Can a single ammonia and water molecule enhance the formation of methanimine under tropospheric conditions?: kinetics of •CH2NH2 + O2 (+NH3/H2O)

The aminomethyl (•CH₂NH₂) radical is generated from the photo-oxidation of methylamine in the troposphere and is an important precursor for new particle formation. The effect of ammonia and water on the gas-phase formation of methanimine (CH₂NH) from the ^•CH₂NH₂ + O₂ reaction is not known. Therefore, in this study, the potential energy surfaces for ^•CH₂NH₂ + O₂ (+NH₃/H₂O) were constructed using ab initio//DFT, i.e., coupled-cluster theory (CCSD(T))//hybrid-density functional theory, i.e., M06-2X with the 6-311++G (3df, 3pd) basis set. The Rice−Ramsperger−Kassel−Marcus (RRKM)/master equation (ME) simulation with Eckart’s asymmetric tunneling was used to calculate the rate coefficients and branching fractions relevant to the troposphere. The results show 40% formation of CH₂NH at the low-pressure (<1 bar) and 100% formation of CH₂NH₂OO^• at the high-pressure limit (HPL) condition. When an ammonia molecule is introduced into the reaction, there is a slight increase in the formation of CH₂NH; however, when a water molecule is introduced into the reaction, the increase in the formation of CH₂NH was from 40% to ∼80%. The calculated rate coefficient for ^•CH₂NH₂ + O₂ (+NH₃) [1.9 × 10⁻²³ cm³ molecule⁻¹ s⁻¹] and for CH₂NH₂ + O₂ (+H₂O) [3.3 × 10^-17 cm³ molecule^-1 s^-1] is at least twelve and six order magnitudes smaller than those for free ^•CH₂NH₂ + O₂ (2 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹ at 298 K) reactions, respectively. Our result is consistent with that of previous experimental and theoretical analysis and in good agreement with its isoelectronic analogous reaction. The work also provides a clear understanding of the formation of tropospheric carcinogenic compounds, i.e., hydrogen cyanide (HCN).

1 Introduction

Methylamine is a simple organic nitrogen compound that is released into the atmosphere from a range of sources, for example, food industries, animal husbandry, marine sources, and biomass burning (Schade and Crutzen, 1995; Ge et al., 2011a; Ge et al., 2011b; Zhang et al., 2012; Almeida et al., 2013). Methylamine forms a particulate salt when reacting with acids such as H₂SO₄, HNO, and CH₃COOH; therefore, it plays a vital role in enhancing atmospheric cloud nucleation (Murphy et al., 2007; Lee and Wexler, 2013). The reaction of methylamine with various tropospheric oxidants such as O₃, OH, and NO₃ radicals leads to the formation of semi-volatile and non-volatile chemical species, consequently leading to the formation of secondary organic aerosols (Schade and Crutzen, 1995; Murphy et al., 2007; Ge et al., 2011a; Nielsen et al., 2012; Qiu and Zhang, 2013). Methylamine is also expected to be present in the interstellar medium (ISM), which leads to the formation of amino acids (Altwegg et al., 2016; Elsila et al., 2009; Gonza´lez et al., 2022). Although glycine (HO₂CCH₂NH₂) has not yet been identified in the ISM medium, it is detected in different comets (Elsila et al., 2009; Altwegg et al., 2016). Methylamines are also possible atmospheric precursors of hydrogen cyanide and nitrous oxide (N₂O) (Nielsen et al., 2012). N₂O is a greenhouse gas and the potential source of stratospheric NOx production. To know the significance of methylamine reactions in the two drastically different environments, several researchers have investigated their atmospheric significance and sinks in both the gas phase and solid phase (Schade and Crutzen, 1995; Ge et al., 2011a; Ge et al., 2011b; Almeida et al., 2013).

Once CH₃NH₂ is released into the Earth’s atmosphere, it reacts with the OH radical via the H-abstraction reaction, leading to the formation of a carbon-centered aminomethyl (^•CH₂NH₂) radical, which is observed as a major product, and nitrogen-centered methyl amino radical (CH₃NH^•), which is observed as a minor product (Figure 1) (Gonza´lez et al., 2022; Onel et al., 2014; Rissanen et al., 2014; Ashraful and Silva, 2020).

FIGURE 1

FIGURE 1. Photo-oxidation mechanism of methylamine (Gonza´lez et al., 2022; Onel et al., 2014; Rissanen et al., 2014; Ashraful and Silva, 2020).

As suggested in the previous studies (Gonza´lez et al., 2022; Onel et al., 2014; Rissanen et al., 2014; Ashraful and Silva, 2020), ^•CH₂NH₂ predominantly reacts with molecular oxygen (O₂), which can lead to the formation of methanimine (CH₂NH) and the hydroperoxy radical (HO₂) as major reaction products via a hydrogen atom transfer (HAT) mechanism (Gonza´lez et al., 2022; Onel et al., 2014; Rissanen et al., 2014; Ashraful and Silva, 2020). The chemical kinetics studies on the ^•CH₂NH₂ + O₂ reaction system have been investigated by various researcher groups (Masaki et al., 1995; Jansen et al., 1999; Rissanen et al., 2014; Ashraful and Silva, 2020; Glarborg et al., 2020). Jansen et al. (1999) used pulse radiolysis and UV-absorption detection to analyze the chemical kinetics of the ^•CH₂NH₂ + O₂ reaction at 298 K and 1 atm of SF₆ as a bath gas. Masaki et al. (1995) investigated the kinetics of the same reaction by employing the photoionization mass spectrometry technique at 298 K and a few torr pressure of N₂. Rissanen et al. (2014) used the laser flash photolysis technique in combination with photoionization mass spectrometry to determine the rate coefficients of the ^•CH₂NH₂ + O₂ reaction. They observed negative temperature-dependent rate coefficients from 267 K to 363 K, independent of the pressure between 0.5 Torr and 2.5 Torr (Rissanen et al., 2014). The reported rate coefficients fall in the range of (2–8) × 10^–11 cm³ molecule⁻¹ s^-1 (Rissanen et al., 2014; Mallick et al., 2018; Ashraful and Silva, 2020; Kumar et al., 2020). Rissanen et al. (2014) also performed quantum chemical calculations coupled with ME simulation to predict the product branching fractions. Their modeling results reproduce the experimentally observed negative temperature dependence and validated the production of CH₂NH under low-pressure conditions. Recently, a chemical kinetic model for the oxidation of methylamine has been characterized by Glarborg et al. (2020) and validated against the results obtained from shock tube experiments. In their work, the potential energy surface of several reactions was studied theoretically starting from the isomerization of CH₃NH and the reactions of CNHx (x = 3–5) molecules with O₂ using the quantum chemistry composite method. In this study, the rate coefficients for ^•CH₂NH₂ + O₂ were re-investigated at high-level quantum chemical calculations with similar statistical rate theories to validate the finding for the role of ammonia and water and molecules in the same reaction. To the best of our knowledge, the branching ratios and temperature- and pressure-dependent rate coefficients have not been available until now.

