Gas-Phase Kinetics Study of Reaction of OH Radical with CH3NHNH2

Article pubs.acs.org/JPCA

Gas-Phase Kinetics Study of Reaction of OH Radical with CH3NHNH2 by Second-Order Multireference Perturbation Theory Hongyan Sun,* Peng Zhang, and Chung K. Law Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, United States ABSTRACT: The gas-phase kinetics of H-abstraction reactions of monomethylhydrazine (MMH) by OH radical was investigated by second-order multireference perturbation theory and two-transition-state kinetic model. It was found that the abstractions of the central and terminal amine H atoms by the OH radical proceed through the formation of two hydrogen bonded preactivated complexes with energies of 6.16 and 5.90 kcal mol−1 lower than that of the reactants, whereas the abstraction of methyl H atom is direct. Due to the multireference characters of the transition states, the geometries and ro-vibrational frequencies of the reactant, transition states, reactant complexes, and product complexes were optimized by the multireference CASPT2/aug-cc-pVTZ method, and the energies of the stationary points of the potential energy surface were refined at the QCISD(T)/CBS level via extrapolation of the QCISD(T)/cc-pVTZ and QCISD(T)/cc-pVQZ energies. It was found that the abstraction reactions of the central and two terminal amine H atoms of MMH have the submerged energy barriers with energies of 2.95, 2.12, and 1.24 kcal mol−1 lower than that that of the reactants respectively, and the abstraction of methyl H atom has a real energy barrier of 3.09 kcal mol−1. Furthermore, four MMH radical−H2O complexes were found to connect with product channels and the corresponding transition states. Consequently, the rate coefficients of MMH + OH for the H-abstraction of the amine H atoms were determined on the basis of a two-transition-state model, with the total energy E and angular momentum J conserved between the two transition-state regions. In units of cm3 molecule−1 s−1, the rate coefficient was found to be k1 = 3.37 × 10−16T1.295 exp(1126.17/ T) for the abstraction of the central amine H to form the CH3N•NH2 radical, k2 = 2.34 × 10−17T1.907 exp(1052.26/T) for the abstraction of the terminal amine H to form the trans-CH3NHN•H radical, k3 = 7.41 × 10−20T2.428 exp(1343.20/T) for the abstraction of the terminal amine H to form the cis-CH3NHN•H radical, and k4 = 9.13 × 10−21T2.964 exp(−114.09/T) for the abstraction of the methyl H atom to form the C•H2NHNH2 radical, respectively. Assuming that the rate coefficients are additive, the total rate coefficient of these theoretical predictions quantitatively agrees with the measured rate constant at temperatures of 200−650 K, with no adjustable parameters.

1. INTRODUCTION Monomethylhydrazine (MMH) is a diamine-based fuel for spacecraft rocket engines. It is usually used together with oxidizers such as nitrogen tetroxide (NTO) or inhibited red fuming nitric acid (IRFNA) as high performance is desired. Because the MMH/NTO or MMH/IRFNA bipropellant combinations are hypergolic in that the two chemicals react exothermically as soon as they come in contact,1 not only is knowledge of the MMH oxidation reactions useful for the development of gelled hypergolic propellant (GHP),2 but it is also an essential component of the full kinetic mechanism involving the oxidative reactions. Reactions of MMH + NO2 and MMH + OH are important in rocket engine combustion, because NO2 and OH are the decomposition products of NTO and nitric acid.3 Furthermore, the H-abstraction of MMH by NO2 produces nitrous acid (HONO),4 which undergoes further decomposition and chain reactions to regenerate the OH radical.5 Recently, the reactions of MMH + OH at temperatures of 1000−1250 K have been found to play a critical role in the modeling of earlier OH time histories in the ignition of MMH with O2 as an oxidizer.6 Consequently, the © 2012 American Chemical Society

theoretical rate data for each individual channel need to be quantified accurately. Two sets of experimental data for the MMH + OH reaction at low temperatures were reported.7,8 Specifically, Harris et al.7 determined the absolute rate constants for the reactions of the OH radical with hydrazine and methylhydrazine by using a flash photolysis-resonance fluorescence technique. The reported rate constants were found to be independent of temperature over the range of 298−424 K, with the values of (6.1 ± 1.0) × l0−11 and (6.5 ± 1.3) × l0−11 cm3 molecule−1 s−l for hydrazine and methylhydrazine, respectively. Vaghjiani8 studied the gas-phase reactions of OH with N2H4, CH3NHNH2, and (CH3)2NNH2 in a discharge flow tube apparatus and a pulsed photolysis reactor with laser-induced fluorescence technique and found that the three reactions did not show discernible pressure dependence on He or N2 bath gas pressure up to 530 Torr. However, the absolute second-order rate coefficients were found to have a weak temperature dependence in the Received: March 5, 2012 Revised: April 27, 2012 Published: April 30, 2012 5045

dx.doi.org/10.1021/jp3021529 | J. Phys. Chem. A 2012, 116, 5045−5056

The Journal of Physical Chemistry A

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temperature range of 232−637 K: (2.17 ± 0.39) × l0−11 exp(160 ± 30)/T, (4.59 ± 0.83) × l0−11 exp(85 ± 35)/T, and (3.35 ± 0.60) × l0−11 exp(175 ± 25)/T cm3 molecule−1 s−l, respectively. For temperatures below 600 K, the reactions of MMH + OH are probably dominated by addition of the OH radical to the N-centered diamine group followed by abstraction of the amine H atoms to form radical products, and the temperature dependence of the rate coefficients can be ascribed to reactions containing multiple transition states. Theoretically, we have found that the reactions of MMH + OH proceed via direct and indirect abstraction mechanisms. Specifically, the abstraction of methyl H atoms by the OH radical is a direct abstraction reaction, whereas the indirect abstraction of amine H atoms proceeds via addition of the OH radical to the diamine N atoms to form an intermediate and subsequently rapid dissociation into products. Similar to the Habstraction reactions of unsaturated alkenes by the OH radical,9 two transition states, outer and inner, exist for the indirect abstraction of MMH + OH. The outer transition state corresponds to a large interfragment distance and hence a weak long-range interaction between the OH radical and MMH, and it is most important to the reaction rate at low temperatures. At relatively high temperatures the inner transition state for the abstraction of amine H atoms controls the reaction rate. Furthermore, the multireference character is significant for the OH abstraction of amine hydrogen atoms; herein the molecular properties in the reactions of MMH + OH were investigated with application of second-order multireference perturbation theory.10 With the energies of the stationary points of the potential energy surface refined by high-level quadratic configuration interaction QCISD(T) calculations and appropriate treatments of torsional anharmonic effects for the each inner transition states, the rate coefficient for each individual abstraction channel was determined by a two-transition-state model at the E and J resolved levels. It was found that the total rate coefficient quantitatively reproduces the measured experimental rate coefficients over 200−650 K, with no adjustable parameters.

