational modes [60, 61].

Results and discussion

Conformational analysis and molecular geometry

The structures of ellagic acid and its three methyl derivatives are given in Fig. 1a. The atomic numbering scheme employed in the present work is shown in this figure. The optimized structures of three conformers of ellagic acid, denoted EA-1, EA-2, and EA-3, are shown in Fig. 1b, c, and d, respectively. In each of these three conformers, the two OH groups located on each side of the ring system are oriented in the same direction, so that an intramolecular hydrogen bond is formed between them. These intramolecular hydrogen bonds stabilize the conformers. The relative Gibbs free energies of the three conformers obtained at different levels of theory in the gas phase and aqueous media are presented in Table 1. It is found that, in the gas phase, the conformer EA-1 is most stable at all four levels of theory; in aqueous media, it is most stable at three out of the four levels of theory employed here. As the B3LYP functional is generally rated somewhat better than the B3PW91 functional [62–64], we considered the results obtained at the B3LYP/AUG-cc-pVDZ level to be more reliable than those obtained at the B3PW91/AUG-cc-pVDZ level in aqueous media. Therefore, the conformer EA-1 of ellagic acid was taken to be the most stable. Mono- and dimethyl derivatives of ellagic acid were obtained by appropriate methyl group substitutions in the conformer EA-1 of ellagic acid.

Fig. 1
figure 1

a Atomic numbering and structures of ellagic acid and its three methyl (Me) derivatives. In ellagic acid, X1 = X2 = X3 = X4 = H, in 3′-O-methyl ellegic acid, X1 = H, X2 = H, X3 = Me, X4 = H, in 3′,4′-di-O-methyl ellegic acid, X1 = H, X2 = H, X3 = Me, X4 = Me and in 3,3′-di-O-methyl ellegic acid, X1 = Me, X2 = H, X3 = Me, X4 = H. b, c, d Optimized structures of the three conformers of ellagic acid

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Table 1 Relative Gibbs free energies (∆G, in kcal/mol) of the three conformers of ellagic acid (EA-1, EA-2, and EA-3) at 298.15 K, obtained at different levels of theory in the gas phase and aqueous media. In each column, the energies are given with respect to that of the conformer EA-1
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Therefore, the reactions of the free radicals with ellagic acid were studied by considering the conformer EA-1 (Fig. 1b). The optimized gas-phase bond lengths and bond angles involving heavy atoms for the most stable conformer are compared with those observed experimentally using X-ray diffraction [65] in Table S1 (see the “Electronic supplementary material,” ESM). The RMS difference between the optimized and XRD bond lengths was found to be 0.025 Å, while the corresponding difference for bond angles was 0.88°. These differences are within acceptable limits, and can be largely ascribed to the forces present in the crystal environment that are absent from the gas phase.

Barrier energies of hydrogen abstraction reactions

Hydrogen abstraction reactions between ellagic acid or its methyl or dimethyl derivatives [66] and different radicals (R·) may be expressed by the following general scheme:

$$ \begin{array}{lllllll}\mathrm{A}\hbox{--} {\mathrm{H}}_{\mathrm{n}}+{\mathrm{R}}^{\cdot}\hfill & \to \hfill & \mathrm{A}\hbox{--} {\mathrm{H}}_{\mathrm{n}}\hbox{--} {\mathrm{R}}^{\cdot}\hfill & \overset{\varDelta {{\mathbf{G}}_n}^{\mathbf{b}}}{\to}\hfill & {\left[\mathrm{TS}\right]}_n\hfill & \overset{-\varDelta {{\mathbf{G}}_{\mathrm{n}}}^{\mathbf{r}}}{\to}\hfill & {\mathrm{A}}^{\cdot}\hbox{--} \mathrm{R}\hbox{--} {\mathrm{H}}_{\mathrm{n}},\hfill \end{array} $$

