Computational studies on the gas phase reaction of methylenimine (CH2NH) with water molecules

In this work, we used quantum chemical methods and chemical kinetic models to answer the question of whether or not formaldehyde (CH2O) and ammonia (NH3) can be produced from gas phase hydration of methylenimine (CH2NH). The potential energy surfaces (PESs) of CH2NH + H2O → CH2O + NH3 and CH2NH + 2H2O → CH2O + NH3 + H2O reactions were computed using CCSD(T)/6–311++G(3d,3pd)//M06-2X/6–311++G(3d,3pd) level. The temperature-and pressure-dependent rate constants were calculated using variational transition state theory (VTST), microcanonical variational transition state theory \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\mu VTST)$$\end{document}(μVTST) and Rice–Ramsperger–Kassel–Marcus/master equation (RRKM/ME) simulations. The PES along the reaction path forming a weakly bound complex (CH2NH⋯H2O) was located using VTST and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μVTST, however, the PES along the tight transition state was characterized by VTST with small curvature tunneling (SCT) approach. The results show that the formation of CH2NH + H2O → CH2NH⋯H2O is pressure -and temperature-dependent. The calculated atmospheric lifetimes of CH2NH⋯H2O (~ 8 min) are too short to undergo secondary bimolecular reactions with other atmospheric species. Our results suggest that the formation of CH2O and NH3 likely to occur in the combustion of biomass burning but the rate of formation CH2O and NH3 is predicted to be negligible under atmospheric conditions. When a second water molecule is added to the reaction, the results suggest that the rates of formation of CH2O and NH3 remain negligible.

computational studies on the gas phase reaction of methylenimine (cH 2 nH) with water molecules Mohamad Akbar Ali in this work, we used quantum chemical methods and chemical kinetic models to answer the question of whether or not formaldehyde (cH 2 o) and ammonia (nH 3 ) can be produced from gas phase hydration of methylenimine (cH 2 nH). the potential energy surfaces (peSs) of cH 2 nH + H 2 o → cH 2 o + nH 3 and cH 2 NH + 2H 2 o → cH 2 o + nH 3 + H 2 O reactions were computed using CCSD(T)/6-311++G(3d,3pd)// M06-2X/6-311++G(3d,3pd) level. The temperature-and pressure-dependent rate constants were calculated using variational transition state theory (VTST), microcanonical variational transition state theory (µVTST) and Rice-Ramsperger-Kassel-Marcus/master equation (RRKM/ME) simulations. the peS along the reaction path forming a weakly bound complex (cH 2 nH⋯H 2 o) was located using VTST and µVTST, however, the PES along the tight transition state was characterized by VTST with small curvature tunneling (SCT) approach. The results show that the formation of cH 2 nH + H 2 o → cH 2 nH⋯H 2 O is pressure -and temperature-dependent. The calculated atmospheric lifetimes of cH 2 nH⋯H 2 O (~ 8 min) are too short to undergo secondary bimolecular reactions with other atmospheric species. our results suggest that the formation of cH 2 o and nH 3 likely to occur in the combustion of biomass burning but the rate of formation cH 2 o and nH 3 is predicted to be negligible under atmospheric conditions. When a second water molecule is added to the reaction, the results suggest that the rates of formation of cH 2 o and nH 3 remain negligible.
The alkylamines especially methylamine is emitted to the atmosphere from various sources such as biogenic, oceanic, anthropogenic, animal husbandry, marine emissions, biomass burning (forest vegetation, savannah grass, firewood and agricultural wastes), chemical manufacturing and carbon capture storage (CCS) technologies 1 .
