Ab Initio Kinetics for Thermal Decomposition of CH3Nâ¢NH2, cis

Article pubs.acs.org/JPCA

Ab Initio Kinetics for Thermal Decomposition of CH3N•NH2, cis-CH3NHN•H, trans-CH3NHN•H, and C•H2NNH2 Radicals Hongyan Sun,* Peng Zhang, and Chung K. Law Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, United States S Supporting Information *

ABSTRACT: The thermal decomposition of the CH3N•NH2, cis-CH3NHN•H, trans-CH3NHN•H, and C•H2NNH2 radicals, which are the four radical products from the H-abstraction reactions of monomethylhydrazine, were theoretically studied by using ab initio Rice−Ramsperger−Kassel−Marcus (RRKM) transition-state theory and master equation analysis. Various decomposition pathways were identified by using either the QCISD(T)/cc-pV∞Z//CASPT2/aug-cc-pVTZ or the QCISD(T)/cc-pV∞Z//B3LYP/6-311++G(d,p) quantum chemistry methods. The results reveal that the β-scission of NH2 to form methyleneimine is the predominant channel for the decomposition of the C•H2NNH2 radical due to its small energy barrier of 13.8 kcal mol−1. The high pressure limit rate coefficient for the reaction is fitted by 3.88 × 1019T−1.672 exp(−9665.13/T) s−1. In addition, the pressure dependent rate coefficients exhibit slight temperature dependence at temperatures of 1000−2500 K. The cis-CH3NHN•H and trans-CH3NHN•H radicals are the two distinct spatial isomers with an energy barrier of 26 kcal mol−1 for their isomerization. The β-scission of CH3 from the cis-CH3NHN•H radical to form transdiazene has an energy barrier of 35.2 kcal mol−1, and the β-scission of CH3 from the trans-CH3NHN•H radical to form cisdiazene has an energy barrier of 39.8 kcal mol−1. The CH3N•NH2 radical undergoes the β-scission of methyl hydrogen and amine hydrogen to form CH2NNH2, trans-CH3NNH, and cis-CH3NNH products, with the energy barriers of 42.8, 46.0, and 50.2 kcal mol−1, respectively. The dissociation and isomerization rate coefficients for the reactions were calculated via the E/J resolved RRKM theory and multiple-well master equation analysis at temperatures of 300−2500 K and pressures of 0.01− 100 atm. The calculated rate coefficients associated with updated thermochemical property data are essential components in the development of kinetic mechanisms for the pyrolysis and oxidation of MMH and its derivatives.

1. INTRODUCTION Monomethylhydrazine (MMH) is an extensively used hypergolic rocket fuel together with either nitrogen tetroxide or red fuming nitric acid. Experimental studies have also shown that the hypergolic ignition occurs in the gas phase over the liquid fuel pool.1,2 Kinetically, the initial gas-phase reactions of MMH are the H-abstraction reactions which are dominant at low temperatures. In particular, the kinetics of H-abstraction reactions of MMH by NO2 was characterized by McQuaid et al.3 via the CCSD(T)/6-311++G(3df,2p)//MPWB1K/6-31+G(d,p) and the CCSD(T)/6-311+G(2df,p)//CCSD/6-31+G(d,p) calculations. Recently, we studied the kinetics of OH abstraction reactions of MMH by using the second-order multireference perturbation theory and two-transition-state kinetic model.4 The H-abstraction of MMH leads to the formation of four MMH radicals: CH3N•NH2, cis-CH3NHN•H, trans-CH3NHN•H, and C•H2NNH2, where the cis and trans notations indicate the orientation of the terminal amine H atom to the methyl group. These MMH radicals undergo further decomposition reactions to produce H, NH2, and CH3 radicals, which further lead to many chain reactions. Consequently, the decomposition of the MMH radicals is crucial to the understanding of the ignition chemistry of MMH and its derivatives. © 2012 American Chemical Society

For the decomposition of these radicals, the major reaction pathways are the β-scission reactions to form diazene, methyldiazene, and methyleneimine products.5 The primary electronic structure changes for the β-scission take place upon breaking the σ bond of NX (X = H, C, N) at the β position of the radical and the simultaneous formation of a new NN or CN π bond. These electronic structure changes also hold for the β-scission of the radicals produced from the MMH derivatives such as symmetrical dimethylhydrazine (SDMH) and unsymmetrical dimethylhydrazine (UDMH). Despite the importance of the decomposition of MMH radicals, there is no experimental information available. Certainly, ab initio kinetics is an alternative method and is particularly useful in calculating the rates of elementary chemical reactions over wide ranges of temperature and pressure. For the dissociation reactions of MMH, the pressure dependence and product branching were recently studied by solving the master equation incorporating the transition-state information obtained from the variable reaction coordinate transition-state (VRC-TST) calculations of the radical−radical Received: May 10, 2012 Revised: July 19, 2012 Published: July 19, 2012 8419

dx.doi.org/10.1021/jp3045675 | J. Phys. Chem. A 2012, 116, 8419−8430

The Journal of Physical Chemistry A

Article

Table 1. Saddle Point Energies (kcal mol−1) Relative to the Energy of CH3 + trans-NHNH •

a

CH3N NH2(DFT) CH3N•NH2(CASPT2)b cis-CH3NHN•H(DFT)a cis-CH3NHN•H(CASPT2)b trans-CH3NHN•H(DFT)a trans-CH3NHN•H(CASPT2)b C•H2NHNH2(DFT)a C•H2NHNH2(CASPT2)b TS1a_cis-CH3NHN•H → trans-CH3NHN•H TS2a_cis-CH3NHN•H → CH3 + trans-NHNH TS3b_cis-CH3NHN•H → cis-CH3NNH + H TS4a_trans-CH3NHN•H → CH3 + cis-NHNH TS5b_trans-CH3NHN•H → trans-CH3NNH + H TS6a_trans-CH3NHN•H → CH3N•NH2 TS7a_cis-CH3NHN•H → CH3N•NH2 TS8a_trans-CH3NHN• → C•H2NHNH2 TS9a_cis-CH3NHN•H → C•H2NHNH2 TS10b_CH3N•NH2 → CH2NNH2 + H TS11b_CH3N•NH2 → trans-CH3NNH+H TS12b_CH3N•NH2 → cis-CH3NNH + H TS13b_CH3N•NH2 → CH3 + NNH2 TS14b_C•H2NHNH2 → CH2NH + NH2 TS15a_C•H2NHNH2 → CH2NNH2 + H TS16a_CH3N•NH2 → C•H2NHNH2

T1 diagnosticc

ZPEd

ZPE+TZe

ZPE+QZf

ZPE+CBSg

0.0207 0.0205 0.0224 0.0222 0.0224 0.0222 0.0182 0.0178 0.0211 0.0161 0.0195 0.0155 0.0238 0.0138 0.0123 0.0157 0.0158 0.0172 0.0207 0.0196 0.0244 0.0313 0.0192 0.0147

42.17 42.93 42.57 43.28 42.48 43.21 42.41 42.93 41.23 38.45 36.59 37.91 36.96 38.67 39.01 38.57 39.11 36.72 36.72 36.29 36.37 40.65 36.71 39.00

−29.60 −28.93 −26.98 −26.27 −27.15 −26.45 −15.28 −14.83 1.05 6.86 20.73 11.24 16.67 16.95 16.63 25.36 21.10 13.48 15.80 19.88 39.04 −2.62 18.59 22.96