Concerning the gas-phase reactivity of ^•CH₂NH₂ toward O₂ in the role of ammonia and water, several studies in the past few years have proposed the role of different species such as H₂O, NH₃, formic acid, and CO₂ on important atmospheric reactions (Vöhringer-Martinez et al., 2007; Iuga et al., 2010; Buszek et al., 2012; Iuga et al., 2011; Thomsen et al., 2012; Jonas et al., 2013; Zhang et al., 2013; Zhang et al., 2014; Jara-Toro et al., 2017; Ali et al., 2018; Inaba, 2018; Mallick et al., 2018; Ali, 2019; Ali et al., 2019; Ali, 2020; Kumar et al., 2020; Wu et al., 2020; Zhang et al., 2020; Ali et al., 2021; Ali and Balaganesh, 2022; Ali et al., 2022; Dash and Ali, 2022). It is well-known that ammonia (NH₃) is highly alkaline and is one of the most common chemicals used in the agriculture sector, and as a fertilizer, it is the major source in the atmosphere. Ammonia is mainly produced industrially and exists naturally as a product of the decomposition of organic matter. It is also used as a refrigerant gas and in the production of plastics, textiles, dyes, explosives, and other chemicals. The emissions of NH₃ into the Earth’s atmosphere have been increasing over the last few decades. The change in NH₃ concentration has essential implications for air quality and the ecosystem. To ascertain the significant influence of NH₃ on many atmospheric reactions, several researchers have investigated the role of NH₃ on many important atmospheric reactions (Jonas et al., 2013; Mallick et al., 2018; Ali, 2019; Kumar et al., 2020; Zhang et al., 2020; Ali et al., 2021). To this end, it is essential to clearly understand the reaction between ^•CH₂NH₂ and O₂ in the presence of NH₃, given its similar catalytic efficiency to water.

Water vapor is an environmentally significant constituent of the Earth’s atmosphere. Numerous investigations have been carried out to determine the catalytic role of a single H₂O molecule in many atmospheric and combustion reaction systems (Vöhringer-Martinez et al., 2007; Iuga et al., 2010; Buszek et al., 2012; Iuga et al., 2011; Thomsen et al., 2012; Zhang et al., 2013; Zhang et al., 2014; Jara-Toro et al., 2017; Ali et al., 2018; Inaba, 2018; Ali et al., 2019; Ali, 2020; Wu et al., 2020; Ali and Balaganesh, 2022; Ali et al., 2022; Dash and Ali, 2022). These studies reveal that water-catalyzed reactions are energetically more favorable than other catalyzed reactions due to the formation of many hydrogen-bonded intermediates and transition states. However, water does not enhance the reaction’s rate coefficients under tropospheric conditions due to its high concentration and lower entropic contribution compared to a free reaction (Ali et al., 2019; Ali, 2020; Ali and Balaganesh, 2022; Dash and Ali, 2022).

In this paper, we have investigated the rate coefficients for the effect of NH₃ and H₂O molecules on the important atmospheric and combustion prototype reactions, i.e., ^•CH₂NH₂ + O₂, for the first time. Using the RRKM/ME simulation, the temperature- and pressure-dependent rate coefficients were calculated between 200 K and 400 K and pressure ranges of 0.0001–1000 atm. The role of enthalpy and entropy contributions on hydrogen-bonded species on the effect of ammonia and water on the ^•CH₂NH₂ + O₂ reaction has been discussed to understand the chemical kinetic behavior of these complexes. In these situations, we have been inspired to model a gas-phase ternary reaction system, ^•CH₂NH₂ ···O₂···X (X = NH₃, H₂O), where H₂O and NH₃ can act as catalysts (vide Infra). To assess the accuracy of the data provided in this work, we have compared the energies and re-calculated rate coefficients and compared them with the available literature data for ^•CH₂NH₂ + O₂ and its isoelectronic similar reaction, i.e., ^•CH₂OH + O₂ (Dash and Ali, 2022). We hope that this study will strengthen the chemical kinetic database for global modeling and provide a thorough understanding for further study on analogous reaction systems.

2 Theoretical and computational methodology

2.1 Quantum chemical calculations

All the electronic structure calculations were carried out with the Gaussian 09 suite of programs (Frisch, 2013). The stationary points on potential energy surfaces (PESs) for ^•CH₂NH₂ + O₂, ^•CH₂NH₂ + O₂ (+NH₃), and ^•CH₂NH₂ + O₂ (+H₂O) reactions were computed using the hybrid-density functional method, i.e., M06-2X (Zhao and Truhlar, 2008) with the Pople 6-311++G (3df, 3pd) basis set (Frisch et al., 1984) and tabulated in Supplementary Table S1. The M06-2X is a frequently used preeminent functional to investigate the non-covalent interactions of transition states, intermediates, and post-intermediates for investigating chemical systems that encounter hydrogen bonding. To add corrections from the van der Waals interaction on M06-2X (Zhao and Truhlar, 2008), the Grimme empirical dispersion “GD3” was used (Grimme et al., 2010). Normal modes of the vibrational frequency for each optimized species were carried out to obtain the zero-point energy (ZPE) and to calculate the rotational–vibrational partition functions. The transition state (TS) shows a single imaginary frequency, whereas reactants, intermediates, and products all show positive vibrational frequencies (see Supplementary Table S2). Intrinsic reaction coordinate (IRC) calculations (Fukui, 1981) were performed to confirm the identity of intermediates and post-intermediates for each TS. The IRC calculation was performed in both directions with the maxpoints=50 and the step size set to 3. The internal degrees of freedom of all species involved in the reaction were treated as harmonic oscillators and rigid rotor approximations, as suggested in previous studies for similar reaction systems (Ali et al., 2018; Dash and Ali, 2022). To improve the accuracy of energy, the single-point energy calculations were carried out at CCSD(T)/6-311++G (3df, 3dp)//M06-2X/6-311++G (3df, 3dp)+GD3 (Frisch et al., 1984; Raghavachari et al., 1989; Zhao and Truhlar, 2008). The result provides values that are accurate enough up to ∼1 kcal/mol, as validated in our previous studies (Ali et al., 2019; Ali, 2020; Ali and Balaganesh, 2022; Dash and Ali, 2022). To check the qualitative contribution of the single-reference wave function, we have carried out the T1 diagnostic calculation at CCSD(T)/6-311++G (3df, 3pd). The calculated T1 diagnostic was found to be ≤ 0.03, which is an acceptable range for a single reference wave function. To understand the spin contamination for each species, the spin expectation value <S²> was calculated and found to be in the range of ∼0.75–0.77, which indicates that spin contamination was negligible.

2.2 State-of-the-art kinetics calculations

All the kinetics calculations were carried out using a software tool in the MultiWell suite of the program (Barker, 2009; Barker, 2011; Barker, 2023). The “me” codes in MultiWell programs calculate the unimolecular rate coefficients k(E) based on the RRKM/master equation as follows (Forst, 2003):

$k\left(E\right)=\left[\frac{m^{\ne }}{m}\frac{{\sigma }_{ext}}{{\sigma }_{ext}^{\ne }}\right]\frac{g_e^{\ne }}{g_e}\frac{1}{h}\frac{G^{\ne }\left(E-E_{\mathrm{0,0}}\right)}{\rho \left(E\right)}.(1)$

To avoid repetition from the previous studies, the details of each term of the equation are given in Supplementary Material S1. To calculate temperature- and pressure-dependent rate coefficients and branching fractions, N₂ bath gases were used with an approximate value of the energy transfer process <ΔE > _down = 200 × (T/300)^0.85 cm⁻¹ (Goldsmith et al., 2012). The Lennard–Jones parameters for collider gases (N₂) εk_B, σ(N₂) = 3.74 Å, and ε/k_B(N₂) = 82 K were obtained from Hippler et al. (1983). The Lennard–Jones parameters of NH₂CH₂O₂ and NH₂CH₃O₂ were approximated based on Rissanen et al. (2014). The double arrays used in me simulations consisted of 1500 array elements with 10 cm^-1 energy grains using a quasi-continuum regime, which is evaluated up to 85,000 cm^-1. At each pressure and temperature value, ME simulations were carried out using the chemical activation energy distribution, which is appropriate for association reactions. The RRKM/ME simulations consisted of 10⁵ stochastic trials, each with a simulated time duration corresponding to an average of 100 collisions.