where A–H n represents ellagic acid or one of its methyl derivatives, and H n is the hydrogen atom (bonded to the C n carbon atom) that is to be abstracted by the radical R·. In the present study, R· represented a hydroxyl radical, nitrogen dioxide radical, or methoxy radical. The free radical initally forms a reactant complex (RC) with ellagic acid or its methyl or dimethyl derivative (A–H n –R·). Subsequently, after the Gibbs activation energy (∆G n b) has become available, a transition state (TS) is formed, which is followed by the formation of the product complex (PC), i.e., A·–R–H n . Thus, at the PC stage (following the abstraction of a hydrogen atom from ellagic acid or one of its methyl or dimethyl derivatives (A–H n ) by an OH·, NO2 ·, or OCH3 · radical), a molecule of water, nitrous acid, or methyl alcohol complexed with a radical of the antioxidant (A·) is formed. Consequent to the formation of the PC, a certain amount of Gibbs free energy (−∆G n r) is released. As is well known, hydroxyl groups of phenolic antioxidants play important roles in their antioxidant activities [42]. Because of this, we only considered the abstraction of hydrogen by each of the three radicals from the hydroxyl groups of ellagic acid and its three methyl derivatives.

The hydrogen abstraction reactions with the lowest barrier energies that involve each of the radicals (i.e., OH·, NO2 ·, and OCH3 ·) along with ellagic acid or 3′-O-methyl ellagic acid are shown in Fig. 2, while the corresponding reactions that involve 3,3′-di-O-methyl ellegic acid and 3′,4′-di-O-methyl ellagic acid are shown in Fig. 3. Thus, only one hydrogen abstraction reaction that involves each of the three radicals and each of the four antioxidant molecules and which corresponds to the lowest barrier energy for that radical–antioxidant combination is shown in each of these two figures. The structures of the RCs, TSs, and PCs along with the barrier and released energies, the important interatomic distances, and the imaginary vibrational frequencies at the TSs involved in these reactions are shown in Figs. 2 and 3.

Fig. 2
figure 2

Gibbs barrier energies the energies released during the scavenging of OH·, NO2 · and OCH3 · radicals by ellagic acid or 3′-O-methyl ellagic acid. RCs, TSs, and PCs are shown on the left side (a, d, g, j, m, q), in the middle (b, e, h, k, n, r), and on the right side (c, f, i, l, p, s), respectively. The hydrogen atom involved in the reaction, the H attached to C3, C4, or C4′, and the reacting radical are indicated below the arrow on the left in each case. The following properties correspond to the transition state in each case: ν is the imaginary frequency (cm−1), O–H is the length of the OH bond of ellagic acid or 3′-O-methyl ellagic acid, H is the hydrogen atom that is abstracted (Å), and H–O is the distance between the hydrogen atom abstracted and the oxygen atom of the radical under consideration

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Fig. 3
figure 3

Gibbs barrier energies the energies released during the scavenging of OH·, NO2 ·, and OCH3 · radicals by 3′,4′-di-O-methyl ellagic acid or 3,3′-di-O-methyl ellagic acid. RCs, TSs, and PCs are shown on the left side (a, d, g, j, m, q), in the middle (b, e, h, k, n, r), and on the right side (c, f, i, l, p, s), respectively. The hydrogen atom involved in the reaction, the H attached to C3 or C4, and the reacting radical are indicated below the arrow on the left in each case. The following properties correspond to the transition state in each case: ν is the imaginary frequency (cm−1), O–H is the length of the OH bond of 3′,4′-di-O-methyl ellagic acid or 3,3′-di-O-methyl ellagic acid, H is the hydrogen atom that is abstracted (Å), and H–O is the distance between the hydrogen atom abstracted and the oxygen atom of the radical under consideration

