Theoretical study on the reactions of CH3NHNH2 with ground state O(3P) atom and excited state O(1D) atom

The reaction mechanisms of methylhydrazine (CH3NHNH2) with O(3P) and O(1D) atoms have been explored theoretically at the MPW1K/6-311+G(d,p), MP2/6-311+G(d,p), MCG3-MPWPW91 (single-point), and CCSD(T)/cc-pVTZ (single-point) levels. The triplet potential energy surface for the reaction of CH3NHNH2 with O(3P) includes seven stable isomers and eight transition states. When the O(3P) atom approaches CH3NHNH2, the heavy atoms, namely N and C atoms, are the favourable combining points. O(3P) atom attacking the middle-N atom in CH3NHNH2 results in the formation of an energy-rich isomer (CH3NHONH2) followed by migration of O(3P) atom from middle-N atom to middle-H atom leading to the product P6 (CH3NNH2+OH), which is one of the most favourable routes. The estimated major product CH3NNH2 is consistent with the experimental measurements. Reaction of O(1D) + CH3NHNH2 presents different features as compared with O(3P) + CH3NHNH2. O(1D) atom will first insert into C–H2, N1–H4, and N2–H5 bonds barrierlessly to form the three adducts, respectively. There are two most favourable paths for O(1D) + CH3NHNH2. One is that the C–N bond cleavage accompanied by a concerted H shift from O atom to N atom (mid-N) leads to the product PI (CH2O + NH2NH2), and the other is that the N–N bond rupture along with a concerted H shift from O to N (end-N) forms PIV (CH3NH2 + HNO). The similarities and discrepancies between two reactions are discussed.


Introduction
Hydrazine (N 2 H 4 ) is the classical rocket fuel with notable advantages such as high reaction capabilities, high energy density, low molecular weight of the combustion products, and no special requirement for the production bases [1]. However, the thermodynamic stability of N 2 H 4 is not good enough, and N 2 H 4 is hard to remain in the liquid state over a wide temperature range. With the substitution of methyl for one hydrogen in N 2 H 4 , the formed compound methylhydrazine (CH 3 NHNH 2 ) presents better thermodynamic stability and better remaining-liquid-state ability over a wide temperature range [1]. Thus, it drew much more attention as an important rocket propellant. Rocket exhaust effluent including raw fuel fragments will not only contaminate the surface of the onboard instrumentation to reduce the lifetime or performance [2], but also degrade the ambient atmospheric optical environment due to chemiluminescent interactions both in the near-and far-fields of the expanding plume [3]. Oxidation by O atoms is one of the main processes that determine the fate of the diamine fuel fragments within the thermospheric plume. As stated by Vaghjiani [3], it is desirable to accurately determine the product distributions and the reactivity trends in O atom reactions with * Corresponding author. Email: zhangjinglai@henu.edu.cn diamines, not only for carrying out reliable plume-radiance calculations but also for properly simulating the combustion of these fuels in N 2 O 4 . Therefore, chemical kinetics studies of CH 3 NHNH 2 with O( 3 P) atoms have attracted lots of attentions.
According to the Lang's report [4], the rate constants for the reaction of CH 3 NHNH 2 + O are larger than those of reaction N 2 H 4 + O. Moreover, it was estimated that the primary reaction step should be hydrogen abstraction or the attacking of methyl group by O atoms. In addition, Vaghjiani [3] pointed out that direct H abstraction by the O atom from N-H or C-H bonds plays a relatively minor role in the overall reaction mechanism since low OH yields are determined. Removal of hydrogen atom may occur in other processes such as addition, elimination, etc. The mechanism and rate constants of H-abstraction process have been studied in our other work [5], but the discrepancy between the theoretical and experimental values in higher temperatures is large beyond the acceptable scope. Therefore, other feasible pathways should be considered for the reaction of CH 3 NHNH 2 + O. Products CH 3 NNH (not CH 3 NHN) and CH 3 NHNH or CH 3 NNH 2 were detected [3]. However, no actual yields for the carbonaceous species and C 2013 Taylor & Francis detailed mechanisms were reported in both literatures [3,4]. It is important and desirable to exactly identify the product distributions and the detailed reaction mechanism of O atom with CH 3 NHNH 2 for elucidating the combustion and oxidation processes. Except for the O( 3 P) atom, excited O( 1 D) species is also a primary component in the atmosphere. Therefore, the reaction of CH 3 NHNH 2 + O( 1 D) should also be considered to obtain more reliable and more complete reaction mechanisms. To our best knowledge, no experimental or theoretical study has focused on the reaction of CH 3 NHNH 2 with O( 1 D). The general purposes of this paper are to provide the detailed information of isomerisation or dissociation pathways for both reactions of CH 3 NHNH 2 + O( 3 P) and CH 3 NHNH 2 + O( 1 D), to determine the products to assist further experiments, and to make a comparison between two title reactions in order to deeply understand the combustion process of CH 3 NHNH 2 .

