Relative Antioxidant Efficiency of a Large Series of Carotenoids in

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J. Phys. Chem. B 2007, 111, 12898-12908

Relative Antioxidant Efficiency of a Large Series of Carotenoids in Terms of One Electron Transfer Reactions Annia Galano* Instituto Mexicano del Petro´ leo, Eje Central La´ zaro Ca´ rdenas 152, 007730 Me´ xico D. F., Me´ xico. ReceiVed: June 5, 2007; In Final Form: August 30, 2007

The relative antioxidant efficiency, expressed as electron donating capability, of a large series of carotenoids has been studied using density functional theory. Their reactivity toward nine different radicals has been modeled as well as the electron transfer between pairs of carotenoids, one of which is present as a radical cation. The influence of the solvent polarity has also been studied. Torulene was found to be the most easily oxidized carotenoid, followed by lycopene. This higher reactivity is proposed in the present work for the first time, and the potential implications of such a finding are discussed. Since torulene has not been previously studied, compared to other carotenoids in terms of oxidation potentials, further experimental studies are suggested in order to confirm or reject this prediction. Ionization potential seems to be a magnitude calculable at low computational cost that correctly predicts the relative ease of oxidation in a series of carotenoids. The nuclear reorganization energy associated with electron-transfer reactions has been calculated in a very simple but apparently efficient way that allows computation of free energy barriers and relative rate constants in good agreement with the experimental values. In addition, an additive correction is proposed to include the •+ processes. The general agreement effect of increasing the size of basis sets on the energies of Carn f Carn-1 between different calculated magnitudes and the corresponding available experimental data supports the predictions from this work.

Introduction Carotenoids (Car) are versatile organic molecules, which are of great relevance to living systems. They serve multiple purposes for their producers as well as for their consumers. Among their diverse functions,1 their free-radical-scavenging antioxidant properties stand out.2,3 However, their broadly defined antioxidant activity strongly depends on a mixture of variables. Consequently, attempts to uniformly characterize antioxidant activity may be a futile task. On the other hand, testing antioxidant systems for a specific function may provide valuable information for a particular application. This work will focus on the electron-transfer (ET) processes, although hydrogen abstraction and adduct formation are also viable mechanisms of carotenoids’ antioxidant activity

Electron transfer: R• + Car f R- + Car•+

(I)

Adduct formation: R• + Car f [R-Car]•

(II)

Hydrogen abstraction: R• + Car f RH + Car(-H)•

(III)

The relative importance of these reaction channels will depend on diverse factors, including the nature of the reacting free radical and the structural features of the carotenoid4,5 and, in biological systems, its location and orientation within the membrane.5 Generally speaking, the antioxidant properties of carotenoids are related to their excellent ability to deactivate excited states and to their high electron donation capability. Although electron donation can immediately deactivate harmful radicals, the antioxidant mechanism can be inseparably ac* To whom correspondence should be addressed. E-mail: agalano@ imp.mx.

companied by the simultaneous formation of oxidized carotenoids such as Car•+. In addition, redox pairs involving Car/ Car•+ conjugates6-10 could regenerate the parent molecule and eliminate the pro-oxidant concerns related to carotenoid radical cations. The electron-transfer reaction (I) will clearly be favored when the R groups are electron withdrawing. For example, the reaction of the trichloromethyl peroxyl radical (CCl3O2) with β-carotene11,12 and several other carotenoids13 has been suggested to involve electron transfer to generate the corresponding anion and carotene radical cation. Everett and co-workers14 have also shown that β-carotene is oxidized by NO2• in solution via reaction I. In a recent study using benzyl peroxyl radicals, it was concluded that carotenoids scavenge peroxyl radicals, which are not highly reactive, by adduct formation and not by electron transfer, while reaction III seems to be much less important than reaction II.15 These results are in line with a previous review article16 showing that carotenoids react with free radicals by addition and/or electron-transfer reactions, with the reaction channel distribution varying according to the nature of the reacting free radical. On the other hand, it seems obvious that there must be a relationship between the structure of carotenoids and their reactivity toward free radicals. There are some reports addressing this issue. Jeevarajan et al.17 found that carotenoids substituted with electron donating groups are more easily oxidized than those with electron accepting substituents. Mortensen and Skibsted18 have studied the reactions of eight carotenoids with phenoxyl radicals. These authors report the following order of reactivity: lycopene (LYC) > β-carotene (BC) > zeaxanthin (ZEA) > lutein (LUT) > echinenone (ECH). They also found that canthaxanthin (CAN) and β-apo-8′-carotenal (APO) hardly

10.1021/jp074358u CCC: $37.00 © 2007 American Chemical Society Published on Web 10/17/2007

Relative Antioxidant Efficiency of Carotenoids

J. Phys. Chem. B, Vol. 111, No. 44, 2007 12899

react, while asthaxanthin (ASTA) does not react at all. Edge et al.19 have studied ET reactions between different pairs of carotenoids with similar outcomes. They found that LYC is the most easily oxidized followed by BC > ZEA > LUT > CAN > APO > ASTA. In addition, El-Agamey and McGarvey20 have recently shown that the profile of carotenoid radical products formed depends on the polarity of the solvent medium. According to these authors, in nonpolar solvents, only addition radicals are formed, while in polar solvents, these adducts decay to carotenoid radical cations. The main aim of this work is to provide a computational strategy that allows reliable predictions of carotenoids’ relative antioxidant efficiency, expressed as electron donating capability, at a reasonable computational cost. The studied species are hydrocarbon carotenoids and oxygen carotenoids. Their reactivity toward nine different radicals has been modeled through reaction I, as well as the electron transfer between pairs of carotenoids, one of which is present as a radical cation. The influence of the solvent polarity has also been investigated.