The T1 diagnostic of Lee et al.14 for the transition states of the abstraction of amine hydrogen atoms from the QCISD(T) calculations was found to be 0.04, implying significant multireference character of the wave function. Therefore, multireference second-order perturbation theory (CASPT2)15 with Dunning’s augmented correlation-consistent double-ξ basis set, aug-cc-pVDZ, and then triplet-ξ basis set, aug-ccpVTZ,16,17 were applied to optimize the geometries of reactants and transition states and then to calculate the rovibrational frequencies. In the CASPT2 calculations, the active space for the reactant, complexes, and transition states was carefully chosen to ensure that it represents the characteristics of frontier molecular orbitals. Specifically, the active space (4e,3o) consisting of the σ,σ* orbital pair of N−N bond and the s orbital of amine N atom was selected for the reactant MMH, the state-averaged (3e,2o) active space consisting of the two degenerated p orbitals of the OH radical was used for the prereactivated reactant complexes, the active space (3e,3o) consisting of the OH radical orbital and the σ,σ* orbital pair of the H being abstracted was used for the transition states of the abstraction of amine H atoms, and the active space (9e,6o) consisting of the σ,σ* orbital pair of the methyl H being abstracted, two p orbitals of the hydroxyl O atom, and two hybrid s orbitals of hydroxyl O and hydroxyl H was used for the transition states of the abstraction of methyl hydrogen. Higher level single-point energies were obtained from the quadratic configuration interaction with single, double and perturbative triple excitation QCISD(T) calculations.18 Specifically, the QCISD(T) calculations employed the correlationconsistent, polarized-valence, triplet-ξ (cc-pVTZ) and quadruple-ξ (cc-pVQZ) basis sets and then the energies were extrapolated to the complete basis set (CBS) limit19 by the asymptotic form:20,21 E∞ = Elmax − B/(lmax + 1)4, where E∞ is the infinite basis-set energy, B a least-squares fit parameter, and lmax the maximum component of the angular momentum in the cc-pVnZ basis set, which is 3 and 4 for the triple (n = 3) and quadrupole (n = 4) basis sets, respectively. Electronic structure calculations were performed by using the MOLPRO22 and Gaussian0923 program packages. 2.2. Kinetic Rate Coefficients. For the reactions of OH + MMH, there are multiple transition states associated with the abstraction of different H atoms. Because the abstraction of the methyl H atom has an energy barrier higher than that of the reactants, it is appropriate to apply the E/J resolved microcanonical transition-state theory for the rate calculation. The abstraction reaction of the amine H atoms proceeds through the formation of two hydrogen bonded preactivated complexes and it has submerged energy barriers lower than that of the reactants. The two-transition-state model proposed by Georgievskii and Klippenstein24 is suitable to determine the rate coefficients for such type of reactions, especially at low to intermediate temperatures. In the model, the outer transition state corresponds to a large interfragment distance and weak long-range interactions between the fragments. The corresponding rate coefficient has a large preexponential Arrhenius factor and small activation energy and is rate-controlling at low temperatures. At relatively high temperatures, the inner transition state associated with the saddle point controls the reaction rate. To determine the overall effect of the two types of controlling bottlenecks at an arbitrary temperature, the formation of preactivated reactant complex followed by its

2. COMPUTATIONAL METHODOLOGY 2.1. Electronic Structure Calculation. For reactions of the OH radical with a stable molecule, which have small or negative energy barriers, the accuracy of calculated rate coefficients greatly depends on the accurate descriptions of both the inner and outer transition states,9 and hence it is crucial to apply a suitable method to locate accurate geometries of the stationary points on the potential energy surface. For the H-abstraction reactions of MMH, the amine H atoms are easier to be abstracted than the methyl H atoms, because the N−H bond energies are 12−14 kcal/mol lower than those of the C− H bond.11 It was found that the density functional B3LYP method with split valence basis set, extended from 6-311G(d,p) to 6-311++G(3df,2pd), predicts reactant-like transition states for the abstraction of amine H atoms. However, the geometries optimized by the BHandHLYP/6-311G(d,p) method, which uses Becke’s half-and-half nonlocal exchange12 with the Lee− Yang−Parr (LYP) correlation functional,13 capture the characteristics of transition states of amine H-abstraction by the OH radical. However, it was found that when the diffuse functions were included in the basis set to approximate more exact molecular orbital for this oxygen and nitrogen containing system, the BHandHLYP/6-311G(d,p) method still predicts earlier transition states, and as such worse interaction energies. 5046



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and 114.7° at the B3LYP/6-311++G(d,p) level, respectively. Considering the experimental N−N bond length is 1.446 Å in NH2NH2,34 and the N−N bond length is 1.433 Å in CH3NHNH2,30 these predicted N−N bond lengths at the MP2 and B3LYP levels seem to be short. The CASPT2/aug-ccpVTZ optimization with the minimum (2e,2o) active space, which consists of the N−H σ,σ* orbital bonding pair between the s orbital of H atom and the p orbital of the central amine N atom, predicts the N−N bond length to be 1.426 Å. Altering the active space to (4e,3o) consisting of one σ,σ* orbital pair of the N−N bonding (as shown in Figure 1) and the s orbital of

dissociation and transformation into a product complex must be considered. Calculation of the rate constant was considerably simplified by the fact that the preactivated reactant complex is weakly bound and therefore relatively short-lived. As a result, for all but extraordinarily high pressures the kinetics of the preactivated complex occurs in a collision-free environment with the total energy E and the angular momentum J conserved.24 The inner, N†inner, and outer, N†outer, transition-state numbers of states for a given electronic state are used to calculate the effective number of states, N†eff, by the following equation:9 1 1 1 = † + † † Neff Ninner Nouter