−30.78 −30.14 −28.25 −27.63 −28.46 −27.81 −16.85 −16.43 −1.09 6.72 20.31 11.15 16.17 16.27 16.24 24.69 20.46 12.49 15.36 19.52 38.90 −3.31 17.55 21.70

−31.59 −30.97 −29.13 −28.57 −29.37 −28.75 −17.93 −17.54 −2.58 6.62 20.01 11.09 15.82 15.79 15.98 24.23 20.02 11.80 15.06 19.27 38.80 −3.79 16.84 20.83

a

Geometry optimized at the B3LYP/6-311++G(d,p) level. bGeometry optimized at the CASPT2/aug-cc-pVTZ level. cT1 diagnostic from the QCISD(T)/cc-pVQZ calculations . dZero-point energy calculated at either the CASPT2/aug-cc-pVTZ or the B3LYP/6-311++G(d,p) level. eZeropoint corrected energy calculated at the QCISD(T)/cc-pVTZ level. fZero-point corrected energy calculated at the QCISD(T)/cc-pVQZ level. g Zero-point corrected energy calculated at the QCISD(T)/cc-pV∞Z level.

association reactions of NH2 + CH3NH and CH3 + NHNH2,6 and from conventional transition-state calculations of the dissociation reactions with energy barriers.7 As a result, the theoretical predictions of the pressure dependence agree very well with the experimental data of Kerr et al.8 for the first-order rate coefficient of the N−N bond dissociation of MMH at 0.01−0.04 atm. This provides a sound judgment of the capability of the adopted theoretical methodologies in calculating the pressure dependent rate coefficients for the MMH radical dissociation reactions. In the present study, the decomposition pathways and energy barriers of CH3N•NH2, cis-CH3NHN•H, trans-CH3NHN•H, and C•H2NNH2 radicals were identified by using several ab initio quantum chemistry methods. The thermochemical properties of MMH and the four radicals were evaluated on the basis of the new ab initio quantum chemistry results, and the temperature- and pressure-dependent rate coefficients were determined by solving the master equation for wide ranges of temperature and pressure. It is noted that the calculated thermochemical and kinetic data are important components in modeling ignition and combustion of MMH, SDMH, and UDMH.

states of other thermal decomposition channels, implying the multireference characters of the wave functions. Furthermore, it was found that some transition states of the β-scission of H atom from the MMH radicals cannot be located by using density functional theory (DFT). Though they can be located by the MP2/6-311++G(d,p) method, the T1 diagnostic for the CCSD(T) calculation is as large as 0.03. Consequently, the multireference second-order perturbation theory (CASPT2)10 with Dunning’s augmented correlation consistent double-ξ basis set, aug-cc-pVDZ, and triplet-ξ basis set, aug-cc-pVTZ,11,12 were applied to locate the transition states. It was found that the CASPT2(3e,3o) active space, consisting of three electrons and three orbitals involved in the cleaving and forming bonds, is able to qualitatively describe the correct frontier orbitals of all the transition states in the present study. Figure 1 illustrates the transition-state geometry of the β-scission of H from the transCH3NHN•H radical to form trans-CH3NHNH + H products, which is optimized at the CASPT2(3e,3o)/aug-ccpVTZ level with the active space (3e,3o) consisting of the π, π* pair of N−N bond (Figure 1a,b) and the s orbital of the H radical (Figure 1c). For the C•H2NHNH2 radical, due to the conjugation of sp2 carbon orbital with p orbitals of amine nitrogen atoms, the (5e,4o) active space was found to be the minimum to properly describe the frontier orbitals of the C•H2NHNH2 radical. Specifically, the (5e,4o) active space consists of a conjugated orbital of the C−N and N−N bonding, a carbon radical orbital, and the σ, σ* orbital pair of the N−N bond, as shown in Figure 2. Subsequently, the CASPT2(5e,4o)/aug-cc-pVTZ method was also used for the geometry optimization and frequency calculation of the CH3N•NH2, trans-CH3NHN•H, and cis-CH3NHN•H radicals. Specifically, the (5e,4o) active space for the CH3N•NH2

2. THEORETICAL METHODOLOGY 2.1. Electronic Structure Calculations. The T1 diagnostic of Lee et al.9 was used herein to estimate the importance of multireference effects and the reliability of the coupled cluster and quadratic configuration interaction calculations. As shown in Table 1, except for the transition states of isomerization between the MMH radicals and β-scission of CH3 from cis- and trans-CH3NHN•H radicals, the T1 diagnostic values are in the range 0.02−0.03 for the MMH radicals and the transition 8420



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Figure 1. Transition-state geometry of β-scission of the H from the trans-CH3NHN•H radical to form trans-CH3NHNH + H, optimized at the CASPT2(3e,3o)/aug-cc-pVTZ level. The active space (3e,3o) consists of the π, π* pair of the N−N bond as shown in (a) and (b) and the s orbital of the H atom as shown in (c).

energies of open-shell species were determined from the spin restricted open-shell quadratic-configuration-interaction method with single and double excitations and correction for triple excitations,15 ROHF-RQCISD(T), with cc-pVTZ and cc-pVQZ basis sets, extrapolated to the complete basis set limit cc-pV∞Z; the RHF-RQCISD(T)/cc-pV∞Z method was applied for closed shell molecules. Specifically, the QCISD(T) complete basis set (CBS) limit was extrapolated from the triple and quadruple-ζ basis set calculations using the asymptotic form:16,17 E∞ = Elmax − B/(lmax +1)4, where E∞ is the infinite basisset energy, B is a least-squares fit parameter, and lmax is the maximum component of the angular momentum in the cc-pVnZ basis set. lmax is 3 and 4 for the triple (n = 3) and quadrupole (n = 4) basis sets, respectively. The QCISD(T)/cc-pV∞Z energy is then determined from the expression QCISD(T) EccQCISD(T) ‐ pV ∞ Z = Ecc‐pVQZ +

44 QCISD(T) (EccQCISD(T) ‐pVQZ − Ecc‐pVTZ ) 4 5 −4 4

It is seen in Table 1 that the zero-point corrected QCISD(T)/ cc-pV∞Z energies are lower than the zero-point corrected QCISD(T)/cc-pVQZ energies, which in turn are lower than the zero-point corrected QCISD(T)/cc-pVTZ energies. This result is consistent with the common practice of that the larger basis set, the lower energies. In the present work, all the CASPT2 QCISD(T), and CCSD(T) calculations were performed by using MOLPRO program packages,18 and the density functional calculations by using Gaussian09.19 2.2. Kinetic Rate Coefficients. The potential energy surface (PES) for the decomposition of the MMH radicals consists of multiple, interconnected potential wells and multiple product channels. Microcanonical rate coefficients as functions of total rotational−vibrational energy (E) and total angular momentum (J) were calculated using Rice−Ramsperger− Kassel−Marcus (RRKM) theory and the multiwell master equation analysis developed by Miller and Klippenstein,20−22 which are implemented in the VARIFLEX code.23 The transition states were treated with the conventional transition-state theory employing rigid-rotor harmonic oscillator assumptions using optimized geometries and vibrational frequencies from the CASPT2/aug-cc-pVTZ or the B3LYP/6-311++G(d,p) calculations for most modes. Hindered rotor corrections for the CH3 and NH2 torsional modes were obtained from onedimensional fits of the torsional potentials, employing Pitzer− Gwinn like approximations24 and the I(2,3) moments of inertia. The I(2,3) moments of inertia were computed from the axis passing through the centers-of-mass of both the rotating group and the remainder of the molecule.25 Tunneling corrections

