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. 2020 Oct 14;5(42):27572–27581. doi: 10.1021/acsomega.0c04144

Substituent Effects on the N–H Bond Dissociation Enthalpies, Ionization Energies, Acidities, and Radical Scavenging Behavior of 3,7-Disubstituted Phenoxazines and 3,7-Disubstituted Phenothiazines

Pham Thi Thu Thao †,‡,§, Binh Thuc Tran ‡, Nguyen Minh Thong ∥,*, Duong Tuan Quang ⊥, Nguyen Khoa Hien #, Minh Tho Nguyen ∇,○, Pham Cam Nam †,*
PMCID: PMC7594321  PMID: 33134721

Abstract

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The substituent effects on the N–H bond dissociation enthalpies (BDE), ionization energies (IE), acidities (proton affinity, PA), and radical scavenging behavior of 3,7-disubstituted phenoxazines (PhozNHs) and 3,7-disubstituted phenothiazines (PhtzNHs) were determined using density functional theory, with the M05-2X functional in conjunction with the 6-311++G(d,p) basis set. These thermochemical parameters calculated in both gas phase and benzene solution with respect to the changes in several different substituents including halogen, electron-withdrawing, and electron-donating groups at both 3 and 7 positions in both PhozNHs and PhtzNHs systems were analyzed in terms of the inherent relationships between them with some quantitative substituent effect parameters. The kinetic rate constants of hydrogen-atom exchange reactions between PhozNH and PhtzNH derivatives with the HOO• radical were also calculated, and the effects of the substituents on the kinetic behaviors of these reactions were thereby quantitatively evaluated.

1. Introduction

The deterioration of physical, chemical, and mechanical properties of a variety of materials in air is caused by many factors and mostly related to chain reactions of free radicals that are generated as pollutants circulating in the atmosphere. Therefore, a study on the relevant processes with the purpose to slow down the oxidative degradation of materials is an actual and important topic for scientific research. From a chemical view point, one of the indispensable methods for treating free radicals is the use of antioxidants with proper content.

The main action of an antioxidant is to terminate the chain of oxidation reactions or prevent oxidation reactions of free radicals from occurring in organic compounds. The antioxidant compounds generally operate according to possible mechanisms involving hydrogen-atom transfer (HAT), proton-coupled electron transfer (PCET), single-electron transfer (SET), single-electron transfer followed by proton transfer (SETPT), sequential proton lost electron transfer (SPLET), sequential proton-loss hydrogen-atom transfer (SPLHAT), and radical trapping adduction (RAF). Of these processes in the gas phase, the most frequently applied mechanisms include the HAT/PCET, SET, and SPLET.1−4 As a result, the hydrogen donating ability of a chain-breaking antioxidant induces a very important effect on its antioxidant activity.

Currently, antioxidants used for organic polymers include hindered phenol and amine compounds as well as their related derivatives. In particular, antioxidants based on aromatic amines exhibit excellent antioxidant properties in which the derivatives from phenoxazine and phenothiazine are considered as promising candidates for this purpose in terms of efficiency.5−7

Phenoxazine (PhozNH) is a heterocyclic compound with a molecular formula of C12H9NO, including an oxazine fused with two benzene rings. Phenothiazine (PhtzNH) has a similar structure to phenoxazine but the oxygen (O) atom is now replaced by a sulfur (S) atom (Figure 1). Based on their chemical and biological properties, they have been widely used as chemotherapeutic agents, antioxidants, and acid–base and redox indicators. As antioxidant agents, their abilities are similar to that of Trolox in terms of prevention of the oxidation of linoleic acid.8,9

Figure 1.

Figure 1

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Molecular structures of phenoxazine, phenothiazine, and their 3,7-disubstituted derivatives considered.

As a matter of fact, antioxidant activities of both phenoxazine and phenothiazine can be preliminarily predicted via the relatively small bond dissociation energies of their N–H bonds, bond dissociation enthalpies (BDE) (N–H) values, which suggest that the separation or transfer of H(N) atom to free radicals is favored.8,10,11 In addition, the ionization energy (IE) and proton affinity (PA) parameters involved in the first step of SETPT and SPLET processes also need to be taken into account. Furthermore, the antioxidant performance evaluated from the nature of substituents and the substituted positions is also an interesting topic for investigation. Regarding the substituent effects, recent papers have approached them more frequently in terms of the changes in thermochemical parameters12−14 but almost rarely on the changes in kinetic behaviors. Therefore, a legitimate question raises here is as to whether there is any relationship between kinetic parameters (i.e., energy barrier, rate constants, etc.) with Hammett constants that are typical substituent parameters.

In this context, we set out in the present study to investigate the effects of a series of selected substituents, as shown in Figure 1, not only on the thermochemical properties such as BDE, IE, and PA in the gas phase15−17 but also on the kinetic behaviors of the reactions between PhozNH and PhtzNH derivatives (Figure 1) and the HOO• radical. The latter is a typical and abundant free radical pollutant present in the atmosphere. Therefore, the main content in this paper is 2-fold: (i) first, we aim to determine the main thermochemical parameters with respect to the changes in the substituents at both 3 and 7 positions in the systems considered (Figure 1) and to analyze the relationships between them with Hammett parameters, and (ii) second, we construct the relevant portions of the potential energy surfaces (PESs) and thereby kinetic calculations on hydrogen-atom exchange reactions between PhozNH and PhtzNH derivatives with the HOO• radical in the gas phase and benzene solution. Based on these results, the effects of the substituents and solvent on the kinetics behaviors of these reactions will be explored.

2. Results and Discussion

2.1. Calibration for Predicted Thermochemical Parameters

The BDEs, IEs, and PAs are important thermochemical parameters that define the three main antioxidant mechanisms, namely, the HAT, SETPT, and SPLET, respectively.15−17

It should be noted that the accuracy of the computed results for these parameters and energy barrier derived from the potential energy surface (PES) of the scavenging radical reactions considerably affects the accuracy of the calculated rate constants. Therefore, the validation of the computational methods used for evaluation of these values is the first task before proceeding further with calculations and analysis.

First, to ensure the accuracy of proposed approaches, the relevant thermochemical results of compounds containing an N–H bond whose experimental data are available are calculated at the M05-2X/6-311++G(d,p) + ZPE level. A set of nine compounds is chosen with the presence of F (halogen), CH3 (electron-donating group, EDG), and CN (electron-withdrawing group, EWG), which represent typical kinds of substituents on both PhozNH and PhtzNH. Their BDEs, IEs, and PAs are calculated and given in Table 1; the differences between the calculated and experimental values are also evaluated. It should be noted here that PA values are calculated for the anion derived from the parent molecule.