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The ellagic acid molecule is planar and has four hydroxyl groups attached at the C3, C4, C3′, and C4′ positions. Since the structure of the molecule is symmetric, we considered hydrogen abstraction by each of the three radicals from the hydroxyl groups attached at the C3 and C4 positions only. The Gibbs barrier energy and the released energy, denoted ∆G i b and ∆G i r (i = 3, 4), respectively, for reactions at 298.15 K between ellagic acid (kcal/mol) and each of the three radicals (OH·, NO2 ·, and OCH3·), as obtained at different levels of theory in both the gas phase and aqueous media, are presented in Table 2. The O–H bond lengths of the four antioxidants are increased at the TSs due to the presence of the OH· radical to values of 1.03–1.06 Å; the corresponding lengths in the presence of OCH3 · and NO2 · radicals are 1.09–1.14 Å and 1.12–1.18 Å, respectively (Figs. 2 and 3). The H–O interatomic distances at the TSs in the presence of the OH· radical are 1.40–1.47 Å; the corresponding lengths in the presence of OCH3 · and NO2 · radicals are 1.27–1.32 Å and 1.24–1.30 Å, respectively (Figs. 2 and 3). Thus, the O–H bonds are the longest while the H–O interatomic distances are the shortest at the TSs when the NO2 group is the reacting radical. The reverse is true for the OH· radical, and the OCH3 · radical lies between the other two radicals in this respect. This correlates with the order of barrier energies, as discussed below.

Table 2 Gibbs barrier energies (∆G i b, i = 3, 4, in kcal/mol) and released energies (∆G i r, i = 3, 4, in kcal/mol) at 298.15 K for the abstraction of hydrogen by OH·, NO2 ·, or OCH3 · radicals from different sites on ellagic acid, as obtained at different levels of theory in the gas phase and aqueous media (results calculated in aqueous media are shown in parentheses)
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The Gibbs barrier energies for hydrogen abstraction by an OH· radical from both the C3 and C4 sites in both the gas phase and aqueous media were found to be negative (Table 2). Negative barrier energies imply that hydrogen abstraction from the hydroxyl groups of ellagic acid occurs barrierlessly. The energies released in these reactions in aqueous media, as obtained at different levels of theory, lie in the range −34.5 to −32.1 kcal/mol, showing that the PCs are quite stable. The Gibbs barrier energies associated with the abstraction of hydrogen by NO2 · and OCH3 · radicals in both the gas phase and aqueous media (Table 2) are all positive. The Gibbs barrier energies associated with the abstraction of hydrogen by the NO2 · radical from the hydroxyl groups attached to both the C3 and C4 sites, considering the values calculated in both the gas phase and aqueous media at all four levels of theory employed here, lie in the range 6–14.2 kcal/mol, while those corresponding to hydrogen abstraction by the OCH3 · radical lie in the range 0.4–5 kcal/mol (Table 2). The Gibbs energies released in the reactions involving the NO2 · and OCH3 · radicals are all negative; reactions involving the former radical usually result in more energy being released than those involving the latter do (Table 2).

The Gibbs barrier and released energies of reactions between 3′-O-methyl ellagic acid (kcal/mol) and each of the three radicals (OH·, NO2 ·, and OCH3 ·), as obtained at different levels of theory in both the gas phase and aqueous media, and denoted ∆G i b and ∆G i r, respectively (i = 3, 4, or 4′), are presented in Table 3. The corresponding results for hydrogen abstraction reactions between 3′,4′-di-O-methyl ellagic acid and each of the radicals are presented in Table 4, while those for hydrogen abstraction reactions between 3,3′-di-O-methyl ellagic acid and each of the three radicals are presented in Table 5. We can make the following observations based on the results presented in Tables 3, 4, and 5. The Gibbs barrier energy for the reaction between the mono- or dimethyl ellagic acid molecule and the OH· or NO2 · radical is usually similar to that between ellagic acid and the corresponding radical. The Gibbs barrier energy for the abstraction of hydrogen from the C3 site of the mono- or dimethyl ellagic acid molecule and the OCH3 · radical is also similar to that for the reaction between ellagic acid and the same radical. However, the Gibbs barrier energies for the corresponding reactions from the C4 sites of the antioxidant molecules and the OCH3 · radical are appreciably larger than those for the reactions between ellagic acid and the corresponding radicals. The reason for this difference is that, at the RC corresponding to the abstraction of hydrogen from the C4 site, one of the hydrogen atoms of the OCH3 group, bearing a Mulliken charge of 0.204, is involved in hydrogen bonding with the O8′ (Mulliken charge −0.491) and O7′ (Mulliken charge −0.565) sites of the antioxidant molecules (Figs. 1a and 2q). Because of this, the RC corresponding to hydrogen abstraction by OCH3 · from the C4 site is appreciably more stabilized than that corresponding to hydrogen abstraction from the C3 site by the same radical. As the RC is appreciably more stabilized in this case, the barrier energy is significantly increased.

