Article pubs.acs.org/JPCA

Atmospheric Gas Phase Chemistry of CH2NH and HNC. A FirstPrinciples Approach Arne Joakim C. Bunkan,† Yizhen Tang,‡ Stig R. Sellevåg,† and Claus J. Nielsen*,† †

Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern 0315, Oslo, Norway ‡ School of Environmental and Municipal Engineering, Qingdao Technological University, Fushun Road 11, Qingdao, Shandong 266033, P.R. China S Supporting Information *

ABSTRACT: Quantum chemical methods were used to investigate the OH initiated atmospheric degradation of methanimine, CH2NH, the major primary product in the atmospheric photo-oxidation of methylamine, CH3NH2. Energies of stationary points on potential energy surfaces of reaction were calculated using multireference perturbation theory and coupled cluster theory. The results show that hydrogen abstraction dominates over the addition route in the CH2NH + OH reaction, and that the major primary product is HCN, while HNC and CHONH2 are minor primary products. HNC is found to react with OH exclusively via addition to the carbon atom followed by O−H scission leading to HNCO; N2O is not a product in the atmospheric photooxidation of HNC. Additional G4 calculations of the CH2NH + O3 reaction show that this is too slow to be of importance at atmospheric conditions. Rate coefficients for the CH2NH + OH and HNC + OH reactions were calculated as a function of temperature and pressure using a master equation model based on the coupled cluster theory results. The rate coefficients for OH reaction with CH2NH and HNC at 1000 mbar and room temperature are calculated to be 3.0 × 10−12 and 1.3 × 10−11 cm3 molecule−1 s−1, respectively. The atmospheric fate of CH2 NH is discussed and a gas phase photo-oxidation mechanism is presented. 10−19 cm2 molecule−1 near 250 nm;10 there is no information concerning the spectrum in the region of relevance to tropospheric chemistry (λ > 300 nm). It is likely that the absorption band stretches into this region such that photolysis may occur in the troposphere in which case the only products will be HCN + H210,11 (the UV spectrum of 2,3,4,5tetrahydropyridine has its maximum at 225 nm and extends to 285 nm; at 280 nm the cross section is less than 1% of the peak value12). Schade and Crutzen13 speculated on the atmospheric chemistry of methanimine in their study of emission of aliphatic amines from animal husbandry, and estimated that with cross sections of 3 × 10−20 to 3 × 10−21 cm2 molecule−1 in the 290−320 nm region and a unity quantum yield to photodissociation, the photolytic lifetime would be around 10−100 h for “overhead sun” conditions. They further suggested that CH2NH could be a potential source of N2O via HNC as intermediate in its atmospheric photo-oxidation. On a global scale the major atmospheric gas phase sink for imines is expected to be reaction with OH radicals, while reactions with O3, Cl atoms, and NO3 radicals will be of limited significance compared to that with OH radicals. The present

1. INTRODUCTION Imines (general formula: R1R2CNR3) have been detected as major products in the atmospheric gas phase photo-oxidation of amines.1−4 The simplest imine, methanimine, CH2NH, is reported to account for around 90% of all primary products formed in the atmospheric photo-oxidation of CH3NH2.2 A vintage review of the chemistry of imines reports rapid hydrolysis reactions (>CNR + H2O → >CO + H2NR) and addition reactions with primary amines (i.e., >CNH + H2NR → >CNR + NH3).5 In addition, simple imines enter a reversible trimerization reaction with the corresponding 1,3,5triazine.6 Virtually nothing is known about the atmospheric chemistry of imines. Tuazon and co-workers found CH2NCH3 as a product in the (CH3)2NH and (CH3)3N reactions with O3 reporting that CH2NCH3 was “essentially non-reactive towards O3”.7 Lazarou and Papagiannakopoulos studied the reaction of CH2NCH3 with Cl atoms employing the VLPR technique at 303 K and reported kCH2NCH3+Cl = (1.9 ± 0.15) × 10−11 cm3 molecule−1 s−1,8 which is comparable to the low pressure rate coefficient for the Cl + CH2CHCH3 reaction (4 × 10−11 cm3 molecule−1 s−1 at 0.33 Torr).9 There is a single experimental study of the electronic spectrum of CH2NH in the region 235−260 nm showing a broad and structureless absorption of the n → π* transition with its maximum of ∼4 × © 2014 American Chemical Society

Received: May 19, 2014 Revised: June 19, 2014 Published: June 20, 2014 5279

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study addresses the reaction of CH2NH with OH radicalsa reaction that will be extremely difficult to carry out in the laboratory due to imine polymerization and surface reactions.

where p(0) contains the initial conditions for each grain, U is an eigenvector matrix obtained from the diagonalization of M, and Λ is the diagonal matrix of corresponding eigenvalues, where the smallest eigenvalues are the chemically significant eigenvalues. Time-dependent concentrations of different species were obtained by summing the normalized populations from eq 2 over the appropriate grains. The phenomenological rate constants were extracted from the chemically significant eigenvalues using a procedure similar to that described by Bartis and Widom.36 Spin−orbit coupling in the OH radical (139.7 cm−1)37 was included in the model by lowering the energy of the OH radical with half of the splitting and including the 2Π3/2 and 2Π1/2 spin−orbit states in the electronic partition function. It was assumed that spin−orbit coupling could be neglected in the prereaction adduct and in the saddle points. Lennard-Jones parameters for the CH2NH + OH and HNC + OH reactions were approximated with values for ethanol38 (ε = 362.6 K, σ = 4.530 Å) and the energy transfer in collisions with N2 and O2, ⟨ΔEdown⟩, was set to 250 cm−1. Variation of these parameters resulted in only minor changes in the calculated rate coefficients; changing ⟨ΔEdown⟩ by ±50 cm−1 resulted in changes of ±3% in the overall rate coefficients. The Lennard-Jones parameters were varied over the 200 K < ε < 500 K and 4 Å < σ < 5 Å range resulting in only ±2% changes in the calculated rate coefficients.