Table 1. Comparison of Thermochemical Parameters Calculated at the M05-2X/6-311++G(d,p) Level and the Experiment for Selected N–H Compounds (kcal/mol)a,b.

  BDE(N–H)c
 IE
 PA
compounds calc. exptl.d calc. exptl.e calc. exptl.e
NH3 107.3(−0.9) 108.2 ± 0.3 234.3(2.1) 232.2 ± 0.5 404.3(0.9) 403.4 ± 1.2
CH3NH2 99.2(−2.4) 101.6 ± 2.0 207.1(3.3) 205.2 ± 2.3 402.9(0.9) 402.0 ± 2.6
(CH3)2NH 93.7(0.4) 94.1 190.3(0.3) 190.0 ± 1.8 394.9(−0.2) 395.1 ± 2.0
NH2CN 99.9(0.2) 99.0 244.2(−1.2) 245.4 345.0(−4.2) 349.2 ± 2.9
C6H5NH2 95.0(2.7/5.3) 92.3/89.7 177.2(−0.7) 178.0 ± 0.05 366.1(−2.1) 368.0 ± 0.3
4F–C6H4NH2 93.9(5.1) 88.8 179.2(−3.2) 182.2 ± 2.3 362.8(−1.4) 364.2 ± 2.1
4Me–C6H4NH2 93.1(5.6) 87.5 170.6(0.6) 170.0 ± 0.5 366.1(−0.8) 366.9 ± 2.1
4CN–C6H4NH2 98.1(2.0) 95.2 195.0(−3.2) 199.2.0 ± 0.9 351.2(2.5) 348.7 ± 2.1
(C6H5)2NH 88.5(1.3) 87.2 168.3(2.5) 165.8 ± 0.3 349.4(−0.5) 350.9 ± 1.3
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a

Differences between both values are in parentheses.

b

σBDE = 2.6 kcal/mol, σIE = 2.4 kcal/mol, and σPA = 1.9 kcal/mol.

c

Restricted open shell (RO) for open-shell radicals is applied to calculate BDEs.

d

Data taken from ref (18)

e

Data taken from ref (19) (https://webbook.nist.gov/chemistry/).

Based on the deviations between the calculated and experimental values, the sample standard deviations (σ) for BDE(N–H), IE, and PA of nine small compounds considered are σBDE = 2.6 kcal/mol, σIE = 2.4 kcal/mol, and σPA = 1.9 kcal/mol. These results indicate that the M05-2X/6-311++G(d,p) level is expected to reasonably generate thermochemical parameters of the N–H bonds with an error margin of ±2.0 kcal/mol.

2.2. Substituent Effects on Thermochemical Parameters and Correlation with Hammett Parameters

2.2.1. Substituent Effects on BDE, IE, and PA Values

The BDE(N–H), IE, and PA values based on M05-2X/6-311++G(d,p) computations for two sets of substituted phenoxazines and phenothiazines are shown in Table 2, in which the data in parentheses are the changes in the corresponding parameters in going from the parent PhozNH/PhtzNH to their substituted one. The reasonably accurate data in Table 2 provide the essential information not only to help us preliminarily evaluate the antioxidant ability but also to clarify the thermochemical effect of substituents for the studied systems.

Table 2. Calculated BDE(N–H), IE, and PA (kcal/mol) Values of PhozNH and PhtzNH Derivatives at the M05-2X/6-311++G(d,p) + ZPE Levela.
  PhozNHs (X = O)
 PhtzNHs (X = S)
substituent Y BDE(N–H) IE PA BDE(N–H) IE PA
H 76.7a(0.0) 159.8(0.0) 343.8(0.0) 80.6b(0.0) 158.4f(0.0) 345.1(0.0)
F 75.3(−1.4) 165.3(5.5) 338.2(−5.6) 79.2(−1.4) 164.6(6.2) 339.4(−5.7)
Cl 76.2(−0.5) 165.3(5.5) 333.8(−10.0) 80.1c(−0.5) 164.6(6.2) 335.5(−9.6)
CH3 75.2(−1.5) 153.2(−6.6) 345.7(1.9) 78.9(−1.7) 152.5(−5.9) 347.3(2.2)
OCH3 72.9d(−3.8) 148.3(−11.5) 346.9(3.1) 76.5d(−4.1) 148.8(−9.6) 347.8(2.7)
NH2 70.7(−6.0) 138.8(−21.0) 350.7(6.9) 75.0(5.6) 140.3(−18.1) 351.8(6.7)
CF3 79.3(2.6) 176.9(17.1) 323.8(−20.0) 82.5(1.9) 174.2(14.8) 325.6(−19.5)
CN 79.4(2.7) 181.3(21.5) 317.2(−26.6) 82.3(1.7) 178.6(20.2) 319.1(−26.0)
NO2 80.4(3.7) 186.0(26.2) 310.7(−33.1) 83.2e(2.6) 182.5(24.1) 313.1(−32.0)
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a

In benzene: a77.6; b81.7; c81.6; d77.3; and e85.3 kcal/mol in this work; a77.2 ± 0.3; b79.3 ± 0.3; c79.8 ± 0.3, d76.3 ± 0.4, and e81.6 ± 1.0 kcal/mol from ref (20) In DMSO: a79.5 and b83.7 kcal/mol in this work and a79.7 and b82.3 kcal/mol from ref (21)f155.4 ± 1.6 kcal/mol (6.73 ± 1.6 eV) and 158.4 kcal/mol (6.87eV) ref (24) Values in parentheses are the differences between the calculated values of substituted derivatives with respect to the parent compounds.

2.2.1.1. Bond Dissociation Enthalpy

In the HAT mechanism, BDE of a given bond is essential for predicting the radical scavenging capacity of the corresponding antioxidant. The gas-phase-calculated BDE(N–H)s for PhozNH and PhtzNH are 76.7 and 80.6 kcal/mol, respectively (Table 2). In the benzene solvent, the calculated values, using the radical-equilibrium electron paramagnetic resonance (REqEPR) technique by Lucarini et al., increased to 77.6 and 81.7 kcal/mol and thus are slightly larger by about 0.4 and 2.4 kcal/mol with respect to the experimental results.20 Moreover, in DMSO, our calculated values of 79.7 and 83.7 kcal/mol are quite close to the respective values calculated by Bordwell and co-workers.21 For 3,7-di-Y-PhtzNHs, our calculated results in benzene are 81.6, 77.3, and 83.0 kcal/mol for Y = Cl, OCH3, and NO2, respectively, whose deviations to the experimental ones20 are 1.8, 1.0, and 1.4 kcal/mol, respectively. This result once again confirms the reliability of the proposed method for further calculations.

