A Computational Study of the Mechanism and Kinetics of the 4-Methyl Aniline Reaction with OH Radicals

: In this study, the mechanism of the reaction between 4-methyl aniline and hydroxyl free radicals was computed using the M06-2X and CCSD(T) methods, along with the 6-311++G(3df,2p) basis set. The kinetics of the reaction were calculated utilizing the transition state theory and the microcanonical Rice–Ramsperger–Kassel–Marcus theory. The calculated results revealed that NH-C 6 H 4 - CH 3 was the key product of the system. The total rate coefficient of the system, k_ total = 2.04 × 10 − 18 T 2.07 exp[(11.2 kJ/mol)/RT] cm 3 /s, was found under the 300–2000 K interval, with P = 760 Torr. At the ambient conditions, the velocity of this reaction was about ten times larger than that of the reaction between C 6 H 5 CH 3 and hydroxyl free radicals, but it was smaller than the aniline + OH rate.


Introduction
The study of the atmospheric chemistry of organic compounds in the gas phase has attracted considerable interest as a specialized area of research.Due to its significance, particular emphasis is placed on studying the atmospheric interaction between the hydroxyl radical (OH) and organic compounds, particularly aromatic species [1,2].
4-methyl aniline, created from toluene, is mainly used as an intermediate for producing dyes, textiles, plastics, paper, medicines, conducting polymers, and agricultural pesticides [3,4].Because of its versatility in manufacturing many items, as stated, there is a growing demand for this species [5,6].Human activities, such as burning garbage, smoking, and fossil fuel combustion, along with natural events like forest fires and volcanic eruptions, are recognized sources of significant 4-methyl aniline emissions into the environment.Many test indicators have shown that 4-methyl aniline is present in the blood and urine of smokers and workers in air-polluted areas [7,8].Some studies have also shown that, if a person inhales a significant amount of 4-methyl aniline, urinary tract diseases can occur; in more severe cases, it can cause cancer or death [9,10].
Hydroxyl free radicals are known as tropospheric detergents; they can remove most of the volatile organic compounds in this layer [11,12].Therefore, the reaction of OH radicals with 4-methyl aniline has practical significance in terms of eliminating or minimizing the concentration of 4-methyl aniline in the atmosphere.In the troposphere, the concentration of hydroxyl radicals is relatively significant, standing at about two million molecules per cm 3 [13].Several investigations have indicated that the temperature and geometric structures of reactants impact the mechanisms of the reactions between aromatic compounds and hydroxyl radicals.in low-temperature regions, the OH addition mechanism in the aromatic cycle is dominant, contrary to the H abstraction mechanism at high-temperature ranges, for example [14 -16].
No research has been undertaken, either theoretically or experimentally, on the reaction between 4-methyl aniline and hydroxyl radicals.Thus, the data from the similar reactions of C 6 H 5 NH 2 and C 6 H 5 CH 3 with hydroxyl radicals were utilized for comparison.The C 6 H 5 NH 2 + OH reaction was implemented by various groups.For example, the experimental results of Atkinson and colleagues [17] demonstrated that, at room temperature, Physchem 2024, 4 147 the NH 2 hydrogen abstraction and the OH addition are favorable, with the measured rate coefficient being (1.18 ± 0.11) × 10 −10 cm 3 /s.This value agrees well with the laboratory numbers of Zetzsch and co-workers [18,19], being about (1.20 ± 0.24) × 10 −10 cm 3 /s.In the study of Nahas and colleagues [11], the rate constant of the C 6 H 5 NH 2 + OH system was found to be larger than the available experimental data [17][18][19], standing at about 4.4 × 10 −10 cm 3 /s.According to their findings, the abstraction of H from the amino group is significantly less favorable compared to the addition of OH to the aromatic ring.However, their result differs from the theoretical value for the reaction of aniline with a chloride atom, predicted by Chen and colleagues [20].In their study, the NH 2 hydrogen abstraction dominated compared to the addition of the Cl atom.The rate coefficient of the C 6 H 6 CH 3 + OH system was also determined by various research groups.At 300 K and 100 Torr(He), Fischer and co-workers [21] measured the rate constants of the reactions of benzene + OH and toluene + OH, with the respective values of 1.59 × 10 −12 and (6.11 ± 0.40) × 10 −12 cm 3 /s.At 304 K, Pitts and colleagues [2] measured the rate coefficients of specific aromatic substances, such as toluene, revealing a value of (4.15 ± 1.49) × 10 −12 cm 3 /s.In the range of 250-298 K, Wine and co-workers [22] studied the rate coefficients for the toluene + OH reaction and indicated that they are pressure-dependent.Additionally, at 299 K, Zetzch and colleagues [23] measured the rate coefficients of the OH + toluene reaction, finding a value of 0.2 × 10 −12 cm 3 /s for the abstraction reaction, whereas there was a measurement of (7.0 ± 2.1) × 10 −10 cm 3 /s for the addition reaction.Through computation, Truhlar and co-workers [24] indicated that the abstraction of hydrogen atoms from the methyl group contributes 30%.
To explore the loss of the 4-methyl aniline compound in the atmosphere under the influence of various factors, this present study aims to explore the mechanism and kinetics of the reaction between 4-methyl aniline and OH radicals across a broad range of temperatures (300−2000 K) and pressures (1−7600 Torr).

