Effect of Water and Formic Acid on · OH + CH 4 Reaction: An Ab Initio /DFT Study

: In this work, we used ab initio /DFT method coupled with statistical rate theory to answer the question of whether or not formic acid (HCOOH) and water molecules can catalyze the most important atmospheric and combustion prototype reaction, i.e., · OH (OH radical) + CH 4 . The potential energy surface for · OH + CH 4 and · OH + CH 4 (+X) (X = HCOOH, H 2 O) reactions were calculated using the combination of hybrid-density functional theory and coupled-cluster theory with Pople basis set [(CCSD(T)/ 6-311++G(3df,3pd)//M06-2X/6-311++G(3df,3pd)]. The results of this study show that the catalytic effect of HCOOH (FA) and water molecules on the · OH + CH 4 reaction has a major impact when the concentration of FA and H 2 O is not included. In this situation the rate constants for the CH 4 + HO ··· HCOOH (3 × 10 − 9 cm 3 molecule − 1 s − 1 ) reaction is ~10 5 times and for CH 4 + H 2 O ··· HO reaction (3 × 10 − 14 cm 3 molecule − 1 s − 1 at 300 K) is ~20 times higher than · OH + CH 4 (~6 × 10 − 15 cm 3 molecule − 1 s − 1 ). However, the total effective rate constants, which include the concentration of both species in the kinetic calculation has no effect under atmospheric condition. As a result, the total effective reaction rate constants are smaller. The rate constants when taking the account of the FA and water for CH 4 + HO ··· HCOOH (4.1 × 10 − 22 cm 3 molecule − 1 s − 1 ) is at least seven orders magnitude and for the CH 4 + H 2 O ··· HO (7.6 × 10 − 17 cm 3 molecule − 1 s − 1 ) is two orders magnitude smaller than · OH + CH 4 reaction. These results are also consistent with previous experimental and theoretical studies on similar reaction systems. This study helps to understand how FA and water molecules change the reaction kinetic under atmospheric conditions for · OH + CH 4 reaction.


Introduction
The tropospheric concentration of important greenhouse gases, i.e., methane (CH 4 ), is steadily increasing [1][2][3][4]. In the atmosphere, · OH (OH radical) plays a crucial role in removing the CH 4 [1][2][3][4]. The atmospheric lifetime of methane is due to loss by · OH is ∼12-17 years [1][2][3][4]. This reaction is also important in high-temperature combustion kinetics [5]. Due to large uncertainty in the rate constants data, many experimental measurements and theoretical studies have been performed [1][2][3][4][5]. To avoid the repetition of previous studies, only a few studies have been discussed here [1][2][3][4][5]. Various experimental measurements were used to estimate the rate constant for · OH + CH 4 reaction into the atmosphere condition and reported its atmospheric lifetime due to loss with the · OH [1][2][3][4]. Experimental measurement on · OH + CH 4 reaction was done by Vaghjian et al. [2] in the temperature range of 295 to 400 K. Due to the limited number of high temperature studies, Srinivasan et al. measured the rate constants of · OH + CH 4 using the reflected shock tube method [5]. The · OH + CH 4 reaction has been extensively studied by using various theoretical approaches [6][7][8][9]. Most of the theoretical studies have focused on calculating the rate constants using a high-level ab initio methods and statistical rate theory [6][7][8][9]. Ellingson et al. [9] proposed the rate constants for OH + CH 4 reaction and its 12 C/ 13 C kinetic k CVT (T) = min s k GT (T, s) = k GT T, s CVT (T (2) where k GT (T, s) is generalized rate constants and k CVT (T) are the temperature dependent rate canonical variational transition state theory (CVT) rate constants, V MEP is the barrier height without zero-point correction, L = is a reaction path degeneracy, 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, Γ is the small curvature tunneling (SCT) correction as implemented in Polyrate [35]. The rate constants were calculated using a dual dynamic approach with CVT and the interpolated single point energies (ISPE) correction calculated using dual level direct dynamic approach CVT/SCT with interpolated single point energies (ISPE) as discussed in the reference [35,36]. PolyRate and GaussRate suite of programs were used to calculate the temperature-dependent bimolecular and unimolecular rate constants based on CVT/SCT (Table S4) approach [35,36].