TABLE 1: Carotenoids Previously Studied by Experimental Techniques and Modeled in the Present Work

Computational Details For all of the modeled species, full geometry optimizations have been carried out using the B3LYP hybrid HF density functional21-23 and the 6-31G(d,p) basis set, while frequency calculations were performed at B3LYP/3-21G level of theory for geometries previously optimized at the same level. The IR spectra of neutral carotenoids have also been computed at this level of calculation. Unrestricted calculations were used for open-shell systems, and local minima were identified by the number of imaginary frequencies (NIMAG ) 0). All of the electronic calculations were performed with the Gaussian 9824 package of programs. Thermodynamic corrections at 298 K were included in the calculation of the relative energies. Solvent effects were included by using the polarizable continuum model (PCM)25,26 with water and benzene as the solvents for polar and nonpolar environments, respectively. The Gibbs free energies of reaction for an aqueous environment were calculated using a mixed discrete-continuum model with two water molecules explicitly included, with a surrounding continuum of bulk solvent for carotenoids + free radical reactions. The corresponding energies were improved by single point (SP) calculations at the B3LYP/6-311++G(d,p) level of theory. The adsorption spectra of neutral and radical cation carotenoids have been computed with time-dependent density functional theory (TDDFT) using the same functional and 6-31G(d,p) basis set. Results and Discussion Since there is previous knowledge about the relative antioxidant activity of seven carotenoids,18,19 they have been included in the present work in order to test the reliability of the results proposed here for the whole studied series. The structures of all modeled carotenoids are shown in Tables 1 and 2. The simplest approach to study the ease of ET processes from different molecules is to analyze their ionization potentials (IP). The IP of an n-electron system (X), calculated at a given level of theory, implies the following energy difference X IP ) En-1 (gn-1) - EXn (gn)

(1)

where EXn (gn) is the energy of the n-electron neutral system X calculated at a geometry gn and En-1 (gn-1) is the energy of the (n - 1)-electron ionic species calculated at a geometry gn-1.

Accordingly, to calculate IPs, two separate geometry optimizations are needed, performed on the neutral and radical cationic species. The IP calculated this way is known as an adiabatic IP and takes into account the geometry relaxation of the radical cation after the electron transfer. Another approximation, known as the vertical IP, is to optimize the geometry of the X species and then to perform the calculation of the radical cation at this very geometry. This approach implies also two calculations but only one geometry optimization and one single point to obtain the electronic energy of the X n-1 species. A special case of a vertical IP is that obtained within the framework of the Koopman’s theorem approximation.27 In this particular case, the vertical IP is evaluated as minus the energy of the molecular orbital of the neutral system from which an electron is removed, usually the highest occupied molecular orbital (HOMO),28-35 provided that the potential is defined in such a way that it vanishes at infinity. This is a very simple, relatively inexpensive way to estimate the IP from a single calculation on the neutral system. Even though the fast development of computers in the last few decades has remarkably enlarged the potential use of computational quantum chemistry for modeling molecular systems of increasing size at reliable levels of calculation, carotenoids can still be considered as large molecules from a computational point of view. Accordingly, it would be of interest to find some parameters that describe their relative ease of electron transfer in a proper way, at least qualitatively, and that, at the same time, could be calculated at a reasonable computational cost. With that purpose in mind, the correlations of the adiabatic IP versus the Koopman IP and the vertical IP versus the Koopman IP have been tested for all of the studied carotenoids in polar and nonpolar media. As Figure 1 shows,

12900 J. Phys. Chem. B, Vol. 111, No. 44, 2007

Galano

TABLE 2: Carotenoids Modeled in the Present Work and with No Previous Data on Their Electron-Transfer Reactions

Figure 1. Correlation between vertical and adiabatic ionization potentials with Koopman’s IP, for polar and nonpolar media.

TABLE 3: Ionization Potentials (eV) in Nonpolar and Polar Environments solvent ) benzene

solvent ) water

Koopman vertical adiabatic Koopman vertical adiabatic ASTA APO CAN LUT ZEA BC LYC DIH ECH NOS OKE SAP TOR CSAN CRUB CRY NEO VIO MYT

there is a good correlation in all of the tested cases. However, the agreement of Koopman’s IP with the more accurate ones is better in polar solvents. According to these results, Koopman’s IP can be used to qualitatively compare the ease of electron donation capability among a series of similar compounds. In the specific case of carotenoids, it can be used as the most

4.808 4.676 4.707 4.493 4.458 4.414 4.321 4.491 4.563 4.472 4.593 4.375 4.313 4.685 4.886 4.625 4.444 4.516 4.741

5.165 5.083 5.069 4.882 4.836 4.790 4.672 4.938 4.922 4.849 4.937 4.721 4.641 5.064 5.269 5.003 4.842 4.917 5.124

5.038 4.914 4.942 4.736 4.681 4.629 4.522 4.779 4.770 4.680 4.790 4.577 4.495 4.902 5.142 4.853 4.689 4.778 4.990

4.701 4.687 4.658 4.495 4.474 4.455 4.388 4.548 4.550 4.489 4.572 4.408 4.361 4.646 4.850 4.627 4.509 4.558 4.723

4.559 4.553 4.518 4.366 4.346 4.328 4.251 4.425 4.415 4.360 4.431 4.276 4.230 4.511 4.706 4.491 4.380 4.429 4.590