Figure 2. Geometry of C•H2NHNH2 radical optimized at the CASPT2(5e,4o)/aug-cc-pVTZ level. The active space (5e,4o) consists of a conjugated orbital of the C−N and N−N bonding (a) a carbon radical orbital (c), and the σ, σ* orbital pair of the N−N bonding (b) and (d).

radical consists of the central N radical orbital, one π orbital of the N−N bonding, and the σ, σ* orbital pair of the N−N bonding. Similarly, the (5e,4o) active spaces for the transCH3NHN•H and cis-CH3NHN•H radicals consist of the terminal N radical orbital, one π orbital of the N−N bonding, and the σ, σ* orbital pair of the N−N bonding. Previously, we have found that the MMH geometry and rovibrational frequencies from the CASPT2(4e,3o)/aug-cc-pVTZ optimization4 are closer to the experimental data13,14 than those obtained from the B3LYP/6-311++G(d,p) and MP2/6-311+ G(d,p) optimizations, indicating that the multireference CASPT2 method predicts more accurate structure and vibrational frequencies of the species involved in the MMH reaction system. Consequently, the CASPT2(5e,4o)/aug-cc-pVTZ geometries and vibratoinal frequencies are considered to be more accurate than the B3LYP/6-311++G(d,p) geometries for the four MMH radicals. Rovibrational frequencies of species were calculated at the same level of geometry optimization. The higher-level single-point 8421



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Table 2. Ideal Gas-Phase Thermodynamic Propertiesa species

ΔHfo298b

So298c

Cp300c

Cp500

Cp800

Cp1000

Cp1200

Cp1500

Cp2000

Cp3000

Cp5000

CH3NHNH2 C−Nd N−Nd CH3N•NH2 C−Nd trans-CH3NHN•H C−Nd cis-CH3NHN•H C−Nd C•H2NHNH2 N−Nd

22.12

65.60 2.74 1.77 64.36 3.01 64.34 2.92 64.22 2.64 64.89 2.62

15.78 1.74 2.03 14.69 1.53 14.61 1.60 14.93 1.91 16.05 1.68

23.08 2.11 2.17 20.45 1.23 20.28 1.27 20.47 1.50 22.34 2.06

30.75 2.28 1.83 26.97 1.09 26.84 1.11 26.93 1.23 28.62 2.28

34.17 2.21 1.63 30.05 1.06 29.94 1.07 30.00 1.15 31.43 2.25

36.77 2.08 1.48 32.44 1.04 32.35 1.05 32.40 1.11 33.57 2.15

39.59 1.87 1.33 35.07 1.02 35.01 1.03 35.04 1.07 35.91 1.95

42.48 1.60 1.20 37.79 1.01 37.75 1.01 37.77 1.04 38.32 1.67

45.11 1.31 1.09 40.27 1.00 40.26 1.00 40.26 1.01 40.54 1.36

46.70 1.12 1.03 41.78 1.00 41.78 1.00 41.78 1.00 41.89 1.14

49.83 52.04 52.23 63.31

Thermodynamic properties are referred to a standard state of an ideal gas at 1 atm. bUnits in kcal mol−1. cUnits in cal mol−1 K−1. dContribution from the internal rotations.

a

−10.98 kcal mol−1 for NH3, −5.62 for CH3NH2, and 22.79 for NH2NH2 from the NIST chemistry database,29 we determined the ΔHf,298 of MMH to be 22.12 kcal mol−1, which is closer to the experimental ΔHf,298 of 22.6 kcal mol−1.30 Based on this theoretical ΔHf,298 of MMH and the bond dissociation energies above, the ΔHf,298 of CH3N•NH2, trans-CH3NHN•H, cisCH3NHN•H, and C•H2NNH2 radicals were found to be 49.83, 52.04, 51.21, and 63.31 kcal mol−1, respectively. The entropy So298 and heat capacities Cp(T) of MMH and the four MMH radicals were determined by the CASPT2/augcc-pVTZ optimized geometries and vibrational frequencies. The contributions from the hindered internal rotors of CH3 and NH2 to So298 and Cp(T) were considered for MMH by using Pitzer-Gwinn approximation.24 For the nitrogen centered cis-CH3NHN•H, trans-CH3NHN•H and CH3N•NH2 radicals, only the CH3 rotor of each radical is considered as hindered rotor because of the significant resonance along the N−N bond. By considering the calculated CASPT2 vibrational frequencies corresponding to the internal rotational motion and the DFT determined rational potentials, we approximated the barrier heights of the CH3 rotors to be 1.7, 1.2, and 1.1 kcal mol−1 for cisCH3NHN•H, trans-CH3NHN•H, and CH3N•NH2 radicals, respectively. Similarly, only the NH2 rotor is treated as hindered rotor for the carbon centered C•H2NHNH2 radical because of the significant resonance along the C−N bond. The rotational potential of the NH2 rotor of the C•H2NHNH2 radical along its dissociation transition state will be discussed in detail in section 3.4.1. Table 2 lists the thermochemical properties of MMH and the four MMH radicals determined in this work, including contributions from the internal rotors to the S and Cp(T). 3.2. Potential Energy Surface. Figure 3 shows the PES for the decomposition pathways of the CH 3 N • NH 2 , cisCH3NHN•H, trans-CH3NHN•H, and C•H2NHNH2 radicals to form H, NH2, CH3, diazene, methyldiazene, and other products. Briefly, the β-scission of NH2 from the C•H2NHNH2 radical has a small barrier of 13.8 kcal/mol to form methyleneimine. The mutual isomerization between the cis- and trans-CH3NHN•H radical has a barrier of 26 kcal/mol. Furthermore, the β-scission of CH3 from cis-CH3NHN•H and trans-CH3NHN•H radicals have the barriers of 35−40 kcal/mol to form trans-diazene or cis-diazene. The β-scission of the H atom from CH3N•NH2 radical has higher energy barriers, 42.7−50 kcal/mol. The transand cis-CH3NHN•H radicals can isomerize to the CH3N•NH2 radical and can also isomerize to the C•H2NHNH2 radical. These isomerization channels have higher energy barriers of

were included for all transition states on the basis of the asymmetric Eckart potentials,26 with the parameters of the potentials computed from the barrier heights and the imaginary frequency of the transition state. The pressure-dependent kinetics analysis for the decomposition of the MMH radicals was performed by solving the time-dependent, multiple-well master equation at the E, J resolved level. Specifically, the phenomenological (thermal) rate coefficients, k(T,p), were determined using either (a) the time-dependent multiple-well master equation, which is limited to a one-dimensional formulation in which E is the independent variable or (b) the single-well master equation for irreversible dissociation with E and J being the independent variables. The collisional energy transfer probability in the master equation analysis was approximated by a single-exponential-down model, employing the temperature dependent form ΔEdown = 200(T/300)0.85 cm−1 for the average downward energy transfer.6 This energy transfer model is used for the collider of argon, which has been considered in the MMH pyrolysis and oxidation mechanism.27 Nitrogen was also considered as a collider in the study for comparison. The Lennard-Jones parameters of the MMH radicals for collision rates were estimated to be the same as those of the MMH molecule, namely, σ = 4.4 Å and ε = 340 cm−1.5 The Lennard-Jones parameters are σ = 3.42 Å and ε = 86.2 cm−1 for argon, and σ = 3.70 Å and ε = 66.1 cm−1 for nitrogen.28