Of course, the change in molecular properties depends on the nature of substituents. In the systems considered, the effects are due to both X and Y substituents. First, for a substituent Y, it is recognized that EDGs such as CH3, OCH3, and NH2 tend to reduce the BDE. Of these substituents, NH2 causes the highest decrease of the BDE value (−6.0 kcal/mol in PhozNH and −5.6 kcal/mol in PhtzNH). In contrast, EWGs are expected to increase the BDEs and more pronounced when X = NO2. Halogen atoms such as F and Cl slightly reduce the BDEs by an amount of only <1.4 kcal/mol.

As shown in Table 2, the BDE(N–H) values are computed in the range of 70.7–80.4 kcal/mol for PhozNH and from 75.0 to 83.2 for PhtzNH derivatives. A smaller BDE indicates the antioxidant activity of this compound will follow the HAT mechanism. Hence, the derivatives containing EDG emerge as promising scavengers following the HAT mechanism.

2.2.1.2. Ionization Energy

On observing the calculated IE values in the gas phase, it is found that the effects of both EDG and EWG on the IEs are quite similar to those exerted on BDE. The largest changes are observed when Y = NH2 and NO2, with the corresponding changes of −21.0 and 26.0 kcal/mol for PhozNHs and −18.1 and 24.1 for PhtzNHs. In the cases of F and Cl, they increase the IEs up to 5.5 and 6.2 kcal/mol in PhozNH and PhtzNH, respectively.

2.2.1.3. Proton Affinity

The gas-phase acidities of PhozNHs and PhtzNHs are determined from the proton affinities (PA) of the corresponding anions derived from PhozNHs and PhtzNHs when donating H+ at the amine group (NH). In this case, the effects of both EDG and EWG are rather opposite to those found above on the BDEs and IEs. The EDGs induce an increase of PA with the values ranging from 2.0 to 7.0 kcal/mol for both systems. On the other hand, the strong EWGs considerably reduce the PA with the value increasing up to 32.0 kcal/mol. The F and Cl atoms, in this case, behave like the EWG (see the values given in parentheses of Table 2 for details). Based on the PA values, the EWGs and halogen atoms at both 3 and 7 positions of disubstituted phenoxazines and disubstituted phenothiazines make these derivatives to be compared to those of the EDGs.

2.2.2. Correlations Between BDE, IE, and PA Values with Hammett Parameters

Substituent effects are very important for understanding and predicting the property/activity of organic compounds based on molecular structures. Up to now, there are mainly three kinds of substituent electronic effect descriptors derived from aromatic rings: ground-state polarity effect constant, spin-delocalization effect constant, and excited-state constant. The most representative ones of these substituent constants are Hammett constants σ,22 spin-delocalization substituent constants σJJ•,23 and excited-state substituent constants σCC,p,24−26 respectively.

Generally, when interpreting the substituent effects, it is of importance to determine any relationship between BDE, IE, and PA quantities with the Hammett constants. The latter are, in fact, characteristics for different classes of substituents. Because the substituents are at the positions of 3 and 7 of the aromatic ring with conjugation effects and resonance stabilization of the negative charge centered by a substituent, the modified Hammett constants for the para position σp+ is better chosen, instead of the regular Hammett constants σp for BDE and IE, and a set of σp parameters applied for PA.22,27,28 Based on the calculated thermochemical parameters for both sets of 3,7-disubstituted phenoxazines and 3,7-disubstituted phenothiazines shown in Table 2 and the σp+ and σp values taken from Table S1 of the Supporting Information, the Hammett plots between BDEs and IEs with σp+ constants, and PAs with σp constants are constructed and shown in Figure 2. All of the correlations are found to be very good with the R2 value being larger than 0.9465, in which the best ones are for the BDEs (R2 > 0.9819). Other analysis factors for evaluating the linear regression are also given in Table S2. The values of root-mean-square error (RMSE) are in the range of 0.4–3.1 kcal/mol, depending on the property, in which the linear equations for BDE have the smallest RMSE. The correlation equations between BDE(N–H)s, IEs, and PAs with Hammett constants can be expressed as follows.

Figure 2.

Figure 2

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Correlations between the modified Hammett parameters with (a) BDE, (b) IE, and (c) PA of PhozNHs and PhtzNHs.

For bond dissociation enthalpy

2.2.2. 1
2.2.2. 2

For ionization energy

2.2.2. 3
2.2.2. 4

For proton affinity

2.2.2. 5
2.2.2. 6

To assess the stability of the obtained fitting equations, a cross-validation is also performed. The data set is split into training and test sets; the latter includes Cl, NH2, and NO2, which characterize for three kinds of substituents (halogen, electron-withdrawing, and electron-donating groups) and the training set is the remains. The RMSE values of cross-validation given in Table S3 of the SI for BDE, IE, and PA in PhozNH/PhtzNH are 0.41/0.15, 3.76/3.48, and 3.91/3.81 kcal/mol, respectively. The RMSE for BDE is a good measure of how accurately the obtained linear model predicts the BDE. However, it should be noted that this sample size contains only nine data points may increase the errors for estimation. For example, in the case of IE and PA, the RMSE values are found to be larger than 3.5 kcal/mol. With the purpose of increasing the accuracy, other fitting models should be taken into account.

It is worth noting that the factors of the substituent affecting the BDE, IE, and PA are not only the Hammett constant but also other substituent effect parameters.24 The contribution of substituent parameters on the same property change of a compound may be different and needs to be clarified. Based on the quantitative substituent effect parameters shown in Table S1, we demonstrate the contribution of the effects of the field/inductive constant σF,22 resonance constant σR,22 and excited-state substituent constant σCC,pex24,26 to the changes in BDE, IE, and PA. As a result, the correlation equations are expressed as follows.

For PhozNHs

2.2.2. 7
2.2.2. 8
2.2.2. 9

For PhtzNHs

2.2.2. 10
2.2.2. 11
2.2.2. 12

It can be seen from eqs 7 to 12that the contributions of the quantitative substituent effect parameters on the property change are explicitly split. For example, the resonance effect is stronger than the field/inductive effect on the BDE(N–H), and the excited-state effect also plays an important role in the PA values instead of only the Hammett constant. These obtained equations are helpful in distinguishing the contribution of substituent parameters from each other.

