How Metal Influence on Reaction Mechanism of Antioxidants Considering the Solvent Effect: A DFT level Study

Introduction

Computational details

Results and discussion

Single electron transfer (SET) mechanism

Relative reaction Gibbs free energy values ($∆G^0$) for the SET-1 and SET-2 mechanisms, calculated at 298.15 K in water and pentylethanoate with radical ˙OOH and ˙OH, are shown in Table 1.

Table 2. Reaction Gibbs free energy (ΔG⁰), in kcal/mol, with the ˙OOH and ˙OH radical, in water and pentylethanoate at 298.15 K.

Table 2. Reaction Gibbs free energy (ΔG⁰), in kcal/mol, with the ˙OOH and ˙OH radical, in water and pentylethanoate at 298.15 K.

Channel	A1(I)		A1(II)		A2(I)		A2(II)
	ΔG0		ΔG0		ΔG0		ΔG0
	˙OOH	˙OH	˙OOH	˙OH	˙OOH	˙OH	˙OOH	˙OH
SET-1	26.04	0.62	64.88	41.35	26.54	0.82	68.21	44.67
SET-2	2.62	-22.97	-	-	0.81	-24.91	-	-

(I) = water (II) = pentylethanoate.

For the SET-1 mechanism, where the radical cation is formed from neutral geometry, the reaction Gibbs free energy ($∆G^0$), in aqueous solution, with the radical ˙OOH is highly endergonic for A1 and A2 and the reaction is not viable. With ˙OH radical, the reaction is slightly endergonic. Activation energy $∆G^{‡}$ values for A2 reaction with ˙OH radicals decrease with respect to A1. The rate order of the apparent rate constant $k_{app}$ for reaction of A1 and A2 with ˙OH radical doesn´t change, 10⁹ M⁻¹ s⁻¹, showing that the presence of the Sn(IV) in A2 contributes to decrease the height of the barrier but not to decrease the width, which is essential in the electron tunnel effect, but this contribution do not influence to improve the scavenger activity.

In pentylethanoate $∆G^0$ is highly endergonic with both ˙OOH and ˙OH radicals because the formation of the ionic specie is not viable. Comparing $∆G^0$ behavior of A1 and A2 in their neutral form, an increase in $∆G^0$ is shown with the ˙OOH and ˙OH radicals in aqueous and lipid media. This shows that the presence of the Sn(IV) in the organometallic moiety acts like an electro-acceptor group, withdrawing electron density to the ester.

For the SET-2 mechanism $∆G^0$ is endergonic with the radical ˙OOH and highly exergonic with the radical ˙OH. For A2, which has a Sn(IV), $∆G^0$ is less endergonic in the reaction with ˙OOH radical and more exergonic with ˙OH radical, in comparison to A1. It shown that the organometallic moiety acts like an electron-donor group, donating electron density to the ester in their deprotonated form favoring the charge transfer. Contrary to that shown for SET-1 mechanism.

Activation energy $∆G^{‡}$ values on the reaction of A2 with ˙OOH radical, slightly decreases in comparison with A1. On the other hand, on the reaction of A2 with ˙OH radical, $∆G^{‡}$ decreases considerably in comparison with A1.

Table 3. Reaction Gibbs activation energy ΔG^‡ in kcal/mol, apparent rate constant k_app in M⁻¹ s⁻¹.

Table 3. Reaction Gibbs activation energy ΔG^‡ in kcal/mol, apparent rate constant k_app in M⁻¹ s⁻¹.

	A1(I)		A2(I)
SET-1	ΔG‡	kapp	ΔG‡	kapp
˙OOH	-	-	-	-
˙OH	1.28	8.55 × 109	0.34	8.78 × 109
SET-2	ΔG‡	kapp	ΔG‡	kapp
˙OOH	4.65	1.25 × 106	4.03	9.13 × 107
˙OH	44.41	8.53 × 10-24	28.40	2.12 × 108

(I) = water.