The pressure-dependent total rate coefficients $k^{bimol}\left(T,M\right)$ for ^•CH₂NH₂ + O₂ were calculated using (Ali, 2020; Dash and Ali, 2022)

$k^{bimol}\left(T,M\right)={\Gamma K}_{eq}\times k_{\infty }^{uni}\left(1-f_{{CH}_2{NH}_2+O_2}\right),(2)$

where ($\mathrm{\Gamma }$) is the quantum mechanical tunneling correction to the microcanonical rate coefficients k(E). $\mathrm{\Gamma }$ was implemented in the MultiWell master equation code, which is based on the 1-D Eckart asymmetric barrier. The k(E) calculated using the modified sums of states of the transition state reflect the tunneling effects. Tunneling was used to initialize the chemical activation distribution if both the “CHEMACT” and “TUN” keywords were selected. The $f_{{CH}_2{NH}_2+O_2}$ is the branching fraction (f) of the reaction going back to the reactants, and $k_{\infty }^{uni}$ is a high-pressure limit rate coefficient. The fall-off behavior of rate coefficients from (pressure = 1000 bar, P→∞) toward the low-pressure limit (p = 0.0001 bar, P→0) was considered.

For the barrierless reactions, i.e., ^•CH₂NH₂ + O₂→ CH₂NH₂OO, ^•CH₂NH₂ … H₂O + O₂→ CH₂NH₂OO … H₂O, ^•CH₂NH₂ … NH₃+O₂→^•CH₂NH₂OO … NH₃, the inverse Laplace transform (ILT) method was used. Since the rate coefficients for association reactions are usually weak and dependent on temperature, the activation energy for the recombination reaction was assumed to be equal to 0. As suggested in many similar reactions (Rissanen et al., 2014), this approach is good, and Arrhenius’s activation energy can be equal to the reaction critical energy (E₀). MultiWell input for ILT calls for only two parameters E₀ and A-factor. In this work, we use statistical rate theories, which do not account for non-statistical effects, such as slow intramolecular vibrational energy redistribution (IVR), as suggested by Ali et al. (2023).

The equilibrium constant (K_eq) for the formation of ^•CH₂NH₂ + O₂→ CH₂NH₂OO^•, ^•CH₂NH₂ … H₂O→CH₂NH₂OO … H₂O, ^•CH₂NH₂ … NH₃→^•CH₂NH₂OO … NH₃,^•CH₂NH₂ … H₂O + O₂→CH₂NH₂OO … H₂O and ^•CH₂NH₂ … NH₃+O₂→^•CH₂NH₂OO … NH₃ was calculated using the “THERMO” code as given: (Barker, 2009; Barker, 2011; Barker, 2023)

$K_{eq}=\frac{Q_{\mathit{INT}}}{Q_R}\mathit{exp}\left(-\frac{E_{\mathit{INT}}-E_R}{k_{B}T}\right).(3)$

The equilibrium constants ($K_{eq}$) for the formation of two-body and three-body complexes calculated by Eq. 3 are tabulated in Supplementary Tables S3, S4. The $Q_{\mathit{INT}}$ and $Q_R$ are total partition functions of the intermediates and reactants, respectively; $E_{\mathit{INT}}-E_R$ is the zero-point corrected energy difference between intermediates and reactants. The calculated rate coefficients in the high-pressure limit ($k_{\infty }$) were fitted to the modified Arrhenius expression $k_{\infty }\left(T\right)=A\times T^n\times \text{ex}p\left(\frac{-E_a}{RT}\right)$ in the temperature range of 200 K–400 K.

3 Results and discussion

3.1 Geometries and Energies

3.1.1 Reaction channels for ^•CH₂NH₂ + O₂

The optimized structures of intermediates and transition states are shown in Figure 2. The zero-point corrected PES for the ^•CH₂NH₂ + O₂ reaction is depicted in Figure 3, and enthalpies values are given in Table 1. In the current reaction system, the O₂ molecule attacks the radical carbon atom, which leads to the formation of the intermediate ^•OO-CH₂NH₂ (INT1). Several conformational isomers of INT1 were observed, and for simplicity, we have considered the lowest energy conformer in our calculation. The calculated stabilization energy for INT1 is −31.7 kcal mol^-1, which is in very good agreement with the reported values by Rissanen et al. (2014) and Zhang et al. (2020) This value is also in very good agreement with its isoelectronic reactions, i.e., the O₂ + ^•CH₂OH value (−31.9 kcal/mol) (Dash and Ali, 2022). The unpaired electron in INT1 resides at the terminal O-atom, which can be decomposed differently. The lowest energy channel is an isomerization process where the terminal O-atom attacks the H-atoms of the NH₂ group via five- and six-membered cyclic transition states (TS5 and TS1), leading to hydrogen-bonded five- and six-membered cyclic complexes, i.e., INT2 and QOOH, respectively. The calculated barrier heights for TS5 and TS1 are 21.9 and 36.1 kcal mol^-1, respectively, with respect to INT1, indicating that the isomerization reaction going through TS5, leading to the formation of INT2, is energetically more favorable than that going through TS1 to QOOH. Supplementary Figure S1 provides an IRC scan that confirms the connectivity of TS5 with INT2 and CH₂NH + HO₂ at the M06-2X/6-311++G (3df, 3pd). It is noted that the influence of the formation of hydrogen-bonded cyclic complexes may change the energetics and kinetics of the reaction system. In INT2, two strong hydrogen bonds are formed between the H-atom of the HO₂ and the N-atom of the CH₂NH (1.72 Å) and O-atom of the HO₂ radical and the H-atom of the CH₂NH (2.55 Å), which leads to the formation of a stable six-membered ring planar cyclic structure. In QOOH, a five-membered ring cyclic structure with one hydrogen bond is formed between the terminal O and H-atoms (2.47 Å). Therefore, INT2 is energetically 6.6 kcal mol^-1 more stable than QOOH. QOOH can further dissociate via TS2 and TS4 to form HO₂ + CH₂NH and OH + OCH₂NH, respectively. Because the barrier height for the formation of QOOH is very high, the formation of CH₂NH and OCH₂NH via QOOH may be negligible under tropospheric conditions. The terminal O-atom of INT1 can also attack the H-atom of a nearby C-atom, leading to the formation of a hydrogen-bonded six-membered cyclic intermediate, INT3, via a four-membered ring transition state (TS3) and subsequently dissociating to form OH + NH₂CHO. In INT3, two strong hydrogen bonds are formed between the H-atom of the OH radical and the O-atom of the NH₂CHO (1.91 Å) and the O-atom of the OH radical and the H-atom of the NH₂CHO (2.16 Å). INT3 is energetically the most stable structure in the PES, with a stabilization energy of −78.9 kcal mol^-1 from the reactants. The barrier height of this reaction channel is 41 kcal mol^-1, which is 20 kcal mol^-1 higher than that of the TS5 and may not contribute to the overall reaction kinetics (vide infra).

FIGURE 2

FIGURE 2. Structural and geometrical changes during the ^•CH₂NH₂ + O₂ reaction calculated using M06-2X/6-311++G (3df, 3pd).

FIGURE 3

FIGURE 3. Potential energy surface for the ^•CH₂NH₂ + O₂ reaction obtained using CCSD(T)/6-311++G (3df, 3pd)//M06-2X/6-311++G (3df, 3pd). The energies shown in the figure include the zero-point energy.

TABLE 1

TABLE 1. Comparison of enthalpies (in kcal mol^-1) of each species for the ^•CH₂NH₂ + O₂ reaction with those found in previous studies and its isoelectronic analogs.