Methylamine (CH 3 NH 2 ) is one of the atmospheric precursors of the greenhouse nitrous oxide (N 2 O) gas and HCN and is one of the sources of the formation of NO x 2-4 . For example: the synthetic nitrogen-based fuel is one the source of NO x emission 5,6 . Methylamine has also received numerous attention due to its potential role in enhancing particle nucleation and growth and affecting secondary organic aerosol (SOA) formation 7,8 . After emission into the atmosphere, methylamine undergoes conversion reactions in both the gas and aqueous phases. The gas phase reaction of methylamine with hydroxyl radical (CH 3 NH 2 + OH) is the most important pathway of degradation of methylamine 9,10 . The OH radical initially abstracts the hydrogen from the C-H and N-H groups of the methylamine to generate carbon-centered aminomethyl radical (·CH 2 NH 2 ) as a major product and nitrogen-centered methylamine radical (CH 2 N·H) as a minor product 10 . The major detected products from the photooxidation of methylamine are 90% methylenimine (CH 2 NH) and ~ 10% nitrosamine, a carcinogen. The photooxidation reaction of methylamine is given below 1,9,10 (1) CH 3 26 calculated the rate constants for OH + CH 2 NH reaction using DFT and CCSD(T) level. Our group has also predicted the rate constants for HO 2 + CH 2 NH reaction using ab initio// DFT methods coupled with microcanonical variational transition state theory 22 . Recently, Ali et al. 23,24 proposed the reaction mechanism of the catalytic effect of a single water molecule on the OH + CH 2 NH, OH + CH 2 O and OH + CH 2 CH 2 reactions. Ali et al. 23,24 concluded that a single water molecule has a negative effect on OH + CH 2 NH, OH + CH 2 O and OH + CH 2 CH 2 reactions. Ali et al. suggested that water-assisted OH + CH 2 NH, OH + CH 2 O and OH + CH 2 CH 2 reactions cannot accelerate the reaction because the dominated water-assisted process depends parametrically on water concentration. As a result, the overall reaction rate constants are smaller 23,24 .
In earlier studies 1,10,27 , various research groups have been proposed that the hydrolysis of methylenimine will produce CH 2 O + NH 3 , but no clear justification has been made so far. They suggested that, CH 2 NH are watersoluble and will be absorbed by aqueous aerosols in the troposphere. In aqueous solution, it is well known that CH 2 NH undergoes hydrolysis to yield ammonia and formaldehyde. The process of formation of ammonia and formaldehyde is acid-catalyzed and should be relatively rapid in aerosol droplets 1,10,27 . The interest of present work is to address the question of whether the gas phase reaction of CH 2 NH with H 2 O will leads to the formation of formaldehyde and ammonia.
The role of the water molecule as a catalyst in the hydrogen transfer reaction of simple atmospheric and combustion product i.e., ketene (H 2 C=C=O) has been studied by various research groups [28][29][30] . Nguyen et al. 28 calculated gas phase pseudo-first-order reaction rate constants for ketene with water molecules at room temperature. The calculated decay rate of ketene was obtained for both the pathways 1.5 × 10 −19 (pathway A) and 1.5 × 10 −16 s −1 (pathway B). They suggested that the gas phase reaction with ketene and water molecules to form acetic acid is many orders of magnitude slower. They also purposed that room-temperature formation of acetic acid from CH 2 CO + 2H 2 O → NH 3 + CH 2 O is almost negligible and maybe provide better understanding in the aqueous phase chemistry 28 . The role of two-water reaction with CH 2 NH is also of great interest from the viewpoint of atmospheric and combustion chemistry research. Because CH 2 NH is also isoelectronic analogous to important atmospheric and combustion species i.e., CH 2 O and CH 2 CH 2 .
To the best of our knowledge, there have been no theoretical chemical kinetics investigations on the hydrolysis of CH 2 NH in the gas phase. To investigate the various possibilities of CH 2 NH + H 2 O and CH 2 NH + 2H 2 O reactions, we used ab initio/DFT method for the potential energy surface and advanced kinetic models to predict the temperature-and pressure-dependent rate constants. Finally, concluding remark whether the formation of CH 2 O and NH 3 is a possible pathway under both atmospheric and combustion conditions are drawn. theoretical methods electronic structure calculations. Geometries of all stationary points were optimized using M06-2X method 31 in conjunction with Pople 6-311++G(3df,3pd) basis set 32 . The M06-2X has been shown to be reliable for handling noncovalent interactions between molecules and widely used to locate the transition states of atmospheric and combustion reaction systems 20,[33][34][35] . The optimized structure of reactants, complexes, intermediates, and transition states (TSs) are shown in Supporting Information Figure S1 and the cartesian coordinates are given in Supporting Information Table S1. Vibrational frequencies were calculated at M06-2X/6-311++G(3df,3pd) to estimate the zero-point corrections (ZPE) for the reactants, complexes, TSs and products. The frequency calculation also shows that the optimized transition states have single imaginary frequency and reactants, complexes, intermediates and products have all positive vibrational frequencies (see Supporting Information,  Table S3). Intrinsic reaction coordinate (IRC) calculations were carried out at M06-2X/6-311++G(3df,3pd) level to confirm the identities of the reactants and products for every transition state. Single point energy calculations were calculated using CCSD(T)/6-311++G(3df,3pd) level of theory [36][37][38][39] (see Supporting Information, Table S4) on M06-2X/6-311++G(3df,3pd) optimized geometries. The combination of CCSD(T)/6-311++G(3df,3pd)//M06-2X/6-311++G(3df,3pd) (designated CC//M06) has been tested by many research groups 20,33-35 and shown to be reasonably accurate. T1 diagnostic was computed using CCSD(T)/6-311++G(3df,3pd) for all important species was < 0.017, which is acceptable for a single reference wave function 40 . The T1 diagnostic for all the species involved in the reaction are given in Supporting Information Table S5. Gaussian 09 suite of programs was used for all ab initio/density functional theory (DFT) calculations 41 .