2.3. Substituent Effect on the Kinetic Behaviors of Hydrogen Atomic Transfer Reactions Between the Studied Compounds with HOO• in the Gas Phase

2.3.1. Evaluation of Hydrogen-Atom Transfer Reaction Gibbs Energies Between the Studied Compounds with the Free Radical HOO• in the Gas Phase

To proceed with the further calculations for examining the kinetic behaviors of the current systems, the spontaneity of the reactions between PhozNHs and PhtzNHs with HOO• in the gas phase is now evaluated by calculating the standard Gibbs energy change (ΔG°) of the respective reaction. The calculated results shown in Table 3 indicate that all relevant reactions are characterized by negative Gibbs energies of the reaction. Therefore, in the next section, all substituents are taken into account for establishing the potential energy profiles and then predicting the rate constants as well as the substituent effect on the kinetic behavior. The substituent effect on such a reaction spontaneity is also clear. The effect trend of the substituents on the changes in ΔG° of reactions is also clear. The higher the negative value of σp+ (i.e., stronger EDG), higher is the negative ΔG° value of the reaction.

Table 3. Calculated Gibbs Energies ΔG° of HAT Reactions of PhozNHs and PhtzNHs with HOO• in the Gas Phase (in kcal/mol, M05-2X-GD3/6-311++G(d,p) + ZPE).
substituent ΔG° of PhozNHs + HOO•
 ΔG° of PhtzNHs + HOO•
Y ΔG° ΔΔG° ΔG° ΔΔG°
H –10.0 0.0 –6.5 0.0
F –11.3 –1.3 –7.9 –1.4
Cl –10.8 –0.8 –7.0 –0.5
CH3 –11.7 –1.7 –8.3 –1.8
OCH3 –14.7 –4.7 –9.7 –3.2
NH2 –15.7 –5.7 –12.2 –5.7
CF3 –7.8 2.2 –5.4 1.1
CN –8.0 2.0 –4.9 1.6
NO2 –5.8 4.2 –3.6 2.9
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2.3.2. Substituent Effects on Thermochemical Parameters of Hydrogen-Atom Transfer Reactions

To get insights into the molecular mechanism of the radical scavenging (HOO•) via an H atom transfer process, the potential energy profiles of these reactions in the gas phase are established and shown in Figure 3a,b, indicating that from the reactants to the products, the reactant complex RC, transition structure TS, and product complex PC always exist along the reaction pathway for all substituents considered (details are given in Table S4 of the SI).

Figure 3.

Figure 3

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Schematic potential energy profiles illustrating the reaction paths of HOO● with (a) PhozNHs and (b) PhtzNHs in the gas phase (R: reagent, RC: precomplex; TS: transition state; PC: postcomplex; and P: Products). Energy values are obtained from M05-2X-GD3/6-311++G(d,p) + ZPE computations.

Concerning the RC species in Figure 3 and Table S4, the trend of the changes in the relative enthalpy induced by substituents is not clear-cut. In contrast, the change in the relative enthalpies of TS and PC with the substituent is consistent with the change in the BDE(N–H)s and IEs, as discussed above. The decrease and enhancement of these parameters correspond to the EDG and EWG, respectively. In cases of halogen atoms, the energy change is not significant and is within 1.0 kcal/mol. Based on the data shown in Tables S1 and S4, plots of both TS and PC values with the modified Hammett constants (σp+) are constructed and drawn, as shown in Figure 4a,b.

Figure 4.

Figure 4

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Correlation between the modified Hammett parameters and (a) TS energy barriers and (b) PC reaction energies in the reaction of HOO• with PhozNHs and PhtzNHs in the gas phase (at the M05-2X-GD3/6-311+G(d,p) + ZPE level).

Of course, the reaction energies, being the relative energy of products (P) with respect to reactants, are expected to follow the linear correlations with Hammett constants because they include PhozNHs or PhtzNHs radicals, a component of the BDE(N–H) values, and therefore they behave similarly as the BDE(N–H) values.

The linear equations between, on the one hand, Hammett constants and on the other hand, energy barriers (via TS) and reaction energies (via PC) can be established and are shown in Figure 4, with R2 being larger than 0.94, indicating a good correlation between them.

2.3.3. Kinetic Parameters for HAT Reactions Between PhozNH and PhtzNH with the Free Radical HOO• in the Gas Phase

The HAT process has been proved to be the most favorable antioxidant mechanism in both the gas phase and nonpolar solvents;29−31 therefore, in this section, we mainly focus on the HAT characteristics in the gas phase and benzene.

Based on the schematic potential energy profiles shown in Figure 3a,b and Table S4 of the SI, the kinetic constants, including the calculated activation free energies ΔG≠, tunneling corrections (κ), and rate constants kgas at 298.15 K in the gas phase are computed and shown in Table 4.

Table 4. Calculated ΔG≠, κ, and kgas for the HOO• Scavenging of the PhozNH and PhtzNH Derivatives in the Gas Phase (M05-2X/6-311++G(d,p) + ZPE).
  PhozNH + HOO•
 PhtzNH + HOO•
substituent ΔG≠ (kcal/mol) κ kgas (M–1·s–1) ΔG≠ (kcal/mol) κ kgas (M–1·s–1)
H 9.5 11.9 8.43 × 106 11.7 27.1 4.33 × 105
F 8.8 6.3 4.11 × 107 11.3 19.6 6.62 × 105
Cl 9.2 10.2 1.2 × 107 12.2 36.7 2.53 × 105
CH3 8.7 4.9 1.26 × 107 10.1 12.5 3.07 × 106
OCH3 6.2 3.6 7.28 × 108 9.6 8.6 5.63 × 106
NH2 5.9 2.3 1.39 × 109 8.1 6.8 5.49 × 107
CF3 11.8 48.6 7.22 × 105 12.8 244.1 7.28 × 105
CN 11.0 76.8 3.97 × 106 13.7 427.6 4.97 × 105
NO2 13.2 167.2 2.17 × 105 14.2 973.1 2.65 × 105
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The rate constants for the HOO• scavenging of the PhozNH derivatives in the gas phase are in the range of 2.17 × 105–1.39 × 109 M–1·s–1, while the ΔG≠ values for these reactions are in the range of 5.9–13.2 kcal/mol. For PhtzNH derivatives, the rate constants are calculated in the range of 2.53 × 105–5.49 × 107 M–1·s–1.

In terms of substituent effects, the EDGs make the velocity of HAT reactions faster, about two orders of magnitude, than the EWG. The obtained results summarized in Table 4 also indicate that with the strongest EWD group such as the NO2, the rate constants of the H-abstraction reactions with peroxyl radical are still larger than 105 M–1·s–1. The high values of kgas in HAT reactions with HOO• suggest that both PhozNH and PhtzNH systems can be considered as potential efficient antioxidants.

2.3.4. Solvent Effect on the Kinetic Behaviors of Hydrogen Atomic Transfer Reactions Between the Studied Compounds with HOO•

Because both PhozNH and PhtzNH and their derivatives are freely soluble in benzene and, in most of the cases, these systems are proposed to be used as an antioxidant or additives in unpolar media,9,14,32,33 we attempt to clarify the effect of benzene, one of typically apolar solvent, on the kinetic behaviors in their reactions with HOO• via the HAT mechanism.

