Atmospheric reaction of hydrazine plus hydroxyl radical. I. Reliable pathways


 Understanding the mechanism of hydrazine oxidation reaction by OH radical accompanied by the rate constants of all possible pathways is important. They are key parameters to explain the fate of hydrazine in the atmosphere. To reach the mentioned parameters, higher-level calculations by using quantum chemical methods have been implemented comprehensively for reliable channels such as H-abstraction, SN2, and addition/elimination reactions. To estimate the barrier energies of H-abstraction channels accurately, large numbers of the CCSD(T)/X calculations (where X denotes the augmented Dunning and Pople double zeta or triple zeta basis sets) have been applied to the optimized geometries of the MP2/aug-cc-pVTZ, MP2/maug-cc-pVTZ, and M062X/maug-cc-pVTZ levels. Contributions of excited states on the computed potential energy surface have been considered by the MR-MP2 (multi-reference) method in conjunction with the large augmented quadruple zeta, aug-cc-pVQZ, basis sets. The direct dynamic calculations have been carried out using the accurate energies of the CCSD(T) method and the partition functions of the second-order MØller-Plesset perturbation theory, and also by the validated M06-2X method with the aug-cc-pVTZ, and maug-cc-pVTZ basis sets. Finally, The VTST and TST theories have been used to calculate the temperature dependence of rate constants of the considered pathways. Also, the pressure-dependent rate constants of the barrierless pathways have been investigated by the strong collision master equation/RRKM theory.


Introduction
Hydrazine has three structural conformers: s-cis (C2h), anti (C2v), and gauche (C2). The gaucheconformer is the most stable, and the anti-conformer is more stable than the cis. In industry, hydrazine and its derivatives have many applications such as polymerization initiators, boiler water treatment, dyes [1][2][3][4][5] , and corrosion inhibitors for steel in contact with hot water [6][7][8] . Also, hydrazine plays an important role in the production of organic compounds 9 . The International Agency for Research on Cancer (IARC) and American Conference of Governmental Industrial Hygienists (ACGIH) take into account hydrazine as a carcinogenic substance with an unknown relevance for both animals and humans 10 . In unsymmetrical structures, the fuels containing hydrazine, methyl hydrazine, and dimethylhydrazine compounds are high-energy and have special applications such as fuels of rockets and spacecraft. All of them are crudely toxic [11][12][13][14] . Usually, some of the oxidizers are added to hydrazine fuels for high performance. The most common oxidizers are dinitrogen tetroxide (NTO) and inhibited red fuming nitric acid (IRFNA). [15][16][17] Because decomposition of NTO and nitric acid can produce hydroxyl radicals and nitrogen dioxide, the reactions of hydrazine with these species are important in designing rockets 18 . Knowledge of hydrazine oxidation reactions has some advantages.
The most important advantage is the development of the gelled hypergolic propellant (GHP) 19 . In the atmosphere, the complete decomposition of hydrazine with reactive species is probable 20 . A few numbers of experimental studies [21][22][23][24] and only one theoretical investigation 25 have been performed previously on the mechanisms and kinetics of the N2H4 + OH reaction in the second-order form. The obtained results have been shown that hydrogen abstraction via hydroxyl radical is the main reaction pathway at temperatures lower than 700 K. N2H4 + OH N2H3 + H2O (1) Also, the main reaction of hydrazine with O3 as other important atmospheric species is as follows: 12,26 N2H4 + O3 N2H3 + OH + O2 Vaghjiani 21  molecule -1 s -1 at the 232-637 K temperature range. Also, he recommended that OH radicals can not be added to one center of diamine in low temperatures, and thus the reaction does not progress by rapid dissociation of the intermediate into products 22 . Harris et al. 23 measured the rate constants of the title reaction by using photolysis-resonance fluorescence in the 298-424 K temperature range. They found a rate expression as k=4.40 × 10 -11 exp[(116±176)/T] cm 3 molecule -1 s -1 . Hack et al. 24 investigated the rate of hydrazine with hydroxyl radical, OH + N2H4  products, in an isothermal flow reactor with helium flow as the carrier gas. The overall rate constant was k(298.15)=2.20 × 10 -11 cm 3 molecule -1 sec -1 at room temperature and pressure around 2 Torr. The reaction of N2H4 + OH was studied by Tang and et al. 25  theory.