3. RESULTS AND DISCUSSION 3.1. Thermochemistry. The Cartesian coordinates, vibration frequencies, moments of inertia, zero-point energies, and total electronic energies at different calculation levels for the four target radicals are listed in Supporting Information Table S1−S4. By using the calculated QCISD(T)/cc-pV∞Z total electronic energies at 0 K, and thermal energy correction to 298 K values based on the CASPT2 frequencies, we found the bond energies at 298 K for dissociation of different H atoms of the MMH to form CH3N•NH2, trans-CH3NHN•H, cisCH3NHN•H, and C•H2NNH2 radicals to be 79.81, 82.03, 82.19, and 93.29 kcal mol−1, which is consistent with those determined in our previous work.5 The enthalpy of formation ΔHf,298 of MMH was found to be 21.6 kcal mol−1 by isodesmic reaction analysis and different ab initio composite methods.5 Re-evaluating the isodesmic reaction, CH3NHNH2 + NH3 → CH3NH2 + NH2NH2, by using the QCISD(T)/cc-pV∞Z enthalpies at 298 K, the enthalpy of reaction was found to be 6.03 kcal mol−1 at 298 K. By using the ΔHf,298 values of 8422



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Figure 3. Potential energy surface of decomposition of the CH3N•NH2, cis-CH3NHN•H, trans-CH3NHN•H, and C•H2NNH2 radicals calculated at the QCISD(T)/cc-pV∞Z//CASPT2/aug-cc-pVTZ level (data marked by blue) and at the QCISD(T)/cc-pV∞Z//B3LYP/6-311++G(d,p) level (data marked by black).

44.5−53.0 kcal mol−1. Reactions with the zero-point corrected energy barriers higher than 53 kcal mol−1 are neglected on the PES. The T1 diagnostic, the zero-point energies, and the zeropoint corrected total energies of the stationary points relative to that of CH3 + trans-NHNH channel are listed in Table 1. Specifically, the cis-CH3NHN•H radical isomerizes to the trans-CH3NHN•H radical (R1) via TS1 with an energy barrier of 26.0 kcal mol−1: •

•

cis‐CH3NHN H → TS1 → trans‐CH3NHN H

were found to have energy barriers over 70 kcal mol−1 and hence are kinetically unfavorable, we did not include them in the PES and also the rate calculations. The trans- and cis-CH3NHN•H radicals can isomerize to the CH3N•NH2 radical via the three-center transition states TS6 and TS7, and also can isomerize to the C•H2NHNH2 radical via the four-center transition states TS8 and TS9, respectively.

(R1)

This reaction is almost thermal neutral because the energy of trans-CH3NHN•H is merely 0.2 kcal mol−1 lower than that of the cis-CH3NHN•H. This also implies the similar energy barrier height for the reverse isomerization. Because of the relatively high energy barrier of the isomerization, the cis- and transCH3NHN•H radicals should be treated as distinct spatial isomers rather than rotamers. The cis-CH3NHN•H radical undergoes β-scission of the CH3 to form CH3 + trans-NH NH products (R2) with an energy barrier of 35.2 kcal mol−1, and also β-scission of the H atom to form H + cis-CH3NH product (R3) with an energy barrier of 48.6 kcal mol−1: (R2)

cis‐CH3NHN H → TS3 → cis‐CH3NNH + H

(R6)

cis‐CH3NHN•H → TS7 → CH3N•NH 2

(R7)

trans‐CH3NHN•H → TS8 → C•H 2NHNH 2

(R8)

cis‐CH3NHN•H → TS9 → C•H 2NHNH 2

(R9)

These isomerization channels are not kinetically favorable because the constrained transition states for the intramolecular H transfer have the higher energy barriers (44.5−53.0 kcal mol−1) and lower entropies than those of the β-scission reactions. Therefore, these isomerization channels will not be considered in the rate coefficient calculations. The β-scission of H atoms from the CH3N•NH2 radical can form CH2NNH2, trans-CH3NNH, and cis-CH3NNH products (R10)−(R12), with energy barriers of 42.8, 46.0, and 50.2 kcal mol−1, respectively,

cis‐CH3NHN•H → TS2 → CH3 + trans‐NHNH •

trans‐CH3NHN•H → TS6 → CH3N•NH 2

(R3)

•

Similarly, the trans-CH3NHN H radical decomposes to CH3 + cis-NHNH products (R4) with an energy barrier of 39.8 kcal mol−1, and to trans-CH3NH + H product (R5), with an energy barrier of 44.6 kcal mol−1: trans‐CH3NHN•H → TS4 → CH3 + cis‐NHNH

CH3N•NH 2 → TS10 → CH 2NNH 2 + H

(R10)

CH3N•NH 2 → TS11 → trans‐CH3NNH + H

(R11)

CH3N•NH 2 → TS12 → cis‐CH3NNH + H

(R12)

These reactions have higher energy barriers than the β-scission of the CH3 in the cis- and trans-CH3NHN•H radicals, which is consistent with the fact that the C−H and N−H bond dissociation energy is stronger than that of the C−N bond. The C−N bond fission of the CH3N•NH2 radical can form NNH2 product:

(R4) •

trans‐CH3NHN H → TS5 → trans‐CH3N = NH + H (R5)

Furthermore, the C−H bond fission of the cis-CH3NHN•H and trans-CH3NHN•H radicals forms cyclic, three-member-ring CH2NHNH in which the two amine H atoms are in either trans or cis position along the N−N bond. Because these reactions

CH3N•NH 2 → TS13 → CH3 + NNH 2 8423

(R13)



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Figure 4. Transition-state geometry of β-scission of the NH2 group from the C•H2NHNH2 radical optimized at the CASPT2(3e,3o)/aug-cc-pVTZ level. The active space (3e,3o) consists of a pair of conjugated C−N(π, π*) and C−N(σ, σ*) bonding orbitals as shown in (a) and (b), and the radical orbital of the C•H2NHNH2 as shown in (c).

Table 3. Zero-Point Corrected Energy Barriersa reaction

RCCSD(T)/MP2

TS5_trans-CH3NHN•H → trans-CH3NNH + H TS3_cis-CH3NHN•H → cis-CH3NNH + H TS10_CH3N•NH2 → CH2NNH2 + H TS11_CH3N•NH2 → trans-CH3NNH+H TS12_CH3N•NH2 → cis-CH3NNH + H TS13_CH3N•NH2 → CH3 + NNH2 TS14_C•H2NHNH2 → CH2NH + NH2

49.75 43.93 48.20 52.77

UCCSD(T)/CASPT2

UQCISD(T)/CASPT2

RQCISD(T)/CASPT2

44.21 48.53 42.88 45.81 50.17 70.20 13.50

44.07 48.55 42.92 45.79 50.16 70.06 12.51

44.57 48.58 42.77 46.03 50.25 69.77 13.75

a Units in kcal mol−1. Zero-point corrected energy barriers were calculated with spin restricted or unrestricted QCISD(T)/cc-pV∞Z and CCSD(T)/ cc-pV∞Z methods.