Kinetics. High-pressure limit rate constants. The high-pressure limit rate constants for title reaction were calculated using canonical variational transition state theory with small curvature tunneling correction (SCT). The generalized rate constants were calculated by minimizing the transition state dividing surface along the reaction coordinate to get the canonical variational transition state theory (CVT) rate constants, which is given by Eqs. (5) and (6): where k GT (T, s) and k CVT (T) are the rate constants of generalized and canonical variational, transition state theory, respectively, V MEP is the classical barrier height, Γ is the small curvature tunneling (SCT) correction as implemented in Polyrate 42 , h is Planck's constant, k B is the Boltzmann constant, and Q = TS and Q R are the total partition functions for the transition state and the reactants, respectively. The rate constants were calculated using dual level direct dynamic approach CVT/SCT with interpolated single point energies (ISPE) 43 . The minimum energy pathway is obtained using direct dynamics for a small range of the reaction path with the mass scaled reaction coordinate 's' from − 1.0 to 1.0 bohr by using the Page-McIver integrator with a step size of 0.005 bohr. The SCT transmission coefficients 44 , that include the reaction-path curvature effect on the transmission probability, are based on the centrifugal-dominant small-curvature semiclassical adiabatic ground-state (CD-SCSAG) approximation were computed as discussed in Ref. 44 . The SCT method 44 was widely used for many atmospheric and combustion reaction systems and provide reasonably accurate value 23,24,33 . All the unimolecular reaction rate constants for non-barrierless reaction were calculated using Polyrate and Gaussrate suites of program 42,45 . The K eq (T) for all the reactants → complexes and complexes → pre-reactive complex were calculated (see Supporting Information Table S6) using THERMO code as implemented in MultiWell Program suite [46][47][48] . The details procedure of K eq (T) calculations are given in the Supporting Information.
For barrierless reaction, ktools program was used to compute rate constants based on variational transition states theory (VTST) and microcanonical variational transition states theory ( µVTST) [46][47][48] . In the ktools program, we supply reactants and the collection of the loose transition states along the reaction coordinate. This can be further achieved by performing a series of constrained optimizations at fixed distances along the reaction path (RP). At each fixed distance, the potential energy was calculated, and optimized geometry was used to obtain the rotational constants and a vibrational analysis was used to obtain the vibrational frequencies of the orthogonal degrees of freedom, after projecting out the reaction coordinate. The zero-point energy from the orthogonal modes, ΔE z (s), and the electronic energy ΔE e (s) at each fixed bond distance s were used to compute the potential energy with ZPE corrections: V(s) = ΔE e (s) + ΔE z (s), where ΔE e (s) = E e (s) − E e (s = 0) and ΔE z (s) = E z (s) − E z (s = 0). The rotational partition functions and vibrational partition functions were computed from rotational constants and the vibrational frequencies, respectively for the orthogonal normal modes evaluated at the fixed distance s. Utilizing these parameters, "trial" rate constants or reaction fluxes were computed at each point along the reaction path [20][21][22] . The point at which the minimum trial rate constant or reaction flux occurs was identified as a variational transition state (VTS). The obtained minimum TS is also compatible to run the master equation (ME) code for pressure-and temperature-dependent rate constants.