The rate constant can then be calculated by k∞(T ) =

1 hQ R

∫

† Neff (E ,J )e−E / kbT dE dJ

where QR is the reactant partition function and kB and h are the † Boltzmann and Planck constants, respectively. Ninner was calculated from rigid-rotor harmonic oscillator evaluations by employing ab initio multireference electron structure determined properties. N†outer was determined by applying the phase space theory. Specifically, the E/J resolved number of states were evaluated by a procedure based on the formal analytical integration over an inner transition-state coordinate, and its conjugate momentum as well as the three Cartesian components of the total angular momentum.25 A more detailed description of the integration is given by Klippenstein.25 Within the framework of the two transition-state theory, the rate constant is usually not sensitive to the shape of the long-range potential as long as it correctly reproduces the outer rate constant in the important range of temperature.24 Therefore, a long-range potential for isotropic interaction, (R = −V0/R6), was used for its simplification and universality.26 The coefficient V0 for the isotropic potential used in the two-transition-state model is 2.2 × 105 Å6 cm−1, which was determined by an approximation of 1.5α1α2E1E2/(E1 + E2), where αi is the polarizability of the fragment i and Ei is approximated as its ionization energy.26 Specifically, the polarizabilities of MMH and the OH radical were determined from the B3LYP/aug-ccpVTZ calculations, and the ionization energies of MMH and the OH radical were the experimental data from the NIST database.27 It was found that the coefficient for the isotropic potential corresponds to an outer rate constant of 4 × 10−10 cm3 molecule−1 s−1, which is a reasonable rate constant for the H-bonded complex formation. By altering the isotropic potential coefficient value to be equivalent of a rate constant of 3 × 10−10 cm3 molecule−1 s−1 for the H-bonded complex formation, the overall rate coefficient was reduced only by 9− 13.5% at the low temperatures of 200−300 K.

Figure 1. Geometry of MMH molecule optimized at the CASPT2(4e,3o)/aug-cc-pVTZ level, with mesh contour showing the active space of σ,σ* orbital pair of the N−N bonding: (a) σ orbital of the N− N bond; (b) σ* orbital of the N−N bond.

amine N atoms, a longer theoretical N−N bond length is predicted, 1.435 Å, which is closer to the experimental data. Meanwhile, the predicted C−N bond length and ∠C−N−N angle are 1.454 Å and 112.9° at the CASPT2(4e,3o)/aug-ccpVTZ level, respectively. The vibrational frequencies of MMH, calculated at the CASPT2(4e,3o)/aug-cc-pVTZ level, are listed in Table 1, with comparison of the data calculated at the B3LYP/6-311+ +G(d,p) and MP2/6-311+G(d,p) levels and experimental Table 1. MMH Rotational and Vibrational Frequencies (cm−1)

3. RESULTS AND DISCUSSION 3.1. Electronic Structures. Reactants. The structures and vibrational frequencies of the MMH molecule and its two equilibrium conformers have been determined experimentally and theoretically.11,28−33 Specifically, the geometry parameters of the lowest energy conformer of MMH were measured to be r(C−N) = 1.463 Å, r(N−N) = 1.433 Å, and ∠C−N−N = 113.47° by gas electron diffraction. 30 The theoretical predictions of these parameters were 1.456 Å, 1.422 Å, and 113.6° at the MP2/6-311+G(d,p) level,32 and 1.458 Å, 1.424 Å,

a

5047

CASPT2/ aug-cc-pVTZ

B3LYP/ 6-311++G(d,p)

MP2/ 6-31G(d)a

observeda

278.58 327.35 426.34 815.55 933.91 1003.90 1148.15 1157.58 1232.61 1317.47 1455.95 1497.46 1507.30 1532.21 1675.53 3004.13 3116.52 3164.73 3452.29 3571.75 3597.44

263.36 353.09 420.83 781.08 902.68 979.63 1134.86 1136.90 1222.84 1313.05 1447.49 1481.00 1492.72 1520.60 1687.42 2926.79 3046.10 3089.47 3403.48 3530.88 3549.67

292 362 441 840 980 1057 1178 1185 1279 1362 1503 1540 1549 1577 1742 3027 3151 3202 3421 3560 3590

281 315 428 767 890 968 1109 1129 1184 1210 1376 1430 1442 1475 1585 2835 2930 2968 3235 3339 3358

Reference 32. dx.doi.org/10.1021/jp3021529 | J. Phys. Chem. A 2012, 116, 5045−5056


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measurements. In Table 1, for the MP2/6-31G(d) frequencies,28 it is noted that the diagonal elements of the force field in internal coordinates were modified with scaling factors of 0.88 for the C−H and N−H bond stretches, 0.9 for the heavy atoms C and N stretches, and 0.75 for the ∠CNH, ∠NNH, and amino torsion.28 In contrast, without multiplying any scaling factor, the CASPT2(4e,3o)/aug-cc-pVTZ frequencies are in very good agreement with the infrared gas-phase spectral measurement,28 especially in the low frequency range. This indicates that the multireference CASPT2(4e,3o)/aug-cc-pVTZ method predicts more accurate structure and vibrational frequencies of the MMH molecule. For the OH radical, the CASPT2/aug-cc-pVTZ level was applied for the geometry optimization and frequency calculation. It was found that the O−H bond stretching frequency is 3715.55 cm−1 at the level of the theory, whereas it was found to be 3743.68 cm−1 at the CCSD(T)/cc-pVTZ level, which is closer to the experimental data of 3737.8 cm−1.35 Hence the geometry optimization and frequency parameters determined with the CCSD(T)/cc-pVTZ method was used for the rate calculations. Reactant Complexes. Because of the electronegativity of nitrogen and oxygen, hydrogen-bonded complexes of MMH and the OH radical are expected to exist. Two preactivated reactant complexes, designated as R-HBC1 and R-HBC2, were found in the reactions of MMH + OH. The complex R-HBC1 is the hydroxyl H atom interacting with the central N atom of MMH, and the complex R-HBC2 is the hydroxyl H atom interacting with the terminal N atom of MMH. Figure 2 shows

Figure 3. Interatomic distance between the hydroxyl H and O atoms and two amine N atoms in the two H-bonded complexes calculated at the CASPT2(3e,2o)/aug-cc-pVTZ level. The interatomic distances are in angstroms.