4.438 4.406 4.412 4.243 4.213 4.186 4.105 4.271 4.282 4.206 4.300 4.158 4.094 4.368 4.600 4.364 4.242 4.310 4.471

economical criteria (computationally speaking) to predict their relative ease of oxidation. As the values in Table 3 show, the ionization potentials calculated within the vertical and adiabatic approaches are lower for polar than those for nonpolar media, as it is expected since a charged species is formed. In general, this effect was found to be less important for hydrocarbon carotenoids than that for oxygen carotenoids. These results agree with those reported by Sliwka et al.10 who found that electron-transfer processes are enhanced in the presence of water, especially for hydrophilic carotenoids. Koopman’s IPs do not show this experimentally validated tendency; therefore, they are good enough to qualitatively compare the ease in electron donation for a series of carotenoids, but they do not properly describe the influence of the solvent in such process, at least when the continuum PCM model is used. Among the different approaches used to calculate ionization potentials, special attention should be paid to that referred to as the vertical IP. The ET reactions can be assumed to mainly occur by electron tunneling from one species to another. Since electrons are much faster than nuclei, the electronic transitions can be considered to take place in fixed nuclear configurations. This process is expected to occur very fast, in such a way that at the moment of the transfer, there is no time for geometry



Figure 2. Relative order of carotenoids in terms of oxidation potentials in nonpolar and polar solvents; 9 ref 18, 0 ref 19.

relaxation. Accordingly, while adiabatic IPs can be related to the energy involved in the completion of the reaction, vertical IPs can be associated with the energetic barrier. Vertical IPs can then be considered as an upper limit of the activation barrier. According to these assumptions, vertical IPs would be better criteria to predict which carotenoid would more readily transfer one of its electrons to another species and then to relatively order a series of carotenoids in terms of their oxidation potentials. To confirm this hypothesis, it is necessary to compare vertical and adiabatic IPs with the available experimental data, which indicates the following order of reactivity in terms of the ease of oxidation: LYC > BC > ZEA > LUT > ECH > CAN > ASTA;18 and LYC > BC > ZEA > LUT > CAN > APO > ASTA.19 For this particular sets of carotenoids, their relative order, based on vertical IPs, is LYC > BC > ZEA > LUT > ECH > CAN > APO > ASTA, which is in perfect agreement with the experimental findings. For this subset of carotenoids, the order is the same in both solvents. On the other hand, the order based on adiabatic IPs is LYC > BC > ZEA > LUT > ECH > APO > CAN > ASTA, which inverts the relative reactivity of canthaxanthin and β-apo-8′-carotenal. Consequently, for the possible interactions between pairs of carotenoids, their relative order, in term of oxidation potential, is shown in Figure 2 based on vertical IPs. This is a schematic representation, standing only for the order of the ease of electron transfer. However, for some of these pairs, the difference may be small, leading to slow reactions (e.g., DIH/ECH pair). The relative ease of electron transfer between carotenoid pairs has been provided in polar and nonpolar media (Figure 2) since these reactions can be studied independently of their hydrophilicity only under special circumstances.36-38 However, in living systems, carotenoids are not likely to always react either in pure lipid or water-based environments but at the typical hydrophilic/ hydrophobic interphase. Accordingly, a better knowledge of their behavior in such extreme environments, which is hard to obtain from experiments, could be helpful since the physicochemical assessment of the carotenoid radical scavenging behavior in aqueous solutions might be a key property in the formulation of parental therapeutics. Torulene was found as the most easily oxidized carotenoid in polar and nonpolar environments. This can be a relevant finding since it implies that TOR is expected to repair other

Figure 3. Correlations between the Gibbs free energy of reactions for TOR/Car•+ and differences in adiabatic ionization potentials (IP•+ Car IPTOR).

damaged carotenoids through redox reactions between pairs Car2/Car1•+, regardless of the environment’s polarity. Since such repairing processes are relevant to the combined antioxidant activity of carotenoids, a more detailed study has been performed. The energy evolution associated with the completion of ET reactions between carotenoid conjugated pairs has been computed as the corresponding adiabatic Gibbs free energies of such processes at 298 K

∆G0ET ) G(Car•+ 1 , gn-1) + G(Car2, gn) G(Car1, gn) - G(Car•+ 2 , gn-1) (2) where gn represents the relaxed geometry of the neutral carotenoid and gn-1 that of the radical cation. BC, LYC, and TOR have been modeled as the repairing carotenoids (Car2). They have been chosen based on the following criteria: BC is the most representative carotenoid of the series; LYC has been predicted as the Car most easily oxidized from all previously studied Car; and TOR has not been comparatively studied before, but according to our results, it oxidizes even more easily than LYC. The values in Table 4


Galano

TABLE 4: Gibbs Free Energies of Reaction (kcal/mol) for Electron Transfer between Pairs of Carotenoids with Respect to BC, LYC, and TOR solvent ) benzene ASTA APO CAN LUT ZEA BC LYC DIH ECH NOS OKE SAP TOR CSAN CRUB CRY NEO VIO MYT