The other reaction channel, such as the conversion from QOOH to INT3 via H-atom shift (C to N) through a three-membered transition state, TS6 (41 kcal mol⁻¹), is expected to have a negligible impact on the total rate coefficient due to its high energy barriers.

The enthalpies of reaction (ΔH_rxn (0 K) for ^•CH₂NH₂ + O₂ → CH₂NH + ^•HO₂ (−10.9 kcal mol^-1) are in very good agreement with those found in the most accurate active thermochemical database (ATcT) (−11.42 kcal mol^-1) (Ruscic et al., 2004; Ruscic and Bross, 2020) and in good agreement with the theoretically calculated value in Rissanen et al. (2014) (−12.2 kcal mol^-1). The computed PES for the ^•CH₂NH₂ + O₂ reaction is also consistent with its isoelectronic analogous reaction system, i.e., ^•CH₂OH + O₂ reported by Dash and Ali (2022) using CCSD(T)//ωB97XD/6-311++G (3df, 3pd) level of theory. The enthalpy values obtained in their calculations are also given in Table 1. The reaction energies for CH₃NH^• + O₂ → CH₂NH + HO₂ (−17.3 kcal/mol) are also calculated and found to be in very good agreement with that in the ATcT (−17.9 kcal/mol) (Ruscic et al., 2004; Ruscic and Bross, 2020). The energies obtained for most of the structures of the ^•CH₂OH + O₂ system (Ali, 2020) along the reaction paths are very close to those of the current system, indicating the reliability of the data presented here. However, the barrier heights for the isomerization pathways Int-1→TS-1 (−7.4 kcal/mol)→QOOH and Int-1 →TS-5 (−18.5 kcal/mol) Int-2 in the CH₂OH + O₂ system (Dash and Ali, 2022) are quite low and more stable compared to those in the same pathways in the current system with respect to the reactant’s energy (Table 1). Moreover, the barrier height for the reaction proceeding from HO···OCH₂O to OCH₂O + OH (Dash and Ali, 2022) is 24 kcal/mol (TS-4), and the stabilization energy for the products is −15 kcal/mol, whereas in the current system, the corresponding energies are 8.3 and 12.3 kcal/mol less stable than the former ones, respectively. These differences in barrier energies can affect the overall rate coefficients between the two systems.

3.1.2 Role of the ammonia molecule on ^•CH₂NH₂ + O₂

When a single ammonia molecule is introduced in ^•CH₂NH₂ + O₂, the simultaneous collision between ^•CH₂NH₂, O₂, and NH₃ is very unlikely to occur; therefore, the probability of a trimolecular reaction is very small under real conditions. Hence, the first step is the formation of a CH₂NH₂···NH₃ complex, followed by collision with O₂. The CH₂NH₂···NH₃ complex (−2.2 kcal/mol) is assumed to be more important than CH₂NH₂···O₂ and NH₃···O₂ due to its lower binding energy (<1 kcal/mol). As discussed in our previous work, we have also used a similar approach for ammonia-assisted reactions (Ali et al., 2019; Ali, 2020; Ali and Balaganesh, 2022; Dash and Ali, 2022). The geometrical changes in ammonia-assisted intermediates and transition states are shown in Figure 4, and the zero-point corrected PES for the ammonia-assisted ^•CH₂NH₂ + O₂ reaction is given in Figure 5. The energy of all the stationary points, i.e., reactants, intermediates (INTs), and transition states, is tabulated in Table 2.

FIGURE 4

FIGURE 4. Structural and geometrical changes for the ammonia-assisted ^•CH₂NH₂ + O₂ reaction calculated using M06-2X/6–311++G (3df, 3pd).

FIGURE 5

FIGURE 5. Potential energy surface for the role of ammonia on the ^•CH₂NH₂ + O₂ reaction obtained using CCSD(T)/6-311++G (3df, 3pd)//M06-2X/6-311++G (3df, 3pd). The energies shown in the figure include the zero-point energy.

TABLE 2

TABLE 2. Enthalpies (in kcal mol^-1) and entropies (in cal K⁻¹ mol^-1) due to the effect of NH₃ on each species involved for the ^•CH₂NH₂ + O₂ reaction.

Figure 5 shows that the effect of the ammonia reaction proceeds via similar reaction pathways as a free reaction. For simplicity, only the most stable structures are shown in the PES. As shown in Figure 5, O₂ attacks the bimolecular complex ^•CH₂NH₂···NH₃ to form a trimolecular hydrogen-bonded complex (INT1n) (Figure 4), whose stabilization energy is −36.1 kcal mol^-1. The resulting ammonia-assisted intermediate (INT1n) is 4.4 kcal mol^-1 more stable than the corresponding ammonia-free intermediate, i.e., INT1. This is due to the formation of strong hydrogen bonds between the terminal O-atom of H₂NCH₂OO and one of the H-atoms of NH₃ (2.20 Å) and the H-atom of H₂NCH₂OO (2.08 Å) with the N-atom of NH₃, whereas no such effect is observed in INT1. On the other hand, Table 2 shows that INT1 is entropically more favorable than INT1n with respect to reactants. This is due to the fact that the hydrogen-bonded complex decreases the entropy of the system. Similar to uncatalyzed reaction pathways, the terminal O-atom intra-molecularly attacks the H-atoms in the NH₂ group in the presence of NH₃, leading to the formation of INT2n and QOOH-n via five-membered cyclic transition states (TS5n/TS7n and TS1n, respectively). The difference in the barrier heights between two isomeric transition states, TS5n and TS7n, is 2.1 kcal mol^-1. TS5n seems to be more stable than TS7n because, in the case of TS5n, all three hydrogen atoms of ammonia face toward the molecular center, leading to the formation of a six-membered ring hydrogen-bonded cyclic structure, whereas in the case of TS7n, hydrogen atoms of ammonia are away from the molecular center, leading to the formation of a similar six-membered ring hydrogen-bonded cyclic structure. Entropy data also support that TS5n is more disordered than TS7n.

Supplementary Figure S2 provides an IRC scan at the same level that confirms that TS5n bridges the OCH₂C(O)OOH radical (INT2n) and CH₂NH + HO₂ +NH₃. The IRC scan confirms that the only stationary point between INT2h and the trimolecular products is that associated. The barrier height of TS1n is 2.5 kcal mol^-1 lower than that of the corresponding ammonia-free transition state TS1. This is due to the formation of two strong hydrogen bonds (H-atoms of ammonia with N and O atoms of the cyclic ring) in TS1n (1.93 and 2.14 Å). On the other hand, the barrier height of TS5n is almost similar to that of TS5, although hydrogen bonds are present in TS5n. The differences in the barrier height can be explained by the formation of two adjacent cyclic ring structures (five- and six-membered), as aforementioned in TS5n, making it sterically hindered compared to only one ring structure in TS5. The stabilization energies of ammonia-assisted QOOH and INT2 are calculated to be −23.3 and −25.5 kcal mol^-1, respectively, which are 8.4 and 4.1 kcal mol^-1 lower than those of the corresponding free-ammonia structures. This can be explained similarly by comparing the presence of hydrogen bonds in the respective structures. In QOOH-n, the formation of two strong hydrogen bonds between the H-atom of ammonia with N atom QOOH (2.26 Å) and N atom NH₃ and terminal H atom of QOOH (1.76 Å) leads to a seven-membered ring-like structure rather than only one hydrogen bond in the case of free QOOH. Similarly, the stability of INT2n can be explained by the formation of an eight-membered ring with three hydrogen bonds, H of HO₂ and N of CH₂NH (1.64 Å), O of HO₂ and N of NH₃ (2.1 Å), and H of CH₂NH and N of NH₃ (2.24 Å) compared to a six-membered ring with two hydrogen bonds in the case of INT2. On the other hand, the structures of QOOH-n and INT2n are entropically less favorable compared to those of uncatalyzed QOOH and INT2n.