With respect to the apparent rate constant $k_{app}$ for reaction of A1 and A2 with ˙OOH and ˙OH radicals, the order of $k_{app}$ increases from 10⁶ M⁻¹ s⁻¹ to 10⁷ M⁻¹ s⁻¹ on the reaction with radical ˙OOH and, from 10⁻²⁴ M⁻¹ s⁻¹ to 10⁸ M⁻¹ s⁻¹ for reaction with radical ˙OH. Therefore, the presence of Sn(IV) contributes to improve the reactivity of the ester increasing its efficiency like a scavenger. The order of $k_{app}$ for A2 with the radical ˙OOH, is comparable with that shown by glutation (2.7 × 10⁷ M⁻¹ s⁻¹) [53] and the propensulphonic acid (2.6 × 10⁷ M⁻¹ s⁻¹) [54].

Hydrogen Transfer (HT) Mechanism

Gibbs free energy values $∆G^0$ in kcal/mol for HT mechanism, regarding reaction channels 4a, 7 y 8 in aqueous media are shown in Table 1. On reaction of A1 y A2 with radical ˙OOH, $∆G^0$ for reaction channel 7 y 8 is endergonic, in both, aqueous and lipid media. In reaction channel 7, $∆G^0$ increases in water and decreases in lipid media with the presence of Sn(IV), which shows that the presence of Sn(IV) favored the reaction in lipid media. For reaction channel 8, the presence Sn(IV) on A2 contribute to increase $∆G^0$, even in water and lipid media. Therefore, reaction channel 8 is the less favored.

Table 4. Reaction Gibbs free energy $∆G^0$ in kcal/mol for A1 and A2 esters with radical ˙OOH and ˙OH.

Table 4. Reaction Gibbs free energy $∆G^0$ in kcal/mol for A1 and A2 esters with radical ˙OOH and ˙OH.

	A1(I)	A1(II)	A2(I)	A2(II)
4a
˙OOH	-6.65	1.75	-6.27	-4.27
˙OH	-41.92	-33.94	-42.04	-39.97
7
˙OOH	12.67	16.06	14.31	15.93
˙OH	-23.09	-19.64	-21.46	-19.76
8
˙OOH	23.16	23.85	87.47	24.79
˙OH	-12.11	-11.86	51.71	-10.92

(I) = water (II) = pentylethanoate.

On the other hand, reaction with ˙OH radical, $∆G^0$ in reaction channels 7 y 8 is exergonic, except for A2 on water, where $∆G^0$ is highly endergonic. In aqueous and lipid media, an increase in $∆G^0$ for reaction channel 7 on A2 is show in presence of Sn(VI) in comparison with A1. For reaction channel 8, $∆G^0$ is exergonic on A1 in water and lipid media. For A2, the presence of the Sn(IV) increases considerably $∆G^0$ in water media. In lipid media the presence of Sn(IV) on A2 contributes to increase $∆G^0$, showing that channel 7 is more viable than channel 8, and that the presence of the Sn(IV) contributes to increase $∆G^0$ of HT mechanism.

For reaction channel 4a, $∆G^0$ is exergonic for the reaction with radical ˙OOH on A1 (except in lipid media) and A2. On water, Gibbs free energy $∆G^0$ slightly increases with the presence of Sn(IV). In pentylethanoate, $∆G^0$ is endergonic for A1, and exergonic when Sn(IV) is present on A2, showing that the presence of Sn(IV) influences the transferring of light atoms like H.

For reaction with radical ˙OH, $∆G^0$ is exergonic, even higher than that shown on channel 7 y 8, therefore, reaction channel 4a is the most viable, in both, pentylethanoate and water media. When Sn(IV) is included in A2, $∆G^0$ is more exergonic than A1, which means, that the presence of the Sn(IV) contributes to increase the hydrogen transfer in both media.

For hydrogen transfer mechanism, transition state geometries were optimized for A1 and A2 with ˙OOH radical, verifying that each transition state has a negative frequency corresponding to the reaction coordinate. Transition state geometries, for reaction with ˙OH radical, cannot be obtained. Even their $∆G^0$ are highly exergonic, and it is probably that the reaction is carried out by diffusion.

Figure 2. Optimized transition state geometry of A1 and A2 with radical ˙OOH in water (I) and pentylethanoate (II) and their imaginary frequencies.

Figure 2. Optimized transition state geometry of A1 and A2 with radical ˙OOH in water (I) and pentylethanoate (II) and their imaginary frequencies.