Computational methods
All electronic calculations were carried out using the GAUSSIAN 09 program package [6]. The geometries of stationary points including reactants, minimum isomers, transition states, and products were fully optimised by modified Perdew-Wang one-parameter model for kinetics (MPW1K) [7] with the 6-311 + G(d,p) basis set (MPW1K/6-311 + G(d,p)) and restricted or unrestricted second-order Møller-Plesset perturbation theory (MP2) [8] with the same basis set (MP2/6-311 + G(d,p)). The stationary nature of structure is identified by the number of imaginary frequency, i.e. 0 is for the local minimum and 1 is for the transition state. The zero-point energy (ZPE) corrections were obtained at the same level of theory. Singlepoint calculation was performed at the MCG3-MPWPW91 [9] level (a multi-coefficient modification of the Gaussian-3 electronic structure method by empirically mixing correlated wave-function methods and density-functional methods) and CCSD(T) level [10] (coupled-cluster approach with single and double substitutions including a perturbative estimate of connected triples substitutions) with the cc-pVTZ basis set. Note that an unrestricted Hartree-Fock based treatment is being used. The minimum energy path was performed by the intrinsic reaction coordinate theory at the MPW1K/6-311 + G(d,p) and MP2/6-311 + G(d,p) levels to confirm that the obtained transition states really connect the designated intermediates.

Results and discussions
Optimised geometries of some local minimum and transition states involved in two reactions O( 3 P) + CH 3 NHNH 2 (R1) and O( 1 D) + CH 3 NHNH 2 (R2) at the MPW1K/6-311 + G(d,p) level are displayed in Figures S1 and S2, respectively, of the Supporting Information. The optimised geometries of OH radical and CH 4 molecule agree well with the experimental values [11,12]. The calculated coordinates and harmonic frequencies of all species involved in the two reactions are given in Tables S1-S4 of the Supporting Information. In addition, the S 2 values are also listed in Table S3. The S 2 values for the triplet range from 2.01 to 2.08 at the MPW1K/6-311 + G(d,p) level, which are slightly higher than the value of a pure triplet (the exact value for a pure triplet is 2.0) with a maximum error within 4%. Since the calculated values of S 2 differ from s(s + 1) (s equals 1/2 times the number of unpaired electrons) by less than the permitted criterion of 10% [13], the spin contamination can be negligible. Similar behaviour is observed for the doublet, which will not be discussed again.
The energetic profiles of two reactions obtained at the MCG3-MPWPW91//MPW1K/6-311 + G(d,p) level are presented in Figures 1 and 2. The ZPE correction is included and the energy of reactants is set to be zero for reference. In this work, the energy of reactant R is set to be zero for reference to calculate the relative energy, while the barrier height is measured from the corresponding complex energy level.