Computational methods
The UMP2 31 and very popular density functional method, UB3LYP 32,33 , with the 6-311++G (3df, 3pd), maug-cc-pVTZ 34 , aug-cc-pVTZ, and aug-cc-pVQZ 35 basis sets and also some other basis sets were applied to geometry optimization of all stationary points in doublet state. Due to serious shortcomings of the most popular density functional method, B3LYP, in determining barrier heights and so kinetics of reactions, especially in reactions containing hydrogen shifts, we have used the UM06-2X 36,37 method. This method is a highly parameterized meta hybrid density functional method and has reasonable results for specifying reaction kinetics.
The harmonic vibrational frequencies were computed by using the abovementioned methods and basis sets to determine the nature of all stationary points, including prereactive collision complexes (MCr), product complexes (MCp), and transition states (TS). In the whole paper, It was used the maTZ, aTZ, and aQZ for shorthand notations of the maug-cc-pVTZ 34 , aug-cc-pVTZ, and aug-cc-pVQZ 35  To estimate the barrier heights of the title reaction more precisely, a dual-level methodology was used similar to previous reactions of hydrazine with atomic oxygen simulated in the atmospheric conditions [40][41][42] . Thus, the CCS(T)/CBS//MP2/aTZ level was chosen. Because (a) (in the mentioned studies) it has been proved that the CCS(T)/CBS level has excellent results in energy prediction (b) the MP2 method along with a large basis set has better results than small basis sets 43 for geometry optimization of all stationary points containing hydrogen bonds 44 like the N2H4 + OH reaction.
Therefore, we used the geometries obtained at the MP2/aTZ level for the CCSD(T)/CBS calculations. higher-level calculations are needed for investigating systems [50][51][52] . The same value for the Largest amplitudes is 0.2, but our results are below 0.2 (0.045) except TS1b (see Table S32). This is obvious for TS1b because we found the structure of TS1b through the scan option as mentioned in the H2NOH + NH2 formation channels section. Also, according to the proposed PES, the path containing TS1b has a very small contribution to hydrazine degradation due to having a transition state with a high energy barrier (see Figure 1). And this path is not observed in experimental studies. This is only a theoretical pathway and does not affect the total rate of hydrazine degradation.
To explore deeper insight about the reaction mechanisms, the bonds taking part in reactions were analyzed based on the natural bond orbital, NBO, and the atoms in molecule, AIM, analyses at the UMP2/aTZ level. Also, the thermodynamic parameters of the predicted adducts were computed in the temperature range of 200-1200 K at the M06-2X/aQZ and MP2/aTZ levels. The topological analyses of the wave functions were implemented by the AIM2000 53 program. Gaussian 09 package program 7 was executed for optimization and electronic structure calculations of all stationary points 54 . All images of molecular structures were created using the GaussView 5.0.8 software 55 .

Rate constant calculations
All rate constants were calculated at the high-pressure limit using the transition state (TST) theory 56 as follows:  57 . For all elementary bimolecular reactions, the high-pressure limit rate constants were computed by the Gpop program 58 . The rate constants at the low-pressure limit and the falloff regime were calculated using the strong collision master equation/Rice-Ramsperger-Kassel-Marcus (RRKM) theory by the Ssumes program 59 .
The main channels of the reaction in this work are hydrogen shift. Thereby, the exact quantum tunneling correction factor is necessary. The quantum tunneling correction factor was calculated at the UMP2/aTZ and M06-2X/maTZ levels. For the mentioned correction, the second-order correction of Shavitt 60 was used as follows: is Boltzmann constant, νim is imaginary frequency of a transition state, c is the speed of light, T is temperature, and E0 is barrier height that may correct by zero-point energy for the considering reaction (ETS1 -ER). 8 As the authors of the UM06-2X 36,37 method have recommended this method has excellent performance for main group thermochemistry, noncovalent interactions, and kinetics. Therefore, the rate constants of the N2H4 + OH reaction were computed at the M06-2X/maTZ level.

Results and discussion
In the following sections, for the N2H4 + OH reaction, the potential energy surface, rate constants of all reliable pathways at low, intermediate, and high pressures, and also thermodynamic data are discussed using different computational methods. Finally, the fate of hydrazine is studied in different heights of the atmosphere. Also, we use the same notation for stationary points as Tang et al. to simplify the PES following in both works.

Potential energy surface
The potential energy diagram of the N2H4 + OH reaction is depicted in Figure 1.  Tables 1, S1, and S2 (see supporting information). The unscaled vibrational frequencies of stationary points are summarized in Table S3. The energetic parameters of all stationary points computed at the CCSD(T)/CBS level are given in Table 2. Also, these parameters are calculated in several methods and various basis sets and collected in Tables S4-S6 (see supporting information Tables 3a and 3b, and Tables S7-S28 in additional information. The pressure-dependent rate constants for all H-abstraction channels are listed in Table   S29.

Reaction entrance channels
Like many gas-phase reactions, the hydrazine reactions with hydroxyl radical begin with pre-reactive collision complexes. In this work, three pre-reaction complexes are predicted and named by MCr1a, MCr1b, and MCr2. The complex MCr1a is a mirror image of MCr1b. Therefore, the electronic structure of MCr1a is the same as MCr1b. Also, the structure of MCr1a (or MCr1b) including N2H4 and OH is associated with the formation of hydrogen-bond. So, they are more stable than MCr2. In Firstly, in the following sections, the H abstraction (barrier-less) reaction channels will be discussed.
Secondly, hydroxyl radical addition to the N site of hydrazine will be investigated. Finally, the SN2 reaction (OH replacement with a hydrogen atom of hydrazine) will be argued.

