Antioxidant Activity of Eugenol And Its Acetyl And Nitroderivatives: A DFT Approach of DPPH Test.

This work evaluates the antioxidant potential of acetyl and nitro derivatives of eugenol through computational techniques. Structural analysis and Hydrogen Atomic Transfer (HAT) antioxidant mechanism were investigated by density functional theory (DFT). Each molecular structure was optimized by the hybrid functional M06-2X with a basis set 6-31+G(d,p), and the HAT mechanism with HO, HOO, CH 3 O, DPPH radicals was evaluated. In agreement with experimental data from previous studies, two steps of hydrogen transfer were tested. Thermodynamic data showed the need for two stages of hydrogen transfer, followed by the formation of quinones to make the reaction with DPPH spontaneous. Theoretical kinetic data showed that the preferred antioxidant site depends on the instability of the attacking radical and conrmed the antioxidant prole of eugenol (E1) and 5-allyl-3-nitrobenzene-1,2-diol (E5) in the DPPH test. This study shows that the 4-allyl-2-methoxy-(4-nitrophenol) (E4) structure also has an anti-radical activity that is not seen in the experimental due to chemoselectivity of DPPH.


Introduction
The inhibition of oxidation has an important role in technology and health. The prolonged storage time of a biofuel causes the modi cation of its physicochemical properties due the oxidation caused by a class of free radicals known as reactive oxygen species (ROS), thus affecting its performance and even causing damage to the engine [1][2][3]. Our body maintains the balance between antioxidants and reactive species naturally. However, as we age, this oxidative balance is lost, generating an excess of reactive species, resulting in a condition known as oxidative stress. This condition is associated with several diseases such as: thrombosis, heart attack, stroke, depression and cancer [4]. Therefore, the search for and development of new compounds with antioxidant properties is of interest to researchers both in materials and health eld.
This toxicity leads to studies for the development of eugenol derivatives, maintaining or improving bene cial activities and reducing the hepatotoxic effect. Studies carried out with eugenol-derived nitro and acetyl showed that the modi cation in the HO-phenolic group leads to loss of antioxidant activity in the 1,1-diphenyl-2-picrylhydrazyl (DPPH • ) assay [12].
Studies of the antioxidant activity of capsaicin (CAP), a vanilloid compound like eugenol, showed the important role of allylic and benzyl radicals in antioxidant pro le of that compound. Density Functional Theory (DFT) calculations in gas phase revealed that benzyl site of CAP is 3.3 kcal·mol −1 more stable than phenoxyl site [13]. When the implicit solvation model was applied, the benzyl and allyl radicals are 0.2 and 2.5 kcal·mol −1 , respectively, more stable than the phenoxyl radical [14] Due to this structural similarity, as well the formation of a more stable allyl-benzyl radical by eugenol, would suggest that the oxidation mechanism by Hydrogen Atomic Transfer (HAT) would occur through this site [13]. However, this is not observed experimentally since acetylated derivatives of eugenol do not show antioxidant activity in the DPPH test [12].
However, kinetic parameters obtained by DFT studies for capsaicin showed that the phenolic radical formation reaction is faster than that of benzyl. This trend tends to increase the greater the polarity of the solvent and the lower the reactivity of the scavenged radical, which may explain the non-antioxidant pro le of some of these derivatives [12,14].
Most computational chemistry studies address the use of bond-dissociation energy (BDE) or in the case of reactivity studies by HAT mechanism, a single step reaction with simple free radicals such as hydroxyl (HO • ) and peroxyl (HOO • ) radicals to evaluate antioxidant activity [13][14][15][16][17][18]. However, there is evidence that a single hydrogen transfer is not su cient to describe the antioxidant mechanism of eugenol. The rst clue is that the stoichiometry of the eugenol-DPPH reaction is approximately 1:2 [19]. In vitro, the oxidation of eugenol by silver oxide leads to the formation of a quinone-methide [8]. Besides, in humans, the main urine-excreted metabolite of eugenol is 2-methoxy-4-propyl-5-sulfanylphenol, a saturated derivative of eugenol with an added SH-group at position-5 [10]. This type of product is commonly formed by the addition of Michael who requires as an intermediate reagent a quinone-methide.
Although the BDE analysis be e cient in some studies, it does not consider the structure of the free radical which will react with the antioxidant molecule. The use of simpler free radicals does not describe well the interaction of side chains of the reagents, as in the case of DPPH • , which is a bulky radical, neglecting both steric hindrance and electrostatic repulsion effects.
In this work, we revisited the work of Hidalgo et al., using DFT to evaluate the antioxidant activity of eugenol and its derivatives. Unlike other studies, a two-step HAT mechanism was considered to evaluate the role of quinone formation in thermodynamic stabilization of reaction. For this simulation, HO • , HOO • , CH 3 O • , as well as the use of DPPH • , were used to evaluate the stereoselectivity of antioxidants with different types of free radicals. Figure 1 shows the structures of eugenol and its derivatives studied by Hidalgo et al, 2009. The same acronyms as the base reference for the antioxidants studied were used.