The Multiwell Thermo code [37] was used calculate the equilibrium constant (K eq ) for the formation of complexes as given in Equation (3): The equilibrium constants (K eq ) for the formation complexes calculated by Equation (3) were tabulated in Tables S5 and S6.

Reaction Pathways for OH + CH 4
The potential energy surface (PES) for · OH + CH 4 reaction is shown in Figure 1. The rotational vibrational parameters of CH 4 , · OH and TS and products are given in Table S2. As shown in Figure 1, the reaction proceeds via the formation of a pre-reactive complex (RC 1 ) whose energy is higher than the reactants. This is due to fact that the orientation of H of · OH is toward the carbon atom of CH 4 . The role of complex in · OH + CH 4 reaction is unimportant as suggested in earlier studies [8]. The barrier height for · OH + CH 4 is 5.0 kcal/mol is in very good agreement with the value reported by earlier theoretical studies (5-6 kcal/mol) [6-9].

Reaction Pathways for OH + CH4
The potential energy surface (PES) for · OH + CH4 reaction is shown in Figure 1. The rotational vibrational parameters of CH4, · OH and TS and products are given in Table S2. As shown in Figure 1, the reaction proceeds via the formation of a pre-reactive complex (RC1) whose energy is higher than the reactants. This is due to fact that the orientation of H of · OH is toward the carbon atom of CH4. The role of complex in · OH + CH4 reaction is unimportant as suggested in earlier studies [8]. The barrier height for · OH + CH4 is ~5.0 kcal/mol is in very good agreement with the value reported by earlier theoretical studies (5-6 kcal/mol) [6-9]. 3.1.1. Reaction Pathways for · OH + CH4 (+HCOOH) As discussed in the earlier studies, [13,14,[25][26][27][28], under true conditions, it is very unlikely that · OH, CH4, and HCOOH collide simultaneously, therefore the probability of a termolecular reaction is negligible. It is expected that either a CH4···HCOOH or · OH···HCOOH and CH4···HO · will form first, followed by an attack on this complex by third molecule · OH or CH4 or HCOOH. In these three cases, the probable reactions are shown in Equations (4-6): CH4···HCOOH + OH →·CH3 + (H2O) + HCOOH (4) CH4···HO + HCOOH →·CH3 + (H2O) + HCOOH CH4 + HCOOH···HO →·CH3 + (H2O) + HCOOH The potential energy surface (PES) for the effect of FA on · OH + CH4 reaction is shown in Figure 2. The optimized geometries and rotational vibrational parameters of CH4, · OH, Figure 1. Potential energy surface for the · OH + CH 4 reaction leading to form methyl radical and water. The stationary point was computed at the CC//M06-2X level and ZPE correction obtained from vibrational analysis using M06-2X.
3.1.1. Reaction Pathways for · OH + CH 4 (+HCOOH) As discussed in the earlier studies, [13,14,[25][26][27][28], under true conditions, it is very unlikely that · OH, CH 4 , and HCOOH collide simultaneously, therefore the probability of a termolecular reaction is negligible. It is expected that either a CH 4 ···HCOOH or · OH···HCOOH and CH 4 ···HO · will form first, followed by an attack on this complex by third molecule · OH or CH 4 or HCOOH. In these three cases, the probable reactions are shown in Equations (4)-(6): The potential energy surface (PES) for the effect of FA on · OH + CH 4 reaction is shown in Figure 2. The optimized geometries and rotational vibrational parameters of CH 4 , · OH, and TS and products are given in Tables S1 and S2. The calculated binding energy (BE) between · OH and FA1 (−3.85 kcal/mol) is in very good agreement with the value (−3.59 kcal/mol) reported previously [19]. The BE of FA2···OH (−2.83 kcal/mol) is 1 kcal/mol higher than the BE of FA11···OH (−3.85 kcal/mol). This is due to fact that the cis and trans orientation of FA. The trans form of FA with · OH leading more strong hydrogen bonding than the cis form. The B.E. of CH 4 ···OH (+0.3 kcal/mol) and CH 4 ···HCOOH (+0.3 kcal/mol) is very small compared to B.E. of HCOOH···OH, therefore, we have neglected these complexes. As shown in Figure 2, beginning with the CH 4 + HCOOH···OH, two three-body complexes PRC FA-1 and PRC FA-2 were formed due to the trans and cis orientation of FA ( Figure 2). The relevant TS structures connected to these PRCs are shown in Figure 2. The other PRC FA was also optimized and found that they are less stable than PRC FA-1 and PRC FA-2 , therefore not included in the PES of CH 4 + · OH···HCOOH reaction (see Figure S1). and TS and products are given in Tables S1 and S2. The calculated binding energy (BE) between · OH and FA1 (−3.85 kcal/mol) is in very good agreement with the value (−3.59 kcal/mol) reported previously [19]. The BE of FA2···OH (−2.83 kcal/mol) is 1 kcal/mol higher than the BE of FA11···OH (−3.85 kcal/mol). This is due to fact that the cis and trans orientation of FA. The trans form of FA with · OH leading more strong hydrogen bonding than the cis form. The B.E. of CH4···OH (+0.3 kcal/mol) and CH4···HCOOH (+0.3 kcal/mol) is very small compared to B.E. of HCOOH···OH, therefore, we have neglected these complexes. As shown in Figure. 2, beginning with the CH4 + HCOOH···OH, two three-body complexes PRCFA-1 and PRCFA-2 were formed due to the trans and cis orientation of FA ( Figure 2). The relevant TS structures connected to these PRCs are shown in Figure. 2. The other PRCFA was also optimized and found that they are less stable than PRCFA-1 and PRCFA-2, therefore not included in the PES of CH4 + · OH···HCOOH reaction (see Figure S1). The BE of PRCFA-1 (−6.96 kcal/mol) and PRCFA-2 (−4.32 kcal/mol) is the result of C···H and O···H interactions. Starting from PRCFA-1 and PRCFA-2, we have identified two reaction pathways, i.e., hydrogen abstraction by · OH on two different orientations of FA. Transition state (TSF1) corresponds to H-abstraction reaction from methane hydrogen via PRCFA-1. The calculated barrier heights for this pathway (~3.76 kcal/mol), which are lower than the barrier height for · OH + CH4 reaction (~5 kcal/mol). The transition state (TSF2) corresponds to the H abstraction reaction from methane hydrogen via PRCFA-2. The calculated barrier height TSF2 (~ 5.32 kcal/mol) which leads to form a product FA-2 (cis-Hydrogen). The BE of PRC FA-1 (−6.96 kcal/mol) and PRC FA-2 (−4.32 kcal/mol) is the result of C···H and O···H interactions. Starting from PRC FA-1 and PRC FA-2 , we have identified two reaction pathways, i.e., hydrogen abstraction by · OH on two different orientations of FA. Transition state (TS F1 ) corresponds to H-abstraction reaction from methane hydrogen via PRC FA-1 . The calculated barrier heights for this pathway (~3.76 kcal/mol), which are lower than the barrier height for · OH + CH 4 reaction (~5 kcal/mol). The transition state (TS F2 ) corresponds to the H abstraction reaction from methane hydrogen via PRC FA-2 . The calculated barrier height TS F2 (~5.32 kcal/mol) which leads to form a product FA-2 (cis-Hydrogen). The barrier height of TS F1 (~4 kcal/mol,) is~1 kcal/mol lower than the value of TS F2 (~5 kcal/mol) expected to play a more important role in the kinetic calculations [13,14,19].