2. COMPUTATIONAL METHODS 2.1. Quantum Chemical Methods. Geometry optimization of stationary points on the potential energy surfaces (PES) of the OH reactions with CH2NH and HNC as well as the HOCH2NH → OCH2NH2 and CHOHNH → CHONH2 tautomerization reactions were performed at the CCSD(T)/ccpVTZ, and for the CH2NH + OH reactions, also at the CASPT2 level of theory using Molpro.14,15 Dunning’s correlation-consistent (aug-)cc-pVXZ (X = D, T, Q) basis sets16−18 were employed in all calculations. Improved single point energies were calculated using CCSD(T)/cc-pVXZ (X = T, Q) for the optimized geometries and extrapolated toward the basis set limit using the extrapolation scheme proposed by Helgaker et al.;19 these energy calculations will be referred to as CCSD(T)/cc-pV(TQ)Z. The HOCH2NH → OCH2NH2 and CHOHNH → CHONH2 tautomerization reactions were also investigated using the complete active space self-consistent field (CASSCF) method using GAMESS.20,21 Dynamical electron correlation was included by using multireference second-order Møller− Plesset perturbation theory (MRMP2).22,23 Reaction enthalpies were calculated from the G324 and G425 model chemistries, which are reported to reproduce the G3/05 test26 set with average absolute deviations of around 4.7 and 3.5 kJ mol−1, respectively. The G3 method is based on MP2/631G(d) structures and HF/6-31G(d) vibrational frequencies, while G4 model chemistry is based on B3LYP/6-31G(2d,f,p) structures and vibrational frequencies. G3 and G4 results are collected in Table S1 (Supporting Information); the results agree within a few kJ mol−1 and the G4 results for reaction enthalpies are presented in the text. The standard state chosen for gases is 1 bar ideal gas. Additional MP2,27 CCSD,28,29 B3LYP,30,31 BHandHLYP as implemented in Gaussian, and M0632,33 calculations were carried out using Gaussian 09.34 The minimum energy path connecting reactants and products was computed employing the intrinsic reaction coordinate (IRC) method as implemented in Gaussian. 2.2. Kinetics Calculations. Master equation calculations were carried out using the program MESMER 3.0 (Master Equation Solver for Multi-Energy-Well Reactions)35 to simulate the kinetics of the OH radical reactions with CH2NH and HNC. The required input parameters for the stationary points were obtained from the ab initio calculations. The problem was set up by dividing the energy of the intermediates into grains, and the time evolution of the system was then obtained by solving the energy grained master equation, eq 1 d p = M·p dt

3. RESULTS AND DISCUSSION 3.1. CH2NH + OH. The initial step in the CH2NH reaction with OH radicals will either be an addition to the πsystem or a hydrogen abstraction:

where the reaction enthalpies listed stem from G4 calculations.25 Energies and geometries of stationary points on the CH2 NH + OH potential energy surface (PES) were calculated using coupled cluster theory and multireference perturbation theory; the results are summarized in Tables S2−S6 (Supporting Information). Figure 1 illustrates the energetics of the stationary points on the PES derived in CCSD(T)/ccpV(TQ)Z //CCSD(T)/cc-pVTZ calculations (Cartesian coordinates of reactants and stationary points are collected in Table S7 in the Supporting Information). All routes, with the exception of 3bthe OH addition to the nitrogen atom in CH2NHhave barriers close to zero at the CCSD(T)/cc-pV(TQ)Z//CCSD(T)/cc-pVTZ level of theory. The T1 diagnostic values39 are, however, rather large for the saddle points, with values of 0.040 for the N−H abstraction and the N−OH addition reactions, and 0.035 for the C−H abstraction reactions. Energies and frequencies for the stationary points were therefore also derived in CASPT2 calculations employing different active spaces and basis sets. For the hydrogen abstraction reactions the minimum active space consists of 5 electrons in 5 orbitals, CASPT2(5,5), and

(1)

where p is the population vector containing the population, n(E), of energy grains from radical species and M is the matrix that describes the population evolution due to collisional energy transfer and reaction, and also includes bimolecular source terms in order to describe formation of prereaction adducts. Equation 1 represents a set of coupled differential equations and is solved to yield eq 2 p = U ·e Λ·t ·U −1·p(0)