Conformational analysis
Conformational analysis was performed in two steps. In the rst, the 10 lowest energy structures were obtained using the Conformers Plugin with the MMFF94 force eld present in ChemAxon's Marvin Sketch Page 4/27 V. 18.1.0. Structure with energy difference of 0.2 kJ·mol −1 were considered identical, being considered only structures with energy difference greater than this diversity range. The optimization limit used was "verystrict".
In the second step, the structures obtained were re-optimized using the DFT-M06-2X [20] method with the 6-31+G(d,p) [21,22] base set using Gaussian 09 program from Gaussian INC. The calculations were performed in the gas phase and at 298.15 K, using tight convergence criterion. Frequency calculations were made to con rm the correct minimization of the structures through the absence of imaginary frequencies. Only the minimum energy structure (with the lowest Gibbs free energy -G°) of each compound was used for the next calculation steps in this work.

Thermodynamic analysis
Reaction spontaneity was evaluated using Standard Gibbs Free Energy of Reaction (Δ r G°) data for HAT mechanism. Hydroxyl (HO • ), peroxyl (HOO • ), methoxyl (CH 3 O • ) and DPPH radicals were used. Phenolic, benzyl and allyl sites were evaluated as atomic hydrogen donors. On the rst step, the antioxidant (ArXH) transferred a single atomic hydrogen to the free radical (R•), forming a more stable pair of radical (ArX•) and molecule (RH), Equation 1. Δ r G° was obtained by subtracting G° of the reactants from G° of the products, Equation 2.
Where X could be oxygen for phenol sites or carbon for both benzyl and allyl sites. Were also considered the quinone formation overall reaction for E1, E4 and E5 structures, Equation 3. The formation of methide quinone for the three structures and ortho-quinone for E5 was considered. Were computed the Δ r G° for the formation of quinones, Equation 4.
Reaction kinetics were evaluated from activation-free energy (ΔG ‡ ) and rate constant (k) at 298.15 K. Transition states (TS) was obtained using the QST3 algorithm [23,24] of Gaussian 09, and the con rmation of this was performed both by the analysis of frequencies from the existence of only an imaginary frequency, in the direction of proton transfer (bonding stretching bending or bond bending or bond).25,26 For rst HAT step, ΔG ‡ was obtained subtracting G° of the reactants from G° of TS, Equation 5.
For second HAT step, the attacker radical (R • ) receives a hydrogen atom from radical (ArX • ) producing a quinone (QN). In this step, ΔG ‡ was obtained following Equation 6:

Statistical treatment
Statistical analysis of the data was performed by multiple linear regression using the proj.lin function of Microsoft Excel. The values of ln (C 0 /Ct) in the DPPH test were used as response variable. [12] Absence and presence of functional groups, as well as reaction and activation-free energy data, in addition to the rate constant were used as regressor variables. For obtained models, the residue (b) was considered being equal to zero, due in the absence of speci c functional groups for HAT mechanisms, the molecule should not present any antioxidant activity (y = 0).

Natural Bond Order (NBO)
The NBO analysis [28] was used to determine Winberg [29] bonding orders and identify electronic factors that contributed to the stabilization of free radicals reactants. The transfer of atomic hydrogen, as well as the presence of unpaired electrons during the formation of a radical, causes a change in the geometry of the molecule seen by changing of bond length and angles values. In case, the incentive to make a connection is an indication of the mesomeric or hyperconjugative effects.