Reaction Pathways for · OH + CH 4 (+H 2 O)
As suggested in the FA case, the simultaneous collisions of · OH, CH 4 , and H 2 O, are very unlikely, therefore the termolecular reaction probability is negligible under real conditions. It is expected that either a CH 4 ···H 2 O or · OH···H 2 O or CH 4 ···OH will form first, followed by an attack on this complex by the third molecule · OH or CH 4 or H 2 O to this complex. In these three cases, the most probable reactions are given in Equations (7)- (9): Out of three, only one OH···H 2 O (−4.1 kcal/mol) as a two-body complex is found to be more stable than CH 4 ···H 2 O (−0.3 kcal/mol) and CH 4 ···OH (+0.3 kcal/mol), therefore the reactions (7) and (8) are not considered in the potential energy surface plot. The potential energy surface (PES) for the effect of water on · OH + CH 4 reaction is shown in Figure 3. As shown in Figure 3, beginning with the CH 4 + · OH···H 2 O reaction, the three-body complex i.e., PRC w was formed depending on the approach of the hydrogen atom in the · OH towards the water oxygen or the hydrogen of · OH ( Figure 3). We tried different way of projecting OH and H 2 O in the reaction, which led to two different PRC ws , i.e., PRC w-1 (−4.3 kcal/mol) and PRC w-2 (−3.1 kcal/mol). The optimized structure is given in the supporting information Figure S1. As suggested in earlier work on a similar reaction system [21], only stable PRC w was considered for the rate constant calculations. Therefore, we restricted our discussion to only stable PRC w-1 . The barrier height of TSF1 (~4 kcal/mol,) is ~1 kcal/mol lower than the value of TSF2 (~5 kcal/mol) expected to play a more important role in the kinetic calculations [13,14,19].

Reaction Pathways for · OH + CH4 (+H2O)
As suggested in the FA case, the simultaneous collisions of · OH, CH4, and H2O, are very unlikely, therefore the termolecular reaction probability is negligible under real conditions. It is expected that either a CH4···H2O or · OH···H2O or CH4···OH will form first, followed by an attack on this complex by the third molecule · OH or CH4 or H2O to this complex. In these three cases, the most probable reactions are given in Equations (7-9): Out of three, only one OH···H2O (−4.1 kcal/mol) as a two-body complex is found to be more stable than CH4···H2O (−0.3 kcal/mol) and CH4···OH (+0.3 kcal/mol), therefore the reactions (7) and (8) are not considered in the potential energy surface plot. The potential energy surface (PES) for the effect of water on · OH + CH4 reaction is shown in Figure 3. Figure 3, beginning with the CH4 + · OH···H2O reaction, the three-body complex i.e., PRCw was formed depending on the approach of the hydrogen atom in the · OH towards the water oxygen or the hydrogen of · OH ( Figure 3). We tried different way of projecting OH and H2O in the reaction, which led to two different PRCws, i.e., PRCw-1 (−4.3 kcal/mol) and PRCw-2 (−3.1 kcal/mol). The optimized structure is given in the supporting information Figure S1. As suggested in earlier work on a similar reaction system [21], only stable PRCw was considered for the rate constant calculations. Therefore, we restricted our discussion to only stable PRCw-1.

Enthalpies of Reactions (∆H rxn (0 K))
The enthalpies (∆H(0 K)) relative to the reactants for · OH + CH 4 , · OH + CH 4 (+HCOOH) and · OH + CH 4 (+H 2 O) reactions are given in Table 1. The calculated ∆H(0 K) of · OH + CH 4  [38][39][40] and is in very good agreement with previous theoretical calculation (−13.9 kcal/mol) [7,9]. As shown in Figure 2, the formation of the complex in · OH···CH 4 ···HCOOH (PRC FA1 ) and · OH···CH 4 ···HCOOH (PRC FA2 ), are in trans-and cis orientation of HCOOH. Due to the different orientations of OH and HCOOH molecules, the BE of PRCF A1 (−6.96 kcal/mol) and PRCF A2 (−4.32 kcal/mol) are different (see Figure 2 and Table 1). The orientation of the H-atom of HCOOH makes a strong hydrogen bond between · OH···CH 4 ···HCOOH leading to more stable PRC FA1 . The calculated BE of · OH···CH 4 ···H 2 O (PRC w ) (−4 kcal/mol) is lower than BE of PRC FA (−6.96 kcal/mol) due to the presence of weak hydrogen bonds. It is clear from Table 1 that barrier height for the effect of FA and water molecules on · OH + CH 4 reaction is smaller than the barrier height of the free · OH + CH 4 reaction, which gives the indication of catalytic behavior of FA and water on · OH + CH 4 reaction. Table 1. Enthalpies of reaction (∆H rxn (0 K)) in kcal mol −1 of · OH + CH 4 reaction.