(2) 5280

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C−H bond is elongated by ∼16 pm, while the O−H bond being formed is ∼124 pm. The CH2NH + OH abstraction routes are, in contrast, characterized by “early transition states” with the broken X−H bonds being elongated by only ∼4 pm (N−H abstraction), ∼7 pm (C−Hcis abstraction), and 11 pm (C−Htrans abstraction), and electronic barriers of −2.9, 5.4, and 12.8 kJ mol−1; the corresponding O−H bonds being formed in the reactions are, respectively, ∼150, ∼143, and ∼132 pm. In summary, there is a pronounced difference between the ethene and methanimine reactions with OH; the CH2NH + OH reaction is a mixed addition/abstraction reaction at atmospheric conditions whereas the CH2CH2 + OH reaction is entirely an addition reaction. Kinetics of the CH2NH + OH Reaction. The kinetics of the CH2NH + OH reaction may in principle be governed by the formation of both a prereaction adduct and one or more tight inner transition states. Microcanonical rate coefficients for the inner transition states were calculated using RRKM theory based on energies and rovibrational data from the CCSD(T)/ cc-pV(TQ)Z//CCSD(T)/cc-pVTZ calculations. Rate coefficients for the outer transition states were calculated using the inverse Laplace transform of capture rate expressions of the form k(T) = C × (T/298 K)−1/6 from long-range transition state theory (LRTST),41 assuming a dipole−dipole potential. The calculated value of C is 4.86 × 10−10 cm3 molecule−1 s−1 and the sensitivity of the overall rate to variations in the capture rate was tested by varying C between 10−9 and 10−10 cm3 molecule−1 s1; only minor changes in the overall and individual rates were found. Consequently, it is concluded that the reaction is controlled by the inner, tight transition states. The barriers to rotation of the OH fragment at the saddle points of reaction are very different in both shape and height; BHandHLYP/aug-cc-pVDZ calculations suggest barriers ranging from 0.5 to 25 kJ mol−1 (Figure S1 in the Supporting Information). Calculations in which the OH torsion was treated as a hindered internal rotor employing the derived rotational potentials were therefore also carried out. The calculated overall rate coefficient at 298 K and 1000 mbar is 3.0 × 10−12 cm3 molecule−1 s−1 and the results show that the hydrogen abstraction routes dominate at all temperatures and pressures relevant to the atmosphere. The branching ratio of reactions 3a−e at 1000 mbar and 298 K is calculated to be 6:0:55:12:26 in the harmonic oscillator approximation, and 4:0:36:12:49 according to the hindered rotor model. Figure 2 shows rate coefficients for the overall reaction of CH2NH with OH radicals as a function of temperature and pressure (data found in Table S8 in the Supporting Information). The reaction shows weak temperature dependency and a positive pressure dependency. The latter originates to a large extent in reaction 3a, while the other routes show very little pressure dependency. Individual and overall reaction rates as a function of temperature are shown in Figure 3 (data found in Table S9 in the Supporting Information). In contrast to the situation for the methyl amines,42 the CH2NH + OH reaction is, as mentioned above, not close to being collision controlled, and minor changes in the relative barrier heights have a relatively large influence on both the rate coefficient and the branching ratio. The sensitivity of the calculated branching ratio to changes in barrier heights was probed by shifting the barrier heights; Table S10 in the Supporting Information summarizes the results. The Jacobean matrix shows that rate coefficient and branching ratio are mostly sensitive to changes in the saddle point energies of

Figure 1. Relative energies of stationary points on the potential energy surface of the CH2NH + OH reaction. Results from CCSD(T)/ccpV(TQ)Z//CCSD(T)/cc-pVTZ calculations.

includes the bonding and antibonding orbitals of the bond being broken, the O−H bond and the unpaired electron in OH. A larger active space, CASPT2(9,9), which includes the bonding and antibonding π and σ orbitals of the CN bond was also investigated. For the addition reactions, the minimum active space consists of 3 electrons in 3 orbitals, CASPT2(3,3), and includes the bonding and antibonding π-orbitals of the C N bond and the unpaired electron in OH. A larger active space, CASPT2(5,5), that includes the bonding and antibonding σ orbitals of the O−H bond was also studied. The CASSCF calculations indicate that the bonds formed and broken in the hydrogen abstraction reactions all have occupation numbers around of 1.975, while the bonds being formed in the addition reactions to the C and N sites have occupation numbers around 1.90. The agreement among barrier heights calculated using CCSD(T) and CASPT2 is in general very good for the hydrogen abstractions but somewhat less satisfactory for the addition reactions. However, the improved single point energies of the saddle points, based on the CCSD(T) and CASPT2 geometries, are in excellent agreement for all reactions. We therefore conclude that the potential multireference character of the saddle points is not seriously affecting the coupled cluster results. The NH abstraction reaction 3e has the lowest barrier at most levels of theory with a barrier (zero point corrected value, ΔE‡v=0) at the CCSD(T)/cc-pV(TQ)Z//CCSD(T)/cc-pVTZ level of theory of −1.9 kJ mol−1, whereas CASPT2 calculations with different active spaces and basis sets indicate the barrier for this reaction to be between −2.7 and +0.9 kJ mol−1. Disregarding the endothermic route 3b of OH addition to the nitrogen atom in CH2NH, the other routes in the OH reaction with methanimine are significantly more exothermic than the corresponding ethene reactions.40 The pre-reaction adduct is ∼25 kJ mol−1 deeper, the saddle point to C-addition is ∼7 kJ mol−1 lower, and the exothermicity of the addition route increases by ∼20 kJ mol−1 in the CH2NH + OH system. More important, the abstraction routes 3c−e increase in exothermicity from ∼35 kJ mol−1 in the CH2CH2 + OH → CH2CH + H2O reaction40 to an average of ∼100 kJ mol−1. This increase is also reflected in the saddle point structures and energies. The CH2CH2 + OH abstraction route having an electronic barrier of ∼20 kJ mol−140 is characterized by a “late transition state” in which the broken 5281

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coefficient to 1.9 × 10−12 cm3 molecule−1 s−1 at 298 K and 1000 mbar. The calculated rate coefficient, as mentioned above, is 3.0 × 10−12 cm3 molecule−1 s−1 at 298 K and 1000 mbar, which is comparable to the experimental atmospheric pressure value for ethene44 (7.8 × 10−12 cm3 molecule−1 s−1), but significantly lower than that for methyl amine42,45,46 (1.9 × 10−11 cm3 molecule−1 s−1). Even lowering all barriers by 4 kJ mol−1, which is considered unrealistic, results in a rate coefficient 30% below that of methylamine. Concerning the branching in reaction 3, the sensitivity study allows a conservative estimate to be made: the addition route will account for less than 20%, and the C H and NH abstraction routes will each account for more than 40% of the reaction. Fate of the CH2Ṅ Radical. The CH2Ṅ radical is expected to undergo H-abstraction by O2 resulting in HCN CH 2Ṅ + O2 → HCN + HO2 ° = −99 kJ mol−1 ΔH298K

Figure 2. Rate coefficients for the OH radical reaction of CH2NH as a function of temperature and pressure calculated using a master equation model based on the CCSD(T)/cc-pV(TQ)Z results.

