1 Introduction

Highly reactive free radicals, such as hydroxyl and peroxyl radicals, are produced in the organism during normal metabolic processes. Imbalance between formation and consumption of free radicals leads to phenomenon known as oxidative stress [1]. These reactive species contribute to oxidative damage to proteins, DNA and lipids and are associated with some diseases [2, 3]. Thus, the compounds able to scavenge free radicals are in the focus of contemporary investigations. Numerous epidemiological studies have shown that dietary antioxidants can reduce development and progression of some chronic diseases [4,5,6,7]. One of the most abundant phenolic acid antioxidants present in fruits and vegetables is chlorogenic acid (5-O-caffeoylquinic acid, 5CQA) (Fig. 1) [8].

Fig. 1
figure 1

Possible antioxidative reaction pathways of 5CQA in nonpolar solvents. The atoms labeling scheme and product names are indicated

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A wide range of experimental assays are used to evaluate antioxidative capacity [9,10,11,12]. Roughly, there are two types of these assays: chemical and biological [13]. In biological assays the damage in biomolecules caused by radical processes is measured. Chemical assays are used in studies which are devoted to evaluation of the rate constants for the reactions between free radicals and antioxidants. In these assays the antioxidative capacity of a compound is compared to that of some reference compound. The most commonly used antioxidant for this purpose is trolox (6-hydroxy-2,5,7,8-tetramethylchroman-2-carboxylic acid, Tx) (Fig. 2).

Fig. 2
figure 2

Possible antioxidative reaction pathways of Tx in nonpolar solvents. The atoms labeling scheme and product names are indicated

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Recently, a computational protocol known as the quantum mechanics-based test for overall free-radical scavenging activity (QMORSA) has been proposed for estimating antioxidative capacity of compound [14]. This approach is based on thermodynamic and kinetic investigation of all possible reactions included in antioxidative processes for examined compound. Namely, this methodology requires calculation of rate constants for all probable mechanistic pathways of an antioxidant in media of different polarity considering the influence of pH. Like experimental studies, this approach also offers possibility for determination of the relative antioxidative activity using Tx as a reference antioxidant. Thus, the ratio between overall rate constants of examined antioxidant and Tx can indicate larger or smaller activity of the antioxidant in comparison to Tx.

There are several theoretical studies devoted to explanation of antioxidative action of 5CQA [15,16,17,18,19] including thermodynamic and mechanistic approaches to the hydrogen atom transfer (HAT), radical adduct formation (RAF), sequential proton loss–electron transfer (SPLET), and single electron transfer–proton transfer (SET-PT) mechanisms. In our recent paper [17], kinetic investigations of the four mechanisms of 5CQA with HO• have revealed that in neutral and acidic media HAT and RAF mechanisms are competitive, whereas in basis media (e.g., at physiological pH) SPLET mechanism is predominant.

This work is an extension of our efforts aimed at elucidation of antioxidative properties of 5CQA. The goal of the work is to determine relative antioxidative capacity of 5CQA using Tx as a reference (rT) in nonpolar solvents. For this purpose, all antioxidative pathways of 5CQA and Tx with two free radicals, HO• (extremely reactive) and CH3OO• (moderately reactive), were investigated by means of two theoretical models. An additional goal is to examine the performances of the applied theoretical models in evaluation of the rT values of 5CQA.

2 Computational details

Within this work all calculations were performed using the Gaussian 09 program package [20]. Two levels of theory were applied: M06-2X/6-311++G(d,p) [21, 22] in combination with the CPCM polarizable continuum solvation model [23] and M05-2X/6-311++G(d,p) [24] in combination with the SMD continuum solvation model [25]. The former theoretical model has recently demonstrated robustness and very good overall performance in investigations of the related problems [15, 17, 21, 26], where it was applied in a manner that the influence of solvent to the structure and energy was estimated by full geometry optimizations, including frequency calculations. The latter density functional and solvation model have often been employed [27,28,29,30,31]. Sometimes, their application was based on the gas-phase calculations [27, 29], and the solvent cage effects were included according to the corrections proposed by Okuno [32] taking into account the free volume theory [33].