Pressure-dependent rate constants. The 2-D microcanonical rate constants, k i (E ′ ) for a specific J ′ were calculated according to Eq. 7: where L = is the reaction path degeneracy can be written as the product of a ratio of symmetry factors and a ratio of optical isomers; h is Planck's constant; G = (E ′ − E 0 , J ′ ) is the sum of states of the transition state as a function of the active energy E ′ − E T 0 ; and E T 0 is the reaction critical energy, which includes zero-point-energy and centrifugal corrections at temperature T; ρ(E ′ , J ′ ) is the 2-D density of states of the reactant molecule. The microcanonical thermally averaged high-pressure limit rate constants were obtained as discussed in Ali et al. work 22 .
For pressure-dependent rate constants, RRKM/ME simulation was used to calculate the rate constants as a function of pressure. The calculated sum of states and density of state from the microcanonical process were used to run master equation (ME) code for pressure-dependent (i.e. falloff curve) rate constants. The vibrational frequencies and the moments of inertia were used to calculate the density of states and the sum of states were based  10 . The initial energy distribution for the simulations was the chemical activation distribution for the combination reaction producing the CH 2 NH⋯H 2 O. The temperature and pressure-dependent rate constants were obtained using MultiWell code. The rate constants were calculated over the temperature range of 200-350 K at N 2 pressures from 0.01 to 1,000 atm.

Results and discussion
All the stationary points on the PESs for CH 2 NH + H 2 O reaction were obtained using CC/M06 level. To examine the possible catalytic effect of water molecule on the CH 2 NH + H 2 O reaction, we explored the PES of the addition of one water molecule. After the depiction of reaction pathways are considered ("Reaction pathways and thermodynamics analysis"), for which temperature and pressure-dependent rate constants predicted, the ensuing "Rate constants" details chemical kinetic results of CH 2 NH + H 2 O and CH 2 NH + 2H 2 O reactions and "Atmospheric and combustion implications" describes the atmospheric and combustion implications of CH 2 NH + H 2 O reaction system.

Reaction pathways and thermodynamics analysis.
The hydrolysis of methylenimine forming formaldehyde and ammonia is shown below: In the first step, hydrogen transfer from water molecule to methylenimine producing aminomethanol. In the second step, hydrogen transfer from aminomethanol followed by removal of ammonia produces formaldehyde (see the scheme in SI).
The zero-point corrected energies of each stationary point on the PES for the CH 2 NH + H 2 O reaction are tabulated in Table 1 and shown in Fig. 1. Our calculated reaction enthalpy for CH 2 NH + H 2 O → CH 2 O + NH 3 (− 0.4 kcal/mol) at CC//M06 is in excellent agreement with the experimentally measured value (− 0.3 kcal/ mol) [52][53][54] . Our calculated value is also in excellent agreement with the value obtained by Riffet et al. 15 . Both water ( µ D = 1.91D ) and methylenimine ( µ D = 2.045D ) are a polar molecule. The partial electric charge on each atom in CH 2 NH and H 2 O are calculated and shown in supporting information Figure S2. Based on charges, we expect they will bind to each other and formed a weakly bound complex i.e., CH 2 NH⋯H 2 O. The calculated binding energies of CH 2 NH⋯H 2 O is 4.4 kcal mol −1 lower than the reactants and is also in very good agreement with previous studies 15,16,23 . A hydrogen atom transfer from the H 2 O to methylenimine to form an aminomethanol via four-membered transition state TS1 (Fig. 1). The barrier heights for this transformation is 46.4 kcal/mol, which is 8.2 kcal/mol higher than H 2 O addition to C=O of H 2 C=C=O and 12.3 kcal/mol higher than H 2 O addition to C=C bond of H 2 C=C=O 28 . Once aminomethanol is produced, it can either lose H 2 O molecule to regenerate methylenimine or leads to another hydrogen migration via transition state TS3 to form formaldehyde and ammonia. The barrier heights for the formation of formaldehyde and ammonia is also high (30.8 kcal/mol). This value is also in good agreement with Riffet et al. value 15 . Table 1. Calculated energies (in kcal/mol) for species associated with the reaction of methylenimine with onewater and two-water molecules. a Calculated at CCSD(T)/6-311++G(3df,3pd)//M06-2X/6-311++G(3df,3pd), b Calculated at CCSD(T)/6-311++G(3df,3pd)//M06-2X/6-311++G(3df,3pd) + ZPE. c Calculated by Riffet et al. work 15 . d From ATcT data [52][53][54] .  Fig. 2 and relative energies are tabulated in Table 1. In the presence of two-water molecules, the simultaneous collision of isolated CH 2 NH, H 2 O and H 2 O molecule is very unlikely, therefore, the reaction will occur through the formation of two body complex and then two body complex collides with a third species to form the three-body complex. The calculated binding energies of two body complex i.e., CH 2 NH⋯H 2 O (− 4.4 kcal/mol) are in very good agreement with previously reported (− 3.8, − 4.7 kcal/mol) 15 15 . It is obvious that water molecule can not only act as reactants but also play an important catalytic role, which makes reaction more thermodynamically feasible (see Fig. 2).