(4)

Reaction 4 has a relatively small barrier and proceeds via a weak HCN·HO2 post reaction adduct; two saddle points, SP4a and SP4b, are located at, respectively, ΔE†vo = 18.3 and 24.4 kJ mol−1 in CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ calculations. Stationary points on the PES are shown in Figure S2, while structures and energies are given in Tables S11 and S12 in the Supporting Information. ΔG‡298 is calculated to be around, respectively, 50 and 39 kJ mol−1 at 298 K in SP4a and SP4b, and a transition state theory (TST) calculation places k2 around 3 × 10−14 cm3 molecule−1 s−1 at 298 K corresponding to a lifetime of around 1 μs with respect to reaction with O2 at tropospheric conditions. In analogy to the established CH3Ṅ H radical reactions, the CH2Ṅ radical may conceivably also react with NO and NO2

Reactions 5 and 6 were found to take place without electronic barriers. However, even with rate coefficients of 10−10 cm3 molecule−1 s−1 and extremely high NOx-levels, the CH2Ṅ + NOx reaction rates will be insignificant compared to the O2 reaction rate at atmospheric conditions. In summary it can be concluded that HCN is the sole product in the atmospheric reactions of the CH2Ṅ radical. Fate of the HĊ NH Radical. The HĊ NH radicals, formed in the highly exothermic reactions 3c and d, are expected to undergo H-abstraction by O2 resulting in either HCN or HNC

Figure 3. Calculated rate coefficients for the individual reaction paths as well as the total reaction as a function of temperature, calculated using a master equation model based on the CCSD(T)/cc-pV(TQ)Zcalculations.

routes 3c and ethe two lowest barriers. The effects of large shifts in barrier heights are included in Table S10. Lowering all barriers by 4 kJ mol−1 results in a branching ratio of 4:0:40:14:43 and a rate coefficient of 1.3 × 10−11 cm3 molecule−1 s−1 at 298 K and 1000 mbar, that is, an increase by a factor of 4. Greenwald et al.43 studied the CH2CH2 + OH addition reaction at a comparable theoretical level to the present and found that the experimental kinetic data from 300 to 600 K could be reproduced by lowering the barrier to addition by around 4 kJ mol−1. In a later work Senosain et al.40 extended the calculations to include the CH2CH2 + OH abstraction reaction and reported that an increase in the barrier to abstraction by around 2 kJ mol−1 was needed to reproduce the high-temperature kinetic data of the system. Similar saddle point energy corrections in the CH2NH + OH system leads to a branching of 31:0:26:8:35 and a lowering of the rate

The cis- and trans-HĊ NH radicals exist in equilibrium via a trans → cis barrier of only 50 kJ mol−1 (Table S13 in the Supporting Information). This barrier is well below the available internal energy of the radicals when formed, and conformational equilibrium is, consequently, expected to be established before collisional deactivation occurs. It therefore 5282

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that is orders of magnitude faster than any competing atmospheric bimolecular reaction.

makes little sense to strictly distinguish between reactions 7a and 8a, and between reactions 7b and 8b. The HĊ NH + O2 reaction proceeds via a dioxy radical (HNC(OȮ )H), which exists in 4 conformations connected by barriers (SPHNC(OO)H) well below the entrance energy of the reactants, over saddle points to N−H or C−H abstraction, and via HO2 adducts on the exit side toward HCN/HNC and HO2 as illustrated in Figure 4. Energies and Cartesian coordinates of the stationary point structures are collected in Tables S13 and S14 in the Supporting Information.

‡ ̇ ̇ ‡ ⇆ OCH HOCH 2NH 2NH 2

° = +11 kJ mol−1 ΔH298K

(9)

The HOCH2Ṅ H radical, in turn, is expected to undergo hydrogen abstraction by O2 leading to formamide ‡ ̇ OCH 2NH 2 + O2 → CHONH 2 + HO2

° = −197 kJ mol−1 ΔH298K

(10)

The potential energy curve for reaction 9 was probed in B3LYP calculations and further investigated using CCSD(T) and CASSCF with an active space consisting of 9 electrons in 9 orbitals. Figure S3 in the Supporting Information shows the results from a B3LYP and CAS(9,9) IRC calculations of the hydrogen shift from the HOCH2Ṅ H radical to Ȯ CH2NH2; Table S15 in the Supporting Information summarizes the relevant energies and the Cartesian coordinates from the CCSD(T) calculations are given in Table S7. The barrier to the hydrogen shift is calculated to be around 120 kJ mol−1 and with 115 kJ mol−1 available as internal energy in the adduct, equilibrium 9 will be established before collisional quenching. The reaction is, however, slightly endothermic and with ΔG°298 = +11.1 kJ mol−1 from G4 calculations and +13.1 kJ mol−1 from G3 calculations. This implies an equilibrium constant of less than 5 × 10−3, and, consequently, that the 1,3-hydrogen shift reaction 9 will not be an important atmospheric route following OH addition to the imine. Other possible reactions of the HOCH2Ṅ H radical include hydrogen abstraction by O2 resulting in formimidic acid, HOCHNH

Figure 4. Stationary points on the HĊ NH + O2 potential energy surface. Results from CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ calculations.