Computational Methods
In this study, the method M06-2X [25,26] and the basis set 6-311++G(3df,2p) [27] were used to calculate the frequencies of the title reaction.This method has been applied for several similar reaction systems [28,29].The vibrational frequencies of each substance calculated using the above method are the basis for distinguishing transition states from other substances such as intermediate states, reactants, and products.The intrinsic reaction coordinate (IRC) model [30] was also utilized to figure out the relationship between transition states and surrounding points.
The high-cost method known as CCSD(T) [31,32] was employed to compute singlepoint energies (E sp ) for each species on the potential energy surface (PES).Therefore, the total enery of each substance was the sum of E sp and zero-point vibrational energy (E zp ), in which E zp was scaled by a 0.971 factor [33][34][35].The reason to use the CCSD(T) method is that it gives very accurate results, with an error of only about 4 kJ•mol −1 [36,37].Furthermore, the accuracy of this method was also proved by the values of the T1 diagnostics, presented in Table S1 of the Supporting Information (ESI).The calculated results reveal that both the multireference characteristics and spin contamination are negligible.The copyrighted software, Gaussian version 16 [38], was used for the calculations in this present study.
To calculate rate the constants for the dominant reaction paths of the title reaction, we used the transition state theory (TST) [39] and the microcanonical Rice-Ramsperger-Kassel-Marcus (RRKM) theory [40,41].Two values, namely, the sum of state (SOS) and density of state (DOS), were calculated based on the activation energies, vibrational frequencies, and moments of inertia.In the process of the computing partition function, the hindered internal rotation (HIR) of the small moieties, including hydroxyl, amino, and methyl, was examined carefully.To solve the master equation and acquire the rate coefficients, dependent on temperature (T) and pressure (P), an energy grain size of 100 cm −1 was employed.The epsilon and sigma values for the bath gas and the adduct 4-methyl_aniline_OH used to the compute rate coefficients are 82 K and 3.74 Å [42] and 770 K and 9.2 Å [42], respectively.The standard form of the "exponential down" model [43] utilizes an average energy transfer per collision, denoted as <∆E down >, which equals 400 cm −1 .Several similar reactions, consisting of C 6 H 5 + NH 2 [44] and C 6 H 5 NH 2 + CH 3 [45], use this number as the input parameter for the calculation of rate coefficients.The calculated results are reliable, indicating that this value should be utilized in this study.To verify the reliability of the methods utilized in this study, some thermochemical parameters of the title reaction, such as the energies of enthalpy (∆Hº 298K ), Gibbs (∆Gº 298K ), and entropy (∆Sº 298K ), were also examined and compared with the data from the existing literature.The kinetics of the title reaction were computed by utilizing the software known as Chemrate 1.5.8 [46] and Mesmer 6.1 [47].

Results and Discussion
The reaction of 4-methyl aniline with the OH radical, comprising the optimized geometries of all stationary points on the PES, is illustrated in Figure S1 of the Supplementary Materials file.The energy values obtained at different levels (M06-2X and CCSD(T)) are presented in Table 1.The other parameters, such as frequencies, cartesian coordinates, and thermodynamics, are shown in Tables S2-S4 of the Supplementary Materials file, in which the thermochemical data shown in Table S4 indicate that many elementary reaction paths of the title reaction can occur quickly.