Following our strategy (full optimizations with frequency calculations included) we performed the calculations taking into account the effects of two solvents of similar polarity: benzene (dielectric constant ε = 2.2706) and pentyl ethanoate (ε = 4.7297). The restricted and unrestricted calculation schemes were applied for the closed-shell and open-shell structures. The nature of the revealed stationary points was determined by analyzing the results of the frequency calculations: no imaginary vibrations for equilibrium geometries and exactly one imaginary vibration for transition states. The intrinsic reaction coordinate (IRC) calculations were carried out to confirm that each transition state connects two corresponding equilibrium geometries.

The following reactions were considered:

$${\text{Phenolic}} + {\text{R}}^{ \cdot } \to {\text{Phenolic}}^{ \cdot } + {\text{RH}}$$
(1)
$${\text{Phenolic}} + {\text{R}}^{ \cdot } \to \left( {\text{Phenolic}} - {\text{R}} \right)^{ \cdot }$$
(2)
$${\text{Phenolic}} \rightleftarrows {\text{Phenolic}}^{ - } + {\text{H}}^{ + }$$
(3)
$${\text{Phenolic}} + {\text{R}}^{ \cdot } \rightleftarrows {\text{Phenolic}}^{ + \cdot } + {\text{R}}^{ - }$$
(4)

In Eqs. (1)–(4) Phenolic stands for 5CQA and Tx, whereas R• denotes the HO• and CH3OO• radicals. Accordingly, Phenolic•, (Phenolic-R)•, Phenolic−, and Phenolic+• represent the free radical, radical adduct, anion, and radical cation issued from the corresponding phenolic compound, respectively. Apparently, RH is the parent compound of R•, and R− is the corresponding anion. The HO• radical is produced during Fenton and Haber–Weiss reactions in organism and represents one of the most potent radicals of biological importance. CH3OO• radical is selected to imitate behavior of larger lipid peroxide radicals. Equations (1) and (2) represent the HAT and RAF mechanisms. Equations (3) and (4) characterize the first steps of the SPLET (proton loss) and SET-PT (electron transfer) mechanisms. The free energies of the reactions at T = 298.15 K in the two solvents were determined. The free energy values of the solvated proton [Eq. (3)] in benzene (− 901.8 kJ mol−1) and pentyl ethanoate (− 1015.5 kJ mol−1) were taken from the literature [34].

The rate constants were calculated for 1 M standard state using the Eckart method, also known as ZCT-0 [35]:

$$k_{{{\text{ZCT}} - 0}} = \sigma \gamma \left( T \right)\frac{{k_{\text{B}} T}}{h}\exp \left( {{\raise0.7ex\hbox{${ - \Delta G_{a}^{\ddag } }$} \!\mathord{\left/ {\vphantom {{ - \Delta G_{a}^{\ddag } } {{\text{R}}T}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${{\text{R}}T}$}}} \right)$$
(5)

For this purpose TheRate program was utilized [36]. In Eq. (5) kB and h stand for the Boltzman and Planck constants, whereas \(\Delta G_{a}^{\ddag }\), σ, and γ(T) are the free activation energy, reaction path degeneracy, and transmission coefficient, respectively [37]. The energy values and partition functions were taken from the quantum mechanical calculations.

Each koverall value was obtained as a sum of the corresponding kZCT-0 values. The rT (antioxidative activity of 5CQA relative to Tx) value was calculated by dividing koverall for 5CQA with koverall for Tx at three different levels of theory. The branching ratio, i.e., the percent contribution of an antioxidative pathway i to the overall reaction of 5CQA, was calculated by dividing kZCT-0(i) with koverall and multiplying with 100.