Results And Discussion
Part A. Thermodynamics of radical formation The rst part of our study aims to obtain de values for free energies of reaction of the antioxidants with HO•, HOO•, CH3O• e DPPH•.

Stability of the tested free radicals
The radicalar stability (RS) was calculated by the difference of energy between free energies of formation of free radical •R and the molecule formed by capture of atomic hydrogen from antioxidant (HR) as describe by Equation 8.
The lower the value of RS, the more stable the free radical and the more selective the hydrogen abstraction it will be. The values of RS are shown in the second column of for molecules and its respective free radicals. Selectivity of antioxidant sites. The selectivity of antioxidants sites was measured in Table 3. Values of Δ r G° for reactions between eugenol and its derivatives with HO • , HOO • , CH 3 O • and DPPH • . These results show the following trends for hydrogen loss of studied functional groups: Benzyl ~ Allyl > Phenoxyl > Methoxyl > Acetyl.
The higher selectivity of the allylic and benzyl radicals is due to the isoenergetic resonance of the electron unpaired with the π* orbitals of allyl and aromatic ring, that allows a better spreading of the unpaired electron density by the structure leading to a more stable radical.  In uence of the attacker radical stability. The Table 4 show the free energies of activation and rates constants as well. In general, the less stable is the attacking radical, the lower the activation free energy. In all evaluated sites, the HO • showed to be the fastest to abstract the atomic H, showing lower values of Δ ‡ G°.
The only exception found was the formation of the BR in E4, where the smallest energy barrier found was for the attack of the radical CH 3 O • . The presence of the nitro group does not allow the methoxyl group to be in the same plane of the ring which assists the formation of a stable intermediate of 6 membered ring.
In uence of the attacker radical reactivity. The eugenol molecule presented Δ ‡ G° of 6.3·kcal·mol -1 for the formation of the phenoxyl radical (P R ) and 6.4·kcal·mol -1 for the formation of BR in the reaction with HO•.
In the reaction with HOO • and CH 3 O • , as the radical becomes more stable, eugenol shows a kinetic preference to oxidize the phenol than the benzyl group.
The nitro group in E4 and E5 shows increasing the free energy of activation for P R formation due to the stronger hydrogen bond that di cult the transfer of H process and BR due to the meta-position substituent effect that destabilizes the formed radical. In E4 the most kinetically favorable site is benzyl hydrogen with value of Δ ‡ G° of 7.5·kcal·mol -1 , whereas in E5, is phenoxyl-2 hydrogen with 8.2·kcal·mol -1 .
Separately, both thermodynamic and kinetic data for a single atomic hydrogen transferred show that eugenol is expected to have a better antiradical activity than its derivatives, which is inconsistent with literature data where E5 has a higher capacity antioxidant that eugenol and E4 has no activity in DPPH assay [12].

Part C. Thermodynamics of quinone formation
The rst transfer of H did not bring satisfactory answers to justify the reactivity or not of eugenol and its derivatives. Moreover, none showed to be spontaneous with the DPPH radical in a stoichiometry of 1:1. This encouraged us to investigate the second abstraction to explain the facts present in the literature. Only the E1, E4 and E5 structures are able to form methide-quinones, and only E5 can form an orthoquinone, as shown in the Figure 2.
The thermodynamics of formation of quinones was evaluated by comparation of Δ r G° for reaction between ArXH and two equivalents of R • . Table 5 shows the values of Δ r G° with free radicals for two consecutive steps of HAT. The results show that the less stable the attacker free radical, the more spontaneous the formation of the quinones. The formation of methide quinones showed be more spontaneous than ortho-quinone, probably due to electrostatic repulsion among lonely electron pairs of the three oxygen centers presents in the last one.
Among the structures that show the highest tendency to form methide quinone is E1, with -91.4·kcal·mol -1 , followed by E5 with -86.9·kcal·mol -1 . The reaction of E4 quinone is only 0.3·kcal·mol -1 less stable than that of E5.
For the three structures analyzed, the formation of the methide quinones (MQ) showed spontaneous reaction with DPPH • . The formation of ortho-quinone (OQ) presented Δ r G° of 8.3·kcal·mol -1 , suggesting that this mechanistic route is the least favorable to occur. The structural inability to form MQ may explain the negative result of antioxidant activity of E2, E3 and E6 derivatives in DPPH assay, but the experimental data for E4 still unclear.