central N atom is 1.846 Å, the distance between the hydroxyl H and the terminal N atom is 2.505 Å, the distance between the hydroxyl O and the central N atom is 2.809 Å, and the angle between the OH and central N atom ∠N···H−O is 163.28°. For the reactant complex R-HBC2, it was found that the interatomic distance between the hydroxyl H and the terminal N atom is 1.884 Å, the distance between the hydroxyl H and the central N atom is 2.535 Å, the distance between the hydroxyl O and the terminal N atom is 2.845 Å, and the angle between the OH and terminal N atom ∠N···H−O is 163.64°. Comparing the above data for the two complexes, it was found that the interatomic distances and angles between the hydroxyl H atom or O atom and the two amine N atoms in R-HBC1 are shorter than those in R-HBC2, implying lower energy of the complex R-HBC1 than that of the complex R-HBC2. Compared with the interatomic distance 2.98 Å of N···H−O in the ammonia−water complex,36,37 the interacting distance of N···O in R-HBC1 (2.81 Å) and in R-HBC2 (2.84 Å) is shorter, due to the additional interactions between the H atoms and electronegtive O and N atoms. On the basis of the optimized geometry above, the rotational and vibrational frequencies of these reactant complexes were calculated at the CASPT2(3e,2o)/aug-cc-pVTZ level, as listed in Table 2. The rotational and vibrational frequencies of the transition states and product complexes calculated at the CASPT2/aug-cc-pVTZ level are also listed in Table 2. Transition States. The geometries of the transition states for the OH radical abstracting different H atoms in MMH were optimized at the CASPT2/aug-cc-pVTZ level, with an active space (3e,3o) consisting of the OH radical orbital and the σ,σ* orbital pair of the hydrogen being abstracted. For example, the (3e,3o) active space and transition-state geometry for the abstraction of the central amine H atom are illustrated in Figure 4. For the transition state of abstracting the methyl H atom, it was found that the active space (3e,3o) consists of the OH radical orbital and the σ,σ* orbital pair of the N−N bond rather than the OH radical orbital and the σ,σ* orbital pair of methyl H being abstracted. Orbital rotation operations were performed to attempt to force the σ,σ* orbital pair of methyl H into the active space; however, this was not achieved. Specifically, by rotating a few orbitals with energies just below those in the active space, it was found that the optimized active space (3e,3o) includes the σ,σ* orbital pair of the C−N bond, the OH radical orbitals, or the σ, σ* orbital pair of C−H bond that is not being cleaved, instead of the σ,σ* orbital pair of methyl H being abstracted. This implies that the active space (3e,3o) is not large enough to describe the frontier molecular orbitals of the methyl H abstraction. Because the N−N and C−N bonding

Figure 2. Geometries of two H-bonded reactant complexes optimized at the CASPT2(3e,2o)/aug-cc-pVTZ level, with mesh contour showing a state-averaged (3e,2o) active space consisting of the two degenerated p orbitals of the OH radical. The top figures are the geometries of complex R-HBC1, and the bottom figures are the geometries of complex R-HBC2.

the geometries of R-HBC1 and R-HBC2 optimized at the CASPT2(3e,2o)/aug-cc-pVTZ level, with a state-averaged (3e,2o) active space consisting of the two degenerated p orbitals of the OH radical. Figure 3 shows the interatomic distance of the hydroxyl H and O atoms interacting with two amine N atoms in the two Hbonded complexes calculated at the CASPT2(3e,2o)/aug-ccpVTZ level. For the reactant complex R-HBC1, it was found that the interatomic distance between the hydroxyl H and the 5048



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Table 2. Rotational and Vibrational Frequencies (cm−1) Calculated at the CASPT2/aug-cc-pVTZ Level R-HBC1

R-HBC2

TS1

TS2

TS3

TS4

P-HBC1

P-HBC2

P-HBC3

P-HBC4

terminal

central

CH3N•NH2

trans-CH3NHNH

cis-CH3NHNH

CH2NHNH2

CH3N•NH2

trans-CH3NHNH

cis-CH3NHNH

CH2NHNH2

48.50 75.61 210.16 279.84 356.79 435.13 613.30 768.31 825.80 961.87 1032.06 1152.32 1164.11 1244.10 1317.86 1457.95 1508.00 1514.45 1539.40 1673.89 3009.96 3122.42 3172.02 3422.57 3441.67 3552.17 3584.70

60.37 79.95 220.17 284.90 330.84 427.65 617.50 789.78 861.18 960.78 1007.35 1155.35 1158.22 1239.58 1341.81 1457.02 1494.77 1509.25 1532.96 1682.91 3030.16 3128.92 3171.30 3354.51 3460.64 3562.92 3582.35

−736.07 116.98 165.60 204.21 265.15 417.50 448.02 714.17 815.65 871.97 1011.75 1144.29 1151.35 1219.32 1329.03 1451.61 1503.67 1511.59 1550.57 1665.30 2194.13 3025.71 3125.01 3179.93 3472.14 3596.41 3697.36

−767.86 64.68 88.35 135.16 263.07 362.50 452.04 691.53 826.65 977.03 1038.15 1135.57 1185.59 1219.35 1304.95 1446.77 1482.77 1497.92 1532.20 1539.77 1738.59 3027.69 3135.49 3185.01 3488.83 3550.19 3760.45

−1057.74 87.03 140.71 275.35 371.70 407.19 481.83 765.17 813.94 863.19 995.77 1139.15 1161.87 1222.15 1365.89 1455.96 1484.02 1509.16 1537.47 1652.22 2020.36 3022.54 3127.80 3176.08 3484.40 3553.60 3700.15

−1509.94 108.56 135.30 183.14 341.22 392.99 443.11 703.81 867.25 911.74 1034.04 1089.75 1140.49 1190.81 1277.33 1366.32 1383.56 1474.67 1493.03 1643.84 1664.69 3056.90 3189.66 3466.58 3513.09 3561.44 3672.95

56.13 64.36 147.61 149.58 159.07 265.00 461.60 482.17 568.11 706.53 986.43 1073.34 1110.45 1302.40 1321.87 1434.91 1500.92 1509.90 1640.16 1653.89 3007.06 3079.78 3188.76 3464.60 3655.58 3726.26 3911.80

53.44 65.22 109.27 160.21 206.01 373.88 443.48 519.51 655.99 692.96 1000.04 1140.24 1157.09 1384.91 1427.74 1469.96 1505.18 1528.24 1590.89 1674.42 3075.98 3166.62 3204.75 3497.41 3529.43 3574.33 3909.10