3 Results and discussion

The first part of our investigation was devoted to thermodynamic consideration of the reactions (1)–(4). The aim of this examination was to select exergonic reaction pathways for further analysis. Bearing in mind that the rate constants for homolytic cleavage of the C–H bonds and corresponding branching ratios are much smaller in comparison to those for homolytic cleavage of the O–H bonds [27, 29, 38,39,40], examination of the HAT mechanism was focused to abstraction of hydrogen atoms from phenolic groups. As for the RAF mechanism, addition of the two free radicals to the sp2 hybridized carbon atoms was simulated. The results are presented in Table 1 and illustrated with Figs. 1 and 2. It is apparent that the ∆ r G values refereeing to the two solvents are in very good agreement. As expected for nonpolar solvents, both compounds show pronouncedly positive ∆ r G values for the loss of carboxylic proton [Eq. (3)] and for the transfer of electron to either HO• or CH3OO• [Eq. (4)]. In accordance with previous findings [15,16,17,18, 38], these results show that neither 5CQA nor Tx undergo the SPLET and SET-PT mechanisms in nonpolar media. For this reason the further steps of these antioxidative pathways were not examined, and they were excluded from the text that follows.

Table 1 Gibbs energies (kJ mol−1) of the reactions (1)–(4) for chlorogenic acid (5CQA) and trolox (Tx) calculated at the M06-2X/6-311++G(d,p) level of theory in combination with the CPCM solvation model
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On the other hand, HAT is thermodynamically favorable mechanism of 5CQA and Tx with both free radicals, where the reactions with HO• are noticeably more exergonic. In addition, the ∆ r G values for the RAF pathways with HO• are in most cases negative, except for the positions 9’ of 5CQA and 1 of Tx (Table 1). Certainly, these positions are not attractive for highly electrophilic HO• because of the large partial positive charge on C9′ of 5CQA and C1 of Tx. All RAF pathways of both phenolics with CH3OO• are endergonic, which can mainly be attributed to significantly lower reactivity of this free radical, and, to some extent, to its voluminosity. The products of all exergonic HAT and RAF pathways are presented in Figs. 1 (those related to 5CQA) and 2 (those related to Tx).

All these exergonic reaction pathways were subjected to kinetic investigation, aimed at revealing the transition states and calculating the corresponding rate constants and rT values. The located transition states for the antioxidative pathways of 5CQA and Tx are depicted in Figs. 3 and 4, whereas the activation energies, as well as the kZCT-0 and rT values related to both solvents, are collected in Table 2. Two examples of the IRC calculations for 5CQA with HO• in benzene are presented in Figs S1 and S2. Also, representative examples, including appropriate discussion, for dependence of rate constants on temperature for both 5CQA and Tx are depicted in Figs S3 and S4, respectively.

Fig. 3
figure 3

Optimized geometries of transition states figuring in the reactions of 5CQA with HO• and CH3OO• in benzene. The key bond distances are given in Å. The calculations were performed at the M06-2X/6-311++G(d,p) level of theory in combination with the CPCM solvation model

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Fig. 4
figure 4

Optimized geometries of transition states figuring in the reactions of Tx with HO• and CH3OO• in benzene. The key bond distances are given in Å. The calculations were performed at the M06-2X/6-311++G(d,p) level of theory in combination with the CPCM solvation model