Table 3 Gibbs free barrier energies (∆G i b, i = 3, 4, or 4′, in kcal/mol) and released energies (∆G i r, i  = 3, 4, or 4′, in kcal/mol) at 298.15 K for the abstraction of hydrogen by OH·, NO2 ·, and OCH3 · radicals from different sites on 3′-O-methyl ellagic acid, as obtained at different levels of theory in the gas phase and aqueous media (results calculated in aqueous media are given in parentheses)
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Table 4 Gibbs free barrier energies (∆G i b, i  = 3, 4, in kcal/mol) and released energies (∆G i r, i  = 3, 4, in kcal/mol) at 298.15 K for the abstraction of hydrogen by OH·, NO2 ·, or OCH3 · radicals from different sites on 3′,4′-di-O-methyl ellagic acid, as obtained at different levels of theory in the gas phase and aqueous media (results calculated in aqueous media are given in parentheses)
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Table 5 Gibbs free barrier energies (∆G 4 b, in kcal/mol) and released energies (∆G 4 r, in kcal/mol) at 298.15 K for the abstraction of hydrogen by OH·, NO2 ·, or OCH3 · radicals from different sites on 3,3′-di-O-methyl ellagic acid, as obtained at different levels of theory in the gas phase and aqueous media (results calculated in aqueous media are given in parentheses)
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Barrier energies for the abstraction of hydrogen by the hydroxyl radical from ellagic acid and its mono- as well as dimethyl derivatives were also calculated in terms of enthalpy. These barrier energies (Table S2 of the ESM) were also found to be negative, just as those calculated in terms of the Gibbs free energy were, and so they support the conclusion that the reactions under consideration are barrierless.

The reactivities of the radicals, as indicated by the barrier energies for all four antioxidant molecules, decrease in the order OH· > OCH3 · > NO2 · [49]. A graphical presentation of the Gibbs barrier energies involved in the abstraction of hydrogen by hydroxyl, nitrogen dioxide, and methoxy radicals from the C3 and C4 sites of ellagic acid and its mono- and dimethyl derivatives in aqueous media is given in Fig. 4. This enables a convenient comparison of the Gibbs barrier energies associated with the abstraction of hydrogen from ellagic acid and its methyl derivatives by the three radicals. It is obvious from this figure that hydrogen abstraction by an OH· radical from the hydroxyl groups of ellagic acid and its methyl derivatives in aqueous media would be barrierless, while the Gibbs barrier energies would be small or moderate (∼1–4 kcal/mol) or fairly large (∼6–8 kcal/mol) in the same medium when the radical involved is NO2 · or OCH3 ·, respectively.

