Introduction

The human body constantly generates free radicals and other reactive species. The state of cells in which the reactive radical species exceed the capacity of the endogenous antioxidative protection system is named oxidative stress [1, 2]. The oxidative degradation of the vital biomolecules, lipids, proteins, and nucleic acids is caused by processes which include the reactive free radical species, especially reactive oxygen species (ROS) [3, 4]. Biomolecules can be exposed to oxidative degradation for years, which promotes aging and increases risk for certain neurodegenerative diseases such as amyotrophic lateral sclerosis, Alzheimer’s disease, and Parkinson’s disease, and many other diseases [1, 4,5,6,7,8]. Modern studies indicate that oxidative stress can be decreased using antioxidants [9,10,11]. The consumption of fruits and vegetables has a preventive role, which is due to a variety of constituents, including minerals, vitamins, fiber, and numerous phytochemicals among which flavonoids and phenolic compounds are very important [12]. The possible association between the consumption of food containing phenolics and a reduced risk of developing several disorders, including cancer and cardiovascular diseases, has been evaluated in several epidemiological investigations [13,14,15,16,17,18]. Phenolic acids are rarely found as free molecules in nature, but they most commonly occur in plant materials as esters, amides, ethers, or as structural components of the cellulose, proteins, and lignin [19,20,21]. As everyday part of a human diet, they are involved in appreciation of good food quality, sensory qualities, color, nutritional, and antioxidant properties of foods. Especially, phenolic acids such as vanillic acid, 2,3-dihydroxybenzoic acid, 2,4-dihydroxybenzoic acid, and gallic acid (GA) have an important role. Their antioxidative efficiency has been related to the number of hydroxy groups in the molecule, and also to their hydrogen atom donating abilities [22].

GA can be found in gallnuts, witch hazel, tea leaves, oak bark, etc., as free and as a part of hydrolysable tannins [22,23,24,25,26]. GA is commonly used in pharmaceutical and chemical industry, as well as foodstuff. Besides being used as a standard for determination of the total phenol content in various analytes, it is also used as starting material in the organic synthesis. It also has great importance and application in medicine, acting as an antioxidant and helping in protection human cells against oxidative damage. It shows cytotoxicity against cancer cells, antiallergic, antitumor, antifungal, anti-inflammatory, antiseptic, antivirus and antiasthmatic effects. GA and its derivatives inhibit insulin degradation, and is particularly effective in treating albuminuria and diabetes, psoriasis and external hemorrhoids, coronary heart disease, cerebral thrombosis, gastric ulcer, snail fever, viral hepatitis, senile dementia and other diseases where oxidative stress is involved [27].

Antioxidant reactions of phenolic compounds take place in highly complex environments. This is a consequence of the presence of numerous different free radicals and antioxidants present in biological media. The concentrations and reactivity of mentioned species, as well as the polarity and the pH value of the environment have significant influence in these reactions. Therefore, in different media, various radicals can react via several mechanisms. The antiradical properties of antioxidants are based on their ability to donate hydrogen atom to a free radical. In these reactions, a newly formed radical is generated from the antioxidant molecule, and that newly formed species is more stable and less reactive than the initial free radical. There are numerous mechanisms of the antioxidant actions, and some of them are: hydrogen atom transfer (HAT), proton coupled electron transfer (PCET), single electron transfer followed by proton transfer (SET-PT), sequential proton loss electron transfer (SPLET), radical adduct formation (RAF), and sequential proton loss hydrogen atom transfer (SPLHAT) [28,29,30,31,32].

Understanding of the leading reaction mechanism involved in the antioxidant action is a challenging task. It is well known that reactions involving HAT mechanism between two oxygen atoms have much lower activation energies and higher rate constants than HAT mechanism between two carbon atoms [33]. HAT mechanism involves transfer of a proton with one of its bonding electrons. However, in the case of PCET mechanism, the proton is transferred from phenolic compound to the radical’s lone pair. On the other hand, electron moves from the 2p lone pair of the phenol to the singly occupied molecular orbital (SOMO) of phenoxy radical [34, 35]. However, there are different approaches for determination which of these two mechanisms reaction obeys, including position of the orbitals between reacting species, tunneling effect, solvent polarity, etc. [36, 37].