Reaction pathways
There are four potential kinds of binding sites in the course of O( 3 P) atom attacking CH 3 NHNH 2 : H atoms and three heavy atoms in CH 3 NHNH 2 . It is an elementary reaction when O( 3 P) atom abstract one of the H atoms in CH 3 NHNH 2 , which is studied in detail in our other work [5]. Therefore, the primary aim of this work is to provide a deep insight into the detailed mechanism of O( 3 P) atom approaching three heavy atoms, i.e. middle-N attack, end-N attack, and end-C attack. The reaction of O( 3 P) + CH 3 NHNH 2 is classified into seven paths, denoted as routes 1-7, leading to six products, as follows: When O( 3 P) atom nears the N atom in the amino group of CH 3 NHNH 2 , a pre-reaction complex is formed barrierlessly. We have failed to locate the transition state from R to a at the MPW1K/6-311 + G(d,p) level. The relaxed potential energy curve for the formative process of CH 3 NHNH 2 O at the MPW1K/6-311 + G(d,p) level of theory is calculated to further confirm whether this process possesses a barrier.  Figure S3 of the Supporting Information corresponds to a at the MPW1K/6-311 + G(d,p) level. In complex a, the bond distance of O-N2 is 2.37 Å , which is longer than the equilibrium O-N covalent bond length (1.26 Å ) but shorter than the sum of the van der Waals radii of N and O atoms (3.07 Å ). It suggests that the weak interaction is formed between O and N2 atoms, which are easy to take isomerisation. There is no big change between the structure of complex a and TSaa1, only with a bit turning of the O atom from N2 atom to the H6 atom to facilitate the H6 shifting between N2 atom and O atom. The bond length of O-H (0.98 Å ) in complex a1 is almost equal to that of O-H bond length in the isolated OH radical, which indicates that the OH radical is combined with the end-N atom through the weak interaction. Consequently, complex a1 would dissociate easily to form product P1 (CH 3 NHNH + OH). The geometry parameters of a1 are close to those of CH 3 NHNH.
Only one transition state is included in the whole process from adduct a to product P1 with the relative energy of 6.60 kcal mol −1 . Thus, route 1 will be one of the most favourable pathways. Alternatively, a can isomerise to another isomer a2 via N-N bond rupture with the relative energy of 24.03 kcal mol −1 , which indicates that the cleavage of N-N bond is hard to happen.
In contrast, no adduct is located when O( 3 P) atom approaches the C atom (route 3) and the imino-N atom (routes 4-7). Route 3 is an elementary reaction corresponding to the break of C-N bond via the transition state TSRb with much high relative energy of 32.94 kcal mol −1 to produce adduct b. Then, adduct b directly dissociates to produce P3 (CH 3 O + NH 2 NH) without any barrier height. Therefore, route 3 has little opportunity to occur.
The association of O( 3 P) atom with the nitrogen of imino group will form an adduct c via the transition state TSRc with a small barrier height of 1.24 kcal mol −1 followed by four routes. The adduct c will either dissociate to product P4 (CH 3 NONH 2 + H) via N1-H4 bond cleavage through transition state TScP4 (route 4), or undergo displacement to form c1 via C-N bond rupture through transition state TScc1 leading to product P5 (CH 3 + NOHNH 2 ) (route 5).
In route 6, three steps are developed by adduct c, i.e. c → c2 → a1 → P1 (CH 3 NHNH + OH). The O atom transfers from N1 atom to H4 atom through TScc2 to form intermediate c2. The structure of TScc2 is similar to that of c except that the N1-O bond length is increased and O-H4 bond distance is decreased to promote the O-H4 bond formation. Subsequently, the complex c2 takes O migration from H4 to H6 atom associated with the N2-H6 bond rupture via transition state TSc2a1. The relative energies of TScc2 and TSc2a1 are 5.98 and −4.61 kcal mol −1 with respect to the reactants, respectively.
As to the route 7, three steps are included. The first two steps are the same with those of route 6, i.e. (1) CH 3 NHNH 2 + O( 3 P) → c and (2) c → c2. The third step is a process to obtain P6 (CH 3 NNH 2 + OH) barrierlessly. Among routes 4-7, routes 4 and 5 have little opportunity to occur because of higher barrier, especially for route 4. As to routes 6 and 7, they have the same rate-determining step. However, the reaction steps of route 6 are one more than those of route 7. Therefore, the more competitive pathway should be route 7 leading to product P6 (CH 3 NNH 2 + OH) due to less reaction steps and lower overall barrier from the intermediate c to the final dissociation products. Lang [4] performed the kinetic study for the reaction of O( 3 P) + CH 3 NHNH 2 and pointed out that it was premature to think that just the simple hydrogen abstraction was involved in the reaction mechanism. Attacking of the methyl group and other possible channels should be considered. However, the product identification had not been obtained by him. Products CH 3 NNH, CH 3 NHNH, and CH 3 NNH 2 were detected by another group [14]. Observed product CH 3 NNH 2 is one species of the favourable product P6 (CH 3 NNH 2 + OH). The product CH 3 NNH is not found in our calculations, but the product CH 3 NNH 2 will react with OH leading to CH 3 NNH via a simple H abstraction. Another product CH 3 NHNH is confirmed as one species of the feasible product P1 (CH 3 NHNH + OH). Except products, the theoretical mechanism is also in line with the experimental assumption. First, both the experimental studies indicate that removal of hydrogen atom could also well occur in an addition-elimination process except abstraction of a single H atom by atomic oxygen, which should be a complex reaction mechanism involving the formation of an initial adduct that then rapidly dissociated into a variety of products. In routes 1-2, an initial adduct a indeed exists, which is formed when O atom attacks end-N in CH 3 NHNH 2 . Next, adduct a will rapidly dissociate into products with lower relative energy and the simplest steps, which is similar to experimental estimation. Second, experimental studies [14,15] pointed out that O-atom migration can take place either across two H atoms at the same nitrogen or between two H atoms, each one of which is situated at the two different nitrogen atoms. In route 6, O atom shifts across two H atoms belonging to different N atoms via a bridging structure of TSc2a1, which is consistent with Foner and Hudson's conclusion [14,15]. They also stated that different-N type of bridging is favourable in O + CH 3 NHNH 2 reaction. Our results present the same conclusion that route 6 is one of the most favourable pathways with the lower barrier height for rate-determining step.