As analyzed above, the M05-2X/6-311++G(d,p) + ZPE level also accurately predicts the BDE parameter in the benzene solvent; this indicates that the computational procedure of M05-2X/6-311++G(d,p) is reliable for constructing the PES for reactions of PhozNHs or PhtzNHs with HOO• in the benzene solvent. The detailed relative energies for all existing species including RC, TS, PC, and P relating to PES are shown in Table S5 of the SI. The obtained data indicate that in comparison with the gas phase, the TS barriers in benzene are higher, resulting in the lower rate constants. The trend of the substituent effects on the change in RC, TS, PS, and P values is similar to those in the gas phase. The linear relationships between Hammett parameters and the relative energies of TS and PC reaction energies are also plotted and are shown in Figure S1 of the SI.

In terms of the kinetic study, the activation Gibbs energies (ΔG≠) and rate constants (kbenzene) calculated using the Eyringpy program34 in the benzene solvent for these reactions are shown in Table 5. The required parameters for calculating the rate constant in benzene are shown in Tables S6 and S7 of the SI. The results in Table 5 indicate that the ΔG≠ values in benzene with the corresponding substituents are higher than those in the gas phase; the values are in the range of 1.3–3.7 kcal/mol for PhozNH and 2.7–3.8 for PhtzNHs. As a result, the rate constants in the benzene solution are 10–1000 times lower than those in the gas phase (see details in Table S8 of the SI). The most decreases of the rate constants are recognized for the EWG in both PhozNH and PhtzNH systems.

Table 5. Calculated ΔG≠ and kbenzene at 298.15 K in Benzene (M05-2X-GD3/6-311++G(d,p) + ZPE).
  PhozNH + HOO•
 PhtzNH + HOO•
substituent ΔG≠ (kcal/mol) kbenzene (M–1·s–1) ΔG≠ (kcal/mol) kbenzene (M–1·s–1)
H 10.8 8.6 × 105 14.4 5.4 × 103
F 11.6 1.4 × 105 14.3 4.5 × 103
Cl 12.2 8.8 × 104 15.4 1.5 × 103
CH3 11.1 2.4 × 105 12.6 4.7 × 104
OCH3 8.5 1.3 × 107 12.2 6.2 × 104
NH2 8.1 1.7 × 107 11.9 7.8 × 104
CF3 14.9 4.6 × 103 16.1 3.5 × 103
CN 14.6 1.3 × 104 17.4 7.2 × 102
NO2 16.9 6.4 × 102 18.0 6.4 × 102
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Obviously, the strong EDG increases the rate constants in the H-transferred reactions; therefore, the pronounced PhozNH and PhtzNH compounds with two strongest EDGs, namely, OCH3 and NH2, are chosen to evaluate the radical scavenging reactivity with a variety of well-known antioxidants; the detailed data are listed in Table 6, in which k/kref is the ratio of the rate constants between the studied compounds with the reference antioxidant.

Table 6. Rate Constants (M–1·s–1) of the HAT Reaction between the Selected Compounds with HOO•.
symbol reaction with HOO• kbenzene kA/kref kB/kref kC/kref kD/kref
PhozNH:            
A (Y = OCH3) A 1.3 × 107        
B (Y = NH2) B 1.7 × 107        
PhtzNH:            
C (Y = OCH3) C 6.2 × 104        
D (Y = NH2) D 7.8 × 104        
reference antioxidant compounds trolox35 3.40 × 103 3823 5000 18 23
ascorbic acid35 5.71 × 103 2277 2977 11 14
α-tocopherol36 1.6 × 105 ∼82 106 ∼0.4 ∼0.5
dopamine37 8.16 × 105 ∼16 ∼21 ∼0.08 ∼0.1
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In nonpolar media, the peroxyl radical scavenging activity of PhozNHs with two strongest substituted EDGs, namely, OCH3 and NH2, at 3 and 7 positions are found to be higher than those of the reference antioxidant compounds. For instance, the computed data show that when Y = NH2, the rate constant amounts to 1.7 × 107 M–1·s–1, being 5000, 2977, 106, and 21 times faster than those of Trolox,35 ascorbic acid,35 tocophenol,36 and dopamine,37 respectively. The peroxyl radical scavenging rate constants of 3,7-disubstituted phenothiazines + HOO• reactions, when Y = NH2 and OCH3, are 11–23 times as faster as compared with ascorbic acid and Trolox but slightly slower than those of α-tocopherol and dopamine. On the basis of this analysis, PhozNHs and PhtzNHs, when Y = OCH3 and NH2, can be considered as the potential radical scavenging antioxidants in apolar media. The antioxidant activities of PhozNH compounds are better than those of PhtzNH counterparts.

2.3.5. Correlation Between log k with Hammett Parameters

It is now of interest to explore whether there exists any relationship between modified Hammett parameters (σp+) with kinetics behaviors of PhozNH/PhtzNHs + HOO• reactions. In this situation, based on the Evans–Polanyi principle,38,39 log k is taken into account instead of the rate constants (k). Linear fitting between these values taken from Tables S1 and S8 is carried out and the obtained fitting graphs are shown in Figure 5.

Figure 5.

Figure 5

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Correlation between modified Hammett parameters with logk of HOO• reactions with (a) PhozNHs and (b) PhtzNHs.

In PhozNHs compounds, relatively good linear correlations are found between both log k and σp+ quantities in both the gas phase and the benzene solvent with R2 being 0.8960 and 0.8917. However, in PhtzNH compounds, the fitting linear equations are not tight; the corresponding R2 are only 0.7831 and 0.8234 in the gas phase and benzene, respectively. However, all of the obtained linear equations (shown in Figure 5) are useful for quantitatively predicting the kinetics behaviors of the same reactions when using different substituents at both 3 and 7 positions.

3. Concluding Remarks

In the present theoretical study, the bond dissociation energy (BDE), ionization energy (IE), and proton affinity (PA) values of the PhozNH and PhtzNH derivatives were calculated using the density functional theory (DFT) with the M05-2X functional in conjunction with the 6-311++G(d,p) basis set. Application of a restricted open-shell formalism for radical species produces more reliable BDE values, as compared to the experiment. Very good linear correlations were found between the BDE and IE values with the modified Hammett constants σp+ and between the PA values with the σp. In addition, to distinguish the contribution of substituent parameters from each other in the changes of BDE, IE, and PA values such as the resonance effect, field/inductive effect, and excited-state effect (σCC,pex), constants are also taken into account.