In addition to our former thermodynamic investigation of antioxidative properties of GA, here we present a thermodynamic and mechanistic study of the reaction between the different peroxy radicals and GA. Since peroxy and methylperoxy (MP) radicals were used in our previous study [38,39,40,41,42], one of the aims of this work was to check the compatibility of thermodynamic and mechanistic approaches for antioxidative action of GA towards some alkyl peroxy radicals (ROO·). These radicals are soluble in membranes and considered to be the major generators of lipid peroxides [43]. They cause many kinds of diseases, including liver injury and cancer [44]. Akaike et al. found that ROO· was generated by heme–iron-catalyzed decomposition of t-BuOOH, and that scavenging activity of various antioxidants towards these radicals can be estimated by electron spin resonance spectroscopy and chemiluminescence [45, 46]. Recently, it was shown that the tert-butylperoxy radical (tBP) has potent bactericidal action, and that the radical scavenging activity of various antioxidants can be quantitatively estimated on the basis of the inhibitory activity against the ROO· induced cytotoxicity toward Staphylococcus aureus [45, 47]. However, there are no reports on the estimation of the free scavenging activity of gallic acid against ROO·.

Methodology

Geometry optimizations for all participants under investigation and frequency calculations have been carried out using a M05-2X method [48] combined with the 6-311++G(d,p) basis set. To account for the solvent effects, two solvents were investigated (water and benzene) using SMD model as implemented in Gaussian 09 [49, 50]. All geometries were fully optimized without imposing any restriction. The nature of the revealed stationary points on potential energy surface was confirmed by analyzing the results of the frequency calculations: no imaginary frequencies for equilibrium geometries, and one imaginary frequency for transition states.

In the case of the transition states, it was verified that the imaginary frequency corresponds to the expected motion along the reaction coordinate by intrinsic coordinate calculations (IRC). These calculations proved that each transition state (TS) connects two corresponding energy minima: reactant complex (RC) and product complex (PC). Natural bond orbital (NBO) analysis was performed for all participants in simulated reaction of the ROO· and GA [51, 52].

Transition state theory (TST) affords one of the simplest theoretical approaches for estimating the rate constants (k), which requires only structural, energetic, and vibrational frequency information for reactants and transition states [53]. The main advantage of using conventional TST is that it requires very limited potential energy information (only on reactants and the transition state), which makes it practical for a wide range of chemical reactions. Despite its relative simplicity, this theory has been proven to be sufficient to reproduce experimental rate constants of free radical scavenging reactions [54].

The rate constants for the reactions of CR3OO· and GA were calculated using TST, implemented in TheRate program [55] and 1 M standard state is calculated as follows:

$$k^{TST} = \frac{{k_{\text{B}} T}}{h}\exp \left( {\frac{{ - \Delta G^{ \ne } }}{RT}} \right).$$
(1)

Here k B and h stand for the Boltzmann and Planck constants, ΔG ≠is the free energy of activation, which is calculated as the difference in energies between transition states and reactants. In the case of HAT/PCET mechanism, reaction path degeneracy (σ) and transmission coefficient γ(T) were taken into account, implying that the Eyring equation was transformed into:

$$k^{{_{ZCT} }} = \sigma \gamma (T)\frac{{k_{\text{B}} T}}{h}\exp \left( {\frac{{ - \Delta G^{ \ne } }}{RT}} \right).$$
(2)

The transmission coefficient γ, corrections for tunneling effects (defined as the Boltzmann average of the ratio between the quantum and classical probabilities), was calculated using the zero-curvature tunneling (ZCT) approach [56].

Results and discussion

In our previous work, we investigated thermodynamic properties of the reactions of GA with ·OH, −·O2, and ·OOCH3 radicals [38]. It was found that position 4 is the most reactive site of GA, while positions 3 and 5 are mutually identical. In extension, here we examine reactions of GA with ROO· such as: methylperoxy (MP), ethylperoxy (EP), iso-propylperoxy (iPP) and tert-butylperoxy (tBP) radicals (Scheme 1), by applying the kinetic approach. The atom labeling presented in Scheme 1 is used through the whole manuscript. In all investigated cases, the transfer of hydrogen atom/proton is the process of interest. This transition is taking place from hydroxy group of GA to the oxygen of each of corresponding radicals. In this way, reactive peroxy radicals are neutralized, and new, more stable radical products are formed from GA. The rate constants k TST and k ZCT for all reaction of peroxy radicals and GA were calculated using Eqs. 1 and 2. The bond dissociation energies (ΔG BDE) as well as the activation energies and the rate constants at 298 K are presented in Tables 1 and 2.