Rate Constants · OH + CH 4 Reaction
The CVT/SCT rate constant for · OH + CH 4 reaction is calculated and tabulated in Table 2 and shown in Figure 4. The calculated value using harmonic oscillator (HO) approximation is a factor of~2 lower than experimentally measured values over the entire temperature range ( Table 2). The rate constant calculated using HO approximation (2.3 × 10 −15 cm 3 molecule −1 s −1 at 300 K) is in very good agreement with the HO approximation of Ellingson et al [9] (2.3 × 10 −15 cm 3 molecule −1 s −1 at 300 K).
As suggested by Ellingson et al. [9], the free-rotor approximation is the correct choice, which is consistent with our study. The calculated value using free-rotor approximation at 300 K (6.1 × 10 −15 cm 3 molecule −1 s −1 ) is in excellent agreement with the experimentally measured [2,41] value (6.7 × 10 −15 and 6.9 × 10 −15 cm 3 molecule −1 s −1 ) and good agreement with theoretically calculated ones (4 × 10 −15 cm 3 molecule −1 s −1 and 6 × 10 −15 cm 3 molecule −1 s −1 ) [7,9]. Our value is in very good agreement over the entire temperature range with the experimentally measured values. The calculated value is also in very good agreement with Srinivasan et al. (Figure 4) [5]. The calculations of rate constant for · OH + CH 4 reaction provide more confidence in our theoretical approach CC//M06-2X with CVT/SCT method. To avoid the repetition of the · OH + CH 4 reaction, we have restricted our comparison to only a few experimental and theoretical values [2,5,7,9,41].  with Srinivasan et al. (Figure 4) [5]. The calculations of rate constant for · OH + CH4 reaction provide more confidence in our theoretical approach CC//M06-2X with CVT/SCT method.
To avoid the repetition of the · OH + CH4 reaction, we have restricted our comparison to only a few experimental and theoretical values [2,5,7,9,41].   . Rate constants for · OH + CH4 reaction. The rate constants were calculated using harmonic oscillator and free-rotor approximation.

Formic Acid Assisted · OH + CH4 Reaction
As suggested in the thermochemistry section, the binding energy of CH4···HCOOH, and CH4···OH smaller than that of HCOOH··· HO · which will result in a shorter lifetime. Therefore, the formation of CH4···HCOOH, CH4···OH is almost negligible compared to HCOOH··· HO · and only one channel, i.e., CH4 + HCOOH··· HO · is considered for the rate constants calculations.  . Rate constants for · OH + CH 4 reaction. The rate constants were calculated using harmonic oscillator and free-rotor approximation.

Formic Acid Assisted · OH + CH 4 Reaction
As suggested in the thermochemistry section, the binding energy of CH 4 ···HCOOH, and CH 4 ···OH smaller than that of HCOOH··· HO · which will result in a shorter lifetime. Therefore, the formation of CH 4 ···HCOOH, CH 4 ···OH is almost negligible compared to HCOOH··· HO · and only one channel, i.e., CH 4 + HCOOH··· HO · is considered for the rate constants calculations.

Water-Assisted · OH + CH 4 Reaction
As discussed in the case of FA assisted reaction, only one CH 4 + · OH···H 2 O channel is considered for the rate constants calculations. The other channels, i.e., the formation of CH 4 ···H 2 O, CH 4 ···OH, are almost negligible.
The reaction pathways for the effect of a water molecule on · OH + CH 4 starting with · OH···H 2 O are presented in Equation (12): (12) The rate constants (s −1 ) for · OH + CH 4 (+H 2 O) (PRC w → TS → P) were tabulated in Table S4. The rate constants (cm 3 molecule −1 s −1 ) were calculated using k 2w = K eq(A) × k TSaw , where K eq(A) is in equilibriumconstants involved in the · OH···H 2 O + CH 4 reaction. The rate constants in the temperature range of 200 K to 400 K for with and without water concentration are shown in Figure 6. The rate constants for CH 4 + H 2 O···OH reaction (3 × 10 −14 cm 3 molecule −1 s −1 at 300 K) is~20 times higher than · OH + CH 4 reaction (6 × 10 −15 cm 3 molecule −1 s −1 at 300 K. As shown in Figure 6, the water-catalyzed reaction has higher rate constants than a water-free reaction in the entire temperature range 200-400 K. Catalysts 2022, 12, 133 11 Figure 6. Rate constants for · OH + CH4 + (H2O) with different relative humidity. CH4 + H2O···O the rate constants without water concentration. The water concentration at this humidity is t from our earlier studies [21,27]. The presented rates are the relative humidity of water from 20 100%.