The transition state TS13 of the C−N bond fission was located by the CASPT2(3e,3o)/aug-cc-pVTZ method. By further performing QCISD(T)/cc-pV∞Z energy calculations, we found that the energy barrier of TS13 to be 69.8 kcal mol−1, which is too high to be considered in the rate calculation. The C•H2NHNH2 radical undergoes the β-scission of NH2 to form methyleneimine (CH2NH): C•H 2NHNH 2 → TS14 → CH 2NH + NH 2

Table 3 listed the zero-point corrected energy barrier of the decomposition of MMH radicals with multireference characters of transition states calculated by spin-unrestricted or spinrestricted, CCSD(T) or QCISD(T) methods. Specifically, the zero-point corrected energy barriers were calculated for the β-scission of the H atom from the nitrogen-centered cisCH3NHN•H, trans-CH3NHN•H, and CH3N•NH2 radicals (TS3, TS5, TS10, TS11, TS12), β-scission of NH2 from the carbon-centered C•H2NHNH2 radical (TS14), and C−N bond fission of CH3N•NH2 radical (TS13). It is seen that the UQCISD(T)/CASPT2 energy barrier of the major channel (R14) is 1 kcal mol−1 lower than those from the RQCISD(T)/ CASPT2 and UCCSD(T)/CASPT2 calculations, whereas the spin-unrestricted or spin-restricted energy barriers at the CCSD(T)/CASPT2 and the QCISD(T)/CASPT2 levels are consistent with other reactions. To seek the accurate energy barrier of this predominant channel (R14), several different theoretical methods were performed as listed in Table 4. It is seen from Table 4 that the T1 diagnostic values from the spinunrestricted CCSD(T) and QCISD(T) calculations are higher than those from the spin-restricted calculations, hence the spinrestricted CCSD(T) and QCISD(T) energy barriers are considered to be more accurate. Here, the RQCISD(T)/cc -pV∞Z//CASPT2 energy barrier of 13.75 kcal mol−1 is chosen for kinetic rate calculations. The transition states for the β-scission of the amine H and methyl H from nitrogen-centered cis-CH3NHN•H and CH3N•NH2 radicals were located by the MP2/6-311+G(d,p) geometry optimizations, and the zero-point corrected energy barriers at the QCISD(T)/cc-pV∞Z level are found to be 1.2−2.5 kcal mol−1 higher than those determined with the CASPT2(3e,3o)/aug-cc-pVTZ geometries, as shown in Table 3. For the QCISD(T)/cc-pV∞Z//MP2/6-311+G(d,p) energy barriers, the MP2 rovibrational frequencies were scaled by a factor of 0.9748 as recommended by Radom et al.31 The higher QCISD(T)/cc-pV∞Z//MP2/6-311+G(d,p) energy barriers might be ascribed to the multireference character of the MP2

(R14)

The energy barrier of reaction R14 was found to be only 13.8 kcal mol−1, which is ascribed to the weak N−N bond and also stable methyleneimine formation. As discussed above, the (5e,4o) active space is the minimum requirement to describe the frontier orbitals of the C•H2NHNH2 radical in the CASPT2 calculations. However, the (3e,3o) active space was found to be able to qualitatively describe the frontier orbitals of the β-scission of NH2 from the C•H2NHNH2 radical. As shown in Figure 4, the (3e,3o) active space of TS14 consists of a pair of conjugated C−N (π, π*) and N−N (σ, σ*) bonding orbitals, and the radical orbital of C•H2NHNH2. The β-scission of the central amine H atom from the C•H2NHNH2 radical forms the product CH2NNH2, with an energy barrier of 34.4 kcal mol−1: C•H 2NHNH 2 → TS15 → CH 2NNH 2 + H

(R15)

The C•H2NHNH2 radical also undergoes isomerization to the CH3N•NH2 radical via the three-center transition state TS16, with an energy barrier of 38.4 kcal mol−1: C•H 2NHNH 2 → TS16 → CH3N•NH 2

(R16) •

The terminal N−H bond fissions of the C H2NHNH2 radical can form cyclic trans-CH2NHNH and cis-CH2NHNH molecules, and the energy barriers were found to be 48.3 and 50.2 kcal mol−1, respectively. Because reaction R14 has smaller energy barrier of 13.8 kcal mol−1, this leads to the terminal N−H bond fissions, the β-scission of central amine H (R11), and the isomerization (R15) are kinetically unimportant. 8424



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Table 4. T1 Diagnostic and Zero-Point Corrected Energy Barrier of C•H2NHNH2 → CH2NH + NH2a

a

calculation level

T1 diagnostic

energy barrier

RCCSD(T)/cc-pV∞Z//CASPT2(3e,3o)/aug-cc-pVTZ UCCSD(T)/cc-pV∞Z//CASPT2(3e,3o)/aug-cc-pVTZ RQCISD(T)/cc-pV∞Z//CASPT2(3e,3o)/aug-cc-pVTZ UQCISD(T)/cc-pV∞Z//CASPT2(3e,3o)/aug-cc-pVTZ RQCISD(T)/cc-pV∞Z//B3LYP/6-31++G(d,p) UQCISD(T)/cc-pV∞Z//B3LYP/6-31++G(d,p)

0.0286 0.0336 0.0313 0.0387 0.0316 0.0392

14.45 13.50 13.75 12.51 13.98 12.39

Units in kcal mol−1.

Figure 5. Transition-state geometries of the β-scission of H atom from cis-CH3NHN•H and CH3N•NH2 radicals optimized at the CASPT2(3e,3o)/ aug-cc-pVTZ level. The major bond length and bond angle from the CASPT2(3e,3o)/aug-cc-pVTZ optimizations as marked by black are compared with those from the UMP2(full)/6-311+G(d,p) optimizations as marked by blue.

optimization are shorter than those from the CASPT2 optimization; for cleaving C−H bond length, the MP2 optimization predicts 0.23 Å shorter than that of the CASPT2 optimization. Furthermore, the MP2 calculation predicts extremely larger imaginary frequency for each transition state than does the CASPT2 calculation. Specifically, the MP2(full)/6-311+G(d,p) predicts an imaginary frequency of 1964.2 cm−1 (TS3) for the βscission of the H from the cis-CH3NHN•H to form cis-CH3N NH + H (R3), and 1613.0 cm−1 (TS11), 1698.0 cm−1 (TS12), 1125.3 cm−1 (TS10) for the β-scission of the different H atom from the CH3N•NH2 radical in reactions of (R10)−(R12). The corresponding imaginary frequencies from CASPT2 calculations are 1262.4, 877.8, 706.9, and 585.9 cm−1, respectively. Recently, we found that the three low frequencies of MMH from the CASPT2(4e,3o)/aug-cc-pVTZ calculation are 278.6, 327.4, and 426.3 cm−1,4 which is very close to the experimental observation of 281, 315, and 428 cm−1, respectively.32 Therefore, the CASPT2 imaginary frequencies of these transition states are deemed to be accurate for the corrections of tunneling effect to rate coefficients. 3.4. Kinetic Rate Coefficients. 3.4.1. Decomposition of the cis- and trans-CH3NHN•H Radicals. Because the isomerizations of cis-CH3NHN•H and trans-CH3NHN•H radicals to the CH3N•NH2 and C•H2NHNH2 radicals are kinetically unfavorable, as discussed in section 3.1, the decomposition of cis- and