solvent ) water

BC

LYC

TOR

BC

LYC

TOR

-8.21 -5.32 -6.17 -2.35 0.08

-11.65 -8.76 -9.60 -5.79 -3.36 -3.44

-4.57 -3.81 -4.16 -1.20 0.65

-7.42 -6.66 -7.00 -4.05 -2.20 -2.85

3.44 -2.60 -1.87 -1.18 -2.50 1.64 4.29 -6.08 -11.31 -4.97 -0.18 -2.42 -6.83

-6.04 -5.31 -4.62 -5.94 -1.79 0.85 -9.52 -14.74 -8.41 -3.62 -5.85 -10.26

-12.50 -9.61 -10.46 -6.64 -4.21 -4.29 -0.85 -6.89 -6.16 -5.47 -6.79 -2.65

2.85 -1.08 -0.82 -0.46 -1.42 1.10 3.34 -4.00 -9.03 -3.90 -0.09 -1.84 -5.06

-3.93 -3.66 -3.30 -4.27 -1.75 0.49 -6.85 -11.87 -6.75 -2.93 -4.69 -7.91

-7.91 -7.15 -7.49 -4.54 -2.68 -3.34 -0.49 -4.41 -4.15 -3.79 -4.76 -2.24

-10.37 -15.60 -9.26 -4.47 -6.71 -11.12

-7.33 -12.36 -7.24 -3.42 -5.18 -8.40

show that the processes involving electron transfer from neutral TOR to any of the other studied radical cations are energetically favored in terms of Gibbs free energies, that is, they are exergonic processes (∆G < 0). Electron transfers from LYC are mostly exergonic, with the logical exception of its reaction with TOR. When the electron transfer is modeled from BC, the calculated ∆Gs predict it as able to repair other Car•+ species than TOR, LYC, SAP, and ZEA. The explanation for the apparent disagreement between calculated ∆G(BC/ZEA•+) and the predicted relative ease of oxidation for these two carotenoids is that the Gibbs free energy evolution associated with this reaction is expected to be negative but very small,19 and the calculated values are slightly positive and smaller than the error inherent to the most accurate quantum mechanical calculations. The mean absolute deviation from experimental data is estimated to be 1.50 kcal/mol for the G2 method39 and the G2/97 test set,40,41 1.07 kcal/mol for G342 and G3/9943 set, and 3.29 and 4.37 kcal/mol for B3lYP using the G2/97 and G3/99 sets, respectively. Accordingly, if the energy evolution associated with a specific reaction is close to zero, the theoretical calculations can predict it to be slightly negative or slightly positive since both alternatives lie within the error range of the methods. Therefore, there is no certainty about the sign of the relative energies in Table 4 highlighted with italic characters. However, due to the great similarity of the chemical structures of all of the studied systems, it is logical to expect errors of similar magnitude and sign for all of the studied electron-transfer reactions. Consequently, the relative order in exergonicity would still be valid. The expected correlation between the adiabatic IP and the energies of reaction, discussed above, has been tested for polar and nonpolar environments. The results for the TOR + Car•+ reactions are shown in Figure 3. As this figure shows, there is a good correlation between the ∆G of reaction and the difference in ionization potentials between each pair of carotenoids. The possible electron-transfer reactions in nonpolar and polar environments have also been modeled for carotenoids in Tables 1 and 2 and for the following radicals: hydrogen peroxyl: HOO• (R1) methyl peroxyl: CH3OO• (R2) methoxyl: CH3O• (R3) benzyl peroxyl: C6H5CH2OO• (R4)

phenoxyl: C6H5O• (R5) acyl peroxyl: CH3C(O)OO• (R6) phenylacetyl peroxyl: C6H5C(O)OO• (R7) trichloromethyl peroxyl: CCl3OO (R8) nitrite: NO2• (R9) The adiabatic Gibbs free energies of reaction have been calculated as

∆G0ET ) G(Car•+, gn-1) + G(Ox-, gn+1) G(Car, gn) - G(Ox•, gn) (3) where Ox represent the oxidant species, that is, free radicals. The values obtained that way for nonpolar media were found to be highly endergonic (∆G from 25 to 80 kcal/mol) and, accordingly, very unlikely to occur. On the other hand, the presence of polar solvent drastically increased the reactivity of carotenoids toward the studied free radicals, through electrontransfer reactions. Accordingly, it can be stated that in nonpolar media, the studied radicals and probably most oxygenated radicals are bound to react by adduct formation instead of electron transfer since the ionic products cannot be solvated, whereas in polar media, carotenoid radical cations and the corresponding anions can be stabilized by the surrounding molecules. In biological systems, these charged species could be solvated at the lipid-water interface. The carotenoids’ reactions with HOO•, CH3OO•, and C6H5CH2OO• remain endergonic in aqueous phase but with ∆G0ET more than 50 kcal/mol lower than those corresponding to benzene as the solvent. On the other hand, the reactions of CH3O•, C6H5O•, CH3C(O)OO•, C6H5C(O)OO•, CCl3OO•, and NO2• become exergonic (Table 5). Accordingly, among the peroxyl radicals, only those with electron withdrawing groups are able to react with carotenoids, via electron-transfer reaction. Thus, peroxyl radicals with electron donating groups are expected to react via adduct formation. All of these findings nicely agree with the available experimental results. The most energetically favored of the modeled reactions are those involving trichloromethyl peroxyl, nitro, acyl peroxyl, and phenylacetyl peroxyl radicals, in that order. The calculations of the Gibbs free energy of electron transfers from carotenoids to free radicals are relatively expensive since frequency calculations of the corresponding Car, Car•+, oxygenated free radical, and its anion are necessary in order to add thermodynamic corrections to the electronic energies. Since they are rather time-consuming calculations, it would be useful to find another magnitude that could be calculated at a lower computational cost and that retains the correct order of relative reactivity. Ionization potentials have been tested for that purpose. Figure 4 shows the correlations of the ∆G of reaction and the carotenoids’ ionization potentials calculated using the different approaches discussed above for their reaction with the acyl peroxyl radical. Even though, for the sake of simplicity, their reactions with the other studied radicals are not shown, the same tendency was obtained in all of the cases. Regardless of the approach chosen for computing the ionization potentials, good correlations were found with the Gibbs energies of reaction. However, and as it was expected, the best correlation was obtained for the adiabatic IP. One of the greatest challenges in computational chemistry is to incorporate explicit solvent effects into quantum mechanical treatments of chemical reactions. The difficulty lies in the large number of degrees of freedom in a condensed-phase system and the collective motions of the solvent molecules that influence the chemical process. Accordingly, approximate



TABLE 5: Gibbs Free Energies (kcal/mol)a of Carotenoids’ Electron-Transfer Reactions with Different Radicals in a Polar Environment (Solvent ) Water) ASTA APO CAN LUT ZEA BC LYC DIH ECH NOS OKE SAP TOR CSAN CRUB CRY NEO VIO MYT a