The barrier to HNC formation is around 8 kJ mol−1 below the entrance energy of reactants, while the barrier to HCN formation is further 80 kJ mol−1 lower. It is therefore obvious that close to 100% of the HĊ NH + O2 reaction would lead to HCN had the HĊ NH radicals been thermalized. However, the HĊ NH radicals are formed in exothermic reactions, and the additional internal energy would result in the formation of a noticeable amount of HNC. A master equation calculation was therefore carried out to quantify the HNC yield in three different scenarios: (1) The HĊ NH radicals reacting are thermalized when reacting with O2; this results in 1‰ HNC yield. (2) The CH2NH + OH → HĊ NH + H2O reaction enthalpy is distributed with 1 quantum of the OH stretching vibration in product water molecule, and the remaining energy in the HĊ NH radical; this leads to a 4% HNC yield. (3) All of the CH2NH + OH → HĊ NH + H2O reaction enthalpy is deposited in the HĊ NH radical; this results in a 16% HNC yield in the HĊ NH + O2 reaction. The first and last of the three scenarios represent extremes, of which the latter is obviously not realistic. A conservative estimate of the HĊ NH + O2 → HCN/HNC + HO2 branching at atmospheric conditions reaction is therefore a yield of less than 5% HNC. Fate of the HOCH2Ṅ H Radical. The kinetic calculations suggest that around 5% of the initial CH2NH + OH reaction will follow route 3a via HOCH2Ṅ H radical formation; taking an uncertainty of 4 kJ mol−1 in the calculated barrier heights into consideration could, however, bring this fraction up to 20%. The addition reaction is highly exothermic (ΔH°298K = −115 kJ mol−1), and the vibrationally hot radical may therefore undergo isomerization reactions such as 1,3-hydrogen shift to Ȯ CH2NH2. Such a tautomerism may take place with a rate

̇ + O2 → HOCHNH + HO2 HOCH 2NH ° = −139 kJ mol−1 ΔH298K

(11)

The imino−enol formation 11 proceeds via a relatively low barrier of around 24 kJ mol−1, which is 6 kJ mol−1 lower than for the corresponding CH3NH + O2 reaction (results from CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ are collected in Tables S16 and S17 in the Supporting Information). ΔG‡298 is calculated to be around, respectively, 68 and 73 kJ mol−1 at the saddle points, and TST calculations place k9 around 3 × 10−19 cm3 molecule−1 s−1 at 298 Kthe corresponding CH3NH + O2 rate coefficient is predicted to be 4 × 10−20 cm3 molecule−1 s−1 at 298 K; the increase in rate coefficient is in accordance with the inductive effect of the OH group. The branching between reactions 9/10 and 11 was investigated by extending the above-mentioned master equation calculations with reactions 9−11; the results show that less than 0.2% of the HOCH2Ṅ H radicals will react via 9/ 10. There are no experimental rate coefficients for the O2/NO/ NO2 reactions with the CH3NH radical, but photo-oxidation experiments show that small amounts of CH3NHNO2 are formed when NO2 is present.2 The HOCH2Ṅ H radical is, in principle, expected to participate in the following NO/NO2 reactions: 5283

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The sequence of reactions leading from methanimine to CHOHNH is exothermic by 254 kJ mol−1, but not all of this will be available as internal energy in CHOHNH. However, even allowing for quenching in 20 collisions with N2 and 2 quanta of the OH stretching mode as vibrational excitation in the HO2 radical formed in reaction 11, ∼60 kJ mol−1, the formed CHOHNH will still have an internal energy around the tautomerization barrier. It can therefore be concluded that the addition route 3a will exclusively lead to formation of formamide at atmospheric conditions. 3.2. HCN/HNC + OH. The major atmospheric gas phase sink for HCN, and presumably also for HNC, is reaction with OH radicals. The HCN + OH reaction was recently studied by Bunkan et al.,49 who derived a theoretical rate coefficient for the HCN + OH reaction based on the mechanism originally proposed by Wine et al.50 and later confirmed by Galano51

Since the O2 reaction with HOCH2NH is predicted to be an order of magnitude faster than the CH3NH + O2 reaction, the NO/NO2 reactions with HOCH2NH are expected to fairly unimportant at atmospheric conditions. When formed in reaction 11 the imine−enol, HOCHNH, has a substantial amount of internal energy available, and it may undergo an internal 1,3 hydrogen shift reaction (keto−enol tautomerization) resulting in formamide before collisional quenching 1,3‐H

CHOHNH‡ ⎯⎯⎯⎯→ CHONH 2 ° = −49 kJ mol−1 ΔH298K

(14)

The ground-state PES of the tautomerization reaction 14 was investigated using CCSD(T) as well as the complete active space self-consistent field (CASSCF) method. The active space selected to describe the keto−enol tautomerization of formamide consisted of 12 electrons in 10 orbitals, hereafter referred to as CAS(12,10), and was created from the Hartree− Fock (7a′)2(8a′)2(9a″)2(10a′)2(11a′)2(12a″)2(13a′)0(14a′)0(15a′)0(16a″)0 orbitals at the transition state toward keto− enol tautomerization. Figure 5 shows the potential energy along

The abstraction reaction (HCN + OH → Ċ N + H2O) is endothermic by around 40 kJ mol−1 and will not be important at atmospheric conditions. Nothing is known about the atmospheric chemistry of nitroso formaldehyde, H(O)CNO, except that it absorbs in the UV−C region.52 We note that a TDDFT calculation places a weak n → π* transition in the conjugated system around 1200 nm (f = 0.0002) suggesting a relatively short tropospheric lifetime. The HNC + OH abstraction route is exothermic, in contrast to the HCN + OH abstraction route ̇ + H 2O HNC + OH → CN ° = −25 kJ mol−1 ΔH298K

(19)

However, the barrier to H-abstraction is quite high (CCSD(T)/cc-pV(TQ)Z: ΔE‡v=0 = 68 kJ mol−1) and this route will therefore not be of any importance at atmospheric conditions. Consequently, N2O, which in principle could be formed via Ċ N radicals (Ċ N + O2 → OCṄ + O ; OCṄ + NO → N2O + CO), is not a product in the photo-oxidation of methanimine. The HNC + OH addition reaction apparently proceeds without any significant electronic barrier ‡ ̇ HNC + OH → HNCOH ° = −152 kJ mol−1 ΔH298K

Figure 5. Minimum energy path for the keto−enol tautomerization of formamide as calculated at the CCSD(T)/cc-pV(TQ)Z, B3LYP/augcc-pVTZ, M06/aug-cc-pVTZ, and CAS(12,10)/aug-cc-pVTZ levels of theory. The energy is relative to the energy of HOCHNH and includes electronic energy only.