As shown in Fig. 2, the reaction proceeds through a transition state (TS1⋯H 2 O), with a barrier of ~ 21 kcal/ mol (with respect CH 2 NH + 2H 2 O) to form an aminomethanol⋯H 2 O. In this process, the six-membered transition state (TS1⋯H 2 O), which has considerably less strain than that of four-membered TS1 of CH 2 NH + H 2 O reaction. The two-water reaction significantly reduced the activation barrier by 25.0 kcal/mol. This result is also consistent with the previous studies on similar reaction system 28,30 . Similar to the one-water reaction, aminomethanol can react catalytically with a single water molecule to either regenerate methylenimine or to form formaldehyde. The barrier heights for the formation of formaldehyde and ammonia is lower (7.6 kcal/mol), and thus should be the dominant channel. As a result, when the aminomethanol is formed, it will rapidly decompose to formaldehyde and ammonia in the presence of water.
Based on the energetics summarized in Table 1, the first barrier heights of a single water reaction is very high (46 kcal/mol). In the case of two water reactions, one water molecule is acting as a catalyst and still does not reduce the barrier heights sufficiently low to allow the hydrolysis of methylenimine to occur readily under typical atmospheric conditions. It has been also reported in the literature that the addition of more water molecules further decreases the barrier heights, but such reactions are not likely to occur in the gas phase 15,28,29 . As discussed in ketene + H 2 O reaction 28 , the gas-phase hydration of ketene by an excess of two water molecules is unlikely to occur at ambient temperatures because the concentration of (H 2 O) n>2 clusters in the gas-phase is negligibly small under these conditions. Therefore, the reaction of methylenimine with (H 2 O) n>2 is beyond the scope of the present work. chemical kinetics results. Rate constants. The CH 2 NH⋯H 2 O complex that plays important roles in the CH 2 NH + H 2 O reaction system are formed via entrance channels that have no intrinsic energy barriers i.e., barrierless. Figure 3 shows the zero-point corrected potential energy for the entrance channel forming CH 2 NH⋯H 2 O. www.nature.com/scientificreports/ To locate the transition state for the dissociation of CH 2 NH⋯H 2 O, the potential energies (including zeropoint energies) were computed in a series of constrained optimizations "trial TS" have one fixed frequency and remaining orthogonal frequency are properly projected as a function of the R N-O bond distance (from 3 to 8 Å). The optimized geometries at some points along the reaction pathways are shown in Fig. 4. All the transition states shown in Fig. 4 have a single imaginary frequency and the normal modes of vibration of these transition states were confirmed to be reliable with the reaction of interest through visualization with GaussView.