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Table 2 Gibbs energies of activation \(\Delta G_{a}^{\ddag }\) (kJ mol−1) and rate constants kZCT-0 (M−1 s−1) for the HAT and RAF reactions of 5CQA and Tx with HO• and CH3OO• radicals. The results were produced at the M06-2X/6-311++G(d,p) level of theory in combination with the CPCM solvation model
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It is well known that HAT and RAF only slightly depend on solvent polarity [15,16,17, 26, 31, 41]. For example, it can be easily calculated from the results presented in Ref. [17] that koverall for the reaction of 5CQA with HO• in polar solvents, ethanol, and water amounts to 9.46 × 108 and 9.60 × 108 (the same order of magnitude as koverall for the reaction in benzene). Since benzene and pentyl ethanoate are of comparable polarity, it is reasonable to expect that the koverall and rT values for a certain free radical will be very similar. Table 2 shows that the rT values for CH3OO• are almost identical. To our surprise, rT for HO• is much larger in pentyl ethanoate than in benzene. To clarify this unexpected finding, we performed additional investigation. Actually, we repeated all calculations related to the kinetics of the HAT and RAF pathways of 5CQA and Tx using the M05-2X/6-311++G(d,p) level of theory in combination with the SMD solvation model. It should be pointed out that all necessary structures and corresponding free energies were obtained by full optimizations and frequency calculations. The results obtained are presented in Table 3.

Table 3 Gibbs energies of activation \(\Delta G_{a}^{\ddag }\) (kJ mol−1) and rate constants kZCT-0 (M−1 s−1) for the HAT and RAF reactions of 5CQA and Tx with HO• and CH3OO• radicals. The results were produced at the M05-2X/6-311++G(d,p) level of theory in combination with the SMD solvation model
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It is worth emphasizing that M05-2X/6-311++G(d,p) in conjunction with SMD was not able to locate the majority of transition states for the HAT pathways of 5CQA in pentyl ethanoate. In these cases geometry convergence could not be achieved, which is illustrated with Fig S5. Thus, this level of theory could not produce either the koverall values of 5CQA in pentyl ethanoate, or the corresponding rT values for both free radicals. On the other hand, all reaction pathways in benzene were revealed, and the corresponding koverall and rT values were calculated. Thus, we can compare three sets of results in Tables 2 and 3 and calculate three sets of branching ratios (Table 4).

Table 4 Branching ratios (Γ) for all favorable mechanistic pathways of 5CQA. The 6-311++G(d,p) basis set was used in all cases
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Analysis of the results presented in Tables 2, 3 and 4 shows that, despite numerical differences, all three operative computational methodologies, M06-2X—CPCM in benzene and pentyl ethanoate, and M05-2X—SMD in benzene (with the same basis set), exhibit similar trends. In nonpolar solvents the two antioxidants undergo both HAT and RAF pathways with HO•, and only HAT mechanism with CH3OO•. As for the reactions of both phenolics with HO•, the RAF pathways are generally faster. The fastest pathways of 5CQA and Tx are RAFs in the positions 4′ and 6, respectively. A common feature of TS4′ and TS6 (Figs. 3, 4) is that both transition states are stabilized with hydrogen bonds between approaching HO• and phenolic groups and, thus, require low activation energies. On the other hand, attractive interactions in the HAT reaction paths [hydrogen bond between the oxygen of the hydroxyl moiety and proximate phenolic group in TS3′(HO•) and TS4′(HO•) and π-interactions between the hydrogen of the hydroxyl moiety and aromatic ring in TS(HO•)] slow down the formation of hydrogen peroxide and its leaving the reaction system. Thus, despite the finding that addition of HO• to the double bond of 5CQA is thermodynamically most favorable (Table 1), the greatest Γ value for the reaction of 5CQA with HO• comes from the RAF pathway in the 4′ position. As for the HAT pathways with CH3OO•, the Γ values for the 4′ position are larger, and in case of the SMD solvation model the difference between the branching ratios is distinct.

5CQA is more reactive toward HO• than Tx (rT > 1), but less reactive toward CH3OO• (rT < 1). Larger reactivity of 5CQA toward HO• is mainly a consequence of very fast RAF pathways. In comparison to Tx, 5CQA has more suitable positions for addition of HO•. Furthermore, the RAF pathway in the 4′ position of 5CQA is the fastest reaction path according to all three operative methodologies. The rT values for CH3OO• are mutually very similar, while those for HO• differ, where rT in pentyl ethanoate particularly deviates (Tables 2 and 3). Such behavior of rT for HO• is probably a consequence of extreme reactivity of this radical that is challenging to be numerically evaluated, whatever computational methodology is used. Thus, it is more practical to use less reactive free radicals in tasks devoted to determination of antioxidative activity of some compound relative to Tx [14, 42, 43]. However, if one’s goal is to examine all possible antioxidative pathways of the compound, they need to use highly reactive free radicals.

