Solvent-Polarity Dependence of Antioxidant Kinetics of Vitamin E
Aya OUCHI, Shin-ichi NAGAOKA and Umpei NAGASHIMA
It is well-known that vitamin E (a-, b-, g-, d-tocopherols: TocH) (Figure 1(a)) inhibits autoxidation of organic molecules. Furthermore, vitamin E is present in cellular membranes and edible oils and acts as an antioxidant by protecting polyunsaturated lipids or fatty acids from peroxidation. Vitamin E combines with a lipid peroxyl radical (LOO.) and produces a lipid hydroperoxide (LOOH) and a tocopheroxyl radical (Toc.) (reaction (1)), which is a part of the antioxidant reaction [1 - 4].
Here, k1 denotes the second-order rate constant for reaction (1).
Mukai et al.  reported the second-order rate constant (ks) for the reaction between TocH's and a stable substituted aroxyl radical (2,6-di-t-butyl-4-(4'-methoxyphenyl)phenoxyl, ArO., Figure 1(b)) (reaction (2)).
Here, ArOH stands for 2,6-di-t-butyl-4-(4'-methoxyphenyl) phenol. It was shown that the rate constants, such as ks, for the reactions between TocH's and some radicals decrease with increasing the solvent-polarity [6, 7]. However, since the reason was not clear, we have here examined the effect of the solvent-polarity on the ks value by calculating atomic charges of hydrogen atoms in the solvent molecules.
Figure 1. Molecular structures of a-TocH and ArO. used in the present work.
2 Experimental and Computational Methods
2. 1 Measurements
We measured the ks values for a-tocopherol (a-TocH) in ethanol, diethyl ether, benzene, hexane, and heptane at 25°C according to the method reported previously . Briefly, ArO. was prepared according to the method of Rieker et al. . The pseudo-first-order rate constant for reaction (2), kobsd, was determined by following the exponential decay of the peak absorbance of ArO. by using stopped-flow spectrophotometry (Figure 2). Since the concentration of a-TocH ([a-TocH]) is much larger than that of ArO. under our experimental conditions, the kobsd for ArO. bleaching by a-TocH is given by
where k0 denotes the natural decay rate constant of ArO.. The ks values were obtained by plotting kobsd against [a-TocH] (Figure 3).
Figure 2. Change in electronic absorption spectrum of ArO. and a-Toc. during reaction of ArO. with a-TocH in ethanol at 25.0°C.
2. 2 Computational Methods
Ab initio molecular orbital calculations of the solvent molecules were carried out with the Gaussian 98 program . Geometries of ethanol, diethyl ether, benzene, hexane, and heptane were optimized at the HF/6-31G** level. Atomic charges for the optimized geometries were calculated with the STO-3G basis set. The reason for this is that the 6-31G** basis set is, of course, more precise than the STO-3G basis set, but the 2s and 2p orbitals of the carbon atom at 6-31G** are large enough to reach the neighboring hydrogen atom in the molecule and the seeming atomic charge of the hydrogen atom increases. By using the STO-3G basis set, such increase of the seeming atomic charge can be avoided. In the interpretation of the experimental results, we used the atomic charges of the hydrogen atoms of the hydroxy group in ethanol and of the methyl groups in diethyl ether, hexane, and heptane.
3. 1 Experimental Results
Figure 3 shows plots of kobsd as a function of [a-TocH] in various solvents. Each of the plots shows a linear relationship. The ks values were obtained from the slope of the linear plot and the order is as follows: heptane > hexane > benzene > diethyl ether > ethanol.
Figure 3. Dependence of kobsd on [a-TocH] in reaction of a-TocH with ArO. in ethanol, diethyl ether, benzene, hexane, and heptane at 25.0 °C.
3. 2 Calculated Results
The atomic charge of the hydrogen atoms in the solvent molecules changes from 0 to 0.2. As the atomic charge decreases, the solvent-polarity decreases. Figure 4 shows plots of the ks values vs. the atomic charges. A linear relationship was obtained except for the point of ethanol. The ks value increased with decreasing atomic charge, that is, with decreasing the solvent-polarity.
Figure 4. Plots of ks vs. atomic charge.
It was shown that the mechanism of reaction (2) is electron transfer followed by proton transfer from TocH to ArO. [11 - 13]. Mukai et al.  reported a linear relationship between logks and the peak oxidation potential of TocH. The ks value is thus controlled by the rate constant of the electron transfer (ket), in which TocH is the electron-donor and ArO. is the accepter.
Figure 5. Potential curves of LE and CT. The solvent molecules are randomly oriented in A and D configurations, and they are reorganized in C and E configurations.
The potential curves in the electron transfer are given in Figure 5, where LE and CT show the potential curves of the precursor (TocH+ArO.) and the product (TocHδ+-ArO.δ-), respectively. The ordinate is the energy and the abscissa is the reorganization of solvent. On the LE potential where TocH and ArO. are neutral, A configuration where the solvent molecules are randomly oriented around TocH+ArO. is more stable than E configuration where the solvent molecules are reorganized. On the CT potential where TocHδ+-ArO.δ- has partial charge separation, C configuration where the solvent molecules are reorganized is more stable than D configuration where the solvent molecules are randomly oriented. The probability of transition from LE to CT is assumed unity at the crossing point of the potential curves (B point).