71.89 113.91 166.68 196.83 224.81 367.24 423.37 481.12 732.32 768.74 996.61 1131.05 1164.66 1352.86 1454.55 1497.11 1502.75 1539.40 1579.16 1656.27 3061.58 3145.27 3187.69 3479.69 3538.25 3576.67 3908.90

83.95 115.07 143.03 183.41 313.37 345.12 379.97 453.97 564.18 593.42 776.48 916.48 1030.15 1242.94 1274.66 1352.55 1470.39 1506.88 1638.94 1684.16 3192.78 3322.35 3475.55 3577.00 3596.19 3670.26 3910.50

Figure 4. Transition-state geometry of abstracting central amine H of MMH optimized at the CASPT2(3e,3o)/aug-cc-pVTZ level, with mesh contour showing the active space (3e,3o) of the σ,σ* orbital pair of the central amine hydrogen being abstracted and the OH radical orbital: (a) σ orbital of central amine H; (b) σ* orbital of central amine H; (c) p orbital of the OH.

orbitals become conjugated in the C•H2NHNH2 radical upon the OH abstraction of methyl H from MMH, a larger active space is necessary to describe such an orbital conjugation. It was found that the active space (9e,6o) is the minimum to include the σ,σ* orbital pair of the methyl H being abstracted. It is shown in Figure 5 that the CASPT2/aug-cc-pVTZ optimized active space (9e,6o) consists of the p and s orbitals of hydroxyl O atom, the σ-bonding orbital of the methyl H being abstracted, the σ,σ* orbital pair of O−H bonding, and the radical orbital. Four transition-state structures for the OH radical abstracting different H atoms of MMH are shown in Figure 6. TS1−TS4 are the transition states which respectively correspond to the abstractions of the central amine H atom of MMH to form the CH3N•NH2 radical, a terminal amine H atom to form the transCH3NHN•H radical, a terminal amine H atom to form the cis-

CH3NHN•H radical, and the methyl H atom to form the C•H2NHNH2 radical. We note that, for the CH3NHN•H radical, the structure with the terminal amine H atom trans to the methyl group is defined as the trans-CH3NHN•H radical, and the structure with the terminal amine H atom cis to methyl group is defined as the cis-CH3NHN•H radical. It is known that the cleaving and forming bond lengths are the major criteria to evaluate the transition-state geometry. From Figure 6, it is seen that the cleaving N−H bond length is 1.072, 1.067, and 1.084 Å in TS1, TS2, and TS3, respectively. Furthermore, the forming O−H bond length is 1.443, 1.504, and 1.411 Å in TS1, TS2, and TS3, respectively. In TS4, the cleaving C−H bond length is 1.167 Å, and the forming O−H bond length is 1.397 Å. In summary, in these transition states, the N−H bonds are lengthened to 1.07−1.08 Å, the C−H bond to 1.17 Å, and the forming O−H bond length is between 5049



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Figure 5. Active space of abstracting methyl H atom of MMH by the OH radical optimized at the CASPT2(9e,6o)/aug-cc-pVTZ level. The active space (9e,6o) consists of six frontier molecular orbitals of total 19 molecular orbitals: the p and s orbitals of hydroxyl O atom (14.1 and15.1), the σbonding orbital of the methyl H being abstracted (16.1), the σ,σ* orbital pair of O−H bonding (17.1 and 19.1), and the radical orbital (18.1).

Figure 6. TS1−TS4 transition-state geometries for the OH radical abstracting different H atoms of MMH optimized at the CASPT2(3e,3o)/aug-ccpVTZ level. Bond lengths and interatomic distances are in angstroms.

Product-Complexes and Products. In addition to the preactivated hydrogen-bonded complexes, four hydrogenbonded product complexes corresponding to the four different transition states were also found. The geometries of the four Hbonded product complexes, CH 3 N • NH 2 −H 2 O, cisCH3NHN•H−H2O, trans-CH3NHN•H−H2O, and C•H2NHNH2−H2O were optimized at the CASPT2(1e,1o)/ aug-cc-pVTZ level with an active space (1e,1o) consisting of the radical orbital of the product, and the predicted H-bond lengths and interatomic distances are shown in Figure 7. The

1.37 and 1.50 Å. For these data, it is seen that the multireference CASPT2 method predicts good transition-state geometries for the H-abstraction reactions. Furthermore, the cleaving N−H bond length is much shorter than that of the C− H bond length, indicating the stronger N−H bond than the C− H bond, and the earlier transition states. In addition, electrostatic interactions between the hydroxyl H, O atoms and amine N atoms, H atom of MMH in these transition states are observed, and some interaction distances are illustrated in Figure 6. 5050



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Figure 7. Geometries of the four H-bonded product complexes optimized at the CASPT2(1e,1o)/aug-cc-pVTZ level with an active space (1e,1o) consisting of the radical orbital of the complex. H-bond lengths and interatomic distances are in angstroms.

Figure 8. Potential energy surface of the reactions of MMH + OH calculated at the QCISD(T)/CBS//CASPT2/aug-cc-pVTZ level, except the geometry of OH radical optimized at the UCCSD(T)/cc-pVTZ level and the geometries of radical products optimized at the B3LYP/6-311+ +G(d,p) level.

hydroxyl H and the nitrogen radical center, 1.900 and 1.905 Å, and as such they are expected to have lower energies than other complexes. For the CH3N•NH2−H2O complex, a hydroxyl H interacts with two nitrogen atoms with the interatomic distances of 2.099 and 2.558 Å, respectively.

geometries of four radical products were optimized at the B3LYP/6-311++G(d,p) level. For the nitrogen radical centered complex, it was found that the cis-CH3NHN•H−H2O and trans-CH3NHN•H−H2O complexes have the smallest interatomic distance between a 5051



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Table 3. Saddle Point Energies (kcal mol−1) at Different Calculation Levels species

T1 diagnostica

ZPEb

ZPEc

E(ADZ)d

E(ADZ+ZPE)e

E(ATZ)f

E(ATZ+ZPE)g

E(CBS+ZPE)h

R-HBC1 (terminal) R-HBC2 (central) TS1_CH3N•NH2 TS2_trans-CH3NHN•H TS3_cis-CH3NHN•H TS4_C•H2NHNH2