A. The addition of hydroxyl radicals
The addition of OH to the 4-methyl aniline can occur in four directions, as displayed in Figure 1.Among these, the addition of OH to the C-NH 2 carbon atom creates the adduct IS1 and the other additions to the locations of C 2 , C 3 , and C 4 generate the respective adducts, namely, IS2, IS3, and IS4.It can be seen from the PES that, at the first step, four addition paths proceed via the well CP1.From the well CP1, the adduct IS1 is formed when the reaction path climbs over the T0/1 transition state.At the location of T0/1, the OH moiety attacks the C 1 atom at a distance of 2.1 Å, where the C 1 -OH bond vibrates with a negative frequency of 961i cm −1 (see Table S3).Similarly, the adduct IS2 is produced when the reaction path overcomes the hilltop T0/2.It is evident that this transition state represents the highest point when compared to other addition-based transition states like T0/1, T0/3, and T0/4.At the location T0/2, the forming bond C 2 -OH is about 2 Å, which is the same as the C 4 -OH bond at the point T0/4.However, the negative frequency of the state T0/2 is higher than that of the T0/4 (439i versus 398i cm −1 ); thus, the C 2 -OH bond vibrates stronger than the C 4 -OH bond.In contrast to the IS2, the adduct IS3 can be formed more easily because the hilltop T0/3 of this reaction path is the lowest compared to T0/1, T0/2, and T0/4 (see Figure 1).The forming bond C 3 -OH of T0/3 vibrates weaker than the bonds C 1 -OH, C 2 -OH, and C 4 -OH due to its longer bond length and smaller negative frequency (~2.2 Å and ~262i cm −1 , respectively).The levels of the four adducts depicted on the PES indicate their high stability under typical conditions.While these adducts could potentially contribute to the formation of the final products PR2 or PR3, the reaction pathways involve exceptionally high transition states, which were not included in this investigation.
The addition of OH to the 4-methyl aniline can occur in four directions, as displayed in Figure 1.Among these, the addition of OH to the C-NH2 carbon atom creates the adduct IS1 and the other additions to the locations of C2, C3, and C4 generate the respective adducts, namely, IS2, IS3, and IS4.It can be seen from the PES that, at the first step, four addition paths proceed via the well CP1.From the well CP1, the adduct IS1 is formed when the reaction path climbs over the T0/1 transition state.At the location of T0/1, the OH moiety attacks the C1 atom at a distance of 2.1 Å, where the C1-OH bond vibrates with a negative frequency of 961i cm −1 (see Table S3).Similarly, the adduct IS2 is produced when the reaction path overcomes the hilltop T0/2.It is evident that this transition state represents the highest point when compared to other addition-based transition states like T0/1, T0/3, and T0/4.At the location T0/2, the forming bond C2-OH is about 2 Å, which is the same as the C4-OH bond at the point T0/4.However, the negative frequency of the state T0/2 is higher than that of the T0/4 (439i versus 398i cm −1 ); thus, the C2-OH bond vibrates stronger than the C4-OH bond.In contrast to the IS2, the adduct IS3 can be formed more easily because the hilltop T0/3 of this reaction path is the lowest compared to T0/1, T0/2, and T0/4 (see Figure 1).The forming bond C3-OH of T0/3 vibrates weaker than the bonds C1-OH, C2-OH, and C4-OH due to its longer bond length and smaller negative frequency (~2.2 Å and ~262i cm −1 , respectively).The levels of the four adducts depicted on the PES indicate their high stability under typical conditions.While these adducts could potentially contribute to the formation of the final products PR2 or PR3, the reaction pathways involve exceptionally high transition states, which were not included in this investigation.

B. The abstraction of hydrogen atoms
The PES of the reaction reveals that there were five abstraction paths, leading to five different products from PR1 to PR4, where the products PR4a and PR4b were produced when the reaction paths proceeded via the well CP2 and two tops of hills T0P4a and T0P4b.It should be noted that T0P4a and T0P4b have the same structures and energy