In Figure 5, the electron-transfer rate-constant (ket) increases with lowering D‡G, which is the transition energy from A configuration to C configuration and decreases with increasing the energy difference between A and C configurations (-DG0). As -DG0 increases, C configuration is stabilized, and the solvent molecules are more strongly reorganized around TocHδ+-ArO.δ- after the electron transfer. As -DG0 increases, the solvent-polarity becomes larger, as does the atomic charge in Figure 4. As a result, as the atomic charge increases, the ket value should increase and the ks value controlled by ket should also increase. However, this explanation contradicts our experimental results (Figure 4). Therefore, it will be natural to consider that the -DG0 value does not change very much in our system.
Next, we will examine the reorganization energy (l in Figure 5), which is another factor affecting D‡G. l in Marcus theory is expressed by the following expressions .
li denotes the work required to change the dimensions of the reactants and is essentially the potential energy of a vibrational displacement. e is the charge on an electron. rD and rA are respectively the radii of the electron-donor and -accepter. rDA is the center-to-center distance, in the complex, between the electron-donor and -accepter during the electron transfer. d stands for the charge change on the electron-donor and -accepter. n refers to the refractive index. er is the dielectric constant.
(1/2rD + 1/2rA - 1/rDA) is positive because of rDA > rA + rD. Accordingly, as (1/n2 - 1/er) increases, the reorganization energy (l) increases (Eq. (4)). On the other hand, as er and (1/n2 - 1/er) increase, the solvent-polarity increases and then the atomic charge estimated above increases. Thus, there is positive correlation among l, (1/n2 - 1/er), the solvent-polarity, and our computational atomic charge. We have plotted the logks as a function of (1/n2 - 1/er) as in Ref.  (Figure 6). Since a linear relationship with a negative slope between the logks and (1/n2 - 1/er) is seen, the ks value decreases with increasing l, the solvent-polarity, and the atomic charge. This explanation is consistent with our experimental results (Figure 4). Therefore, the origin of the solvent-polarity dependence of ks can be attributed to the reorganization energy (l). The negative slope in Figure 6 corresponds to the normal-regime of Marcus theory.
Figure 6. Plots of logks vs. 1/n2 - 1/ r.
Like this, the reorganization energy (l) has an important influence on the ks value. So we examined how the form of the potential curve changes with l. When l increases, the curvatures of the potential curves of LE and CT increase (broken curves in Figure 7). As a result, D‡G increases and the ket value decreases together with its controlling ks value.
Figure 7. Increase in curvatures of LE and CT potential curves when solvent-polarity increases.
Why does the point of ethanol deviate from the linear relationship between the ks value vs. the atomic charge of the solvent (Figure 4)? The reason for this can be understood by considering that strong intermolecular hydrogen bonds prevent reorganization of the ethanol solvent around the product (TocHδ+-ArO.δ-). On A configuration, ethanol molecules construct an intermolecular network through the hydrogen bonds. Accordingly, on going from A configuration to C configuration, ethanol molecules are not easy to be reorganized, and thus the solvent reorganization is insufficient on C configuration (Figure 5). As a result, the potential curve of CT approaches that of LE along the abscissa (broken curve in Figure 8). Therefore, l decreases, D‡G decreases, and the ks value controlled by ket increases. Such an effect would induce deviation of the point of ethanol from the linear relationship shown in Figure 4.
Figure 8. Approach of potential curves of CT and LE along abscissa in ethanol solvent.
As noted above, the data points of Figure 4 can be divided into two groups; ethanol with intermolecular hydrogen bonding and the others. In contrast, the data points showing a linear relationship in Figure 6 can be divided into three groups; hydrocarbons, diethyl ether, and ethanol. This division cannot be explained in terms of the intermolecular hydrogen bonding alone. It is interesting that a linear relationship between the logks and the dipole moment of the solvent (m)  is also seen with division into the same three groups of the data points (Figure 9). m may also have an influence on ks.
Figure 9. Plots of logks vs. m.
We have studied the effect of solvent-polarity on the antioxidant reaction rate of vitamin E (ks) and we especially paid attention to the intermolecular hydrogen bonding of ethanol. We have understood through this study that the reorganization energy (l) has an important influence on the ks value. We can predict the ks value by calculating the atomic charges of the solvents other than those studied in this study if any effects such as intermolecular hydrogen bonding are absent. The intermolecular hydrogen bonding has a great influence on the ks value, because it prevents the reorganization of the solvent.
A.O. expresses her sincere thanks to Professor Emeritus Kazuo Mukai of Ehime University for his continuous encouragement. A.O. and S.N. thank Eisai Co. Ltd. for the generous gift of d-a-TocH. We also thank the Research Center for Computational Science at the Okazaki Research Facilities of the National Institutes of Natural Sciences for the use of the computers and the Library Program Gaussian 98.
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