The reactions of 5CQA with two simple free radicals in pentyl ethanoate indicate disadvantage of the combination of the M05-2X functional and SMD solvation model to accomplish some routine computational tasks, such as finding energy maxima. On the other hand, the koverall values related to the reaction of Tx with both free radicals were obtained in this way and are mutually comparable (Tables 2, 3). Now we can compare the rate constants and koverall related to the reactions with HO• obtained in this work (Table 3) to those presented in Ref. [38]. General impression is that the values presented here are by two orders of magnitude smaller than those suggested by Alberto et al. [38]. The most noteworthy difference is that we revealed a reaction path for homolytic cleavage of the O–H bond of the phenolic group and calculated the rate constant of 5.54 × 106 M−1 s−1, whereas Alberto et al. found that this process is diffusion controlled and assigned it the rate constant of 1.91 × 109 M−1 s−1. Inconsistency between the two sets of results is, certainly, a consequence of already explained difference in applied computational methodology. We approve the approach based on geometry optimization and frequency calculation in conjunction with some continuum solvation model, as such tasks are nowadays routine.

A logical next step of our investigation is to determine rT of 5CQA in water. In slightly basic aqueous solution 5CQA exists in the form of monoanion and dianion. Extremely complex behavior of these species toward free radicals is under our intense scrutiny.

4 Summary

The quantum mechanics-based test for overall free-radical scavenging activity (QMORSA) is a very useful computational protocol for estimating rT of a compound, i.e., its antioxidative activity relative to some reference compound, usually Tx [14]. It is practical that QMORSA calculations are conducted by using a unique approach, so that the results of different investigations can be mutually compared. In this work we evaluated the rT values of 5CQA for the HO• and CH3OO• radicals in two nonpolar solvents by applying two different methodologies. It turned out that repeatedly suggested M05-2X functional in conjunction with the SMD solvation model failed to estimate the influence of pentyl ethanoate, selected to mimic lipid environment, because of unusual convergence failures. This finding is quite unexpected since SMD employs a set of parameters optimized over the M05-2X/MIDI!6D, M05-2X/6-31G(d), M05-2X/6-31+G(d,p), M05-2X/cc-pVTZ, B3LYP/6-31G(d), and HF/6-31G(d) theoretical methods [25]. On the other hand, other three methodologies, M06-2X—CPCM in benzene and pentyl ethanoate and M05-2X—SMD in benzene, proved to be operative and showed similar trends. Namely, 5CQA and Tx undergo both HAT and RAF paths with HO•, and only HAT path with CH3OO•, where 5CQA is more reactive toward HO• than Tx, but less reactive toward CH3OO•. Discrepancy of the results related to HO•, particularly in pentyl ethanoate, can be attributed to general inability of computational methodologies to numerically evaluate extreme reactivity of this radical.

Our research confirms that if one’s goal is to determine antioxidative activity of a compound relative to Tx, it is more useful to include less reactive free radicals in investigation [14, 42, 43]. However, if one’s goal is to examine all possible antioxidative pathways of the compound, it is necessary to employ highly reactive free radicals, and in such case different approaches can lead to inconsistent results.

As a final point, which approach should be applied in investigations of antioxidative activity? We strongly suggest the approach based on geometry optimization and frequency calculation in conjunction with continuum solvation model, because energy is highly dependent on structure, and geometry of a molecule in the gas-phase differs from that of solvated molecule. M06-2X is more robust than M05-2X [14, 24]. Bearing in mind that radical and negatively charged species participate in antioxidative processes basis set needs to add diffuse functions to all atoms, including hydrogen.