N2H3 + H2O formation channels
The H abstraction channels start with MCr1a and MCr1b complexes. The electronic charge density of the ring critical point (RCP) for MCp1 and MCp2 is ρ (rrcp) = 0.0129, and 0.0128 e bohr -3 , respectively. Also, the Laplacian of the charge density for that rings is 2 (rrcp) =0.0706 and 0.0714 e bohr -5 , respectively. The variation of the electronic charge density and its Laplacian confirms the hydrogen shift in path 1. Finally, the complex products, MCp1 and MCp2, by barrier-less processes release to the N2H3 and H2O adducts.

H2NOH + NH2 formation channels
The H2NOH + NH2 generation pathways (SN2 and addition/elimination reactions) are summarized as follows: 3 An NBO analysis of TS4 shows that the sp 3.00 hybrid orbital of the atom N2 has a weak covalent interaction with the sp 8.59 hybrid orbital of the atom O6. The sp 3.00 hybrid orbital of the atom N2 is varied to sp 2.60 . It shows that the p orbital contribution is decreased in the N-H bond during the SN2 process. The instability of MCp4 is related to the separated hydrogen atom.
The last path is another route for the production of the NH2OH + NH2 adducts. After MCp4 generation, MCP3b post reactive complex is created through TS1c by surmounting on the barrier height of 59.91 kcal/mol. This path is long, so kinetically it has less importance compared to the other pathways discussed above. section, we consider the production pathways of N2H3 + OH, NH2OH + NH2, and H2N2HOH + H products that need to pass just one transition state.
As explained above, the data used by Tang et al. 25  computed and listed in Tables S11, S15-S18, and S24-S26 in the supplementary data. In summary, comparing the rate constant reported here with different experimental results shows that our used methods have adequately precise in describing the title reaction kinetics.

The low-pressure limit rate constant and its behavior in the falloff regime.
To investigate the pressure-dependent rate constant, the strong collision master equation Rice-Ramsperger-Kassel-Marcus (RRKM) theory is used. The rate constant of the title reaction in the lowpressure limit and its behavior in the falloff range is investigated in the 200-800 K temperature range.
The chemical activation mechanism is implemented in the pressure-dependent rate constant as follows: where M is the third body. If we apply the steady-state approximation to the concentration of Cr*, the rate of conversion of Cr to final adducts is At high pressure limit ([M] → ∞), k(T,p) is the first order and at low-pressure limit (where [M] → 0) k(T,p) is the second order. Therefore, in the high and low-pressures, k(T,p) expressions in Eq.1 can be written as follows: If we divide the numerator and the denominator of equation 1 into k-1 [M] and substitute equations 2 and 3 in it, we have: Finally, for the calculation of pressure dependence of the rate constant, the following relation is used: where  is tunneling correction, and K(T) is the temperature dependent equilibrium constant. Similar to temperature dependent rate constants, the Shavitt transmission coefficient was used for the  In the zero-pressure limit, P → 0, k(T,p)/[N2] is called the low-pressure limit rate constant k0(T). k0(T) is a termolecular rate constant with the units of cm 6 molecule -2 s -1 and also called pseudo third order rate constant. Our calculated rate constants at the low-pressure limit in the temperature range of 200-800K are listed in Table S29. The results show that k0(T) is 7.87 × 10 -32 , 2.8 × 10 -32 , and 1.09 × 10 -32 cm -6 molecule -2 s -1 at 298.15, 400 and 600 K, respectively. To our knowledge, the rate constant is not determined experimentally at the low-pressure limit for the generation of main reaction products.
Our calculated rate constants at different pressures in the falloff regime in the temperature range of 200-800K are depicted in figure 4 and collected in Table S29. According to the origin of Gibbs free energy and Table 4 information, the stability of P1 is related to the entropy of reaction that increases with temperature. The variation of TΔS° for P1 in the temperature range 200-1200 K equals 0.8-4.78 kcal/mol. The same behavior for the stability of P2 adducts is observed, but it is changed inversely for P3 adducts that relate to whose electronic entropy. With increasing temperature from 200 to 1200 K, the amount of TΔS° for these species decreases from -1.88 to -6.86 kcal/mol. Another factor for the instability of P3 adducts is the enthalpy function by total variation about +2.53 kcal/mol that is related to the instability of the atom H. For P1 and P2 adducts, the variation of enthalpy is low in the mentioned temperature range.
In summary, with increasing temperature, the P1 and P2 generations are more favorable not only thermodynamically but also kinetically. The production of P3 adducts is favorable just kinetically at a temperature above 1000 K.

The fate of hydrazine in the atmosphere
The lifetimes of hydrazine in the atmosphere at altitudes from 0 to 50 km (corresponding to pressures from 1013 to 0.801 mbar) are listed in Tables 5, S7,  degradation was about 2.6 hours or longer 62 . As we know, the concentration of O3 in the ozone layer is larger than the other parts of the atmosphere, and O3 concentration is also less than the concentration 19 of OH radical in the urban area. Therefore, hydroxyl radical is an important factor for hydrazine degradation in urban areas.

Conclusion
The       is the lifetime of N2H4 in the atmospheric concentration of OH.