At R N-O = 8 Å, the interactions between CH 2 NH and H 2 O are very weak. As the two species approach one another, the potential energy decreases monotonically until it reaches the bottom of the potential well (Fig. 3). The PES decreases to ~ 1 kcal/mol at R N-O = 4 Å and decreased further as CH 2 NH and H 2 O come close to each other. The CVTST "trial" rate constants computed in the temperature range of 200-400 K along the reaction path  www.nature.com/scientificreports/ are shown in Supporting Information Figure S4. At each temperature, the plot shows a single minimum between 5.8 to 6.6 Å. The rate constants for dissociation and association reaction were computed using both canonical and microcanonical approaches and values are tabulated in Supporting Information, Table S7. Our calculation shows that both canonical and microcanonical rate constants for CH 2 NH + H 2 O → CH 2 NH⋯H 2 O reaction is very similar. It is also interesting to know that rate of formation of CH 2 NH⋯H 2 O increases as temperature increases. The sum of states obtained from µVTST process was used to run the master equation (ME) code for pressuredependent (i.e., falloff curve) rate constants. Figure 5 shows that microcanonical chemical activation k (E,J) for CH 2 NH + H 2 O reaction as a function of temperature (200-350 K) and pressure (0.01-1,000 atm). The rate constants are pressure-dependent and show negative temperature-dependence. At lower pressure, rate constants decrease with an increase in temperature and are almost independent of temperature at high-pressure limit. ME simulations show that the formation of CH 2 NH⋯H 2 O is dominant under all the conditions investigated and all other channels i.e., CH 2 NH 2 OH, CH 2 O⋯NH 3 and CH 2 O + NH 3 are almost negligible. This result is due to the fact that the barrier heights for the formation of CH 2 NH 2 OH, CH 2 O⋯NH 3 and CH 2 O + NH 3 are significantly higher. Our results also suggest that rate constants at high-pressure limit have positive temperature-dependence. This result is similar to the OH + CO and H + O 2 reaction systems (see examples posted on the MultiWell web site) and the result obtained previously for the CH 2 O + NH 3 reaction system 20 . We believe that the current microVTST results are accurate to within about a factor of 2.
In some cases, where the rate constant is pressure-independent or depends only weakly on pressure, one does not need to solve ME numerically, and an analytical solution can be obtained. As suggested in earlier studies for a similar reaction system i.e., H 2 O + H 2 C=C=O, the formation of products is almost pressure-independent 28,29 , therefore the rate constants for the reactions of methylenimine with one and two water molecules were calculated based on the high-pressure limit condition as discussed in the method section. The rate constants for the reactions of methylenimine with one water and two water molecules were calculated as a function of temperature are tabulated in Table 2 and shown in Fig. 6.
As discussed in "Reaction pathways and thermodynamics analysis", reactions of methylenimine with twowater molecules proceeds through a seven-membered complex, followed by H 2 O addition leading to products.   Step 0A Step 1 A   Figure 6. Rate constants for the reaction of methylenimine with one-water and two-water molecules. Dash lines correspond to reaction without water-concentration. It should be noted that these are infinite pressure limit rate constants, which are assumed to be valid from the range T ≥ 300 K, and p ≥ 1 atm. www.nature.com/scientificreports/

Pathway B
Step 0 B Step 1 B Step 2 B As discussed in earlier works 23,24 , locating the TS of backward reaction (i.e., PRC → CH 2 NH + H 2 O⋯H 2 O or PRC → CH 2 NH⋯H 2 O + H 2 O) is more difficult due presence of two or more hydrogen bonds in PRCs, therefore, the equilibrium approach was used to account the presence of forward and backward reactions. This model is reasonably correct when the pre-reactive complex can be stabilized by collisions with other atmospheric species. This approach has been widely used in the literature for the water-assisted reaction and predicted rate constants that are in reasonably good agreement with literature value 23,24 .
As suggested by the reviewer, we have also carried out temperature-and pressure-dependent rate constant calculations for two-water reaction using ME method and results are shown in the supporting information Figure S6. Because of the complexity in locating the TS of loose bonds due to the presence many hydrogens bonded complex in the PRC, we have used Inverse Laplace Transform (ILT) method to account for the barrierless reaction. The ILT parameters used in our calculation are based on our previous work i.e., CH 2 NH + HO 2 → CH 2 NH⋯HO 2 . Because the first barrier heights is too high (i.e., 32 kcal/mol w.r.t. PRC, see Fig. 2) our ME calculation suggests that the formation of other species (Intermediates and products) are negligibly small in all the temperature and pressure range studied. Based on ME simulation, we have observed that the infinite pressure condition k (T,p), with T ≥ 300 and p ≥ 1 atm for the two-water reaction.