R1

R2

R3

R4

R5

R6

R7

R8

R9

9.26 8.73 9.02 5.78 3.96 4.48 2.07 5.59 5.81 5.69 6.31 3.96 1.52 8.84 14.03 8.42 4.98 6.38 9.92

1.55 1.02 1.31 -1.92 -3.75 -3.23 -5.64 -2.11 -1.90 -2.01 -1.40 -3.75 -6.19 1.13 6.32 0.71 -2.73 -1.33 2.21

-10.84 -11.37 -11.08 -14.32 -16.14 -15.62 -18.03 -14.51 -14.29 -14.40 -13.79 -16.14 -18.58 -11.26 -6.07 -11.68 -15.12 -13.72 -10.18

4.11 3.58 3.86 0.63 -1.20 -0.67 -3.08 0.44 0.66 0.54 1.16 -1.20 -3.64 3.69 8.87 3.26 -0.18 1.23 4.76

2.71 2.18 2.46 -0.77 -2.59 -2.07 -4.48 -0.96 -0.74 -0.86 -0.24 -2.59 -5.03 2.29 7.47 1.87 -1.58 -0.17 3.37

-14.46 -14.99 -14.71 -17.94 -19.77 -19.24 -21.65 -18.13 -17.91 -18.03 -17.41 -19.77 -22.21 -14.88 -9.70 -15.30 -18.75 -17.34 -13.80

-11.03 -11.56 -11.27 -14.51 -16.33 -15.81 -18.22 -14.70 -14.48 -14.60 -13.98 -16.33 -18.77 -11.45 -6.26 -11.87 -15.32 -13.91 -10.37

-20.69 -21.22 -20.93 -24.17 -25.99 -25.47 -27.88 -24.36 -24.14 -24.25 -23.64 -25.99 -28.43 -21.11 -15.92 -21.53 -24.97 -23.57 -20.03

-14.50 -15.03 -14.75 -17.98 -19.81 -19.28 -21.69 -18.17 -17.95 -18.07 -17.45 -19.81 -22.25 -14.92 -9.74 -15.34 -18.79 -17.38 -13.84

Energies: SP/B3LYP/6-311++G(d,p); geometries: B3LYP/6-31G(d,p); thermodynamic corrections: B3LYP/3-21G.

TABLE 6: Carotenoid Rate Constants, Relative to Those of BCa R1

R2

R3

R4

R5

R6

R7

R8

a Experimental data available for the values highlighted in bold in ref 18.

methods are essential for that purpose. The Marcus theory44-46 of electron-transfer reactions relies on the transition-state formalism defining the ET activation barrier (∆GqET) in terms of two thermodynamic parameters, the free energy of reaction (∆G0ET) and the nuclear reorganization energy (λ)

(

)

ASTA APO CAN LUT ZEA BC LYC DIH ECH NOS OKE SAP TOR CSAN CRUB CRY NEO VIO MYT a

488 454b 476 443 452 450 470 461 448 483 478 484 470 471 472 452 436 475

calculated oscillator λmax strength λcalc/λexp CHCl3 hexane hexane methanol hexane hexane hexane cyclohexane methanol hexane acetone methanol hexane hexane hexane benzene methanol ether

598 553 588 541 554 555 580 470 598 555 614 596 623 577 564 581 526 527 580

3.90 2.64 3.90 3.80 3.87 3.83 4.43 3.37 3.59 3.85 3.85 4.36 4.54 3.41 3.97 3.37 3.94 3.86 3.23

1.22 1.22 1.23 1.22 1.23 1.23 1.22 1.04 1.30 1.24 1.27 1.25 1.29 1.23 1.20 1.23 1.16 1.21 1.22

From ref 49, unless specified otherwise. b From ref 50.

where ∆EET has been calculated as the nonadiabatic energy difference between reactants and vertical products, that is, Car•+ and Ox- in the geometries of Car and Ox•

∆EET ) E(Car•+, gn) + E(Ox-, gn) E(Car, gn) - E(Ox•, gn) (9)

2

(4)

As its very name claims, λ is the energy associated with the nuclear rearrangement involved in the formation of products in an ET reaction, which implies not only the nuclei of the reacting species but also those of the surrounding solvent. Figure 5 shows the relaxed geometries of one of the studied radicals with two explicit water molecules, before and after the electron transfer, that is, the radical and the corresponding anion. In this work, a very simple approximation has been made in order to calculate λ

λ ≈ ∆EET - ∆G0ET

experimentala λmax

R9

ASTA 0.00 0.02 0.33 0.01 0.01 0.51 0.30 1.08 0.31 APO 0.01 0.04 0.39 0.02 0.02 0.57 0.35 1.11 0.36 CAN 0.01 0.04 0.42 0.02 0.02 0.60 0.38 1.13 0.39 LUT 0.25 0.42 0.84 0.37 0.48 0.92 0.81 1.09 0.81 ZEA 1.82 1.51 1.08 1.58 0.86 1.03 1.10 0.93 1.11 BC 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 LYC 10.77 4.67 1.20 5.61 1.65 1.02 1.30 0.73 1.35 DIH 0.27 0.41 0.81 0.37 0.34 0.90 0.79 1.11 0.78 ECH 0.25 0.42 0.84 0.36 0.28 0.92 0.81 1.09 0.81 NOS 0.27 0.43 0.84 0.38 0.52 0.92 0.81 1.09 0.81 OKE 0.13 0.27 0.75 0.22 0.20 0.86 0.71 1.13 0.71 SAP 2.32 1.94 1.14 2.05 1.36 1.04 1.18 0.85 1.20 TOR 19.92 7.16 1.21 8.93 1.82 0.98 1.35 0.62 1.44 CSAN 0.01 0.03 0.38 0.02 0.02 0.55 0.34 1.10 0.35 CRUB 0.00 0.00 0.05 0.00 0.00 0.12 0.04 0.58 0.05 CRY 0.01 0.05 0.45 0.03 0.04 0.62 0.41 1.13 0.42 NEO 0.62 0.75 0.95 0.72 0.52 0.98 0.94 1.03 0.94 VIO 0.13 0.28 0.77 0.23 0.22 0.88 0.73 1.12 0.73 MYT 0.00 0.01 0.29 0.01 0.00 0.46 0.26 1.05 0.27