Fig. 4
figure 4

Graphical representation of the Gibbs barrier energies (kcal/mol) associated with the abstraction of hydrogen from ellagic acid and its three methyl derivatives by hydroxyl, nitrogen dioxide, and methoxy radicals in aqueous media. Here C3, C4, and C4′ are the sites from which the hydrogen is abstracted

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Rate constants for hydrogen abstraction reactions

According to transition state theory [59], the rate constant for a chemical reaction is given by

$$ K=\left({K}_{\mathrm{B}}T/h\right) \exp \left(-\varDelta {G}^{\mathrm{b}}/ RT,\right) $$

where K is the thermal rate constant, K B is the Boltzmann constant, T is the absolute temperature (298.15 K), h is Planck’s constant, R is the gas constant, and ∆G b is the Gibbs barrier energy involved in the reaction under consideration. Ideally, the above expression should also be multiplied by a tunneling factor, but this factor is very close to 1, so it was ignored here. The calculated rate constants for the abstraction of hydrogen at 298.15 K by OH·, NO2 ·, and OCH3 · radicals from different sites on ellagic acid and its monomethyl and dimethyl derivatives, as calculated at the B3LYP/6-31G(d,p) and B3PW91/6-31G(d,p) levels of density functional theory in the gas phase (R i G) and aqueous media (R i A, where the subscript i corresponds to the number label of the oxygen atom to which the hydrogen atom to be abstracted is attached), are given in Table S3 of the ESM, while the corresponding results obtained at the B3LYP/AUG-cc-pVDZ and B3PW91/AUG-cc-pVDZ levels of theory are given in Table 6. We can make the following observations based on the results presented in Tables S3 and 6. (i) When NO2 · is the hydrogen-abstracting radical, the rate constants in the gas phase or aqueous media obtained using the AUG-cc-pVDZ basis set in some cases are appreciably smaller than those obtained using the 6-31G(d,p) basis set. However, when OH· and OCH3 · are the hydrogen-abstracting radicals, the rate constants obtained using the AUG-cc-pVDZ and 6-31G(d,p) basis sets are similar. (ii) In many cases, the rate constants substantially increase upon going from the gas phase to aqueous media, although the reverse is also true in a few cases.

Table 6 Rate constants in the gas phase (R i G, i  = 3, 4, or 4′, in M−1S−1) and aqueous media (R i A, i  = 3, 4, or 4′, in M−1S−1) at 298.15 K for the abstraction of hydrogen by OH·, NO2 ·, or OCH3 · radicals from different sites on ellagic acid and its monomethyl and dimethyl derivatives, as obtained at the B3LYP/AUG-cc-pVDZ and B3PW91/AUG-cc-pVDZ levels of theory (results calculated at the B3PW91/AUG-cc-pVDZ level are given in parentheses)
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The rate constants for the scavenging of OH radicals by ellagic acid and its monomethyl and dimethyl derivatives are mostly found to be on the order of 1013 M−1S−1 or more in the gas phase, while those calculated in aqueous media lie mostly in the range 1013–1016 M–1S−1. When OCH3 · is the hydrogen-abstracting radical, the rate constants in the gas phase lie in the broad range of 109 to 1012 M−1 S−1 while those in aqueous media lie in the broad range of 108 to 1012 M−1 S−1. When NO2 · is the hydrogen-abstracting radical, the rate constants in the gas phase are found to be quite small, lying in the range 104 to 106 M−1 S−1, while those in aqueous media mostly lie in the range 104 to 108 M−1 S−1. However, in some cases when NO2 · is the hydrogen-abstracting radical, the rate constants in aqueous media are quite small. Rate constants for hydrogen abstraction by OH· and NO2 · radicals have been determined experimentally at pH 7 and 8.5 [49]. Our calculated rate constants, particularly those obtained at the B3LYP/6-31G(d,p) and B3PW91/6-31G(d,p) levels in the gas phase, are quite similar to those obtained experimentally [49]. The calculated rate constants show that ellagic acid and its monomethyl and dimethyl derivatives are good radical scavengers, and their scavenging rates decrease in the order OH· >> OCH3 · > NO2 ·. Nitrogen dioxide (NO2 ·) is one of the most reactive species in the RNOS family [17, 49]. However, as shown by the results discussed above, it would be less efficiently scavenged by ellagic acid than OH· and OCH3 ·. Therefore, it appears that RNOS would, in general, be less efficiently scavenged than ROS.