B. The abstraction of hydrogen atoms
The PES of the reaction reveals that there were five abstraction paths, leading to five different products from PR 1 to PR 4 , where the products PR 4a and PR 4b were produced when the reaction paths proceeded via the well CP2 and two tops of hills T0P4a and T0P4b.It should be noted that T0P4a and T0P4b have the same structures and energy levels (see Figure 1 and Figure S1).Therefore, these two paths should be considered as one reaction path.
As depicted in Figure 1, the H abstraction of the C 3 -H bond makes it necessary to surpass the top of hill T0P3, whose barrier height is 13 kJ/mol.The structure of this transition state shows that the lengths of the forming bond H-OH and the breaking bond C 3 -H are 1.2 and 1.31 Å, respectively.The negative frequency of the T0P3 is 1078i cm −1 , which is suitable for the abstraction of an H atom.In terms of energy, the final product PR 3 is higher than the remaining products of the title reaction.Nevertheless, it can be said that this reaction path still takes place quickly at room temperature.Similarly, the H-abstraction at the C 2 location can occur when the reaction path surpasses the hilltop of T0P2.At this position, the breaking bond C 2 -H and the forming bond H-OH were shown to be 1.195 and 1.317 Å, respectively.Their vibrations were characterized by a negative frequency of 1035i cm −1 , which was weaker than that of the T0P3 point.
Last but not least, the product PR 1 can be formed by the route going via the low hilltop T0P1 at the level of approximately 1 kJ/mol.It can be seen from the PES that this reaction route is the most exothermic, followed by the direction producing the PR 4 product (115 kJ/mol versus 111 kJ/mol, respectively).It is worth noting that, among the four H-abstraction directions mentioned above, the PR 4 direction is the most dominant, followed by the PR 1 direction.This proves that the H-abstraction from the amino group is more favorable than that from the methyl group.

Rate Constant Computations
As shown in Figure 1, eight reaction paths are considered in the kinetics calculation.The four addition paths going from the reactants to IS1, IS2, IS3, and IS4 are denoted as k 1 , k 2 , k 3 , and k 4 , respectively, while the four abstraction paths going from the reactants to the products PR1, PR2, PR3, and PR4 are denoted as k 5 , k 6 , k 7 , and k 8 , respectively.
In this part, the TST model was used to compute k 1 , k 2 , and k 3 , whereas the RRKM model was utilized to calculate the remaining rate coefficients k 4 -k 8 .The wide intervals of temperature (from 300 to 2000 K) and pressure (from 1 to 7600 Torr) were considered in these calculations.The calculated results are shown in Tables S5-S10 of the Supplementary Materials file and plotted in Figures 2-7.For the H-abstraction routes, the numbers of k5-k7 increase rapidly when the temperature goes from 300 K to 2000 K.They do not depend on pressures, as stated above.Among them, the k6 number increase most (~1.8 × 10 −16 -4.7 × 10 −12 cm 3 /s), followed by the k7 number (~2.3 × 10 −16 -2.1 × 10 −12 cm 3 /s).However, these two numbers are still smaller Generally, the rate constants of the addition reaction routes are P-and T-dependent, while those of the H-abstraction routes are T-dependent but P-independent.In the considtemperature range, the k -k numbers increase significantly, contrary to the decline in k 1 -k 4 numbers.Nevertheless, these numbers exhibit a minor rise with rising pressures under the given range.Most notable is k 8 , which is almost independent of pressure and temperature and is the most dominant number (see Tables S5-S9).
As shown in Tables S5-S9, the k 3 number is higher than the numbers of k 1 and k 4 under the low-temperature intervals.Conversely, under the high-temperature intervals, these numbers are approximately equal.In addition, in the high-temperature intervals, these values are found to be lower than the numbers of k 5 -k 7 .The value of k 2 is extremely T-and P-dependent.For example, at a pressure lower than or equal to 76 Torr, this value increases and then rapidly declines, in contrast to its increase at a pressure over 76 Torr.In comparison with the numbers of k 1 , k 3 , and k 4 , the k 2 number is smaller at any temperature or pressure.This is appropriate because the hilltop of T0/2 is remarkably higher than those of T0/1, T0/3, and T0/4 (cf.Figures 2-6).
For the H-abstraction routes, the numbers of k 5 -k 7 increase rapidly when the temperature goes from 300 K to 2000 K.They do depend on pressures, as stated above.Among them, the k 6 number increase most (~1.8 × 10 −16 -4.7 × 10 −12 cm 3 /s), by the k 7 number (~2.3 × 10 −16 -2.1 × 10 −12 cm 3 /s).However, these two numbers are still smaller than the k 5 values (~8.1 × 10 −14 -8.9 10 −12 cm 3 /s), that the PR 1 route is dominant compared to the routes of PR 2 and PR 3 .This result agrees well with the calculated energies, as shown on the PES.The total values, k_ total = sum(k 1 :k 8 ), are found to decrease under the low-temperature intervals, but increase gradually under the high-temperature ranges; for example, the 1 Torr value of k_ total reduces in the range of 2.19 × 10 −11 -8.69 × 10 −12 cm 3 /s with T = 300-700 K before going to 2.74 × 10 −11 cm 3 /s at 2000 K.At room temperature and 760 Torr pressure, k_ total = 2.16 × 10 −11 cm 3 /s, which is about ten times higher than that of the similar reaction, C 6 H 5 CH 3 + OH [21][22][23][24][25], but it is still lower than the total number of the reaction between C 6 H 5 NH 2 and OH radical [11,[17][18][19].This outcome indicates that the current reaction occurs at a faster rate than the C 6 H 5 CH 3 + OH reaction, but at a slower pace compared to the C 6 H 5 NH 2 + OH reaction.At 760 Torr and T = 300-2000K, by using the modified Arrhenius form, the total value is presented as k_ total = 2.04 × 10 −18 T 2.07 exp [11,200/(RT)] cm 3 /s.
Branching ratios, shown in Figure 7 and Table S10, reveal that the k 8 value of the route forming the product PR 4 is significantly dominant over the given temperature range.This value increases about 1.4 times in the 300-900 K interval, with a maximum product yield of over 70%, then decreases to well over 40% when the temperature reaches 2000 K.The contribution of the k 3 route over the 300-800 K range is about 34%-10%, whereas the contribution of the k 5 route, from 900 K to 2000 K, is from ~10% to ~32%.In the high-temperature regions, the k 3 contribution declines quickly, contrary to the rise in the k 5 route.The contributions of the routes k 4 and k 6 are also notable, in which the former contributes significantly at low temperatures, and the latter is significant at high temperatures.For the k 7 route, its product yield can go up to nearly 10% at temperatures over 2000 K, but is trivial at temperatures below 1400 K. Lastly, trivial contributions can be seen at the k 1 and k 2 routes, with a total product yield of less than 5%.These calculations demonstrate that the product PR 4 predominates over the specified temperature range and at 760 Torr, with the IS3 adduct prevailing at low temperatures and the product PR 1 doing so at high temperatures.