Scheme 1
scheme 1

Atomic numbering of gallic acid and examined alkyl peroxy radicals

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Table 1 The calculated ΔG BDE (kJ/mol) for the reactions of GA with alkyl peroxy radicals
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Table 2 The calculated values of kinetic parameters for the reaction of GA and free peroxy radicals. ΔG ≠, k TST, k ZCT, γ and ΔG r denote activation free energy, rate constants, transmission coefficient (γ = k ZCT/k TST) and reaction free energy, respectively
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Hydrogen atom transfer-thermodynamics

Among the three hydroxy groups of GA, 4-OH group is the most responsible for the antiradical activity [38,39,40,41,42]. It is well known that ΔG BDE for the HAT mechanism can be calculated using the following equation:

$$\Delta \varvec{G}_{BDE} = \varvec{G}({\text{GA}{-}\text{O}}^{ \cdot } ) + {\text{G}}\left( {{\text{CR}}_{3} {\text{OOH}}} \right) - \varvec{G}\left( {{\text{GA}{-}\text{OH}}} \right) - \varvec{G}\left( {{\text{CR}}_{3} {\text{OO}}^{ \cdot } } \right)$$

Here G(GA–O·), G(CR3OOH), G(GA–OH), and G(CR3OO·) are the free energies of the gallic acid radical, molecule formed when corresponding peroxy radical accepts hydrogen atom from the gallic acid, gallic acid, and different free radical species, respectively. Lower values of ΔG BDE mean higher ability of GA to donate a hydrogen atom to corresponding radical species.

The results with all free radicals indicate that all reactions with p-OH group of GA both in water and benzene are exergonic. As regards, H transfer from m-OH of GA all reactions are endergonic in both solvents, except for the case of MP radical (Table 1). This indicates that the HAT reaction mechanism of GA with all ROO· is thermodynamically possible for p-OH group of GA in both solvents, while this mechanism is not preferable for m-OH. These results are in accordance with the results of previous investigation [38, 57].

To explain the differences in the reactivity of the individual OH sites the assessment of the spin density distribution was undertaken on the radicals of GA (positions 3 and 4). The lower ΔG BDE values implicate easier formation of the radicals and more delocalized spin density. The spin density values in water, obtained by the NBO analysis, as well as SOMOs of GA are depicted in Figs. 1 and S1. The results show that the radical formed from GA in position 4 is more stable. This is consequence of delocalization of the unpaired electron over oxygen and ortho and para carbons of aromatic core of GA (Fig. 1). In addition, appearance of low values of spin density in the GA–4O· on the two adjacent OH groups, as well as carboxyl group, suggests that unpaired electron is additionally delocalized, explaining higher stability compared to GA–3O·.

Fig. 1
figure 1

Spin density distribution in GA radicals in water

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Kinetics of HAT and PCET mechanism

There are several approaches examining g differences between HAT and PCET mechanisms, including different positioning of the reacting species and different electronic characters [58]. In this study, we considered differences between HAT and PCET mechanisms examining geometry orientations of all alkyl peroxy radicals toward GA in transition states as given. Potential energy surfaces and the optimized structures of stationary points along reaction pathways of HAT mechanism in water, and PCET mechanism in benzene are presented in Fig. 2, while the optimized structures of all other transition states are provided in Figs. S2 and S3.

Fig. 2
figure 2

Reaction pathway for the H-atom transfer from the C4–OH position of GA to the MP radical, in water (HAT) and benzene (PCET). The distances between C=O, O–H and H–O9 bonds are given in pm

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It was found that the barrier is slightly higher in benzene than in polar media for reaction of MP with 3-OH group, while in the case of EP, iPP, tBP the barriers are slightly lower in benzene (Table 2). Comparing the reactivity of the GA (both 3 and 4 positions in both solvents), it was found that the energy barrier for H transfer from phenolic site 4 is significantly lower than for 3. The difference is about 20 kJ/mol in the case of HAT and about 10 kJ/mol for PCET. The obtained results strongly suggest a higher reactivity of the para hydroxy group.