QOOH-n further dissociates to INT2n (via TS2n) and INT3n (via TS6n) and then subsequently forms HO₂+CH₂NH + NH₃ and OH + OCH₂NH + NH₃ via TS4n and OH + NH₂CHO + NH₃. INT2n and INT3n are eight-membered ring hydrogen-bonded structures, and their stabilization energies are 4.1 kcal mol^-1 and 7.4 of kcal mol^-1 lower than those of the corresponding uncatalyzed intermediates. Ammonia-assisted intermediates are more stable than ammonia-free ones because of the formation of an eight-membered ring structure with three strong hydrogen bonds between HO₂···NH₃ (2.1 Å), NH₃···CH₂NH (2.24 Å), and HO₂···CH₂NH (1.64 Å) in INT2n and OH···NH₃ (2.04 Å), NH₃···NH₂CHO (1.87 Å), and HO···NH₂CHO (1.72 Å) in INT3n. The barrier heights of TS2n (−5.6 kcal mol^-1), TS3n (2.5 kcal mol^-1), TS4n (9.7 kcal mol^-1), and TS6n (24.2 kcal mol^-1) were also consistently lower than those of the corresponding ammonia-free transition states due to similar hydrogen bonding interactions. Overall, the reaction in the presence of an ammonia-assisted intermediate is thermodynamically more favorable than the free reaction, and vice versa entropically.

3.1.3 Role of the water molecule on ^•CH₂NH₂ + O₂

As previously discussed in the case of ammonia reactions, we have also employed a similar approach for water reactions. When a single H₂O molecule is added to ^•CH₂NH₂ + O₂, the first step is the formation of a CH₂NH₂···H₂O complex, followed by collision with O₂. The CH₂NH₂···H₂O (-2.7 kcal/mol) is assumed to be more important than CH₂NH₂···O₂ and H₂O···O₂ (<1 kcal/mol) due to lower binding energy. The geometrical changes in water-assisted intermediates and transition states are shown in Figure 6 and the Cartesian coordinates of all the optimized geometries are given in Supplementary Table S1.

FIGURE 6

FIGURE 6. Optimized structures of water-assisted intermediates and transition states were obtained using M06-2X/6-311++G (3df, 3pd).

The zero-point-corrected PES for the water-assisted ^•CH₂NH₂ + O₂ reaction is given in Figure 7, and the energy of all the stationary points, i.e., reactants, INTs, and TSs, is tabulated in Table 3. As shown in Figure 6 and Figure 7, the O₂ molecule attacks the bimolecular complex ^•CH₂NH₂···H₂O to form a trimolecular hydrogen-bonded complex (INT1h) with a stabilization energy of −36.1 kcal mol^-1. The INT1h is 4.4 kcal mol^-1 lower than that of the water-free intermediate (INT1) and identical to the energy of ammonia-assisted INT1n. The result indicates water- and ammonia-assisted reactions are energetically more favorable than free reactions.

FIGURE 7

FIGURE 7. Potential energy surface for the role of water on the ^•CH₂NH₂ + O₂ reaction obtained using CCSD(T)/6-311++G (3df, 3pd)//M06-2X/6-311++G (3df, 3pd). The energies shown in the figure include the zero-point correction.

TABLE 3

TABLE 3. Enthalpies (in kcal mol^-1) and entropies (in cal K⁻¹ mol^-1) due to the effect of H₂O on each species involved for the ^•CH₂NH₂ + O₂ reaction.

In INT1h, two strong hydrogen bonds are observed between the terminal O-atom of H₂NCH₂OO and one of the H-atoms of H₂O (1.91 Å) and O-atom H₂O and terminal H-atom H₂NCH₂OO (2.12 Å) (see Figure 6). On the other hand, Table 3 and Table 1 show that INT1h is entropically least favored than INT1n and INT1. Similar to the free reaction, the terminal O-atom of INT1h intra-molecularly attacks the H-atoms in the NH₂ group, leading to the formation of cyclic structures, i.e., INT2h and QOOH-h, via five-membered cyclic transition states, i.e., TS5h and TS1h, respectively. The barrier heights of TS5h and TS1h are 2 kcal mol^-1 and 3 kcal mol^-1 lower than those of water-free transition states TS5 and TS1, respectively. In a similar manner, TS5h and TS1h are 1.8 kcal mol^-1 and 0.4 kcal mol^-1 lower than TS5n and TS1n, respectively. These differences in barrier heights indicate that water-assisted transition states are energetically more stable than ammonia-assisted and water-free species. The stabilization energies of water-assisted QOOH-h and INT2h are calculated to be −22.3 kcal mol^-1 and −27.1 kcal mol^-1, which are 7.8 kcal mol^-1 and 5.7 kcal mol^-1 lower than those of the corresponding free structures. This can be understood by comparing the presence of hydrogen bonds in the respective structures. Supplementary Figure S3 provides an IRC scan at the same level that confirms TS5h bridges the OCH₂C(O)OOH radical (INT2h) and CH₂NH + H₂O + HO₂ products. The IRC scan confirms that the only stationary point between INT2h and the trimolecular products is that associated. In QOOH-h, the formation of two strong hydrogen bonds between the H-atom of water with the N atom of QOOH (1.95 Å) and the O atom of H₂O and the terminal H atom of QOOH (1.82 Å) led to the formation of a seven-membered ring-like structure. Similarly, the stability of INT2h can be found by the formation of an eight-membered cyclic ring with three hydrogen bonds, H of HO₂ and N of CH₂NH (1.65 Å), O of HO₂ and H of H₂O (1.87 Å), and H of CH₂NH and O of H₂O (2.13 Å), which are compared to that of a six-membered ring with two hydrogen bonds, as indicated in the case of INT2. Between water- and ammonia-catalyzed QOOH and INT2, QOOH-n is more stable than QOOH-h and INT2h is more stable than INT2n.

In general, the water-free pathways are entropically more favorable than water-free ones. The QOOH further dissociates to INT2h (via TS2h) and INT3h (via TS6h) and then subsequently forms HO₂+ CH₂NH + H₂O, OH + OCH₂NH + H₂O via TS4h, and OH + NH₂CHO + H₂O. In general, the water-assisted reaction channels are thermodynamically more favorable and entropically less favorable than the free reaction. It is also clear from Table 3 that all other pathways are thermodynamically less important compared to R + O₂→INT1h→TS5h→INT2h→ CH₂NH + HO₂+H₂O, whose barrier height is the lowest with respect to reactants. Therefore, the other reaction channels may have less contribution under tropospheric conditions.

3.2 Kinetics

3.2.1 Rate coefficients for the ^•CH₂NH₂ + O₂ reaction

To obtain the rate coefficients for ^•CH₂NH₂ + O₂ in temperatures between 200 K and 400 K and pressures from 0.000001 bar to 1000 bar, the RRKM/ME simulation has been used. The rate coefficients as a function of the temperature at 1 bar pressure are shown in Figure 8. The rate coefficients for the formation of O₂-CH₂NH and CH₂NH are observed to be pressure-dependent and negative temperature-dependent. This result is consistent with that of the previous reports by Rissanen et al. (2014) and a similar reaction system, i.e., ^•CH₂OH + O₂ (Dash and Ali, 2022). The calculated rate coefficient at 300 K (1.6 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹) is a factor of ∼2 lower than the experimentally measured ones (3.2 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹) (Rissanen et al., 2014). The calculated value is in good agreement with the lower temperature range <250 K when the positive error is considered. In light of the expected errors in computed thermochemistry, which may be up to 1 kcal/mol, we believe that this level of accuracy is sufficient for these purposes. A recent study by Ali et al. (2023) indicates that the barrier heights of similar reactions are very sensitive to quantum chemical calculations. The computed rate coefficients are compared with previously reported values and also with its isoelectronic analogous reaction system, i.e., ^•CH₂OH + O₂ (see Figure 8) (Dash and Ali, 2022). The calculated values at 300 K are a factor of 2 lower than the theoretically calculated values (Dash and Ali, 2022). The presence of the N atom in CH₂NH and the O atom ^•CH₂OH can explain this, leading to the development of various chemical kinetics conclusions.