In order to gain correct insight into the effect of FA/water on · OH + CH4 reaction free energy profiles for all the channels were computed and shown in supporting in mation Figure S2. Due to the high entropy of activation of (ΔS ‡ ) of FA/H2O assisted r tion than free OH + CH4 reaction, rate constants are higher. It is also important to p out that, in the gas phase reaction, the barrier height ΔE ‡ and ΔG ‡ are calculated as energies difference between the transition state and those of the two-body complex, RC complex, while in the water-assisted and FA-assisted reaction, ΔE ‡ and ΔG ‡ are ca lated from energies difference of transition state and termolecular complex i.e., PR Thus, if step 0 is ignored and the rate constant is calculated as keff = Keq × k2 and the reac rate constant is higher in the presence of FA/H2O and catalytic effect is favorable for + CH4 The total rate constants for · OH + CH4 and effective rate constants for · OH + Figure 6. Rate constants for · OH + CH 4 + (H 2 O) with different relative humidity. CH 4 + H 2 O···OH is the rate constants without water concentration. The water concentration at this humidity is taken from our earlier studies [21,27]. The presented rates are the relative humidity of water from 20% to 100%.
As suggested in our earlier studies [25][26][27], the concentration of water at varying humidity levels must be used to estimate the accurate rate constant. Therefore, the correct expression to calculate the total effective rate constants is given by Equation (13) k e f f where K eq(2) are equilibrium constants of H 2 O + · OH →RC 2w reactions, [H 2 O] is water concentration as discussed in earlier studies [21,27]. The effective rate constant (7 × 10 −17 cm 3 molecule −1 s −1 at 300 K) is factor of~100 lower than the water-free OH + CH 4 reaction (~6 × 10 −15 cm 3 molecule −1 s −1 at 300 K) at 100% humidity. The result is also consistent with similar atmospheric reactions, i.e., · OH + CH 2 NH, · OH + CH 2 CH 2 , · OH + CH 2 O, and OH + CH 3 OH [25][26][27].
In order to gain correct insight into the effect of FA/water on · OH + CH 4 reaction, the free energy profiles for all the channels were computed and shown in supporting information Figure S2. Due to the high entropy of activation of (∆S ‡ ) of FA/H 2 O assisted reaction than free OH + CH 4 reaction, rate constants are higher. It is also important to point out that, in the gas phase reaction, the barrier height ∆E ‡ and ∆G ‡ are calculated as the energies difference between the transition state and those of the two-body complex, i.e., RC complex, while in the water-assisted and FA-assisted reaction, ∆E ‡ and ∆G ‡ are calculated from energies difference of transition state and termolecular complex i.e., PRCs. Thus, if step 0 is ignored and the rate constant is calculated as k eff = K eq × k 2 and the reaction rate constant is higher in the presence of FA/H 2 O and catalytic effect is favorable for · OH + CH 4 The total rate constants for · OH + CH 4 and effective rate constants for · OH + CH 4 (+HCOOH) and · OH + CH 4 (+H 2 O) reactions are tabulated in Table 3 and shown in Figure 7.  The result of this study suggests that the catalytic effect of FA and water takes place if the concentration of these molecules were not included, which is unrealistic. Therefore, to calculate the correct reaction rate constants we must include the concentration of HCOOH and H 2 O in the final rate constant calculations. In that situation, the results explain that the total effective rate constants for systems · OH + CH 4 (+HCOOH) (~7 order) and · OH + CH 4 (+H 2 O) (2 order) are magnitudes smaller than the free situation. The total effective rate constants · OH + CH 4 (+HCOOH) (~4 × 10 −22 cm 3 molecule −1 s −1 at 300 K) and · OH + CH 4 (+H 2 O) (~7 × 10 −17 cm 3 molecule −1 s −1 at 300 K) are smaller than · OH + CH 4 (~6 × 10 −15 cm 3 molecule −1 s −1 at 300 K). Similar results were reported in an earlier study [13,[25][26][27][28]. It is clear from geometries of PRCs and TSs, which are different in OH + CH 4 (+HCOOH) than reaction · OH + CH 4 (+H 2 O) resulted in different computed enthalpies and rate constants. Because of that, the kinetics of · OH + CH 4 (+HCOOH) are quite different from those · OH + CH 4 (+H 2 O) reaction systems. In the case of the FA, the rate constants show positive temperature dependence, and in the case of water, the rate constants show negative temperature dependence. This is due to water concentration varying greatly with temperature, whereas HCOOH concentration is nearly temperature independent.