0.0091 0.0092 0.0400 0.0402 0.0402 0.0275

59.03 59.02 56.00 55.15 55.98 55.79

59.24 59.33 56.97 55.94 56.92 56.19

−7.66 −8.18 −0.59 1.86 1.12 4.39

−5.38 −5.92 −1.35 0.26 0.34 3.43

−8.64 −9.17 −1.66 0.83 0.00 3.78

−6.49 −6.93 −1.78 −0.31 −0.17 2.88

−5.90 −6.16 −2.95 −2.12 −1.24 3.09

a

T1 diagnostic calculated at the QCISD(T)/cc-pVQZ//CASPT2/aug-cc-pVTZ level. bZero-point energy calculated at the CASPT2/aug-cc-pVDZ level. cZero-point energy calculated at the CASPT2/aug-cc-pVTZ level. dEnergy relative to reactants MMH + OH calculated at the CASPT2/aug-ccpVDZ level. eZero-point corrected energy relative to reactants MMH + OH calculated at the CASPT2/aug-cc-pVDZ level. fEnergy relative to reactants MMH + OH calculated at the CASPT2/aug-cc-pVTZ level. gZero-point corrected energy relative to reactants MMH + OH calculated at the CASPT2/aug-cc-pVTZ level. hZero-point corrected energy relative to reactants MMH + OH calculated at the QCISD(T)/CBS//CASPT2/augcc-pVTZ level.

determined at the CASPT2/aug-cc-pVTZ level is 0.2−0.4 kcal mol−1 higher than those at the CASPT2/aug-cc-pVDZ level. For the saddle points with the T1 diagnostic value of 0.04, the zero-point energies determined at the CASPT2/aug-ccpVTZ level is 0.8−1.0 kcal mol−1 higher than those at the CASPT2/aug-cc-pVDZ level. This indicates that the barrier heights with zero-point energies calculated by using the aug-ccpVTZ rovibrational frequencies are increased by at least 0.5 kcal mol−1 compared with those using the aug-cc-pVDZ rovibrational frequencies. This energy increase could significantly affect the rate coefficients which are sensitive to submerged energy barrier heights. For the two hydrogen-bonded complexes, the T1 diagnostics are small and therefore the QCISD(T)/CBS//CASPT2/augcc-pVTZ single point energies of −5.90 and −6.16 kcal mol−1 relative to reactants MMH + OH are quite reliable. Compared with these two QCISD(T)/CBS energy values, the zero-point corrected CASPT2/aug-cc-pVDZ and CASPT2/aug-cc-pVTZ relative energies for the two H-bonded complexes are within the absolute error of 0.8 kcal mol−1. Furthermore, it was found that R-HBC1 and R-HBC2 have the QCISD(T)/CBS// B3LYP/6-311++G(d,p) energies of −6.41 and −6.74 kcal mol−1 relative to the reactants MMH + OH, which differ from the QCISD(T)/CBS//CASPT2/aug-cc-pVTZ energies by less than 0.6 kcal/mol. These comparisons suggest the density functional B3LYP/6-311++G(d,p) as an alternative method for the geometry optimization of the hydrogen bonded complexes with small T1 diagnostics value. For the transition states of amine hydrogen abstraction, it was found that the zero-point corrected CASPT2/aug-cc-pVTZ energies are 0.4−0.6 kcal mol−1 lower than those of the CASPT2/aug-cc-pVDZ energies. Furthermore, the zero-point corrected QCISD(T)/CBS energies were found to be 1.1−1.8 kcal mol−1 lower than those of the zero-point corrected CASPT2/aug-cc-pVTZ energies, as shown in Table 3. This result is consistent in that the larger basis set, the better electron correlation for the lower energy. The T1 diagnostic values are 0.04 for the abstraction of amine hydrogen atoms, and 0.03 for the abstraction of methyl hydrogen atom, which indicates that multireference character is significant but not overwhelming. Therefore, the uncertainties arising from the QCISD(T)/CBS calculations for the transition states are expected to be sufficiently small for kinetic calculations. Figure 8 shows that the transition state TS1 for the abstraction of the central amine hydrogen atom has an energy that is 2.95 kcal mol−1 lower than that of the entrance channel. For the abstraction of the terminal amine hydrogen atom, TS2

Furthermore, a methyl H atom also interacts with the hydroxyl O atom in the interatomic distance of 2.833 Å. Therefore the CH3N•NH2−H2O complex is also expected to have lower energy. For the C•H2NHNH2−H2O complex, the electrostatic interaction occurs between the H2O and NHNH2 groups rather than the carbon radical center, such that it is expected to have a higher energy. In this complex, the interatomic distance between a hydroxyl H and the central nitrogen is 2.041 Å and that between a hydroxyl O and a terminal amine nitrogen atom is 2.341 Å. In these four complexes, the nearest interatomic distance between the N atom and the hydroxyl O atom is 2.749−3.042 Å, such that these product complexes are also H-bonded complexes. 3.2. Potential Energy Surface. Using intrinsic reaction coordinate (IRC) analysis, it was found that the abstractions of the central and terminal amine H atoms by the OH radical proceed through the following reaction steps. As shown in Figure 8, the abstraction of the central amine H by the OH radical proceeds through the formation of the R-HBC2 complex, in which the hydroxyl H atom interacts with the terminal N atom of MMH and then abstracts the central amine H via TS1 to form the product complex P-HBC1, which then dissociates to the products CH3N•NH2 + H2O. For the abstraction of the terminal H atoms, it proceeds through the formation of the R-HBC1 complex, in which the hydroxyl H atom interacts with the central N atom of MMH, and then abstracts the terminal amine H via TS2 to form the product complex P-HBC2, which in turn dissociates to the products trans-CH3NHN•H + H2O. Furthermore, it also proceeds through the reactant complex R-HBC1 to form the product complex P-HBC3 via TS3 and then dissociates to the products cis-CH3NHN•H + H2O. The abstraction of the central and terminal amine H atoms proceeds via the formation of the respective R-HBC2 and R-HBC1 complexes, which might be ascribed to the fact that the reorientation of the OH is unnecessary and it is kinetically favorable. The abstraction of methyl hydrogen proceeds via the direct abstraction of the methyl H atom to form the product complex P-HBC4 via TS4 and then dissociates to the products C•H2NHNH2 + H2O. The zero-point energies, energies, and zero-point corrected energies relative to MMH + OH for the preactivated reactant complexes and transition states calculated at the CASPT2/augcc-pVDZ and the CASPT2/aug-cc-pVTZ levels are listed in Table 3. The T1 diagnostic values calculated at the QCISD(T)/cc-pVQZ//CASPT2/aug-cc-pVTZ level are also listed in Table 3. It is seen that for the saddle points with the T1 diagnostic value less than 0.03, the zero-point energies 5052