wave function as reflected by its T1 diagnostic value of 0.03, and also the tight MP2(full)/6-311+G(d,p) transition-state structures as described in the following section. 3.3. β-Scission of Amine H and Methyl H from the MP2 Calculation. The MP2 method has been used to locate the transition-state structures of hydrocarbon oxidation and propellant combustion for its simplicity and reasonable accuracy. For the methylhydrazine radical decomposition system, it was found that the MP2/6-311+G(d,p) method predicts significantly shorter cleaving N−H and C−H bond lengths for the β-scission of the H atom compared with those predicted by the CASPT2 method. Figure 5 illustrates a comparison of the CASPT2(3e,3o)/aug-cc-pVTZ and the MP2/6-311+G(d,p) optimizations for major bond lengths and bond angles in the transitionstate geometries of the β-scission of the H atom from the cis-CH3NHN•H and CH3N•NH2 radicals. It shows that, for the β-scission of the amine H atom in TS3, TS11, and TS12, the MP2/6-311+G(d,p) geometry has longer C−N bond length, shorter N−N bond length, and larger ∠CNN bond angle compared to the CASPT2(3e,3o)/aug-cc-pVTZ geometry. Particularly, the cleaving N−H bond length of 1.60−1.67 Å from the MP2 optimization is significantly shorter than the bond length of 1.81−1.84 Å from the CASPT2 optimization. For the β-scission of the methyl H atom from the CH3N•NH2 radical in TS10, the C−N and N−N bond lengths from the MP2 8425



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trans-CH3NHN•H radicals can be considered by following reactions with the bimolecular reaction of CH3 + trans-NH NH as an entrance channel:

are relatively slow, and the formation of cis-methyldiazene is the slowest. Figure 7 shows the theoretical rate coefficients for the isomerization and β-scission channels of cis- and trans-CH3NHN•H

CH3 + trans‐NHNH ↔ cis‐CH3NHN•H* → cis‐CH3NHN•H → cis‐CH3NNH + H

(R3)

→ trans‐CH3NHN•H

(R1)

→ CH3 + cis‐NHNH

(R4)

→ trans‐CH3NNH + H

(R5)

where cis-CH3NHN•H* indicates an energized complex, and its collisional stabilization competes with the decomposition to cisCH3NNH + H (R3) and the isomerization to the trans isomer (R1), which is followed by decomposition to CH3 + cisNHNH (R4) and trans-CH3NNH + H (R5). Consequently, the decomposition kinetics of cis- and trans-CH3NHN•H radicals can be analyzed on the basis of a two-well and multiple-product channel master equation analysis. Figure 6 shows the theoretical rate coefficients for the isomerization and dissociation of cis- and trans-CH3NHN•H

Figure 7. Theoretical rate coefficients of the β-scission channels and isomerization channel of the CH3NHN•H radical as functions of temperature and pressure.

radicals as functions of both temperature and pressure. At the temperatures of 800−2500 K and pressures of 0.01−100 atm, it is seen the rate coefficients for these reaction channels exhibit strong temperature- and pressure-dependence, namely, increasing with increasing temperature and pressure, as expected. The rate coefficients for the isomerization and dissociation channels of the CH3NHN•H radical at T = 300−2500 K and p = 0.01− 100 atm with argon as collider were fitted in Arrhenius threeparameter format as tabulated in Table 5. 3.4.2. Decomposition of the CH3N•NH2 Radical. The major decomposition channels for the CH3N•NH2 radical are the β-scission of different H atoms (R10)−(R12). As discussed in section 3.1, the isomerization of CH3N•NH2 to other MMH radicals is kinetically unfavorable; the pressure-dependent decomposition kinetics of CH3N•NH2 can be simplified to the rate calculation for a single-well and multiple-product master equation analysis. The rate coefficients k10, k11, and k12 as functions of temperature and pressure are shown in Figure 8. It is seen that all the reactions show strong temperature and pressure dependence. Furthermore, β-scission of the methyl H atom to CH2NNH2 + H (k10) is the dominant channel, followed by β-scission of the terminal amine H to trans-CH3NNH + H (k11) and to cis-CH3NNH + H (k12). For the CH3N•NH2 radical decomposition channels, by variation of the α value in the ΔEdown form, the pressure dependent rate does not change much at low temperatures, though it changes the same magnitude of the α variation at high temperatures. At 1 atm and with nitrogen as collider, it was found that k10, k11, and k12 are monotonically increased by 0−11.1%, 0−12.3%, and 0.6−15.9%, respectively, for temperatures of 300−2500 K, indicating that the bath gas effect of nitrogen and argon on the rate coefficients is not significant. The theoretical rate coefficients for the dissociation channels of the CH3N•NH2 radical at T = 300−2500 K and p = 0.01−100 atm with argon as collider were fitted in the Arrhenius three-parameter format and are also tabulated in Table 5. Because of the relatively high energy barriers for the CH3N•NH2 decomposition, the CH3N•NH2 radical may undergo oxidative reactions for further decomposition.33

Figure 6. Theoretical rate coefficients of the β-scission channels and isomerization channel of the CH3NHN•H radical at p = 1 atm.

radicals at 1 atm pressure and temperatures of 500−2500 K with argon as collider. The high pressure limit rate coefficient of dissociation of cis-CH3NHN•H to CH3 + trans-NHNH, k2,∞ = 2.23 × 1014T0.126 exp(18498.78/T) s−1, is also shown in Figure 6 for comparison. It is seen that the isomerization between the cis-CH3NHN•H radical and trans-CH3NHN•H radical (k1) dominates over other dissociation channels up to 2000 K. The reaction of cis-CH3NHN•H → CH3 + trans-NHNH (k2) is the fastest dissociation channel, followed by the reaction of trans-CH3NHN•H → CH3 + cis-NHNH (k4). The β-scission of H atom from the trans-CH3NHN•H radical (k5) and cisCH3NHN•H radical (k3) to form trans- and cis-methyldiazene 8426



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Table 5. Pressure Dependent Rate Coefficients of Dissociation of MMH Radicalsa cis-CH3NHN•H → CH3 + trans-NHNH p (atm) 0.01 0.1 1 2 5 10 50 100 ∞

5.23 2.80 3.98 8.61 2.06 7.62 5.58 4.93 2.23

n

× × × × × × × × ×

1032 −6.721 1033 −6.639 1032 −6.109 1031 −5.834 1030 −5.263 1029 −5.060 1027 −4.269 1026 −3.891 1014 0.126 cis-CH3NHN•H → trans-CH3NHN•H

A

0.01 0.1 1 2 5 10 50 100

× × × × × × × ×

3.71 3.08 2.38 1.21 3.15 7.42 6.06 3.88

p (atm) 0.01 0.1 1 2 5 10 50 100 ∞

2.54 7.13 1.15 8.36 1.78 1.09 3.91 2.32

× × × × × × × ×

1.29 1.90 9.05 8.27 1.49 9.51 4.11 6.74

A

24.02 25.28 26.62 26.92 27.20 27.32 27.22 26.99 +H

0.01 0.1 1 2 5 10 50 100

× × × × × × × ×

7.21 9.83 3.39 2.85 2.53 1.19 1.34 4.20

10 1037 1032 1031 1032 1031 1031 1029

Ea (kcal mol−1)

−3.859 −5.353 −5.866 −5.980 −5.896 −5.699 −5.269 −4.228

44.08 46.06 47.23 47.81 48.36 48.66 49.62 48.35

A 3.98 3.88 3.34 2.42 8.08 2.13 2.65 3.20 3.88

× × × × × × × × ×

1033 1033 1033 1033 1032 1032 1030 1028 1019

Ea (kcal mol−1)