FIGURE 8

FIGURE 8. Rate coefficients for the ^•CH₂NH₂ +O₂ reaction at 1 bar pressure.

Figure 9 reports the rate coefficients in the fall-off regions for the ^•CH₂NH₂ + O₂ reaction at different temperatures. The rate coefficients increase as pressure increases, and the HPL condition is observed at ∼100 bar. As shown in Figure 9, the largest difference between the two limits occurs at about 250 K, which reaches a factor of 2. However, at 200 K, the difference between the two regimes is about a factor of 2. To provide more detailed insights, the relative branching fractions of these channels were determined at 200 K, 300 K, and 400 K and shown in Supplementary Figure S4. For simplicity, the branching fraction at different pressures and at 300 K is shown in Figure 10. At all temperatures and pressures, the branching fractions of QOOH are almost negligible; therefore, they are not shown in Figure 10. The branching fraction for the formation CH₂NH/HO₂ contributes 40% at 300 K and increases as temperature increases to 400 K. The formation of CH₂NH decreases to 0% as pressure increases to 100 bar. At the same time, the formation of CH₂NH₂OO increases as pressure increases to 100 bar (100%). The plot shows that backward reaction to regenerate reactants is prominent at <0.01 bar. These results are also consistent with the previously reported branching ratio by Rissanen et al. (2014). At all the pressure rates, it is more advantageous to lose HO₂ via the formation of CH₂NH rather than through OH loss via formamide formation due to an energetically favorable pathway (see Figure 10). As temperature increases from 300 K to 400 K, the product branching ratio increases (see Supplementary Figure S4). The result is due to the fact that the relevant stationary points on the respective potential energy surfaces have a dominant entropy factor over the enthalpy factor.

FIGURE 9

FIGURE 9. Total rate coefficients as a function in the fall-off regions for the ^•CH₂NH₂ +O₂ reaction.

FIGURE 10

FIGURE 10. Pressure-dependent branching fractions for the ^•CH₂NH + O₂ reaction at 300 K.

3.2.2 Rate coefficients for ^•CH₂NH₂+O₂ (+NH₃)

As discussed in the previous section, only the entry channel ^•CH₂NH ···NH₃ + O₂ is considered for the rate coefficient calculations.

${\text{CH}}_2{\text{NH}}_2+{\mathrm{O}}_2+{\text{NH}}_3\underset{{\mathrm{k}}_{-1\mathrm{n}}}{\overset{{\mathrm{k}}_{1\mathrm{n}}}{\rightleftharpoons }}{\text{CH}}_2{\text{NH}}_2---{\text{NH}}_3+{\mathrm{O}}_2\underset{{\mathrm{k}}_{-2\mathrm{n}}}{\overset{{\mathrm{k}}_{2\mathrm{n}}}{\rightleftharpoons }}{\mathrm{O}}_2-{\text{CH}}_2{\text{NH}}_2---{\text{NH}}_3\stackrel{{\mathrm{k}}_{\text{uni}-\mathrm{n}}}{\to }{\text{CH}}_2\text{NH}+{\text{HO}}_2+{\text{NH}}_3$

The equation to calculate the effective pressure-dependent rate coefficients $k_{eff}^{bimol}\left(T,M\right)$ is as follows:

$k_{eff}^{bimol}\left(T,M\right)={K_{eq-1n}\times \left[{NH}_3\right]\times K}_{eq-2n}\times k_{\infty }^{uni}\left[1-f_{\left(•\mathrm{C}{H}_2\mathrm{N}{H}_2\dots {NH}_3+O_2\right)}\right],(4)$

where $K_{eq-1h}=\frac{k_{1n}}{k_{-1n}}and$ and $K_{eq-2n}=\frac{k_{2n}}{k_{-2n}}$ are equilibrium constants of each pathway involved in a reaction, [NH₃] is the concentration, and f is the branching fraction for the reaction proceeding to the reactant. The ammonia concentration used at 10 ppbv is based on the observations from previous studies (Ali et al., 2021). The rate coefficients for the ammonia-assisted reaction are almost similar to those of ^•CH₂NH₂ + O₂ in the temperature range of 200 K–400 K (see Table 4). In fact, some lower values were obtained at higher temperatures. The catalytic behavior does not take place if step 0 is not included in the reaction mechanism. The result could be due to the lower entropy change in the reaction. The total effective rate coefficient for ^•CH₂NH₂ + O₂ (2.7 × 10⁻²¹ cm³ molecule⁻¹ s^-1 at 300 K) is ∼12 orders of magnitude lower than that for the ^•CH₂NH + O₂ reaction (8.8 × 10⁻¹³ cm³ molecule⁻¹ s^-1). This result is due to the fact that the ammonia-assisted pathway depends on the ammonia concentration (see Table 4).

TABLE 4

TABLE 4. Calculated rate coefficients for the ^•CH₂NH₂ + O₂, ^•CH₂NH₂ +O₂ (+NH₃), and ^•CH₂NH₂ +O₂ (+H₂O) in the temperature range of 200 K–400 K at 1 bar pressure.

The relative branching fractions of these channels determined at 200 K, 300 K, and 400 K are shown in Supplementary Figure S5. For simplicity, the branching fraction at 300 K is shown in Figure 11. The branching fraction for the formation of CH₂NH/HO₂ contributes 50% at 300 K, and almost the same temperature increases to 400 K (see Supplementary Figure S5). At the same time, the formation of CH₂NH₂OO … NH₃ increases as the pressure increases to 100 bar (100%). The plot shows the back-reaction that regenerates ^•CH₂NH₂ … NH₃ + O₂. When the results are compared with those of the free reaction, it is easier to lose HO₂ via the formation of CH₂NH than through OH loss via formamide formation. We can say that the effect of ammonia has a negligible impact on the product branching ratios, and the results are almost similar to those of a free reaction, except at very low pressure (Supplementary Figure S5).

FIGURE 11

FIGURE 11. Pressure-dependent branching fractions for the ^•CH₂NH₂ … NH₃ +O₂ reaction at 300 K.

3.2.3 Rate constant for ^•CH₂NH₂ + O₂ (+H₂O)

The scheme for the formation of INT1h, CH₂NH, and HO₂ from ^•CH₂NH₂ + O₂ reactions with the effect of a water can be written as follows.