Reaction mechanism
From the preceding analysis, seven reaction paths (routes 1-7) are obtained for the reaction of O( 3 P) + CH 3 NHNH 2 . The atomic O( 3 P) will attack three heavy atoms (carbon, middle-N, and end-N) in CH 3 NHNH 2 . A low-lying adduct a is formed without barrier when the O( 3 P) atom associates with the CH 3 NHNH 2 at end-N site. However, no adduct is formed when O( 3 P) atom attacks carbon position and middle-N position. Routes 1 and 7 are two competitive pathways since the barrier heights of rate-determining step are 8.32 kcal mol −1 for TSaa1 and 8.66 kcal mol −1 for TScc2. Moreover, route 1 is one of the simplest paths through only one transition state. Route 6 is the secondary favourable path, which needs to proceed one more transition state as compared with route 7. Routes 2-5 are less probable channels with the relative energy of the corresponding transition states TSaa2 in route 2, TSRb in route 3, TScc1 in route 5, and TScP4 in route 4, increasing in sequence with the values of 24.03, 32.94, 37.74, and 48.46 kcal mol −1 , respectively.
As to the product, P6 (CH 3 NNH 2 + OH) is a favourable product. P1 (CH 3 NHNH + OH) may have comparable branching ratio since P1 is the common product of routes 1 and 6. Other products are much less feasible.

Reaction O( 1 D) + CH 3 NHNH 2 (R2)
Note that the relative energy discussed in Section 3.2 is relative to the energies of corresponding reactants O( 1 D) + CH 3 NHNH 2 .