The radical scavenging of both PhozNH and PhtzNH derivatives via a hydrogen-atom transfer process in the gas phase was evaluated by thermodynamic and kinetic calculations. The kinetic behaviors in the HAT reactions with the free radical HOO• were studied based on the potential energy profiles and kinetic rate constants. Interestingly, very good correlations are found between the enthalpies for activation and reaction followed by the Evans–Polanyi principle.38,39 In the case of rate constants (k), the linear equations between log k and Hammett-modified parameters (σp+) are also obtained. This finding provides us a useful way of preliminarily estimating the antioxidant reactivity of a new derivative. The rate constants for both studied systems are larger than the limiting rate value of 105 M–1·s–1, reconfirming that both substituted phenoxazine and phenothiazine derivatives are promising candidates as efficient antioxidants for trapping radicals in the gas phase via the HAT mechanism.

4. Computational Methods

The structures of the phenoxazine, phenothiazine, and their 3,7-disubstituted derivatives considered (Figure 1) in the neutral state and their radical, radical cation, and anion forms are optimized using density functional theory (DFT) with the M05-2X functional and the d,p-polarization plus the diffuse functions 6-311++G(d,p) basis set. The unrestricted formalism is used for open-shell species. Their general structures are shown in Figure 6.

Figure 6.

Figure 6

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Optimized structures of (a) 3,7-disubstituted phenoxazines and (b) 3,7-disubstituted phenothiazines considered in neutral, radical cation, anion, and radical forms.

All thermochemical properties of both sets of PhozNHs and PhtzNHs derivatives are also calculated using the M05-2X/6-311++G(d,p) method. The accuracy of the combination of the 6-311++G(d,p) basis set with the M05-2X density functional was previously validated by comparing the calculated thermochemical parameters with the available experimental data.18,19 In general, the error margin of the computed values is expected to be at ±2.0 kcal/mol with respect to available experimental values, as discussed in the following section.

Parts of the potential energy surfaces are constructed based on the computed data obtained at the same level of theory but including the addition of dispersion interaction corrections based on the GD3 approximation for the complexes with the weak bonds40 (hereafter denoted as M05-2X-GD3).

All geometry optimizations, harmonic vibrational frequencies, and energy calculations are carried out using the Gaussian 09 program.41 Cartesian coordinates for all species in PhozNHs and PhtzNHs systems are shown in Tables S9–S12 of the SI.

Based on the potential energy profiles, the kinetic parameters in the gas phase are determined using the Eyringpy code.42,43 Rate constants (k) of the relevant H-abstraction reactions are computed following the conventional transition state theory and at standard conditions according to eq 13(44−49)

4. 13

where σ is the reaction symmetry number,50,51 κ is tunneling correction, which is calculated using an Eckart barrier,52kB is the Boltzmann constant, h is the Planck constant, and ΔG≠ is the Gibbs energy of activation.

In the benzene solvent, the TST rate constant is corrected including the diffusion-limit according to the Collins Kimball theory.34,53

Acknowledgments

This research is financially supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 104.06-2020.17 (P.C.N.).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.0c04144.

  • Modified Hammett, filed/inductive, and resonance and excited electron constants of para substituents; the fit of linear regression; calculated data for cross-validation; Cartesian coordinates and relative enthalpies of all species optimized at the M05-2X-GD3/6-311++G(d,p) level of theory; and data for rate constant calculations such as radius of the reactants (RADn), the reaction distance (RXD), and dynamic viscosity (Pa·s) of benzene (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao0c04144_si_001.pdf (1.8MB, pdf)