−1.687 −3.147 −5.250 −5.679 −5.857 −5.947 −5.524 −5.169

47.12 47.45 49.84 50.57 51.11 51.68 52.28 52.29

5.1 4.2 3.2 2.2 9.6 4.7 6.6 2.3 7.2

53.50 54.07 52.31 52.14 53.91 53.61 55.70 55.27

Ea (kcal mol−1)

−6.716 −6.525 −6.393 −6.319 −6.128 −5.915 −5.246 −4.599 −1.672

22.39 22.48 22.55 22.55 22.49 22.38 21.99 21.56 19.20

10 1031 1032 1032 1031 1030 1028 1026

× × × × × × × × ×

1038 1036 1033 1032 1033 1032 1032 1031 1011

× × × × × × × ×

n 33

10 1036 1033 1033 1031 1029 1027 1025

× × × × ×

10−2 10−1 10−3 10−3 10−2

× 107 × 1011 × 1013

42.47 44.10 45.16 45.49 45.62 45.57 45.10 44.85

Ea (kcal mol−1)

−8.054 −7.237 −6.122 −5.723 −6.045 −5.611 −5.460 −4.993 0.810 CH3N•NH2 → cis-CH3NNH + H

A 1.28 2.33 1.76 3.72 4.58 2.30 4.17 2.08 1.11

Ea (kcal mol−1)

−5.743 −6.382 −6.325 −6.213 −5.849 −5.473 −4.407 −3.921 CH3N•NH2 → CH2NNH2 + H n

A 7.01 1.84 5.42 1.05 1.74 9.23 4.08 7.87

n

× × × × × × × ×

n 27

A

Ea (kcal mol−1)

−8.373 −7.852 −6.031 −5.649 −5.779 −5.334 −5.152 −4.669 C•H2NNH2 → CH2NH + NH2

1011 1017 1025 1027 1029 1029 1029 1028

A 9.99 3.02 3.92 4.10 7.48 9.03 1.25 5.51

n

n 38

× × × × × × × ×

n

trans-CH3NHN•H → CH3 + cis-NHNH

Ea (kcal mol−1)

−5.411 10 1026 −5.048 1026 −4.696 1026 −4.519 1025 −4.235 1024 −3.972 1022 −3.198 1021 −2.790 trans-CH3NHN•H → trans-CH3NNH 1019 1025 1029 1029 1030 1030 1029 1026

39.93 40.76 41.11 41.05 40.62 40.65 40.29 40.11 36.76

A

CH3N•NH2 → trans-CH3NNH + H

p (atm)

0.01 0.1 1 2 5 10 50 100 ∞

n

Ea (kcal mol )

26

A

p (atm)

a

A

p (atm)

cis-CH3NHN•H → cis-CH3NNH + H −1

52.01 51.87 51.41 51.17 53.68 53.36 55.70 55.27 45.04

Ea (kcal mol−1)

−7.293 −7.637 −6.572 −6.269 −5.610 −5.159 −4.277 −3.717 C•H2NNH2 → CH2NNH2 + H

55.44 56.75 56.35 56.40 56.21 56.00 56.20 55.74

n

Ea (kcal mol−1)

2.127 2.044 2.890 2.860 2.630 2.207 0.331 −0.603 0.184

39.20 39.05 35.49 34.45 33.01 32.10 31.62 32.15 36.64

Rate coefficients were fit to the Arrhenius three parameter expression, ATn exp(−Ea/RT), unit in s−1, where R is the gas constant in units of cal mol−1 K−1.

3.4.3. Decomposition of the C•H2NHNH2 Radical. As discussed earlier, the isomerizations of the C•H2NHNH2 radical to other MMH radicals are kinetically unfavorable due to the constrained transition states for the intramolecular H

transfer. By the same token of simplifying the analysis of the CH3NHN•H decomposition, the pressure-dependent decomposition kinetics of C•H2NHNH2 radical can be simplified by solving a single well master equation analysis. 8427



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Figure 8. Theoretical rate coefficients for the dissociation of the CH3N•NH2 radical to three product channels of CH2NNH2 + H, trans-CH3NNH + H, and cis-CH3NNH + H as functions of temperature and pressure.

The torsional mode of NH2 corresponds to a frequency of 282.8 cm−1 in the C•H2NHNH2 radical, and corresponds to a frequency of 147.2 cm−1 in the transition state TS14. The internal rotational potentials of the CH2NH--NH2 rotor in the radical and TS14 determined by the B3LYP/6-311++G(d,p) calculations are shown in Figure 9. It is seen that the potential of the NH2 rotor in the C•H2NHNH2 radical is 2-fold asymmetric whereas it is 1-fold asymmetric in TS14. By examining the structures of local extrema on the potential curves, we found that the structures for the local maxima for both the C•H2NHNH2 radical and TS14 correspond to the structure in which the NH2 group eclipses to CH2NH along the N−N bond. On the potential curve of the NH2 rotor in the C•H2NHNH2 radical, the structure corresponding to the second minimum has the shortest interatomic distance between the terminal amine N atom and the H(8) atom in the CH2 group, 2.593 Å. Furthermore, this geometry configuration enables the lone pair orbital of the terminal amine N atom to orient toward the H(8) atom of the CH2 group for maximizing attraction between them, and as such locally minimizing the energy to form the second minimum of the potential. For the second maximum on the potential curve of the NH2 rotor, the interatomic distance between the terminal amine N atom and the H(8) atom in the CH2 group is increased to 2.627 Å, with the lone pair orbital of the terminal amine N atom being oriented toward different directions and hence repulsed to the p orbital of the CH2 group. However, the potential of the NH2 rotor in TS14 does not have distinct second minimum and second maximum, as shown in Figure 9. By scrutinizing the structure of the inflection points, we found that, for the first inflection point, the interatomic distance between the terminal amine N atom and the H(8) atom in the CH2 group is 2.966 Å because the N−N bond length is increased to 1.878 Å in TS14. For the second inflection point, the structure has the configuration that one terminal amine H atom eclipses to the central amine H atom, and the interatomic distance between the terminal amine N atom and the H(8) atom in the CH2 group is 2.999 Å. This longer interatomic distance weakens the

Figure 9. Rotational potentials of the CH2NH--NH2 rotor in the radical and the transition state of the β scission of NH2.

attraction and repulsion between the NH2 and CH2 groups and therefore leads to the absence of distinct second extremum on the potential curve of the NH2 rotor in TS14. The calculated hindered internal rotation potentials were fitted to a Fourier series as described in our previous work,4 and the torsional modes were treated as uncoupled 1-dimensional hindered rotors with a Pitzer−Gwinn-like approximation24 that reproduces the coupled harmonic oscillator limit at low temperatures and the free rotor limit at high temperatures. Clearly, the dissociation of the C•H2NHNH2 radical to CH2 NH + NH2 (Rl4) is the predominant channel. The rate coefficients (k14) at pressures of 0.01, 0.1, 1, 5, 10, 50, and 100 atm and the high-pressure limit with argon as bath gas are shown in Figure 10. These rate coefficients increase with pressures but are still well below the high-pressure limit at temperatures of 1500− 2500 K. A plot of k/k∞ as a function of pressure at T = 300, 400, 500, 800, 1000, 1200, 1500, 1800, and 2500 K, with the details of the falloff regions for channel CH2NH + NH2 is shown in Figure 11. Specifically, it shows that at T = 300 K, the falloff region starts at pressure of 1 atm, and reaches to the high pressure limit at about 100 atm. However, as the temperature increases, the falloff region spans a wide pressure range. Typically, even though at the pressure of 100 atm, they are still far from the high pressure limit. The theoretical rate coefficients k14 and k15 as functions of temperature and pressure are shown in Figure 12. Obviously, it shows that the R14 is predominant, exhibiting weak temperature dependence at the temperatures of 1000−2500 K due to its small energy barrier of 13.8 kcal mol−1. At 1 atm pressure and nitrogen as bath gas, it was found that k14 monotonically 8428



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Figure 10. Temperature dependence of rate coefficients in the dissociation channel C•H2NHNH2 → CH2NH + NH2 at pressures of p = 0.01, 0.1, 1, 5, 10, 50, 100 atm and at the high pressure limit. Figure 12. Theoretical rate coefficients of the dissociation channels C•H2NHNH2 → CH2NH + NH2 and C•H2NHNH2 → CH2 NNH2 + H as functions of temperature and pressure.