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has an energy that is 2.12 kcal mol−1 lower than that of the entrance channel to form trans-CH3NHN•H + H2O, and TS3 has an energy that is 1.24 kcal mol−1 lower than that of the entrance channel to form cis-CH3NHN•H + H2O. The negative energies of the transition state for the H-abstraction of amine hydrogen atoms are due to the existence of preactivated reaction complexes on the potential energy surface, as well as the high exothermicity of 38−40 kcal mol−1 in these channels. In contrast, the abstraction of the methyl H atom is direct, and it has an energy that is 3.09 kcal mol−1 higher than that of the entrance channel with a smaller exothermicity of 27 kcal mol−1. For the H-bonded product complexes, the nitrogen centered radical complexes were found to have similar energies. Specifically, the CH3N•NH2−H2O, cis-CH3NHN•H−H2O, and trans-CH3NHN•H−H2O complexes have energies of 42.82, 43.42, and 42.83 kcal mol−1 below that of the entrance channel, respectively, whereas the C•H2NHNH2−H2O complex has an energy 30.26 kcal mol−1 below that of the entrance channel, which is higher than those of the nitrogen-centered radical complexes. As shown in Figure 7, the hydrogen-bonded product complexes, CH3N•NH2−H2O and C•H2NHNH2− H2O, can dissociate to water and the corresponding radical products via barriers of 2.49 and 3.58 kcal mol−1. The cis and trans forms of the hydrogen-bonded CH3NHN•H−H2O product complexes have higher barriers of 5.30 and 4.93 kcal mol−1 to dissociate to the products cis-CH3NHN•H + H2O and trans-CH3NHN•H + H2O. The increased energy barriers for the dissociation of the CH3NHN•H−H2O product complexes are ascribed to the stronger H-bonding between the hydroxyl H atom in water and the terminal amine radical of CH3NHN•H moiety with the interatomic distance of 1.90 Å. 3.3. Kinetic Rate Coefficients. For rate coefficient calculations, the inner transition-state numbers of states were determined on the basis of the rigid-rotor harmonic oscillator approximation. Because the spin−orbit interactions split the ground state OH (2Π) into two doubly degenerate states, 2Π3/2 and 2Π1/2, and the 2Π1/2 doublet state lies only 139.7 cm−1 above the 2Π3/2 doublet state,38 the low-lying state 2Π1/2 of the OH radical was included in the electronic partition function. The CH3, NH2, and OH group torsional modes in the reactant and transition states were treated as hindered rotors, and their internal rotational potentials were determined to account for their contribution to the partition functions. As discussed above, the CASPT2 method enables us to obtain accurate transition states for the OH abstraction of MMH; however, it is not practical method for determining internal rotational potentials. Because the BHandHLYP/6-311G(d,p) method was found to be able to capture the characteristic of the transition states of the OH abstraction of alkene39,40 and MMH as discussed in section 2.1, it should be reasonably accurate for the internal rotational potentials of the transition states associated with the reactions of MMH + OH. Figure 9 shows the rotational potentials of methyl group and amine group calculated at the BHandHLYP/6-311G(d,p) level. For the rotational potential of the methyl group in MMH, it is not exactly 3-fold symmetric, indicating that the three methyl hydrogen atoms are not superimposable upon an internal rotation. Because the energy barrier for the abstraction of methyl hydrogen is higher than those of the abstraction of amine hydrogen atom, the three methyl hydrogen atoms were treated as equivalent to the symmetry number of three. The barrier height for the methyl group rotation was found to be 4.11, 4.11, and 4.16 kcal mol−1 at the BHandHLYP/6-

Figure 9. Rotational potentials calculated at the BHandHLYP/6311G(d,p) level: (a) methyl group rotation; (b) amine group rotation.

311G(d,p), B3LYP/6-311++G(d,p), and QCSD(T)/CBS// B3LYP/6-311++G(d,p) levels, respectively. For the rotational potential of the NH2 group in MMH, it is 2-fold asymmetric, and the barrier heights at the BHandHLYP/6-311G(d,p) level were found to be slightly higher than those predicted values at the QCSD(T)/CBS//B3LYP/6-311++G(d,p) level. This implies the BHandHLYP/6-311G(d,p) rotational barrier height is reasonably accurate. Therefore, for the rate calculations, the internal rotational potentials as a function of the dihedral angle for both transition states and the reactant were determined at the BHandHLYP/6-311G(d,p) level for partial cancellation of errors in the partition function. Because of many electrostatic interactions in the four transition states, the cleaving N−H and C−H bond lengths, the forming O−H bond length, and the angle between the cleaving and forming bond were fixed to determine the rotational potentials. The calculated hindered internal rotation potentials then were fit to a Fourier series: V(ϕ) = V0 + ∑3i=1ai cos(iϕ) + ∑8i=1bi sin(iϕ) with the constraints of V0 = −∑3i=1ai and ∑8i=1ibi = 0, which are equivalent to the potential and first derivative of the potentials being zero at ϕ = 0. For the symmetric methyl group torsion potential, the sine term in V(ϕ) is omitted in the Fourier series fit. These torsional modes were then treated as 5053