Part D. Kinetics of quinone formation
The achieving of the transition state for the formation of quinones was performed from the most stable radical of each structure. For E1, phenoxyl radical was used, while for E4 and E5 were used its respective benzyl radicals. Table 6 shows the values of Δ ‡G° and k for formation of quinones. Similarly, to the transition state of the formation of radicals, the free energy of activation is less, the less stable the attacker radical. The Δ ‡G is 6.6·kcal·mol -1 in the E1 reaction with HO • and shows only the transfer of hydrogen, as expected. However, the second transfer for E4 and E5 occurs in a different way.
First occurs the addition of radical to 1-carbon of the aromatic ring. This intermediary is so stabilized by hydrogen bonding that when the reaction with HO • , that Δ ‡ G° computed directly from ArX • and R • show negative values: -3.3·kcal·mol -1 for E4 and -1.7·kcal·mol -1 for E5. The IRC calculation shows that in the next step evolves in a concerted mechanism with the effective transfer of phenolic hydrogen and elimination of water. Figure 3 shows a scheme of this quinone formation path.
The same effect was seen when were used HOO • and CH 3 O • , forming 4-membered and 5-membered rings, respectively. The formation of these intermediaries is responsible for decreasing of free energy of transition state.
Contrary to what is observed for reactions with other radicals, the energy barrier for the reaction with HOO • is higher for nitrated derivatives in relation to activation-free energy compared to the reaction of this radical with eugenol. These results suggest that the more reactive the radical, the greater its selectivity to attack nitrated derivatives for the formation of methide quinones.
Since the DPPH • is more stable than HOO • , is expected that it is more susceptible to the formation of quinone from eugenol, which still did not explain well the fact that E5 presents antioxidant activity superior to eugenol in the test.