Effect of specific water molecules on the barrier energy

We examined the possible roles of specific water molecules located near the reaction sites in two representative cases. One of these two cases was that of ellagic acid, where the Gibbs barrier energy was more negative than the other one for the same molecule, while the other case was that of 3′-O-methyl ellagic acid, where the Gibbs barrier energy was the most negative of all the cases considered in the present study. We studied the mechanisms of these two reactions by placing two specific water molecules near the reaction sites and fully optimizing the corresponding reactant complexes, transition states, and product complexes. It was found that the two specific water molecules stabilized the reactant complexes but did not interfere with the reaction mechanisms, as shown in Fig. S1a–f of the ESM. Consequently, the barrier energies in the cases of ellagic acid and 3′-O-methyl ellagic acid increased somewhat, becoming small positive (i.e., 0.74 and 1.02 kcal/mol) from small negative (i.e., −0.6 and −1.3 kcal/mol, respectively). Thus we find that including specific water molecules does not alter the reaction mechanism, although it does increase the barrier energy by a small amount. It is expected that similar situations will also occur in the other cases.

Single electron transfer reactions

We considered single electron transfer from ellagic acid or any of its monomethyl and dimethyl derivatives (A) to any of the three radicals (R·) considered here [66]. Electron transfer reactions may be expressed by the following general scheme:

$$ \begin{array}{lll}\mathrm{A}+{\mathrm{R}}^{\cdot}\hfill & \overset{\mathrm{A}\mathrm{IP}}{\to}\hfill & {\mathrm{A}}^{\cdot +}+{\mathrm{R}}^{-}.\hfill \end{array} $$

In this reaction, ellagic acid or any of its monomethyl or dimethyl derivatives (A) acts as an electron donor while the radical (R·) acts as an electron acceptor. The possibility of single electron transfer reactions can be studied using the adiabatic ionization potential (AIP). The value of this parameter was calculated for ellagic acid and all of its methyl derivatives mentioned above in combination with each of the three radicals considered here in both the gas phase and aqueous media at different levels of theory, and the results are presented in Table S4 of the ESM. We note the following from this table. (i) The AIP values are appreciably sensitive to the density functional and basis set used. (ii) In most cases, the AIP values in the gas phase are quite large. This suggests that the electron transfer mechanism is barely operative in the gas phase, except, say, in the presence of ionizing radiation. (iii) The AIP values in aqueous media are much less than those in the gas phase in all cases. Therefore, the electron transfer process would be much more likely to occur in aqueous media than in the gas phase. Further, the AIP values obtained at the B3LYP/AUG-cc-pVDZ and B3PW91/AUG-cc-pVDZ levels in aqueous media for the OH radical are negative, while those obtained using the same functionals and the 6-31G(d,p) basis set are positive. If we consider the values obtained using the AUG-cc-pVDZ basis set, the present results (Table S4 of the ESM) show that the electron transfer mechanism involving any of the antioxidant molecules and the OH radical would occur very efficiently in aqueous media, but the same processes involving the other two radicals would be much less efficient, even in aqueous media.