Reaction pathways
The first step for reaction of CH 3 NHNH 2 + O( 1 D) is different from that of the triplet potential energy surface. There are three possible insert modes for the O( 1 D) atom approaching CH 3  Path A is confirmed starting from 1a; paths B and C are confirmed starting from 2a; and 3a is prophase complex for paths D and E. For clarity, these processes are simply written as follows: With respect to path E, 3a first isomerises to isomer 3c, followed by a concerted N1-N2 bond rupture and H migration from C to O atom via a five-member-ring transition state TS3c3d to form hydrogen-bonded complex 3d, which dissociates into P V (CH 2 NH + NH 2 OH) directly. Obviously, path D is more favourable than path E, due to lower barrier height and less reaction steps.

Reaction mechanism
O( 1 D) can barrierlessly insert into C-H, N1-H, and N2-H bonds to form the low-lying isomers 1a, 2a, and 3a, respectively. There are total five energetically accessible paths starting from respective isomers. Among these channels, paths A and D should be the most two competitive pathways because the energies of rate-determining transition states TS1aP I in path A and TS3a3b in path D are much lower than those involved in other three paths. The barrier heights of TS1aP I and TS3a3b are 40.91 and 36.94 kcal mol −1 . Moreover, both paths A and D are one-step pathways. Therefore, two products, P I (CH 2 O + NH 2 NH 2 ) corresponding to path A and P IV (CH 3 NH 2 + HNO) corresponding to path D, may have comparable branching ratios, while other products produced via paths B, C, and E may have less yields.
To testify the accuracy of mechanism obtained at the MCG3-MPWPW91//MPW1K/6-311 + G(d,p) level, all the stationary points involved in the reaction O( 3 P) + CH 3 NHNH 2 (R1) are optimised at the MP2/6-311 + G(d,p) level. It is unfortunate that the TSaa1 is not located since MP2 method is not good to search for a looser transition state. Since the barrier heights of other routes are much higher than those of routes 1 and 7, they are impossible to be favourable reaction routes. As a consequence, only the energies of route 1, route 7, and all products are refined at MCG3-MPWPW91 and CCSD(T)/cc-pVTZ levels based on the optimised geometries. The relative energies (the energy of reactants is set to be zero) obtained at various levels are summarised in Table 1 level, routes 1 and 7 are competitive with the similar barrier height. However, route 7 is more favourable than route 1 with relative lower barrier height at the CCSD(T)/cc-pVTZ//MPW1K/6-311 + G(d,p) level. We are struggled by the question which result is more reliable. Therefore, the reaction energies are calculated at the following levels, i.e. MCG3-MPWPW91//MPW1K/6-311 + G(d,p), CCSD(T)/cc-pVTZ//MPW1K/6-311 + G(d,p), MCG3-  [27][28][29][30]. The reaction energies calculated at the CCSD(T)/cc-pVTZ levels based on different optimised geometries are much higher than the experimental values. Thus, it is reasonable to infer that the energies obtained at the MCG3-MPWPW91 level are reliable for title reactions.
For the reaction of O( 3 P) + CH 3 NHNH 2 , O( 3 P) atom will approach three heavy atoms, i.e. middle-N, end-N, and end-C to form seven routes and six products. Products CH 3 NNH 2 and CH 3 NHNH will have more yields. In contrast, reaction of O( 1 D) + CH 3 NHNH 2 presents totally different mechanism and products. O( 1 D) can barrierlessly insert into C-H, N1-H, and N2-H bonds to form the lowlying isomers 1a, 2a, and 3a; then, five reaction pathways are located. P I (CH 2 O + NH 2 NH 2 ) is the most favourable product and P IV (CH 3 NH 2 + HNO) is the secondary feasible product. The present work is expected to be useful and helpful for deeply understanding the mechanism of title reactions and CH 3 NHNH 2 -combustion chemistry.