On the basis of the obtained results from Table 2, it is evident that Gibbs activation energies and rate constants for HAT mechanisms are not heavily influenced by the solvent polarity. In addition, we were not able to locate transition states responsible for PCET mechanism in water, as polar solvent. As a consequence of the previously mentioned lower activation barriers for position 4, k TST values are larger in comparison to those in position 3, implying that reaction in position 4 is significantly faster. Studies of kinetic solvent effects (KSEs) for the reaction in water and for related reaction in benzene, demonstrated that HAT in water and benzene exhibited gentle influence of KSEs, for example for MP k TST = 8.59 × 105 in water, while k TST = 6.79 × 105 in benzene. It means that the reactions which are taking place via the HAT mechanism are somewhat slower in a non-polar solvent. Similarly to the case of HAT, position 4 of GA is more reactive via PCET mechanism (Table 2). In contrast to the HAT mechanism, here the KSEs play an important role, since the reaction by PCET mechanism takes place only in the non-polar solvent (Table 2). The influence of the branched alkyl group of investigated peroxy radicals on the rate of chemical reaction showed that there is a slight decrease in the rate of the reaction with increase in the branching of alkyl group, in the case of both mechanisms.

Insight into k ZCT and γ points out tunneling effects as the responsible one for making the reaction between GA and alkyl peroxy radicals faster, in both positions and in both solvents (Table 2). Namely, values for MP radical reaction in position 4 of k ZCT = 8.54 × 108 in water, and k zct = 5.17 × 107 in benzene clearly show that tunneling effect is playing very important role. It is worth pointing out that the tunneling effect is responsible for the increase in reactions rate constants in all positions, and all solvents (Table 2; Figs. 3, S4 and S5). This effect rapidly decreases with the increase in the temperature. Since the abstraction reaction involves the motion of a light particle (hydrogen atom) that can easily tunnel through the reaction barrier, this action is to be expected (reaction of “pure” HAT mechanism). In addition, the reactions in position 4 of GA are distinctly exergonic (Table 2), while the activation energies are low and corresponding rate constants high. As in the case of the HAT reactions for the trapping of peroxy radicals by GA, reactions in positions 3 and 4 of PCET reaction in benzene have pronounced tunneling effect, too. In addition, transmission coefficients (γ) are obviously much higher in the case of PCET, implying different pathways for proton and electron motion [58]. The tunneling effect can be attributed to the formation of a compact H-bonded complex via two H bonds between the donor and acceptor and the short path length for hydrogen transfer indicating that the H transfer proceeds via a PCET mechanism [58,59,60]. Nevertheless, although tunneling effect is more pronounced in the case of PCET mechanism, the values for k ZCT show the same trends as k TST values, and point out HAT as preferable reaction pathway. It is worth pointing out that with the increase in branching of alkyl group of radical, i.e. increase in electron donating ability of alkyl moiety, the tunneling effect is becoming more pronounced.

Fig. 3
figure 3

Dependence of lnk TST and lnk ZCT (M−1 s−1) on reciprocal temperature 1/T (K) in the HAT (top) and PCET (bottom) pathways of GA with alkyl peroxy radicals, in benzene

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All these facts suggest that the reaction pathway of HAT mechanism in position 4 is predominant in both solvents [61]. Therefore, this process exposes the highest rate constant values, which can be attributed to the involvement of O4 from gallic acid radical in the relatively strong hydrogen bonds with H3 and H5, contributing to the weakening of the O4–H4 bond. The reaction of MP is slightly favored, by both thermodynamic and kinetic parameters. Inspection of the rate constant values in benzene for PCET mechanism indicated that, again, position 4 is also more probable reacting site. However, if one compares these parameters with those obtained for HAT, it is obvious that HAT is more probable mechanism.

Taking into account pK a value of carboxylate group of GA (4.4) [62], and that GA is deprotonated in aqueous solution (87.3%) [57, 63], it means the carboxylate anion of GA might play an important role is antioxidative action under physiological conditions (pH 7.4). Therefore, radical scavenging action of GA carboxylate anion against all investigated peroxy radicals has been investigated (Table S2). Based on the obtained values of activation energies, it is clear that corresponding reaction with all investigated radicals are slightly faster than those with GA itself.