The bimolecular rate constants of pathway A and pathway B were calculated using k A = K eq(A) × k CVT A and k B = K eq(B) × k CVT B , respectively. The rate constants for these pathways are tabulated in Table 2 and shown in Fig. 6. As shown in the Fig. 6 and tabulated in Table 2, the kinetics of the two-water reaction is more favorable than one-water reaction. This result is due to the fact that the barrier heights of two-water reaction are significantly lower than one-water reaction. As expected, pathway A is more kinetically favorable than pathway B. This result is due to the formation of strong N-H hydrogen-bonded complex (CH 2 NH⋯H 2 O) than weak O-H hydrogen-bonded complex H 2 O⋯H 2 O, which is also consistent with our previous studies 23,24 . It can be seen from Fig. 6, the rate constants for CH 2 NH⋯H 2 O + H 2 O and CH 2 NH + H 2 O⋯H 2 O at < 1000 K are larger than the CH 2 NH + H 2 O reaction and the difference becomes smaller as the temperature increases and is almost similar at the higher temperature (~ 2000 K). It is also clear from this analysis that all reactions involving additional catalytic water are entirely negligible at high temperatures.
The calculated rate constants predict the positive temperature-dependence i.e., rate constants increase with the increase of temperature (see Fig. 6). The tunneling correction for single water and two-water reactions are tabulated in Supporting Information, Table S8. It can be seen from Table S8 (a), the tunneling correction decreases with temperature and at temperature > 1500 K, tunneling correction is almost negligible i.e., Ŵ = 1. In other words, at the combustion condition where the formation of CH 2 O + NH 3 occurred, tunneling is almost negligible. This result is consistent with previous work on similar reaction system 28 . The tunneling correction of two water reaction is greater than one water reaction at lower temperature and almost negligible at temperature > 1300 K (see Table S8 (b). It should be noted that the k(T) given in Table 2 has a non-Arrhenius behaviour because of quantum mechanical tunneling effects.
The effective bimolecular rate constants were calculated using with water concentration, which is based on previous works 23,55,56 , therefore the correct expression to calculate the effective rate constants of pathway A and pathway B is given in Eqs. (8) and (9), respectively:  Table S4). The k A and k B are the bimolecular rate constants of pathway A and pathway B (see Table 2). The [H 2 O] concentration ~ 7.5 × 10 16 molecule/cm 3 was used in our calculation is based on the previous study 28 . As shown in Fig. 2, the kinetic scheme O → Products, the rate-determining step is at step 2, which is the same in both pathways. Therefore, the correct equation to calculate the total effective rate constants (k P ) is expressed by Eq. 10 As shown in Fig. 6 and given in Table 2, that effective rate constant at 500 K is five times larger than the one-water reaction. This result suggests that catalytic reaction takes place at a temperature ≤ 500 K. In general, the effective rate constants of the two-water reaction are smaller than the single-water reaction system in the temperature range of 600-2000 K. As a result, H 2 O + CH 2 NH reaction catalyzed by another H 2 O molecule play a minor role for the sink of CH 2 NH in gas phase combustion reaction. Unfortunately, experimental data are not available to validate our predicted rate constants. But we have examined the consistency of present work with earlier theoretical works on similar reaction system 28 Figure S5) 28 Figure S5).
Atmospheric and combustion implications. As reported in previous studies that the methylenimine are likely to hydrolyze easily under atmospheric conditions and hydrolysis of methylenimine will produce NH 3 + CH 2 O 1,15,27 . It is our interest to know whether or not formaldehyde and ammonia can be produced from the reaction of methylenimine with a single-water and two-water molecules. For this reason, we calculated the pseudo-first-order rate constants for the decay of methylenimine at 1500 K. The water concentration of [H 2 O] ~ 7.5 × 10 16 molecule cm −3 at 50% of relative humidity was used in calculation 28 . The calculated lifetime of methylenimine is ~ 8 min within a factor of 2 errors. The calculated lifetime of methylenimine (~ 8 min.) is also in good agreement with the lifetime of ketene i.e., ~ 5 min. Our calculations suggest that methylenimine can convert to formaldehyde and ammonia only under the combustion condition.