∆G0ET λ ∆GqET ) 1 + 4 λ

TABLE 7: Experimental and Calculated Data for the UV/Vis Spectra of Neutral Carotenoids

(5)

This approach is similar to that previously used by Nelsen and co-workers47,48 for a large set of self-exchange reactions. Within this approach, the values of ∆GqET for all possible reactions between carotenoids in Tables 1 and 2 and the abovespecified radicals have been computed, as well as the corresponding rate constant values (k) at 298 K

kBT exp(-∆Gq/RT) h

k)κ

(10)

where κ represents the tunneling corrections. Their values relative to those of BC are reported in Table 7 and were calculated as


Galano

Figure 4. Correlations between the Gibbs free energy of electrontransfer reactions (Car + R7) and carotenoids’ ionization potentials calculated using different approaches.

Figure 5. Fully optimized geometries of CH3O, with two explicit water molecules, before and after the electron transfer.

kRel_BC (Car) 298

)

kCar 298 kBC 298

)

exp(-∆GqCar/RT) exp(-∆GqBC/RT)

(11)

assuming that tunneling corrections are of the same magnitude for all modeled reactions. For Car2/Car1•+ systems, the analyzed energies were always those computed with the 6-31G(d,p) basis set, and this level of theory seems to be adequate to qualitatively reproduce the experimentally observed tendencies of carotenoids in their oxidation reactions. However, since there are experimental data available for the rate constants of the reactions of several carotenoids with phenoxyl radical, relative to that of BC, it would be desirable to quantitatively reproduce them. Accordingly, the reliability of the used approach has been tested by comparison of the calculated relative rate constants with those from the experimental determination of Mortensen and Skibsted.18 The corresponding calculated values have been highlighted in bold in Table 6. At this point, it could be of concern whether larger basis sets should be used or not in the modeling and how much it would affect the quality of the results. Accordingly, single point calculations at the B3LYP/6-311++G(d,p) level of theory have also been performed for all of the studied reactions, in polar environments. For the sake of shortness, Table 6 only shows those values of kRel_BC obtained at the higher level of theory. 298 However, the correlation between relative rate constants, calculated within three different levels of accuracy, and experimental ones have been included in Figure 6 to illustrate the relevance of using larger basis sets including diffuse functions. The red and black plots in this figure correspond to 6-31G(d,p) and 6-311++G(d,p) basis sets, respectively. Even though both levels of theory reproduce the experimental trend,

Figure 6. Calculated versus experimental18 rate constants, relative to BC, for the reactions of several carotenoids with the phenoxyl radical.

there is a significant improvement in the quantitative agreement with the experimental results when the systems are modeled using basis sets with diffuse functions; R2 increases from 0.83 to 0.93, the slope is much closer to one, and the intercept is much closer to zero. Accordingly, the correspondence between the values theoretically predicted and those obtained from the experiment is very good when the 6-311++G(d,p) basis set is used. This agreement seems to validate the approach used to calculate λ, as well as the relative rate constants proposed here for the first time. It also seems to validate the assumption that the tunneling corrections of all modeled Car + Ox reactions are of similar magnitude. However, due to the size of the carotenoids, the use of the 6-311++G(d,p) basis sets could not always be feasible in a reasonable time. Since it is one of the main goals of this work to propose a strategy of calculation that allows one to obtain reliable data on the studied systems but at a relatively low computational cost, a viable alternative has been analyzed. The Car + Ox reaction can be considered as two simultaneous processes, the removal of one electron from the carotenoid and the gain of one electron by the free radical. Accordingly, eq 3 can be reorganized as

∆G0ET ) [G(Car•+, gn-1) - G(Car, gn)] + [G(Ox-, gn+1) G(Ox•, gn)] (12) Ox ∆G0ET ) ∆GCar ET + ∆GET

(13)

The effect of increasing basis sets has been analyzed separately for both processes. As it was expected, this effect is larger for the smaller system (Ox•n f Oxn+1 ), where a relatively small •+ anion is formed, than that for Carn f Carn-1 , where the long polyene chain helps to distribute the charge. The corresponding values for the BC + R5 reaction are 6.49 kcal/mol higher and Ox -11.64 kcal/mol lower for ∆GCar ET and ∆GET, respectively, when using the 6-311++G(d,p) instead of the 6-31G(d,p) basis set. Since there is a great variety in the chemical structure of the studied free radicals, it is not possible to predict the magnitude of the energy lowering due to the increase in the basis set for other free radicals. However, this does not seem to be an issue since the modeling of these radicals does not represent a computational challenge. On the other hand, the chemical structures of carotenoids are very similar, and the effect



Figure 7. Experimental49 (a) and computed (b) IR spectra of BC.