References

  1. Galano A.; Mazzone G.; Alvarez-Diduk R.; Marino T.; Alvarez-Idaboy J. R.; Russo N. Food antioxidants: chemical insights at the molecular level. Annu. Rev. Food Sci. Technol. 2016, 7, 335–352. 10.1146/annurev-food-041715-033206. [DOI] [PubMed] [Google Scholar]
  2. Thong N. M.; Vo Q. V.; Le Huyen T.; Van Bay M.; Dung N. N.; Thao P. T. T.; Nam P. C. Functionalization and antioxidant activity of polyaniline–fullerene hybrid nanomaterials: a theoretical investigation. RSC Adv. 2020, 10, 14595–14605. 10.1039/D0RA00903B. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Thong N. M.; Dao D. Q.; Ngo T. C.; Le Huyen T.; Nam P. C. Antioxidant activities of [60] fullerene derivatives from chalcone, flavone and flavanone: A ONIOM approach via H-atom and electron transfer mechanism. Chem. Phys. Lett. 2016, 652, 56–61. 10.1016/j.cplett.2016.04.036. [DOI] [Google Scholar]
  4. Boulebd H.; Khodja I. A.; Bay M. V.; Hoa N. T.; Mechler A.; Vo Q. V. Thermodynamic and Kinetic Studies of the Radical Scavenging Behavior of Hydralazine and Dihydralazine: Theoretical Insights. J. Phys. Chem. B 2020, 124, 4123–4131. 10.1021/acs.jpcb.0c02439. [DOI] [PubMed] [Google Scholar]
  5. Mark H. F.; Kroschwitz J. I.. Encyclopedia of Polymer Science and Engineering; Wiley, 1985. [Google Scholar]
  6. Kumar A.Antioxidants Applications and Global Markets; BCC Research, 2015.
  7. Valgimigli L.; Pratt D. A. Maximizing the reactivity of phenolic and aminic radical-trapping antioxidants: just add nitrogen!. Acc. Chem. Res. 2015, 48, 966–975. 10.1021/acs.accounts.5b00035. [DOI] [PubMed] [Google Scholar]
  8. Liu Z. Q.; Tang Y. Z.; Wu D. Antioxidant effects of phenothiazine, phenoxazine, and iminostilbene on free-radical-induced oxidation of linoleic acid and DNA. J. Phys. Org. Chem. 2009, 22, 1009–1014. 10.1002/poc.1554. [DOI] [Google Scholar]
  9. Fukuzumi K.; Ikeda N.; Egawa M. Phenothiazine derivatives as new antioxidants for the autoxidation of methyl linoleate and their reaction mechanisms. J. Am. Oil Chem. Soc. 1976, 53, 623–627. 10.1007/BF02586274. [DOI] [Google Scholar]
  10. Foti M. C.; Amorati R. Non-phenolic radical-trapping antioxidants. J. Pharm. Pharmacol. 2009, 61, 1435–1448. 10.1211/jpp.61.11.0002. [DOI] [PubMed] [Google Scholar]
  11. Gautam V.; Sharma M.; Samarth R.; Gautam N.; Kumar A.; Sharma I.; Gautam D. J. P. Synthesis of Some Substituted 10H-Phenothiazines, Ribofuranosides, and their Antioxidant Activity. Phosphorus, Sulfur Silicon Relat. Elem. 2007, 182, 1381–1392. 10.1080/10426500601161023. [DOI] [Google Scholar]
  12. Poliak P.; Vagánek A.; Lukeš V.; Klein E. Substitution and torsional effects on the energetics of homolytic N–H bond cleavage in diphenylamines. Polym. Degrad. Stab. 2015, 114, 37–44. 10.1016/j.polymdegradstab.2015.01.019. [DOI] [Google Scholar]
  13. Krygowski T. M.; Stępień B. T. Sigma-and pi-electron delocalization: focus on substituent effects. Chem. Rev. 2005, 105, 3482–3512. 10.1021/cr030081s. [DOI] [PubMed] [Google Scholar]
  14. Yamamura T.; Suzuki K.; Yamaguchi T.; Nishiyama T. Antioxidant activities of phenothiazines and related compounds: correlation between the antioxidant activities and dissociation energies of O–H or N–H bonds. Bull. Chem. Soc. Jpn. 1997, 70, 413–419. 10.1246/bcsj.70.413. [DOI] [Google Scholar]
  15. Ingold K. U.; Pratt D. A. Advances in radical-trapping antioxidant chemistry in the 21st century: a kinetics and mechanisms perspective. Chem. Rev. 2014, 114, 9022–9046. 10.1021/cr500226n. [DOI] [PubMed] [Google Scholar]
  16. Wright J. S.; Johnson E. R.; DiLabio G. A. Predicting the activity of phenolic antioxidants: theoretical method, analysis of substituent effects, and application to major families of antioxidants. J. Am. Chem. Soc. 2001, 123, 1173–1183. 10.1021/ja002455u. [DOI] [PubMed] [Google Scholar]
  17. Vo Q. V.; Nam P. C.; Bay M. V.; Thong N. M.; Mechler A.; Hieu L. T. A theoretical study of the radical scavenging activity of natural stilbenes. RSC Adv. 2019, 9, 42020–42028. 10.1039/C9RA08381B. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Luo Y.-R.Handbook of Bond Dissociation Energies in Organic Compounds; CRC Press, 2002. [Google Scholar]
  19. Linstrom P. J.; Mallard W. G. The NIST Chemistry WebBook: A chemical data resource on the internet. J. Chem. Eng. Data 2001, 46, 1059–1063. 10.1021/je000236i. [DOI] [Google Scholar]
  20. Lucarini M.; Pedrielli P.; Pedulli G. F.; Valgimigli L.; Gigmes D.; Tordo P. Bond dissociation energies of the N–H bond and rate constants for the reaction with alkyl, alkoxyl, and peroxyl radicals of phenothiazines and related compounds. J. Am. Chem. Soc. 1999, 121, 11546–11553. 10.1021/ja992904u. [DOI] [Google Scholar]
  21. Bordwell F.; Zhang X. M.; Cheng J. P. Bond dissociation energies of the nitrogen-hydrogen bonds in anilines and in the corresponding radical anions. Equilibrium acidities of aniline radical cations. J. Org. Chem. 1993, 58, 6410–6416. 10.1021/jo00075a041. [DOI] [Google Scholar]
  22. Hansch C.; Leo A.; Taft R. A survey of Hammett substituent constants and resonance and field parameters. Chem. Rev. 1991, 91, 165–195. 10.1021/cr00002a004. [DOI] [Google Scholar]
  23. Jiang X. -K. Establishment and Successful Application of the σJJ• Scale of Spin-Delocalization Substituent Constants. Acc. Chem. Res. 1997, 30, 283–289. 10.1021/ar950121h. [DOI] [Google Scholar]
  24. Cao C.; Wu Y. Recent progress in quantifying substituent effects. Sci. China: Chem. 2013, 56, 883–910. 10.1007/s11426-013-4890-0. [DOI] [Google Scholar]
  25. Cao C. -T.; Chen M.; Fang Z.; Au C.; Cao C. Relationship Investigation between C (sp2)–X and C (sp3)–X Bond Energies Based on Substituted Benzene and Methane. ACS Omega 2020, 5, 19304–19311. 10.1021/acsomega.0c02964. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Cao C. T.; Yuan H.; Zhu Q.; Cao C. Determining the excited-state substituent constants of ortho-substituents from 2, 4′-disubstituted stilbenes. J. Phys. Org. Chem. 2019, 32, e3962 10.1002/poc.3962. [DOI] [Google Scholar]
  27. Chandra A. K.; Uchimaru T. The OH bond dissociation energies of substituted phenols and proton affinities of substituted phenoxide ions: a DFT study. Int. J. Mol. Sci. 2002, 3, 407–422. 10.3390/i3040407. [DOI] [Google Scholar]