Conclusions
Through studying the reaction routes and the rate constants of the OH + 4-methyl aniline reaction, it can be concluded that the species NH-C 6 H 4 -CH 3 is the main product of the title reaction in the studied conditions of temperatures and pressures.This product contributes up to over 70% of the reaction, larger than two times of the IS3 adduct and the PR1 product.
Compared with the reactions of toluene and aniline with OH radicals at ambient conditions, the total rate constant of the title reaction is more significant than that of the former.Still, it is smaller than that of the latter.Therefore, it can be said that the rate of removal of organic compounds given above by OH radicals is in the following order: toluene < 4-methyl aniline < aniline.

Figure 1 .
Figure 1.The energies of the key paths of the title reaction are predicted by the CCSD(T) method.The units of energy are kJ/mol.

Figure 1 .
Figure 1.The energies of the key paths of the title reaction are predicted by the CCSD(T) method.The units of energy are kJ/mol.

Figure 2 .
Figure 2. Graph of the k 1 -k 8 values under the given temperature range and 1 Torr pressure.

Figure 2 .
Figure 2. Graph of the k1-k8 values under the given temperature range and 1 Torr pressure.

Figure 3 .
Figure 3. Graph of the k1-k8 values under the given temperature range and 7.6 Torr pressure.

Figure 3 . 7 Figure 4 .
Figure 3. Graph of the k 1 -k 8 values under the given temperature range and 7.6 Torr pressure.

Figure 4 ., 4 152Figure 4 .
Figure 4. Graph of the k 1 -k 8 values under the given temperature range and 76 Torr pressure.

Figure 5 .
Figure 5. Graph of the k1-k8 values under the given temperature range and 760 Torr pressure.

Figure 5 . 8 Figure 6 .
Figure 5. Graph of the k 1 -k 8 values under the given temperature range and 760 Torr pressure.

Figure 6 .
Figure 6.Graph of the k 1 -k 8 values under the given temperature range and 7600 Torr pressure.

Figure 6 .
Figure 6.Graph of the k1-k8 values under the given temperature range and 7600 Torr pressure.

Figure 7 .
Figure 7. Branching ratios of the k1-k8 numbers under the given temperature range and 760 Torr pressure.

Figure 7 .
Figure 7. Branching ratios of the k 1 -k 8 numbers under the given temperature range and 760 Torr pressure.

Table 1 .
Single-point energies, zero-point vibrational energies (ZPVE), and relative energies of all species of the title reaction at the two levels.