of increasing the level of theory from 6-31G(d,p) to 6-311++G(d,p) on ∆GCar ET could be expected to be similar in magnitude for all of them. In fact it was found that, for all of the modeled carotenoids, differences between ∆GCar ET computed at the 6-31G(d,p) and 6-311++G(d,p) levels ranged from 6.49 to 7.25, with the largest difference of 0.76 between BC and NOS. Since this variation was very small, a correction for ∆GCar ET was proposed to take into account the effect of the diffuse function. This effect was estimated as the average value of ∆GCar ET [6-311++G(d, p)] - ∆GCar ET [6-31G(d, p)] and was found to be equal to 6.82 when the B3LYP functional was used. The effect of such an a posteriori correction has been tested and included in Figure 6, blue line, and named as Car corr. As this figure shows, this approximation significantly improves the quality of the results compared to those obtained at the B3LYP/6-31G(d,p) level of theory at no computational cost for the carotenoid term in eq 13. The proposed expression to calculate the free Gibbs energies, comparable to those obtained using the larger basis set, would be

∆G0ET[6-311++G(d, p)] ≈ {∆GCar ET [6-31G(d, p)] + 6.82} + ∆GOx ET[6-311++G(d, p)] (14) Even though this correction was tested for the B3LYP method with 6-31G(d,p) and 6-311++G(d,p) basis sets, the variation of ∆GCar ET , when increasing the basis and including diffuse functions, is also expected to be similar among all carotenoids for other methods and basis sets, provided that the lower level of calculation is performed using at least the 6-31G(d,p) basis set. Accordingly, for other methods, an equivalent correction could be calculated just for BC and applied to a whole set of carotenoids. Accordingly, it could be calculated as BC Car corr ) ∆GBC ET [larger basis] - ∆GET [smaller basis]

(15)

In addition, the finding that differences in energies associated •+ with the Carn f Carn-1 processes, ∆GCar ET [6-311++G(d, p)] -

Figure 8. Computed IR spectra of CAN (a), ZEA (b), and ASTA (c).

∆GCar ET [6-31G(d, p)], are of similar magnitude for all modeled carotenoids supports the use of the smaller basis set for the study of reactions between carotenoid pairs Car2/Car1•+. The inclusion of diffuse functions would increase the energy associated with the transition Car2 f Car2•+ and lower the energy of the transition Car1•+ f Car1 in similar proportion. Thus, the energy evolution associated with the overall reaction Car2 + Car1•+ f Car2•+ + Car1 would be approximately the same when calculated with 6-31G(d,p) and 6-311++G(d,p) basis sets. The only carotenoid that seems to have higher antioxidant efficiency than LYC, expressed as electron donating capability, is TOR. This seems to be the case in both polar and nonpolar media and in Car + free radical reactions as well as in redox reactions between carotenoid pairs. This new finding suggests that this Car could be of great use for repairing other oxidationdamaged carotenoids and can be easily explained in terms of the length of the polyene chain. TOR has 13 conjugated bonds,


Galano

TABLE 8: Experimental and Calculated Absorption Maxima of Selected Car•+ in Benzene experimental ref 18 ASTA APO CAN LUT ZEA BC LYC ECH TOR CSAN CRUB CRY NEO VIO MYT

840 860 882 907 930 975 907

calculated

ref 19 920 880 940 950 1000 1020 1050

897 836 907 885 936 944 977 941 1073 882 802 887 818 822 853

TABLE 9: Frequencies (cm-1) of Selected Vibrational Modes from Calculated (Experimental49) IR Spectra O-H ASTA APO CAN LUT ZEA BC LYC DIH ECH NOS OKE SAP TOR CSAN CRUB CRY NEO VIO MYT

C-H polyene

3325 (3486) 3144 3135 3144 3449 3141 3449 3142 3141 3143 3145 3142 3414 (3390) 3142 3143 3479 3143 3461 3144 3465 (3464) 3146 3465 (3440) 3144 3469 3142 3465 3143 3468 (3390) 3145

CdOconj

CdCconj

1667 (1664) 1593 (1557) 1604 1576 1690 (1650) 1599 1623 1622 1622 (1629) 1605 1636 1680 (1657) 1570 (1550) 1622 1660 1568 3143 1592 1606 1684 1566 1688 (1669) 1580 (1556) 1687 (1668) 1566 (1516) 1628 1625 1775 (1738) 1659

H out of plane 1019 1019 1020 1016 1017 1019 1010 1028 1019 1019 1020 1004 1016 1018 1019 1018 1017 1018 1017

that is, the largest number among all of the modeled structures, while LYC and BC have 11, but in the case of BC, two of them are in cyclohexane rings, which are nonplanar with the rest of the molecular backbone, reducing the effective length of the conjugated system. The larger reactivity of BC compared to that of ZEA, however, cannot be explained by the length of the conjugated chain but by the presence of two OH’s, which comparatively reduces the stability of the carotenoid radical cation. In the case of ASTA and CAN, the presence of the two carbonyl groups at the end of the conjugated systems also seems to lower the stability of the products. UV/Vis and IR Spectra. Table 7 shows the experimental and calculated data for UV/vis spectra of neutral carotenoids. The calculated maxima of adsorption are systematically red shifted compared to the experimental values. However, and as discussed below, the relative position of the spectral bands shows an acceptable agreement with the experimental data. The ratio λcalc/λexp is, in all cases, around 1.23, which allows an easy correction for the computed spectra of the carotenoids, provided that they are calculated at the B3LYP/6-31G(d,p) level of theory. As the length of the polyene chain increases, electrons are more delocalized, and the excitation energy decreases. Therefore, for larger conjugated chains, the maximum absorption is expected to occur at longer wavelengths. As the values in Table 7 show, the shortest wavelength was found for DIH and the longest one for TOR, which have 8 and 13 conjugated double bonds,