(20)

The vibrationally excited HNĊ OH radical adduct may undergo H-abstraction by O2 or, alternatively, N−H or O−H scission reactions; the net reactions for the latter two are both exothermic

the minimum energy path of the 1,3-hydrogen shift reaction obtained in CAS(12,10), CCSD(T)/cc-pV(TQ)Z, B3LYP, and M06 calculations. Energies from the various calculations are collected in Table S18 in the Supporting Information. The present calculations are in good agreement with recent results from benchmark calculations (ΔE = −44.4 and ΔE‡ = 154.3 kJ mol−1),47 and assessment of theoretical procedures for calculating barrier heights (ΔE = −44.4 and ΔE‡ = 154.3 kJ mol−1).48

To verify the feasibility of these routes at atmospheric conditions, the HNC + OH addition reaction was therefore investigated at a higher level of theory. CCSD(T)/ccpV(TQ)Z//CCSD(T)/cc-pVTZ calculations reveal that the addition route 20 proceeds via a linear prereaction adduct (HNC···HO) and a saddle point with energy below that of the 5284

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reactants to a highly energetic HNĊ OH radical adduct. The barrier to N−H scission is around 10 kJ mol−1 above, whereas the barrier to O−H scission is around 40 kJ mol−1 below the entrance energy of the reactants (Figure 6; energies and

The rate coefficient for the overall reaction of HNC with OH radicals as well as the branching between hydrogen abstraction with O2 and unimolecular hydrogen atom loss from HNĊ OH was examined using a master equation model based on the potential energy surface shown in Figure 6. Hydrogen abstraction was included as a bimolecular sink with rate coefficient k = 10−10 cm3 molecule−1 s−1 and 20% O2 in 1 atm with N2 as bath gas. Unimolecular loss of a hydrogen atom to form HNCO was found to be the most dominant process (>99%) and the contribution from hydrogen abstraction by O2 was found to be around 0.5%. By setting the rate coefficient for the hydrogen abstraction reaction by O2 to 10−10 cm3 molecule−1 s−1 we are essentially assuming a reaction efficiency close to 1, and the calculations therefore provide an upper estimate of the importance of the hydrogen abstraction reactions. Rate coefficients for the overall HNC + OH → HNCO + H reaction are given in Table S23 in the Supporting Information. The reaction rate was found to be independent of pressure and the rate coefficient at 298 K was calculated to be 1.3 × 10−11 cm3molecule−1s−1 using the hindered rotor model for the (H)NĊ −OH torsional mode at the saddle point (the (H)NĊ −OH torsional potential is shown in Figure S4 in the Supporting Information), and 1.6 × 10−11 cm3 molecule−1 s−1 with all internal modes treated as harmonic oscillators. For comparison, the theoretical high temperature value for reaction 22, obtained from BAC-MP4 calculations,53 is reported to be in the range (1.4−2.1) × 10−11 cm3 molecule−1 s−1 for the 1500− 2400 K range. 3.3. CH2NH + O3 Reaction. N-Methyl methanimine, CH2NCH3, was reported to be “essentially non-reactive towards O3”.7 This somewhat surprising inertness warrants further investigation, and a comparative study of the CH2NH + O3 and CH2CH2 + O3 reactions was therefore undertaken. The 1,3-dipolar cycloaddition of ozone to a double bond is problematic to compute accurately. Wheler et al.,54 however, have shown that the G4 approach performs quite well for the CH2CH2 + O3 reaction, and this model was consequently employed in the comparative study. The HOMO−LUMO gap is more than 100 kJ mol−1 larger in CH2NH than in CH2

Figure 6. Stationary points on the HNC + OH potential energy surface of the addition reaction. Results from CCSD(T)/cc-pV(TQ)Z//CCSD(T)/cc-pVTZ calculations.

geometries are summarized in Table S19−S22 in the Supporting Information). It is intuitively clear from the figure that the by far dominant product in the OH reaction with thermalized HNC will be HNCO. Kinetics of the HNC + OH Reaction. Rate coefficients for the reaction of OH radicals with HNC were calculated as outlined above for the CH2NH + OH reaction. The capture rate for formation of the pre-reaction complex was calculated using LRTST to be 6.4 × (T/298 K)−1/6 10−10 cm3 molecule−1 s−1. The rate of formation of the HNCOH adduct was found to have a negative temperature dependency and a positive pressure dependency, but since the HNĊ OH adduct will dissociate before any significant collisional stabilization can take place, it is necessary to include the possible fates of the adduct in order to describe the kinetics of the HNC + OH reaction.

Figure 7. Relative energies of stationary points on the CH2NH + O3 and the C2H4 + O3 potential energy surfaces. Results from G4 calculations. 5285

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isocyanic acid, HNCO; N2O is not a product in the tropospheric photo-oxidation of HNC. The addition route comprises hydrogen abstraction by O2 followed by 1,3-H shift to give formamide as the only product. There is no experimental rate coefficient for the CHONH2 + OH reaction, but an estimate based on the OH reaction being 10 times slower than the Cl reaction suggests a rate coefficient of 4 × 10−12 cm3 molecule−1 s−1,59 corresponding to a lifetime of around 3 days. The sole product in the CHONH2 + OH reaction is HNCO.59 Scheme 1 summarizes the major reaction routes in the OH initiated photo-oxidation of CH2NH at atmospheric

CH2, and this is reflected in the thermochemistry of all steps in reactions 23−26.