  28. Chandra A. K.; Nam P.-C.; Nguyen M. T. The S–H bond dissociation enthalpies and acidities of para and meta substituted thiophenols: a quantum chemical study. J. Phys. Chem. A 2003, 107, 9182–9188. 10.1021/jp035622w. [DOI] [Google Scholar]
  29. Litwinienko G.; Ingold K. Abnormal solvent effects on hydrogen atom abstraction. 2. Resolution of the curcumin antioxidant controversy. The role of sequential proton loss electron transfer. J. Org. Chem. 2004, 69, 5888–5896. 10.1021/jo049254j. [DOI] [PubMed] [Google Scholar]
  30. Stepanić V.; Matijašić M.; Horvat T.; Verbanac D.; Kučerová-Chlupáčová M.; Saso L.; Žarković N. Antioxidant Activities of Alkyl Substituted Pyrazine Derivatives of Chalcones—In Vitro and In Silico Study. Antioxidants 2019, 8, 90. 10.3390/antiox8040090. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Lee C. Y.; Sharma A.; Semenya J.; Anamoah C.; Chapman K. N.; Barone V. Computational Study of Ortho-Substituent Effects on Antioxidant Activities of Phenolic Dendritic Antioxidants. Antioxidants 2020, 9, 189. 10.3390/antiox9030189. [DOI] [PMC free article] [PubMed] [Google Scholar]
  32. Farmer L. A.; Haidasz E. A.; Griesser M.; Pratt D. A. Phenoxazine: a privileged scaffold for radical-trapping antioxidants. J. Org. Chem. 2017, 82, 10523–10536. 10.1021/acs.joc.7b02025. [DOI] [PubMed] [Google Scholar]
  33. Poon J.-F.; Pratt D. A. Recent insights on hydrogen atom transfer in the inhibition of hydrocarbon autoxidation. Acc. Chem. Res. 2018, 51, 1996–2005. 10.1021/acs.accounts.8b00251. [DOI] [PubMed] [Google Scholar]
  34. Dzib E.; Cabellos J. L.; Ortíz-Chi F.; Pan S.; Galano A.; Merino G.. Eyringpy 1.0.2; Cinvestav: Mérida, Yucatán, 2018.
  35. Alberto M. E.; Russo N.; Grand A.; Galano A. A physicochemical examination of the free radical scavenging activity of Trolox: mechanism, kinetics and influence of the environment. Phys. Chem. Chem. Phys. 2013, 15, 4642–4650. 10.1039/c3cp43319f. [DOI] [PubMed] [Google Scholar]
  36. Navarrete M.; Rangel C.; Espinosa-García J.; Corchado J. C. Theoretical study of the antioxidant activity of vitamin E: reactions of α-tocopherol with the hydroperoxy radical. J. Chem. Theory Comput. 2005, 1, 337–344. 10.1021/ct0498932. [DOI] [PubMed] [Google Scholar]
  37. Iuga C.; Alvarez-Idaboy J. R.; Vivier-Bunge A. ROS initiated oxidation of dopamine under oxidative stress conditions in aqueous and lipidic environments. J. Phys. Chem. B 2011, 115, 12234–12246. 10.1021/jp206347u. [DOI] [PMC free article] [PubMed] [Google Scholar]
  38. Evans M.; Polanyi M. On the introduction of thermodynamic variables into reaction kinetics. Trans. Faraday Soc. 1937, 33, 448–452. 10.1039/tf9373300448. [DOI] [Google Scholar]
  39. Chatgilialoglu C.; Studer A.. Encyclopedia of Radicals in Chemistry, Biology, and Materials; John Wiley & Sons Chichester: U.K., 2012; Vol. 2. [Google Scholar]
  40. Grimme S.; Antony J.; Ehrlich S.; Krieg H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104 10.1063/1.3382344. [DOI] [PubMed] [Google Scholar]
  41. Frisch M. J.; Trucks G. W.; Schlegel H. B.; Scuseria G. E.; Robb M. A.; Cheeseman J. R.; Scalmani G.; Barone V.; Mennucci B.; Petersson G. A.; Nakatsuji H.; Caricato M.; Li X.; Hratchian H. P.; Izmaylov A. F.; Bloino J.; Z G.; Sonnenberg J. L.; Hada M.; Ehara M.; Toyota K.; Fukuda R.; Hasegawa J.; Ishida M.; Nakajima T.; Honda Y.; Kitao O.; Nakai H.; Vreven T.; Montgomery J. A.; P J. E. Jr.; Ogliaro F.; Bearpark M.; Heyd J. J.; Brothers E.; Kudin K. N.; Staroverov V. N.; Keith T.; Kobayashi R.; Normand J.; Raghavachari K.; Rendell A.; Burant J. C.; Iyengar S. S.; Tomasi J.; Cossi M.; Rega N.; Millam J. M.; Klene M.; Knox J. E.; Cross J. B.; Bakken V.; Adamo C.; Jaramillo J.; Gomperts R.; Stratmann R. E.; Yazyev O.; Austin A. J.; Cammi R.; Pomelli C.; Ochterski J. W.; Martin R. L.; Morokuma K.; Zakrzewski V. G.; Voth G. A.; Salvador P.; Dannenberg J. J.; Dapprich S.; Daniels A. D.; Farkas O.; Foresman J. B.; Ortiz J. V.; Cioslowski J.; Fox D. J.. Gaussian 09, revision A.02; Gaussian, Inc.: Wallingford, CT, 2009.
  42. Dzib E.; Cabellos J. L.; Ortíz-Chi F.; Pan S.; Galano A.; Merino G. Eyringpy: A program for computing rate constants in the gas phase and in solution. Int. J. Quantum Chem. 2019, 119, e25686 10.1002/qua.25686. [DOI] [Google Scholar]
  43. Dzib E.; Cabellos J. L.; Ortiz-Chi F.; Pan S.; Galano A.; Merino G.. Eyringpy 1.0.2; Cinvestav: Mérida, Yucatán, 2018.
  44. Evans M. G.; Polanyi M. Some applications of the transition state method to the calculation of reaction velocities, especially in solution. Trans. Faraday Soc. 1935, 31, 875–894. 10.1039/tf9353100875. [DOI] [Google Scholar]
  45. Eyring H. The activated complex in chemical reactions. J. Chem. Phys. 1935, 3, 107–115. 10.1063/1.1749604. [DOI] [Google Scholar]
  46. Truhlar D. G.; Hase W. L.; Hynes J. T. Current status of transition-state theory. J. Phys. Chem. A 1983, 87, 2664–2682. 10.1021/j100238a003. [DOI] [Google Scholar]
  47. Furuncuoglu T.; Ugur I.; Degirmenci I.; Aviyente V. Role of chain transfer agents in free radical polymerization kinetics. Macromolecules 2010, 43, 1823–1835. 10.1021/ma902803p. [DOI] [Google Scholar]
  48. Vélez E.; Quijano J.; Notario R.; Pabón E.; Murillo J.; Leal J.; Zapata E.; Alarcón G. A computational study of stereospecifity in the thermal elimination reaction of menthyl benzoate in the gas phase. J. Phys. Org. Chem. 2009, 22, 971–977. 10.1002/poc.1547. [DOI] [Google Scholar]
  49. Vo Q. V.; Bay M. V.; Nam P. C.; Mechler A. Is Indolinonic Hydroxylamine a Promising Artificial Antioxidant?. J. Phys. Chem. B 2019, 123, 7777–7784. 10.1021/acs.jpcb.9b05160. [DOI] [PubMed] [Google Scholar]
  50. Pollak E.; Pechukas P. Symmetry numbers, not statistical factors, should be used in absolute rate theory and in Broensted relations. J. Am. Chem. Soc. 1978, 100, 2984–2991. 10.1021/ja00478a009. [DOI] [Google Scholar]
  51. Fernández-Ramos A.; Ellingson B. A.; Meana-Pañeda R.; Marques J. M.; Truhlar D. G. Symmetry numbers and chemical reaction rates. Theor. Chem. Acc. 2007, 118, 813–826. 10.1007/s00214-007-0328-0. [DOI] [Google Scholar]
  52. Eckart C. The penetration of a potential barrier by electrons. Phys. Rev. 1930, 35, 1303 10.1103/PhysRev.35.1303. [DOI] [Google Scholar]
  53. Collins F. C.; Kimball G. E. Diffusion-controlled reaction rates. J. Colloid Sci. 1949, 4, 425–437. 10.1016/0095-8522(49)90023-9. [DOI] [Google Scholar]

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