respectively. On the other hand, BC and LYC have π chains of the same length, 11 conjugated bonds. However, since two of them are in the rings which are nonplanar with the rest of the molecular backbone in BC, the effective length of the conjugated system is reduced. This causes a blue shift that was found to be equal to 25 nm, which is in excellent agreement with the experimental shift of 21 nm. The experimental spectra of BC and ZEA are practically the same, as should be expected since the OH groups are not involved in the π-electron conjugation. The calculated λmax for these two carotenoids are also almost identical. The carbonyl groups, however, are incorporated into the π-electron conjugation, which is reflected in the position of the absorption bands. The experimental spectra show a blue shift of 26 nm for CAN compared to that of BC, which is also in line with the computed one of 32 nm. The influence of the epoxy groups is also correctly predicted. Comparing the λmax of VIO and ZEA, the first one is found to be shorter by 27 (25) nm from the calculated (experimental) spectra. Thus, even if the absolute values of λmax from calculated spectra are not accurate, relative comparisons are expected to properly reproduce the experimental tendencies for neutral carotenoids. The absorption spectra of selected Car•+ have also been computed. The available experimental data are limited for these species, concerning only 8 of the 19 modeled carotenoids. In contrast to what was observed for their neutral partners, the calculated absorption maxima of Car•+ are not systematically shifted with respect to the experimental data but rather between the experimental values reported by different authors. In this case, the calculations also seem to properly predict the correct tendencies. The longest and shortest wavelengths (in the set of eight Car species) are predicted for LYC•+ and APO•+, respectively, in agreement with the experimental data. Assuming that the computed tendency is correct, TOR•+ is predicted to have the longest absorption maximum among the whole set of studied radical cations, and CRUB•+ has the shortest one. It has been previously suggested18 that the absorption maxima of the carotenoids radical cations may be used as an indicator of the carotenoids ability as free radical scavengers. However, from a theoretical point of view, thermodynamic results are more reliable since, in general, quantum mechanical calculations describe better systems in their ground states than in their exited states. On the other hand, when comparing carotenoids with substantially different oxidation potential, the λmax criterion could also be effective. The computed IR spectrum of neutral BC has been compared with the experimental one in Figure 7. It shows the general agreement between theoretical and experimental results. Since the available data on carotenoids’ IR spectra are scarce, additional information on them has been provided for all of the modeled carotenoids. The IR spectra of selected carotenoids with OH, CdO, and both groups in their structure are shown in Figure 8. Five normal vibrational modes have been analyzed for all of the studied carotenoids, and their frequencies are reported in Table 9. These modes are the O-H, C-H (in the polyene), CdO, and CdC stretchings and the H bendings, involving motions out of the polyene plane. The band of the H bending out of the plane appears for all of the studied systems around 1030 cm-1 and corresponds to strong signals in the spectra. The CdC stretchings also appear as strong signals and around 3140 cm-1, which is characteristic of large polyene systems. In addition to those reported in Table 9, some particular modes deserve to be mentioned to allow potential comparison with further data. For APO the C-H stretching involving the aldehydic hydrogen and the C-CHO

Relative Antioxidant Efficiency of Carotenoids stretchings appear at 2900 and 934 cm-1, respectively. The frequency associated with the stretching involving the allenic group (-CHdCdCH-) in NEO was found to be 2036 cm-1. For MYT, there are two other vibrational modes of interest, the CtC stretching and the band associated with the enolic β-diketone; they appear at 2285 and 1672 cm-1 in the calculated spectrum and at 2165 and 1588 cm-1 in the experimental one.49 The agreement between the calculated and experimental frequencies, corresponding to the variational modes that have been analyzed, is good in general. However, it is important to point out that the aim of the theoretical calculations on vibrational spectra of large systems, at least in this work, is not to reproduce the experimental data to a high wavenumber accuracy but to reflect the major general features and trends and luckily to help in the assignment of the most prominent bands. In general, the calculated wavenumbers are expected to diverge to a certain extent from the experimental ones due to anharmonicity effects. Even though the calculated spectra of chemical systems as large as carotenoids are not expected to be very accurate, in terms of wavelengths (UV/vis) or frequencies (IR), a general agreement between calculated and experimental spectroscopy data has been obtained within the frame of DFT and quite modest basis sets. This agreement seems to support the results obtained in the present work using the same level of theory. Concluding Remarks The relative order of 19 different carotenoids, in terms of oxidation potentials, is proposed for polar and nonpolar solvents. The same order was obtained for Car + oxygenated free radical and Car2 + Car1•+ reactions. Ionization potentials seem to be capable of predicting the correct relative ease of oxidation in a series of carotenoids at a low computational cost. The nuclear reorganization energy associated with ET reactions has been calculated in a very simple but apparently efficient way that allows computing of free energy barriers and, at least, relative rate coefficients in good agreement with the experimental values. In addition, a simple correction is proposed to include the effect of diffuse functions in the energies associated with Carn •+ f Carn-1 processes. TOR is predicted as the carotenoid with the highest antioxidant efficiency from the modeled set, expressed as the electron donating capability, in polar and nonpolar media and in Car + free radical reactions as well as in carotenoid pair redox reactions. The general agreement between different calculated magnitudes and the corresponding available experimental data supports the predictions from this work. Since TOR was found to be the most easily oxidized from all of the studied carotenoids, experimental studies on the antioxidant capabilities of this carotenoid, relative to other carotenoids would be of great interest, especially relative to LYC, which up to date has been thought of as the most efficient one. Such experimental studies might also help to validate the accuracy of the methodology used in this work for describing electron-transfer reactions. They might also support the utility of this kind of calculations in the design of new antioxidants with increasing efficiency in terms of electron donating capabilities, which might potentially help to prevent or repair oxidative damage in living systems. Acknowledgment. The author thanks the Computing Center of the Instituto Mexicano del Petro´leo (IMP) for supercomputer

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Relative Antioxidant Efficiency of a Large Series of Carotenoids in

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