It is important to mention that the reaction of H 2 O + CH 2 NH is still slower than other important reactions for example radical-molecules reaction i.e., CH 2 NH + OH, CH 2 NH + HO 2 and CH 2 NH + OH (+ H 2 O). Based on our previous works, the CH 2 NH + OH reaction is faster than the H 2 O + CH 2 NH in both atmospheric and combustion conditions [21][22][23] . The estimated timescales of 8 min are too large to be competitive with the fast-radical reactions i.e., CH 2 NH + OH (+ H 2 O) ~ 1 ns. Therefore, we believe the kinetic of H 2 O + CH 2 NH is even slow in the combustion process compared to radical molecule reactions. Experimental studies are required to validate the formation of CH 2 O and NH 3 from CH 2 NH + H 2 O reaction. Now it is important to address the question of whether two-water molecules reaction can produce the formaldehyde and ammonia under atmospheric condition. To understand that, we calculated the pseudo-first-order reaction rate decay of methylenimine at 300 K and at [H 2 O] = 7.1 × 10 17 molecule/cc at 100% relative humidity. The calculated decay rate is ~ 4.2 × 10 11 s −1 suggest that two-water molecule reaction to form formaldehyde and ammonia is even slower. Therefore, the reaction of two-water molecules on methylenimine cannot produce formaldehyde and ammonia under atmospheric conditions 1 .
To investigate the possibility of the secondary atmospheric reaction with CH 2 NH⋯H 2 O, the atmospheric lifetime of CH 2 NH⋯H 2 O at 225 K and 0.1 atm (i.e., at an altitude of ~ 10-11 km) were calculated and found to be ~ 10 ms. This is a too short lifetime for CH 2 NH⋯H 2 O to undergoes significant bimolecular reactions with other atmospheric species. Thus, although this is an interesting complex, our pressure-dependent rate constants calculation suggests that its formation under the atmospheric condition is unimportant.
Our observation shows that room-temperature formation of formaldehyde and ammonia cannot have come from either of the mechanism of one-water and two-water reaction under atmospheric conditions. Hence, either another mechanism exists or surface reactions similar to that was observed previously are responsible for the formation of formaldehyde and ammonia 28 The present finding is also consistent with previous studies on the similar type of reactions 28,29 . conclusions The potential energy surfaces and rate constants for the reaction of methylenimine with one-water and two-water molecules in the gas phase reaction have been calculated using CCSD(T)/M06-2X with 6-311++G(3df,3pd) basis set. For barrierless reactions, rate constants were calculated using canonical and microcanonical variational transition state theory coupled with RRKM/ME simulations and for non-barrierless reactions CVT/SCT approach was used to compute the rate constants. The relative energies of stationary points on the PES are in good agreement with previous values. The barrier heights of one-water reaction are very high. When an additional water molecule is added to the reaction, barrier heights significantly reduced by 25 kcal/mol. Therefore, we can say that an additional water molecule plays a role of a catalysis.
The rate constants for the formation of CH 2 NH⋯H 2 O is both temperature-and pressure-dependent. At the high-pressure limit, the formation of CH 2 NH⋯H 2 O shows weak positive temperature-dependence. Because the lifetime CH 2 NH⋯H 2 O is too short, it is expected to play a negligible role in the atmosphere.
The one-water reaction is to form formaldehyde and ammonia (within a few minutes) is dominant at high temperatures, whereas the two-water reaction becomes the major channel at a lower temperature if step 0 is not included in the calculation. Ignoring step 0 is equivalent to assuming that all the methylenimine is complexed with water, which is not true. Therefore, the correct reaction pathways should have [H 2 O] in the rate constants calculations. In that case, our calculations demonstrate that two-water reaction has the potential to accelerate a www.nature.com/scientificreports/ gas phase reaction ≤ 500 K, but the rate of formation of formaldehyde and ammonia is predicted to be negligibly slow. This result is also consistent with previous studies on the similar reaction system, i.e., H 2 O + H 2 C=C=O. Experimental studies are required to understand the formation of CH 2 O and NH 3 from CH 2 NH + H 2 O, and other formation schemes must be explored. Once the laboratory characterization is complete, CH 2 O and NH 3 will be an ideal target for observational search. Although this is an interesting reaction system, our results demonstrate that CH 2 NH + H 2 O is not important under atmospheric and combustion conditions compared to an important radical molecule reaction. Such results are encouraging, and chemical kinetic mechanism can be useful for the future implementation of hydrolysis of other imine compounds.

Data availability
All data generated through this study are given in the Supporting Information file.