Activation energy $∆G^{‡}$ and rate constant k were computed and show in Table 6. For reaction of A1 and A2 with ˙OOH radical on water, computed values of $∆G^{‡}$ were 13.07 y 12.26 kcal/mol respectively. With respect to k, computed values were 1.24 × 10⁶ y 4.64 × 10⁶ M⁻¹ s⁻¹, for A1 and A2 respectively. Even though, the presence of the Sn(IV) on A2 contribute to decrease the $∆G^{‡}$ barrier, the rate order of k remains without change. It can be due to the presence of the metal, which contribute to decrease the activation energy barrier, but do not contribute to modify the width of the barrier during the tunnel effect through the hydrogen transfer.

Table 5. Activation energy barrier ΔG^‡ in kcal/mol and rate constant k in M⁻¹ s⁻¹.

Table 5. Activation energy barrier ΔG^‡ in kcal/mol and rate constant k in M⁻¹ s⁻¹.

	A1(I)		A1(II)		A2(I)		A2(II)
	ΔG‡	k	ΔG‡	k	ΔG‡	k	ΔG‡	k
˙OOH	13.07	1.24 × 106	18.47	4.12 × 103	12.26	4.64 × 106	12.56	1.25 × 105

(I) = water, (II) = pentylethanoate.

In pentylethanoate, $∆G^{‡}$ for reaction of A1 and A2 were 18.47 and 12.56 kcal/mol respectively, and computed k values were of 4.12 × 10³ M⁻¹ s⁻¹ for A1 and 1.25 × 10⁵ M⁻¹ s⁻¹ for A2. In non-polar face, it was shown that the influence of the Sn(IV) contributes to decrease the activation barrier improving the tunnel effect, and increasing the rate order on A2, which means that the presence of the metal contribute to improve its efficiency like scavenger, on this type of systems.

Reaction Abduct Formation (RAF)

On Table 7 computed values of total rate constant k_T are shown. Contribution of each rate constant, for electron transfer and hydrogen transfer mechanism, were included with ˙OOH and ˙OH radicals.

Table 6. Total rate constant k_T in M⁻¹ s⁻¹.

Table 6. Total rate constant k_T in M⁻¹ s⁻¹.

	A1(I)	A1(II)	A2 (I)	A2 (II)
	kT	kT	kT	kT
˙OOH	2.5 × 106	4.12 × 103	9.59 × 107	1.25 × 105
˙OH	8.55 × 109	-	8.99 × 109	-

(I) = water, (II) = pentylethanoate.

Contribution of each mechanism in the scavenger activity of A1 and A2 was computed by calculating the contribution ratio.

$$\Gamma =\frac{k_i}{k_T}x100\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}ec.5$$

where $\Gamma$ is the contribution ratio, $k_i$ is the rate constant of the reaction mechanism and $k_T$ is the total rate constant. Rate contribution is represented in percentage, Table 8.

For the reaction of A1 with ˙OH radical, the main contribution comes from SET-1 mechanism, which contribute with a 100 %, because of the very low-rate order of k, shown in SET-2 mechanism. On the other hand, in the reaction with A2, the contribution is 97.6 %, the lower contribution is due to the deprotonated specie, which contributes with a 2.36 %. This means that both esters are good scavengers in their neutral form.

Table 7. Contribution $\left(\Gamma \right)$ of each mechanism to the scavenger activity.

Table 7. Contribution $\left(\Gamma \right)$ of each mechanism to the scavenger activity.

	A1(I)		A1(II)		A2(I)		A2(II)
	$\Gamma$		$\Gamma$		$\Gamma$		$\Gamma$
SET-1
˙OOH	-		-		-		-
˙OH	100				97.6
SET-2
˙OOH	50		-		95.2		-
˙OH	0		-		2.36		-
HT
˙OOH	49.6		100		4.84		100
˙OH	-		-		-		-

(I) = water, (II) = pentylethanoate.

For reaction of A1 with OOH radical, SET-2 and HT mechanism contributes to almost the same rate, 50.4 % and 49.6 % respectively. With respect to A2, the contribution changes due to the presence of Sn(IV), where the main contribution comes from SET-2 mechanism with a 95.2 % and a 4.84 % from HT mechanism, showing that the presence of Sn(IV) contributes to significantly increase the donor electron character of the ester to neutralize peroxy radicals, but not the transfer of light atoms like hydrogen. In lipid media, the main contribution comes from HT mechanism, due to the ester cannot form ionic species. This shows that metal could improve the scavenger capability of the ester derived from p-cumaric acid against peroxy type radicals.

Conclusions

References

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