Figure 7 compares the stationary points on the PES for the two systems (structures and energies from G4 calculations are summarized in Tables S24 and S25 in the Supporting Information). Both reactions proceed via weak van der Waal complexes and unmistakable barriers to formation of the primary ozonides. The barrier to ozonide formation is significantly higher for methanimine (ΔE‡v=0 = 51.8, ΔG‡298 = 99.2 kJ mol−1) than for ethylene (ΔE‡v=0 = 19.3, ΔG‡298 = 61.8 kJ mol−1). Accordingly, the reactivity toward ozone is considerably lower, and transition state theory predicts the rate coefficients to be 3.7 × 10−18 cm3 molecule−1 s−1 for the CH2 CH2 + O3 reaction, and 1.0 × 10−24 cm3 molecule−1 s−1 for the CH2NH + O3 reaction. For comparison the recommended value for the CH2CH2 + O3 reaction is 1.6 × 10−18 cm3 molecule−1 s−1 at 1000 mbar and 298 K.55 Even allowing for a significant error in the calculated barrier to the CH2NH + O3 reaction, it can be concluded that the reaction is too slow to be of any importance at atmospheric conditionsmethanimine is “essentially non-reactive towards O3”.

Scheme 1. Major Routes in the OH-Initiated Atmospheric Gas Phase Photo-Oxidation of CH2NH

conditions and includes conservative estimates of the branching. In summary, the relatively short-lived CH2NH is through a series of gas phase oxidation steps converted to two relatively long-lived species: HCN and HNCO with conservatively estimated yields of, respectively, 80% HCN. A recent modeling study of atmospheric HNCO in California and Colorado (USA) suggests methylamine and formamide as HNCO precursors, but it does not consider the branching in the photo-oxidation sequences leading to HNCO.60 Smog chamber studies of CH3NH2 photo-oxidation show a roughly 10:90 ratio in the yields of formamide and methanimine.2 The present theoretical study places a conservative upper limit of 20% HNCO yield in OH initiated photo-oxidation of methanimine, and considering the additional heterogeneous loss of methanimine, it is reasonable to place a conservative upper limit of 25% HNCO yield in the atmospheric photooxidation of methylamine.

4. CONCLUSIONS AND IMPLICATIONS The atmospheric photo-oxidation of the simplest imine, CH2 NH, has been outlined in detail on the basis of quantum chemistry calculations. The potential energy surface of the CH2NH + OH reaction was characterized in multireference perturbation theory and coupled cluster theory calculations, and master equation modeling reveals a weak pressure dependency and a small negative temperature dependency of the reaction, with typical values of kOH around 3 × 10−12 cm3 molecule−1 s−1 at tropospheric conditions. With a diurnal OH radical concentration of 106 cm−3,56 the atmospheric lifetime of CH2NH with respect to reaction with OH will therefore be around 4 days. Given the readiness with which imines in general are known to interact on surfaces, it is likely that heterogeneous loss processes, including hydrolysis to CH2O and NH3, will be as important to the atmospheric removal of CH2NH as the gas phase reaction with OH. The master equation results imply that the most dominating reaction pathway in the OH-initiated gas phase photo-oxidation of CH2NH is hydrogen abstraction leading to HCN, although minor amounts of HNC may also result. The tropospheric residence time of HCN is around 5 months,57,58 and the main sink for HCN in the troposphere is ocean uptake while oxidation by OH represents an additional minor sink.58 For HNC, in contrast, our theoretical calculations show that reaction with OH radicals will constitute a major sink; the rate coefficient for HNC + OH reaction is typically around 10−11 cm3 molecule−1 s−1 at tropospheric conditions, that is, the HNC will have an atmospheric liftime of around 1 day; one may also envisage that HNC converts to HCN on aqueous particles. The HNC reaction with OH radicals is exclusively an addition reaction followed by O−H bond scission leading to

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ASSOCIATED CONTENT

S Supporting Information *

Energies, enthalpies and Gibbs free energies from G3 and G4 calculations (Table S1). Energetics of the CH2NH + OH → HOCH2NH reaction (/kJ mol−1) relative to that of the reactants (Table S2). Energetics of reaction CH2NH + OH → CH2NHOH relative to that of the reactants (Table S3). Energetics of the CH2NH + OH → trans HCNH + H2O reaction relative to that of the reactants (Table S4). Energetics of reaction CH2NH + OH → cis HCNH + H2O relative to that of the reactants (Table S5). Energetics of the CH2NH + OH → CH2N + H2O reaction relative to that of the reactants (Table S6). Cartesian coordinates of reactants, intermediates, and products in the reactions between the OH radical and CH2NH (Table S7). Rotational potentials for rotation of the OH fragment in the saddle points of reactions 3a and 3c−e (Figure S1). Calculated rate coefficients for the reaction of CH2NH + OH reaction as a function of pressure at different temperatures (Table S8). Calculated rate coefficients for the individual reaction channels of the CH2NH + OH reaction as a function of temperature (Table S9). Stationary points on the potential 5286