HAT versus PCET

The values of the partial negative charge and the spin density in benzene, obtained by NBO analysis, on corresponding oxygen atoms for the RCs, TSs, and PCs are presented in the Table 3. On the basis of the obtained results, one can see that during the reaction the partial negative charge on peroxy O9 increases, and has the highest value in PCs. In the contrast to this, the partial negative charge on the phenolic oxygen O4 decreases in all cases. The partial positive charges on phenolic hydrogens are around 0.5, with small variations during the reactions. On the other hand, the spin density value on O9 is about 0.7 in all RCs, while the spin density values on all other atoms are practically equal to zero. The spin density is shared between O9 and the phenolic oxygen O4 in TSs (Table 3). Finally, in all PCs, the spin density is distributed over the GA moiety, while its value on O9 is decreased to zero. This finding confirms that every PC consists of alkyl peroxide and the corresponding GA–4O· species. Spin delocalization in this product is in agreement with the fact that more stable radical is formed. During all reaction pathways, the spin density on the phenolic hydrogens (H4) remains close to zero. All these facts indicate that the spin density on the transferred hydrogen cannot be generally used to distinguish HAT from PCET mechanism [35], but some other results point out differences between PCET and HAT mechanism.

Table 3 Partial charge and spin density values of the oxygen atoms of interest in benzene
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Mayer et al. used DFT to examine the self-exchange reactions of the phenoxy radical/phenol, methoxy radical/methanol and the benzyl radical/toluene systems [64]. They identified the geometrical differences of HAT and PCET in transitions states. The identification was based on the analysis of the SOMO of the transition state. The HAT mechanism is characterized by a significant SOMO density along the donor ···H··· acceptor transition vector. On the other hand, SOMO of PCET transition state involves p type orbitals, which are orthogonal to the transition vector.

The analysis of SOMOs shapes in the corresponding HAT and PCET transition states provides deeper insight into the differences between these mechanisms (Fig. 4). SOMOs of all TSs of HAT and PCET are mostly localized over aromatic ring of GA. On the other hand, differences are obvious along the O4···H4···O9 vectors. Namely, in all HAT transition states, SOMOs are also localized along this transition vector, implying that the transfer of hydrogen atom is taking place. On the other hand, the SOMOs of PCET in TSs involve the p orbitals in the H acceptor (O4), and they are not localized along O4···H4···O9 transition vector. Here, the transfer of a proton and electron follows different pathways, indicating that the proton is transferred from the OH group in position 4 of GA to oxygen’s lone pair of radical, while the electron moves from the 2p lone pair of the GA–4OH to the SOMO of alkyl peroxy radical. These findings are in good agreement with literature data [65].

Fig. 4
figure 4

The shape of SOMOs in different transition states of HAT and PCET mechanisms in position 4, in benzene

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Additionally, delocalization of SOMO is significantly weaker in transition states of PCET than in those for HAT mechanism. These differences rationalize the higher activation energies for the reactions via PCET mechanism (Table 2). Namely, PCET is energetically disfavored for about 24 kJ/mol in all cases.

Conclusion

In this paper, we presented thermodynamic and kinetic approach for the antioxidative action of gallic acid with some alkyl peroxy radicals, via HAT and PCET mechanisms, in polar and non-polar solvents. Based on the obtained results, it can be concluded that PCET mechanism is not possible in water for the examined system. Furthermore, ΔG BDE as well as k TST rate constants are undoubtedly showing that HAT is predominant mechanism in both solvents. Thermodynamic and kinetic data clearly point out position 4 as more reactive site of the GA. In addition, the large tunneling effect is sharpening the potential barriers for both mechanisms. Moreover, the obtained k ZCT values are in agreement with those for k TST also implying that HAT is prevailing mechanism. Furthermore, it is shown that differences between HAT and PCET mechanisms cannot be distinguished using NBO charges and spin densities. Instead, for this purpose, SOMOs are used to interpret these differences. The obtained results showed that, unlike HAT TSs structures, there is no SOMO localization over O4···H4···O9 transition vector in PCET transition states. Consequently, HAT activation barriers are favored by about 24 kJ/mol, in all cases. This additionally points out HAT as preferred mechanistic pathway under examined reaction conditions.