Part E. Statistical analysis of structure and reactivity
Based on the data obtained, a statistical study was carried out in three parts: (a) structural aspects, (b) reaction-free energy and (c) reaction kinetics.
Structural Aspects.
In the structural study, a multiple linear regression was performed using the following factors: presence of phenolic (PR 1 and PR 2 ), benzyl sites (BR) and ability to form methyl quinone (MQ) and orthoquinone (OQ). PR 1 was de ned as original phenolic group and PR 2 , as the phenolic group produced by demethylation of the methoxy group in E5. The response variable was de ned as ln(Co/Ct) values of the antioxidant capacity in the DPPH test present in the work of Hidalgo and in this work it was called antioxidant activity (AA) [12].
In case of the presence of the antioxidant site was interpreted as 1 and the absence was represented by 0. The ability to form quinone of molecule was interpreted as 1 (e.g. E1, E4 and E5) and the inability to form, as 0 (e.g. E2, E3 and E6). In the model the term B was considered being equal to 0, because in the absence of speci c functional groups, the molecule should not present any antioxidant activity. Table 7 show the results for structural analysis.  Free Energy of Reaction.
The second study was based on the free energy data of the formation of phenolic and benzyl radicals as the quinones, maintaining the equal response variable. The Table 8 shows the data for Δ r G° for the main reactive sites. In the absence of the site, the free energy value was de ned as being equal to zero.
The evaluated data set formed the following relationship with the antioxidant activity represented by the Equation 11. AA = -0.356 × Δ r G°(RF1) + 0.111 × Δ r G°(QM) -0.0249 × Δ R G°(OQ) (11) According to this equation, the more negative the reaction-free energy for the formation of the phenoxyl radical-1 and ortho-quinone, the greater the anti-radicalar activity. The positive coe cient of Δ R G° (QM) may suggest that greater stability of MQ may decrease the antioxidant activity in the DPPH test. This can be explained because there would be a side reaction where two PR can disproportionate into a methide quinone and regenerating the original antioxidant molecule. This reaction competes with the reaction with the DPPH radical which could slow down the change in the absorption band of the DPPH at 515 nm. The third statistical study was based on the constants of bimolecular reaction rates obtained by the Eyring equation. Table 9 show values of k for formation of PR1, PR2, BR, QM and OQ, using as y the results in DPPH test [12]. From data analysis of Table 9, was obtained the Equation 12, correlating kinetics data with antioxidant activity. AA = 0.0220 × k(PR 1 ) + 0.2082 × k(PR 2 ) + 0.0782 × k(QM) (12) This equation showed that the activity is in uenced by the activation barriers for the formation of PR 1 , QM and mainly PR 2 . These results suggest that the presence of PR 2 assists the reaction kinetics, while the thermodynamic of antioxidant activity depends on the Δ R G°(PR 1 ). Nevertheless, only possession of these data is impossible to suggest the chemical explanation for the improvement of the antioxidant pro le by PR 2 .
Part F. Rates of Reaction With DPPH Radical.
In order to understand the lack of activity of E4 and the greater reactivity of E5 in relation to E1, the transition states were obtained for the reaction of these three antioxidants with the DPPH • . They were used as phenolic sites for the transfer of H, since the statistical study disposes the in uence of the allyl and benzyl sites in the test.
The Table 10 show the value of ΔG ‡ and k for these reactions. These results show perhaps one of the best results of this work: the stereoselectivity of the DPPH to E1 and E5. The data of free energies of activation with DPPH • show values of 20.6 kcal·mol -1 for the PR and 24.0 kcal·mol -1 for the BR of E1, following the trend seen that the greater the stability of the radical, the greater the preference of reaction with the phenolic site.  Figure 4 show the transitions states of hydrogen transfer from phenolic sites to DPPH of E1, E4 and E5.
The arrangement almost parallel of the aromatic rings suggests that the reaction appears should be facilitated by an π-stacking interaction. The presence of the nitro group gives rise to a repulsion force that prevents the stacking of the aromatic rings. Only E1 and PR 2 of E5 be able to reach this arrangement, due to the absence of nitro group in E1 and to considerable distance between this group in meta to second phenoxyl group.
From this perspective, the second phenol group (PR 2 ) in the structure should act in two different ways: as an ampli er of the reactive surface area, because the two sites of E5 have close activation free energies; or intramolecular catalyst as shown in Figure 5. The reaction in only one step is about ten times slower.
The PR 1 formation indirect route has 3 steps: rst, the H-transfer from E5 to DPPH producing PR 2 by a

Conclusions
Free energies of reaction data showed that the benzyl-allyl radical is the most stable to be formed by the HAT mechanism in the gas phase. However, the transfer of only one hydrogen atom does not appear to be spontaneous against the DPPH radical. The formation of the both methide and ortho-quinones has be shown to be an important key for antioxidant activity in DPPH assay, since the second transfer of atomic hydrogen, releases more energy than the rst and the formation of the quinone showing negative Δ r G values for the global reaction of E1, E4 and E5 with two DPPH equivalents, which corroborates with literature data.
Kinetic data showed, except for eugenol, the more stable the attacking radical, the greater the kinetic a nity for the phenolic sites. This may explain the reason for E2, E3 and E6 did not show antioxidant activity in the DPPH test. Statistical analysis of structural and kinetic data showed that the presence of the catechol group increases antioxidant activity.
Although this study suggests that E4 has an antioxidant pro le like E1 and E5. Its antioxidant activity is not detected in the DPPH test due to the electrostatic repulsion between DPPH • and its nitro groups. The increased antioxidant activity of E5 is attributed to the presence of the catechol group, because the replacement of the OCH 3 by OH group allows a faster and more favorable approximation and pairing with DPPH • aromatic rings, forming PR2 rst. Then the radical formed undergoes tautomerism, occurring an intramolecular hydrogen transfer forming the thermodynamic more stable PR 1 radical.

Declarations
Author contributions Luiz Antônio Soares Romeiro, Emmanuel Silva Marinho, Norberto de Kássio Viera Monteiro, and Pedro de Lima-Neto: Contribution to the writing and revising of the manuscript. José Roberval Candido Júnior: Contribution to the theoretical calculations and to the writing and revising of the manuscript.
Code availability Not applicable.

Data Availability
All data are available on request to the corresponding author.

Figure 5
Possibilities of PR 1 formation from E5: (a) single step; (b) three steps catalysed by PR 2.

Supplementary Files
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