The result of this study suggests that the catalytic effect of FA and water takes p if the concentration of these molecules were not included, which is unrealistic. There to calculate the correct reaction rate constants we must include the concentratio HCOOH and H2O in the final rate constant calculations. In that situation, the results plain that the total effective rate constants for systems · OH + CH4 (+HCOOH) (~7 or and · OH + CH4 (+H2O) (2 order) are magnitudes smaller than the free situation. The effective rate constants · OH+CH4 (+HCOOH) (~4 × 10 −22 cm 3 molecule −1 s −1 at 300 K) · OH + CH4 (+H2O) (~7 × 10 −17 cm 3 molecule −1 s −1 at 300 K) are smaller than · OH + CH4 ( 10 −15 cm 3 molecule −1 s −1 at 300 K). Similar results were reported in an earlier study [13 28]. It is clear from geometries of PRCs and TSs, which are different in OH + (+HCOOH) than reaction · OH + CH4(+H2O) resulted in different computed enthalpies rate constants. Because of that, the kinetics of · OH + CH4 (+HCOOH) are quite diffe from those · OH + CH4 (+H2O) reaction systems. In the case of the FA, the rate const show positive temperature dependence, and in the case of water, the rate constants s negative temperature dependence. This is due to water concentration varying greatly w temperature, whereas HCOOH concentration is nearly temperature independent.
In general, the effective rate constants of the FA and water-assisted reaction is smaller than the · OH + CH 4 reaction system. As a result, the catalytic effect of FA/H 2 O on · OH + CH 4 reaction is of minor importance in gas-phase atmospheric reaction chemistry. This result is consistent with previously reported results on similar reaction system [13,[25][26][27][28]. To understand the upper troposphere consequences of CH 4 [42].
As discussed in this study, the rate constants for the effect of FA and water are almost negligible as compared to the naked reaction. It is important to mention that the comparison of effective rate constant with naked reaction does not provide the complete picture for the degradation mechanism of CH 4 . Experimental measurement is required to validate the current study. Based on this study, we believe that the effect of FA and water on the formation of formaldehyde will even be slower. We believe the current finding provides better insights into the gas-phase catalytic activity of FA and water molecules on · OH + CH 4 .

Conclusions
The effect of FA and water molecules on · OH + CH 4 was explored. The potential energy surfaces for OH + CH 4 , CH 4 + HO··· HCOOH, and CH 4 + HO···H 2 O have been explored using CC//M06-2X. The rate constants for these reactions were computed using CVT/SCT approach.
In the presence of FA, the two different channels of the hydrogen abstraction reaction were identified. In the case of the water reaction, only one reaction pathway was identified. Under the atmospheric condition, the kinetics of · OH + CH 4 (+HCOOH) is quite different from those of · OH + CH 4 (+H 2 O). This difference is possibly due to the FA concentrations being much lower than H 2 O. Our results demonstrate that a FA and water molecule has the potential to catalyze the gas-phase reaction if the atmospheric concentration of these species is not included in the kinetic calculations. However, as suggested, the total effective rate constant must include the concentration of FA and water. In that situation, the total rate is constants for the effect of FA and water than the · OH + CH 4 reaction is lower. The present study provides a comprehensive model of how the acidic nature of these catalysts affects the gas-phase reaction kinetics. The atmospheric degradation mechanism suggests that CH 3 can further react with O 2 molecules to form the formaldehyde under atmospheric and combustion conditions. The effect of FA and water molecules could be even slower in the formation of formaldehyde. These kinds of results are interesting and can be used to identify the effect of FA and water on higher chain alkane compounds.