${\text{CH}}_2{\text{NH}}_2+{\mathrm{O}}_2+{\mathrm{H}}_2\mathrm{O}\underset{{\mathrm{k}}_{-1\mathrm{h}}}{\overset{{\mathrm{k}}_{1\mathrm{h}}}{\rightleftharpoons }}{\text{CH}}_2{\text{NH}}_2---{\mathrm{H}}_2\mathrm{O}+{\mathrm{O}}_2\underset{{\mathrm{k}}_{-2\mathrm{h}}}{\overset{{\mathrm{k}}_{2\mathrm{h}}}{\rightleftharpoons }}{\mathrm{O}}_2-{\text{CH}}_2{\text{NH}}_2–––{\mathrm{H}}_2\mathrm{O}{\displaystyle \stackrel{{\mathrm{k}}_{\text{uni}-\mathrm{h}}}{\to }}{\text{CH}}_2\text{NH}+{\text{HO}}_2+{\mathrm{H}}_2\mathrm{O}$

The equation to calculate the effective pressure-dependent rate coefficients $k_{eff}^{bimol}\left(\exp \left(-\mathrm{B}/\mathrm{T}\right)\right)$ is as follows:

$k_{eff}^{bimol}\left(T,M\right)={K_{eq-1h}\times \left[H_{2}O\right]\times K}_{eq-2h}\times k_{\infty }^{uni}\left[1-f_{\left(•\mathrm{C}{H}_2\mathrm{N}{H}_2\dots H_2\mathrm{O}+O_2\right)}\right],(5)$

where $K_{eq\left(1\right)h}=\frac{k_{1h}}{k_{-1h}}$ and $K_{eq-2h}=\frac{k_{2h}}{k_{-2h}}$ are the equilibrium constants of each reaction pathway involved in equation (iii), [H₂O] is the concentration, and f is the branching fraction for the reaction proceeding to the reactants. The [H₂O] is calculated using a typical humidity concentration, as discussed in the previous paper (Dash and Ali, 2022). The rate coefficients were also calculated using different water concentrations, as shown in Supplementary Figure S6. The effect of relative humidity from 20% to 100% on calculated rate coefficients is a factor of 10 difference. The effective rate coefficient calculated based on Eq. 4 (2.04 × 10⁻¹⁷ cm³ molecule⁻¹ s^-1 at 298 K) is ∼six to seven orders of magnitude lower than that of the water-free ^•CH₂NH₂ + O₂ reaction (∼2.2 × 10⁻¹¹ cm³ molecule⁻¹ s^-1 at 298 K). This is due to the fact that the water-assisted pathway depends parametrically on water concentration and entropy reduces the rate coefficients. Our results are also consistent with the previously reported values for similar reaction systems (Ali et al., 2022; Dash and Ali, 2022).

Our calculation shows that the total effective rate coefficients for systems ^•CH₂NH₂ + O₂ (+NH₃) (∼10^–11 order) and ^•CH₂NH₂ + O₂ (+H₂O) (6 order) are smaller than that of the free reaction (see Figure 12).

FIGURE 12

FIGURE 12. Comparison between rate coefficients for ^•CH₂NH₂ + O₂, ^•CH₂NH₂ + O₂ (+NH₃), and ^•CH₂NH₂ + O₂ (+H₂O) in the temperature range of 200 K–400 K at 1 bar pressure.

It is clear that the geometries of INT and TSs are different in ^•CH₂NH₂ + O₂ (+NH₃) reaction systems compared to their isoelectronic analogous ^•CH₂NH₂ + O₂ (+H₂O) reactions, resulting in different computed enthalpies and rate coefficients. Because of this, the kinetics of ^•CH₂NH₂ + O₂ (+NH₃) is quite different from those of ^•CH₂NH₂ + O₂ (+H₂O) reaction systems. In the case of free reactions and ammonia, the rate coefficients exhibit negative temperature dependence, whereas in the case of water, positive temperature dependence was observed. This may be due to the fact that water concentration is highly dependent on temperature, and ammonia concentration is nearly independent of temperature. The branching fractions for the formation of ^•OOCH₂NH₂ and ^•CH₂NH and the reaction going back to ^•CH₂NH₂ + O₂ with the effect of a single water molecule at 300 K and pressure range 0.001 bar–1000 bar are shown in Figure 13, and a comparison of branching fractions for ^•CH₂NH₂ + O₂, ^•CH₂NH₂ + O₂ (+NH₃), and ^•CH₂NH₂ + O₂ (+H2O) at 200 K, 300 K, and 400 K is shown in Supplementary Figure S7.

FIGURE 13

FIGURE 13. Pressure-dependent branching fractions for the ^•CH₂NH₂ … H₂O+ O₂ reaction at 300 K.

As previously discussed in water- and ammonia-free reactions, the product branching ratios for the formation of CH₂NH + HO₂ decrease, and the reaction goes back to the reactants, i.e., ^•CH₂NH₂ + O₂, when the pressure increases from 0.1 bar. When a water molecule is added to the reaction, the product branching ratio changes significantly (∼80%), and a single water reaction favors the formation of CH₂NH + HO₂ at a temperature of <300 K; however, the effect of ammonia favors only ∼10%. Despite the slower water reaction, our ME calculations indicate that a favorable CH₂NH + HO₂ formation is observed under tropospheric conditions.

3.3 Atmospheric fate of methylamine and methanimine

The atmospheric degradation of CH₃NH₂ with and without ammonia and water molecules is shown in Figure 14. The atmospheric lifetime ($\tau$) because of its interaction with OH and species ^•CH₂NH₂ with O₂ radicals is calculated as follows:

$\tau =\frac{1}{k_{\left[X=OH,O2\right]}\times \left[X\right]}.(6)$

FIGURE 14

FIGURE 14. Atmospheric degradation reaction of CH₃NH₂ with and without ammonia/water molecules.

The average OH radical concentration at tropospheric conditions 225 K and <1 bar is ∼1 × 10⁶ cm³ molecule⁻¹ s^-1, and a concentration of [O₂] = 1 × 10¹⁶ molecules cm^-3 was used, which is based on a previous study (Dash and Ali, 2022). We can say that the photo-oxidation lifetime of methylamine to the sink of ^•CH₂NH₂ is nearly 13–14 h. Based on current data and previous results, we can say that the CH₃NH₂ + OH/O₂ → CH₂O + HO₂ via ^•CH₂NH₂ leading to the formation of CH₂NH is both kinetically and thermodynamically more favorable than the CH₃NH₂ + OH/O₂ → CH₃NH + HO₂ via CH₃NH^• under tropospheric conditions. This result is also consistent with its isoelectronic analogous (Ali et al., 2019) reaction ^•CH₂OH + OH/O₂ → CH₂O+ HO₂. Generally, the effective rate coefficients for the role of water and ammonia reactions are smaller than those of the free ^•CH₂NH₂ + O₂ reaction system in the temperature range of 200 K–400 K. Therefore, the effect of ^•CH₂NH₂ + O₂ with H₂O/NH₃ is less important for the sink of ^•CH₂NH₂ in a gas-phase atmospheric reaction.

To understand the impact of INT1 in budget calculations, we have calculated the atmospheric lifetime of ∼3 microseconds of ^•CH₂NH₂ with its reaction O₂, indicating that the formation of CH₂NH is fast under tropospheric conditions (i.e., at 225 K and an altitude of ∼10–11 km) when taking an average concentration of O₂ radicals in the upper troposphere of ∼1 × 10¹⁶ molecule cm^-3. It is of interest to know whether HO₂···CH₂NH₂···H₂O can be produced from the reaction of CH₂NH···H₂O + O₂ reaction under atmospheric conditions. For this purpose, we calculated the pseudo-first-order rate coefficients of decay of ^•CH₂NH₂···H₂O+ O₂ at 300 K using concentration [O₂] = 1 × 10¹⁶ molecules cm^-3. The decay rate of INT2h producing CH₂NH₂+H₂O-HO₂ was found to be 8 × 10⁻³ s^-1, which led to the 2 min of the lifetime of HO₂···CH₂NH₂···H₂O. Therefore, we can say that under tropospheric conditions, HO₂···CH₂NH₂···H₂O can be produced from the reaction of ^•CH₂NH₂ + O₂ (+H₂O).