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amine and Trimetahylamine; Climit Project No. 201604; NILU OR 2/ 2011, ISBN 978-82-425-2357-0; NILU: 2011. (3) Nielsen, C. J.; D́ Anna, B.; Bossi, R.; Bunkan, A. J. C.; Dithmer, L.; Glasius, M.; Hallquist, M.; Hansen, A. M. K.; Lutz, A.; Salo, K., et al. Atmospheric Degradation of Amines (Ada); University of Oslo: Oslo, 2012; ISBN 978-82-992954-7-5, http://urn.nb.no/URN:NBN:no30510. (4) Nielsen, C. J.; Herrmann, H.; Weller, C. Atmospheric Chemistry and Environmental Impact of the Use of Amines in Carbon Capture and Storage (CCS). Chem. Soc. Rev. 2012, 41, 6684−6704. (5) Layer, R. W. Chemistry of Imines. Chem. Rev. 1963, 63, 489−510. (6) Gowenloc, B. G.; Thomas, K. E. Gaseaous Equilibrium of 1,3,5Triazine and N-Methylenemethylamine. J. Chem. Soc. B 1966, 409− 410. (7) Tuazon, E. C.; Atkinson, R.; Aschmann, S. M.; Arey, J. Kinetics and Products of the Gas-Phase Reactions of O3 with Amines and Related Compounds. Res. Chem. Intermediat. 1994, 20, 303−320. (8) Lazarou, Y. G.; Papagiannakopoulos, P. Kinetic Studies of the Reactions of Atomic Chlorine with N-Methylmethylenimine and 1,3,5Trimethylhexahydro-1,3,5-Triazine. J. Phys. Chem. 1993, 97, 4468− 4472. (9) Kaiser, E. W.; Wallington, T. J. Pressure Dependence of the Reaction Cl + C3H6. J. Phys. Chem. 1996, 100, 9788−9793. (10) Teslja, A.; Nizamov, B.; Dagdigian, P. J. The Electronic Spectrum of Methyleneimine. J. Phys. Chem. A 2004, 108, 4433−4439. (11) Nguyen Minh, T.; Sengupta, D.; Ha, T.-K. Another Look at the Decomposition of Methyl Azide and Methanimine: How Is HCN Formed? J. Phys. Chem. 1996, 100, 6499−503. (12) Darwich, C.; Elkhatib, M.; Steinhauser, G.; Delalu, H. ChlorineAtom Transfer Reactions between Chloramine (=Chloramide) and Piperidine: Kinetic Reactivity and Characterization in a Raschig Medium. Helv. Chim. Acta 2009, 92, 98−111. (13) Schade, G. W.; Crutzen, P. J. Emission of Aliphatic-Amines from Animal Husbandry and Their Reactions - Potential Source of N2O and HCN. J. Atmos. Chem. 1995, 22, 319−346. (14) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schuetz, M. Molpro: A General-Purpose Quantum Chemistry Program Package. Wiley Interdisciplinary Reviews-Computational Molecular Science 2012, 2, 242−253. (15) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M.; Celani, P.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G., et al. Molpro, version 2012.1, a Package of Ab Initio Programs, 2012. (16) Dunning, T. H., Jr. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007−23. (17) Kendall, R. A.; Dunning, T. H., Jr.; Harrison, R. J. Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96, 6796−806. (18) Woon, D. E.; Dunning, T. H. Gaussian-Basis Sets for Use in Correlated Molecular Calculations. 3. The Atoms Aluminum through Argon. J. Chem. Phys. 1993, 98, 1358−1371. (19) Helgaker, T.; Gauss, J.; Jorgensen, P.; Olsen, J. The Prediction of Molecular Equilibrium Structures by the Standard Electronic Wave Functions. J. Chem. Phys. 1997, 106, 6430−6440. (20) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J.; et al. General Atomic and Molecular Electronic Structure System. J. Comput. Chem. 1993, 14, 1347−1363. (21) General Atomic and Molecular Electronic Structure System (Gamess); http://www.msg.ameslab.gov/index.html. (22) Hirao, K. Multireference Møller-Plesset Method. Chem. Phys. Lett. 1992, 190, 374−380. (23) Hirao, K. Multireference Møller-Plesset Perturbation Theory for High-Spin Open-Shell Systems. Chem. Phys. Lett. 1992, 196, 397−403. (24) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. Gaussian-3 (G3) Theory for Molecules Containing First and Second-Row Atoms. J. Chem. Phys. 1998, 109, 7764−7776. (25) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-4 Theory. J. Chem. Phys. 2007, 126, 084108.

energy surface of the CH2N + O2 reaction (Figure S2). Rate coefficients and branching ratios at 298 K and 1000 mbar in the CH2NH + OH reaction as functions of barrier heights (Table S10). Cartesian coordinates of stationary point structures in the CH2N + O2 reaction (Table S11). Energies of and energy differences between s stationary point structures in the CH2N + O2 reaction (Table S12). Energies of species included in Figure 4 in the main text and energy differences between stationary points on the PES of the HCNH + O2 reaction (Table S13). Cartesian coordinates of species included in Figure 4 (Table S14). Minimum energy path of the 1,3hydrogen shift HOCH2NH → OCH2NH2 (Figure S3). Energetics of the 1,3-hydrogen shift reaction HOCH2NH → OCH2NH2 (Table S15). Cartesian coordinates of reactants and saddle points in the HOCH2Ṅ H + O2 and CH3Ṅ H + O2 reactions (Table S16). Energies and energy differences between reactants and saddle points in the HOCH2Ṅ H + O2 and CH3Ṅ H + O2 reactions (Table (S17). Energetics of the keto− enol tautomerization in formamide (Table S18). Energetics of the HNC + OH → HNCOH reaction (Table S19). Energetics of the HNCOH → HNCO + H reaction (Table S20). Energetics of the HNCOH → HOCN + H reaction (Table S21). Cartesian coordinates of reactants, intermediates, and products in the reactions between the OH radical and HNC (Table S22). Calculated rate coefficients of the HNC + OH reaction (Table S23). Cartesian coordinates of reactants, intermediates, products and saddle points in the CH2CH2 + O3 and CH2NH + O3 reactions (Table S24). Energies, enthalpies and Gibbs free energies from G4 calculations on the CH2CH2 + O3 and CH2NH + O3 reactions (Table S25). Rotational potential for rotation of the OH fragment in the saddle points of reaction 20 (Figure S4). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +47 2285 5441. Tel: +47 2285 5680. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to Dr. Robin Shannon and Dr. Mark Blitz, University of Leeds, and to Prof. Trygve Helgaker, University of Oslo, for helpful advice and discussions. This work is part of the Atmospheric Degradation of Amines (ADA) project supported by Masdar, Statoil, Vattenfall, Shell, and the CLIMIT program under contracts 193438, 201604, and 208122, from the VISTA-program (project 6157 “Study of the formation and stability N-nitrosamines, N-nitramines and N-nitroamides resulting from degradation of amines emitted to the atmosphere”), and from the Research Council of Norway through a Centre of Excellence Grant (Grant No. 179568/ V30).

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