NH2 rotor in the transition state is rather small, 147.2 cm−1; hence it has a relatively large contribution to the partition function. However, the rotational potential of the NH2 rotor is quite high, 7.6 kcal mol−1, due to the electronic repulsion between the NH2 and CH2NH group in the transition state. This leads to less contribution to the partition function and a smaller rate coefficient with increasing temperatures.

4. CONCLUDING REMARKS Thermal decomposition of the CH3N•NH2, cis-CH3NHN•H, trans-CH3NHN•H, and C•H2NNH2 radicals were theoretically investigated by ab initio RRKM theory and master equation analysis at the E- and J-resolved level. The multireference character of the wave functions of the radicals and the transition states were observed in most decomposition channels. Accordingly, the QCISD(T)/cc-pV∞Z//CASPT2/augcc-pVTZ quantum chemistry method was applied to locate the geometries and energies of the stationary points on the potential energy surface. The results reveal that the β-scission of NH2 to form methyleneimine is the predominant channel for the decomposition of the C•H2NNH2 radical because of its small energy barrier of 13.8 kcal mol−1, and as such the rate coefficient exhibits relatively weak temperature dependence at 1000−2500 K. The cis-CH3NHN•H radical and transCH3NHN•H radical are the two distinct spatial isomers with an energy barrier of 26 kcal mol−1 for their isomerization. The β-scissions of CH3 from the cis- and the trans-CH3NHN•H radicals have energy barriers of 35.2 kcal mol−1 and 39.8 kcal mol−1, respectively. The CH3N•NH2 radical undergoes the β-scission of methyl hydrogen and amine hydrogen to form CH2NNH2, trans-CH3NNH, and cis-CH3NNH products, with energy barriers of 42.8, 46.0, and 50.2 kcal mol−1, respectively. The temperature- and pressure-dependent theoretical rate coefficients for these dissociation and isomerization channels were determined via RRKM and multiple-well master equation analysis at the E and J conserved level. The rate coefficients and thermochemical property data provided in the work will be the essential inputs for the development kinetic mechanism in the pyrolysis and oxidation of MMH,

Figure 11. k/k∞ as a function of pressure at T = 300, 400, 500, 800, 1000, 1200, 1500, 1800, and 2500 K, for the dissociation channel C•H2NHNH2 → CH2NN + NH2.

increases by 1.8−5.4% from 300 to 2500 K, whereas k15 increases by 40.4−16.7% for the same temperature range. The theoretical rate coefficients for the dissociation channels of the C•H2NHNH2 radical at T = 300−2500 K and p = 0.01− 100 atm with argon as collider were fitted in the Arrhenius threeparameter format and are tabulated in Table 5. For the C•H2NHNH2 radical to dissociate to form the products CH2NH + NH2 (R14), the ΔEdown only affects slightly its pressure dependent rate constant because of its small energy barrier. In contract, it significantly affects the rate constant for the higher energy barrier dissociation channel CH2NHNH + H (R15). Consequently the uncertainties of the rate coefficients k15 at different pressures in Table 5 could be large. The numerical estimate for the effect of hindered rotors in the calculated reaction rate constants was discussed in our recent work.4 For example, by considering the NH2 as hindered internal rotors, a theoretical rate coefficient for the Habstraction of the central amine hydrogen is increased monotonically by 6.3−27.7% over 200−2500 K. In this work, it was found when the NH2 rotor is considered as a hindered rotor, the rate coefficient for the β-scission of NH2 from the C•H2NHNH2 radical is reduced by 2.9−40.8% over 300−2500 K. This is because the vibrational frequency corresponding to the 8429



Article

(20) Miller, J. A.; Klippenstein, S. J. J. Phys. Chem. A 2006, 110, 10528. (21) Fernández-Ramos, A.; Miller, J. A.; Klippenstein, S. J.; Truhlar, D. G. Chem. Rev. 2006, 106, 4518. (22) Miller, J. A.; Klippenstein, S. J. J. Phys. Chem. A 2003, 107, 2680. (23) Klippenstein, S. J.; Wagner, A. F.; Dunbar, R. C.; Wardlaw, D. M.; Robertson, S. H.; Miller, J. A. VARIFLEX, version 2.02m; 2010. (24) Pitzer, K. S.; Gwinn, W. D. J. Chem. Phys. 1942, 10, 428. (25) East, A. L. L.; Radom, L. J. Chem. Phys. 1997, 106, 6655. (26) Johnston, H. S.; Heicklen, J. J. Phys. Chem. A 1962, 66, 532. (27) Sun, H.; Zhang, P.; Law, C. K. Detailed Chemical Kinetic Mechanism for Modeling MMH Oxidation, 7th International Conference on Chemical Kinetics: MIT, Cambridge, MA, July 10−14, 2011. (28) Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular theory of gases and liquids; Wiley: New York, 1954. (29) NIST Chemistry Web Book, http://webbook.nist.gov/ chemistry/. (30) Cole, L. G.; Gilbert, E. C. J. Am. Chem. Soc. 1951, 73, 5423. (31) Merrick, J. P.; Moran, D.; Radom, L. J. Phys. Chem. A 2007, 111, 11683. (32) Durig, J. R.; Gounev, T. K.; Zheng, C.; Choulakian, A.; Verma, V. N. J. Phys. Chem. A 2002, 106, 3395. (33) Sun, H.; Law, C. K. Ab initio Multireference Study of the Reactions of CH3N•NH2 + OH, Fall Technical Meeting of the Eastern States Section of the Combustion Institute, University of Connecticut, Storrs, CT, Oct 9−12, 2011.

symmetrical dimethylhydrazine (SDMH), unsymmetrical dimethylhydrazine (UDMH), and other MMH derivatives for understanding the ignition and combustion chemistry of propellants in rocket engines.

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ASSOCIATED CONTENT

* Supporting Information S

Cartesian coordinates, vibration frequencies, moments of inertia, zero-point energies, and total electronic energies at different calculation levels for the four target radicals (Tables S1−S4). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Fax: (609) 258-6233. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr. Stephen J. Klippenstein at the Argonne National Laboratory for providing us with the latest version of the VARIFLEX code. This work was supported by the U.S. Army Research Office via a multidisciplinary university research initiative (ARO/MURI) program. The research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0205CH11231.

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REFERENCES

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Ab Initio Kinetics for Thermal Decomposition of CH3Nâ¢NH2, cis

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