To understand the fate of the CH₃NH^• radical with its reaction with O₂ under the PES (see Supplementary Figure S8), rate coefficients for the addition of O₂ to CH₃NH^• are investigated using the RRKM/ME simulation. The O₂ radical mildly reacts with CH₃NH^• with the ∼6 kcal/mol below the reactants. Unlike the formation of common aminoperoxy radicals, O₂ addition to CH₃NH^• proceeds with a transition state TS1a with ∼5 kcal/mol of barriers, leading to the formation of Int2 and dissected to Int-2 via a five-membered ring transition state with the barrier height of ∼13 kcal/mol (with respect to Int-ad) and dissociated with barrierless process to CH₂NH + HO₂. We predicted the rate coefficients using the direct reaction, i.e., CH₃NH^• + O₂→TS2a→CH₂NH + HO₂ (Supplementary Figure S8, in blue), and the indirect reaction, i.e., CH₃NH^• + O₂ →TS1a→CH₃NHOO→TS2a→Int2→CH₂NH + HO₂ (Supplementary Figure S8, in black). The calculated rate coefficient for the direct formation of CH₂NH + HO₂ is 7 × 10⁻¹⁶ cm³ molecule⁻¹ s^-1, which is at least two orders of magnitude smaller than the indirect reaction. Based on our ME calculation, we can say that the formation of CH₂NH does not come from the CH₃NH^• +O₂ reaction because the reaction is quite slow under tropospheric conditions.

The mechanistic and kinetic analysis suggests the formation of these two ^•CH₂NH₂ and CH₃NH^•, and our overall understanding of atmospheric and interstellar oxygen chemistry remained uncertain. Although many experimental and computational efforts over the past decade on reaction rate coefficients and branching ratios have been made, our knowledge of the chemical pathways theorized for the O₂ reaction in two different environments is not clear. Therefore, as suggested in a previous study, at a low temperature, i.e., <100 K, the formation of CH₃NH^• is dominated over the formation of ^•CH₂NH₂ under an interstellar cold medium (Gonza´lez et al., 2022). We have performed the RRKM/ME simulation at below 100 K and found that the formation of CH₃NOO is dominated under high-pressure limit conditions, i.e., >10 bar and below 100 K. Under low pressure and low temperature, the reaction goes back to the reactant. The formation of CH₃NOO in the ISM medium is not clear, but our analysis suggests that the reaction CH₃NH^•+O₂ does nothing under ISM conditions. We have also carried out our RRKM/ME simulation under combustion conditions (>1000 K and HPL), and our analysis suggests that the formation of CH₃NOO^• and CH₂NH is even negligible. It may also be suggested that such a reaction might take place in a more polluted situation.

There has been considerable speculation about what will happen after the formation of CH₂NH (Rissanen et al., 2014; Ali et al., 2018; Ali, 2020). Figure 15 shows the atmospheric degradation reaction of CH₂NH with various possible atmospheric species. The result in the figure shown is based on our previous calculation, except for the reaction of CH₃NH^• + O₂, which is re-calculated. As shown in Figure 15, we can see that the reaction with water does not lead to the formation of NH₃ and CH₂O as suggested in our previous work under tropospheric conditions (Ali, 2020). We also tried to find out if the backward reaction was favorable; for that, we have set up an ME simulation and predicted that this reaction would do nothing in the troposphere (Ali et al., 2016). We also calculated the rate coefficients for the reaction of CH₂NH + OH radicals, and the mechanism has already been discussed in our previous work (Ali and Barker, 2015). The results show the formation of CH₂N^•+ and ^•CHNH as major products and show a similarity between isoelectronic analogous systems, i.e., CH₂O and CH₂CH₂. As suggested in Rissanen et al. (2014) and Ashraful and Silva (2020), water may favor the formation of CH₂N^• and ^•CHNH; therefore, we have also analyzed the effect of water molecules on the CH₂NH + OH reaction (Ali et al., 2019). We have found that the reaction rate coefficients increase when the concentration of water molecules is not included in the calculation and decrease in the presence of water (Ali et al., 2019). Based on our current and previous findings, we propose that the formation of HCN could be the major product when O₂ radicals react with ^•CHNH radicals. We also suggest that the gas-phase formation of CH₂NH from the CH₂N^• + O₂ reaction will be even slower, as shown in the previous degradation mechanism (see Figure 14). Again, this is due to less favorable N—O-O bond formation than C—O-O bond formation. We can also suggest that the formation of HCN in its presence may be unimportant under tropospheric conditions. Our calculation suggests that oxidation pathways may also contribute to the HO_x abundance under the tropospheric conditions, as shown in the degradation reaction mechanism (Figure 15 and Figure 14). Such state-of-the-art kinetics provides a clue to the formation of HCN under tropospheric conditions. Our result may be helpful in setting up an experimental analysis for the formation of HCN under tropospheric conditions.

FIGURE 15

FIGURE 15. Atmospheric degradation of CH₂NH with various possible atmospheric species.

4 Conclusion

In this work, the rate coefficients and branching fraction for ^•CH₂NH₂ + O₂, ^•CH₂NH₂ + O₂ (+H₂O), and ^•CH₂NH₂ + O₂ (+NH₃) for the formation of methanimine (CH₂NH) and HO₂ have been investigated using CCSD(T)//M06-2X/6-311++G (3df, 3pd) coupled with the RRKM/ME simulation. The results show that ^•CH₂NH₂ + O₂ leads to the formation of CH₂NH at temperatures <300 K and goes back to reactants (^•CH₂OH + O₂) at high temperatures (>300 K). When the water/ammonia molecule is added to the ^•CH₂NH₂ + O₂ reaction, it favors the formation of CH₂NH at a temperature <300 K. The NH₃- and H₂O- assisted rate coefficients are at least 10¹⁰–10¹² (Gonza´lez et al., 2022) and 10⁶ times, respectively, smaller than those of the free reaction; thus, we can say that the effect of NH₃/H₂O on ^•CH₂NH₂ + O₂ has less importance in the troposphere. Under tropospheric conditions, the reaction CH₃NH₂ + OH/O₂→ CH₂NH + HO₂ via ^•CH₂NH₂ leading to form CH₂NH + HO₂ is both kinetically and thermodynamically more favorable than reaction CH₃NH₂ + OH/O₂ → CH₂NH + HO₂ via ^•CH₃NH. The mechanism indicates that a single NH₃/H₂O molecule has the potential to increase the branching fraction in a gas-phase reaction at a lower temperature <300 K and slower reaction at a higher temperature. Such results are promising, and chemical kinetic data can be beneficial for the future implementation of ammonolysis and hydrolysis of other carbon-centered hydroxyl compounds. In previous studies, researchers stated that the reaction CH₂NH may be favorable in water; our study demonstrated that water increases the formation of CH₂NH. Our results also indicate the formation of HCN may have come from the reaction going via a carbon-centered radical instead of an N-centered radical. Experimental analysis is required to validate this finding. Such chemical kinetic analysis is interesting; chemical kinetics details can be useful to understand the bigger amine/imine that may lead to the formation of HCN, and N₂O may increase the reaction rate.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding author.

Author contributions

MD and MA completed all the electronic structure calculations, and MA completed the chemical kinetic calculations. MD and MA prepared the draft of the manuscript. All authors contributed to the article and approved the submitted version.

Funding

The work is supported by the faculty startup grant # 8474000461 at Khalifa University Abu Dhabi UAE.

Acknowledgments

MA thanks the Department of Chemistry at College of Art and Science at Khalifa University of Science and Technology, Abu Dhabi UAE, to carry out the research. MA thanks the supercomputer facility computational support at Khalifa University of Science and Technology, at Abu Dhabi, UAE. The authors thank reviewers for their valuable suggestions.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fchem.2023.1243235/full#supplementary-material

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