Spin density and molecular electrostatic potential distributions

Spin density distributions in the various RCs, TSs, and PCs corresponding to hydrogen abstraction by OH·, NO2 ·, and OCH3 · radicals at the C3 and C4 sites of ellagic acid for the iso-spin density value of 0.001 electrons/bohr3 are presented in Fig. S2 of the ESM. In this figure, the spin density distributions in RCs, TSs, and PCs are shown on the left side, in the middle, and on the right side in each case, respectively. Molecular electrostatic potential (MEP) distributions in the same RCs, TSs, and PCs (Fig. S3 of the ESM) corresponding to hydrogen abstraction by the same three radicals at the same sites of ellagic acid for the iso-MEP values of ±15.7 kcal/mol are presented in Fig. S3 of the ESM. In this figure, the pink and yellow colors correspond to negative and positive MEP values, respectively. It should be noted that spin density is localized at the attacking radicals in the various RCs, while it is usually delocalized over fairly broad regions including the radicals and ellagic acid at the TSs (Fig. S2 of the ESM). Also, at the PCs, spin density is delocalized over fairly extended regions of the ellagic acid radical created by the loss of a hydrogen atom from ellagic acid. Further, at the PCs, spin density is most pronounced near the site on ellagic acid from which the hydrogen atom is abstracted.

It is well established that negative MEP is a sensitive indicator of electron density. At the RCs of reactions involving the attack of an OH· radical on ellagic acid (Fig. S3a, d of the ESM), the negative-MEP regions for the chosen MEP value are pronounced near the carbonyl group oxygen atoms, the oxygen atoms of the OH groups attached to the C3 and C3′ sites of ellagic acid, and near the oxygen atom of the attacking OH· radical. Broadly speaking, the same is true for the corresponding transition states (Fig. S3b, e of the ESM), while, at the PCs, fairly broad negative-MEP regions are localized near the sites from which hydrogen atoms are abstracted. At the RCs of reactions involving the NO2 · radical (Fig. S3g, j of the ESM), no negative-MEP region is located near this radical, but such regions are located on the corresponding TSs (Fig. S3h, k of the ESM). At the PCs, negative-MEP regions are located near HNO2, which is formed from the NO2 · radical after this radical abstracts a hydrogen atom. In this case, an extended negative-MEP region is also located near the site from which hydrogen is abstracted. At the RCs and TSs of reactions involving the attack of the OCH3 · radical on ellagic acid (Fig. S3m, q of the ESM), negative-MEP regions are located mainly near the oxygen atom of this radical, the carbonyl group oxygen atoms, and the oxygen atoms of the hydroxyl groups attached to C3 and C3′. At the PCs formed due to the reaction of the OCH3 · radical with ellagic acid (Fig. S3p, s of the ESM), broad negative-MEP regions occur near the regions from which hydrogen was abstracted in each case. Thus, we find that both spin density and MEP are distributed over broad regions near the site at which hydrogen abstraction occur. This shows that the sites from which hydrogen atoms are abstracted are quite reactive and would readily capture hydrogen atoms, if available.

Conclusions

We can draw the following conclusion from theGibbs barrier energies and rate constants calculated in the present work. The Gibbs barrier energies involved in the abstraction of hydrogen by an OH· radical from the hydroxyl groups of ellagic acid and its monomethyl and dimethyl derivatives in both the gas phase and aqueous media were all found to be negative, which implies that the reactions are barrierless, and the corresponding rate constants, including those calculated in gas phase and aqueous media, are in the range 1013–1016 M−1 S−1. Therefore, these reactions would occur very efficiently. Specific water molecules located near the reaction sites increase barrier heights by ∼1–2 kcal/mol by stabilizing reactant complexes, but they do not interfere with the reaction mechanisms. The Gibbs barrier energies are moderately to notably large and positive when the radical involved in the hydrogen abstraction reactions is OCH3·. In this case, the rate constants, including those calculated in both the gas phase and aqueous media, lie in the range 108–1012 M−1 S−1. When NO2 · is the radical involved in hydrogen abstraction, barrier energies are appreciably increased, meaning that the rate constants mostly lie in the range 104–108 M−1 S−1, although, in some cases, the rate constants are much smaller. Hence, the scavenging efficiencies of ellagic acid and its monomethyl and dimethyl derivatives towards the three radicals decrease in the order OH· >> OCH3 · > NO2 ·. The available experimental results on the scavenging rate constants of ellagic acid towards OH· and NO2 · radicals broadly agree with our theoretical results.