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amine H to form the cis-CH3NHN•H radical, and k4 = 9.13 × 10−21T2.964 exp(−114.09/T) for the abstraction of the methyl H atom to form the C•H2NHNH2 radical. Assuming the rate coefficients are additive, the total rate coefficient ktotal = 1.94 × 10−18T2.306 exp(1272.81/T) cm3 molecule−1 s−1 is obtained by summing the rate coefficients of above individual channels, which again exhibits negative temperature dependence. Excellent agreement is observed by comparing this total rate coefficient k total (blue curve) with the two available experimental data over 232−637 K,7,8 as shown in Figure 10. For the OH abstraction channels, it was found that contributions from the internal rotors, the outer transition states, and tunneling are considerable on the chemical accuracy of rate coefficients. For the abstraction of central amine hydrogen in TS1, by considering the rotational motion of the OH group as a hindered rotor instead of vibrational motion, the rate coefficient is increased by 25−36% over 200−2500 K. While considering the similar OH motion as a hindered rotor in TS3 for the abstraction of the terminal amine hydrogen, we found that the rate coefficient k3 is increased monotonically by 2.7−54.3% over 200−2500 K. This implies that the contribution of the OH rotor to the microcanonical rate coefficient k1 is probably overpredicted at low temperatures by using the uncoupled 1-dimensional hindered rotor approximation. The overprediction might ascribed to the branched transition-state structure of TS1 in which the OH group interacts with neighboring methyl H though a H-bonding with interacting distance of 2.216 Å, as shown in Figure 11. In

uncoupled 1-dimensional hindered rotors with a Pitzer− Gwinn-like41 approximation that reproduces the coupled harmonic oscillator limit at low temperatures and the free rotor limit at high temperatures. The tunneling effect through the saddle point was modeled with asymmetric Eckart forms. The kinetic rate calculations were carried out with the VARIFLEX code.42 The calculated rate coefficients for the abstraction of different H atoms in MMH by OH are shown in Figure 10, with the

Figure 10. Theoretical rate coefficients for the abstraction of different H atoms in MMH by OH radical, with a total rate compared with the experimental data.

abstraction of the central amine H atom illustrated by black curve, and the abstraction of the terminal amine H atom to form trans-CH3NHN•H−H2O and cis-CH3NHN•H−H2O by red and green curves, respectively. It is seen that the rate coefficients for the abstraction of the amine H atoms have negative temperature dependence; i.e., the rate constant decreases with increasing temperature below 600 K. It is also seen that the rate coefficient k2 for the abstraction of the terminal amine H to form trans-CH3NHN•H + H2O is the most dominant channel at all temperatures. Furthermore, the rate coefficient k2 is close to the experimental data for total abstraction rate coefficients at 200−300 K,7,8 which implies the OH only abstracts a terminal H atom at 200−300 K. The abstraction of the central amine H is the second dominant channel at the temperatures below 1000 K. The rate coefficient for the abstraction of the methyl H atom is represented by the pink curve, which is far below those of the abstraction of amine hydrogen atoms at temperatures below 500 K. However, the reaction becomes an important channel above 1000 K. It is therefore concluded that the initial reactions of MMH oxidation are governed by the abstraction of amine hydrogen atoms. However, in our kinetics study on the decomposition of MMH radicals, it was found that the β-scission of NH2 from the C•H2NHNH2 radical is the fastest reaction among the decomposition of the four radicals.43 Therefore, the methyl hydrogen abstraction of MMH by OH is also an important path for MMH oxidation, especially at higher temperatures. In units of cm3 molecule−1 s−1, the rate coefficient was fitted as k1 = 3.37 × 10−16T1.295exp(1126.17/T) for the abstraction of the central amine H to form the CH3N•NH2 radical, k2 = 2.34 × 10−17T1.907 exp(1052.26/T) for the abstraction of the terminal amine H to form the trans-CH3NHN•H radical, k3 = 7.41 × 10−20T2.428 exp(1343.20/T) for the abstraction of the terminal

Figure 11. Hindered internal rotation potential of OH group in TS1 calculated at the BHandHLYP/6-311G(d,p) level. The global minimum of the potential corresponds to a transition-state structure in which the OH group interacts with neighboring methyl hydrogen though a H-bonding with interacting distance of 2.216 Å.

addition, it was found that the NH2 rotor contributes the rate coefficient of the abstraction of the central amine hydrogen by 6.3−27.7% over 200−2500 K. Because of many electrostatic interactions in the transition states for this nitrogen and oxygen containing reaction system, an explicit treatment of rotational anharmonicities of the transition states demands significant work. However, the subchemical accuracy of rate coefficients is worth such an effort. It is also noted that more rigorous treatment of the rotational anharmonicities for the geometries containing hydrogen bonds requires a multidimensional rotor model. For the H-abstraction amine hydrogen atoms of MMH + OH, comparison of the theoretical rate coefficients determined 5054



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atom (k4) and moderate for the abstraction of terminal amine H atom to form cis-CH3NHN•H radical (k3). Without considering the tunneling effect, k1 is reduced by factors of 1.1−1.2, k2 by factors of 1.1−1.3, k3 by factors of 1.1−2.2, and k4 by factors of 1.2−26.6 for 1000−200 K, respectively. The moderate tunneling effect for k3 is due to its increased energy barrier and moderately large imaginary frequency of 1057.7 cm−1 of TS3. The significant tunneling effect for k4 is ascribed to the relatively higher energy barrier and larger imaginary frequency of 1509.9 cm−1 of TS4. Recently, a dynamic study by Liu et al.44 on the reactions of MMH + OH was performed on the basis of quantum chemistry calculations at the BMC-CCSD//B3LYP/6-31G(d,p) level, yielding the total rate coefficient at temperatures of 200−1000 K as ktotal = 0.16 × 10−23T4.03 exp(1411.5/T) cm3 molecule−1 s−1, which is lower than the experimental data8 over 250−600 K by factors of 20−36. As discussed above, the density functional B3LYP method with split valence basis set predicts reactant-like transition states and hence poor interaction energies for the abstraction of amine hydrogen atoms. Furthermore, at low to intermediate temperatures, the rate coefficients of the OH abstraction of weakly bonded amine hydrogen atoms are greatly sensitive to the accurate description for both the molecular properties including torsional anharmonicity and the energetics of the inner and outer transition states. Consequently, the employment of multireference electron structure theory and sophisticated kinetic theory is essential for fundamental understanding and accurate prediction of the rate coefficients.

with (solid line) and without (dashed line) considering the outer transition states is shown in Figure 12. Without

Figure 12. Comparison of the theoretical rate coefficients determined with (solid lines) and without (dashed lines) considering the outer transition state for the abstraction of amine H atoms in MMH.

considering the outer transition state for the formation of the H-bonded complexes, the rate coefficients k1 and k2 were found to be a factor of 2.8 higher, and k3 a factor 1.7 higher at 200 K. At room temperature, the effect of the outer transition state is reduced, as the rate coefficients k1 and k2 were found to be a factor of 1.6 higher, and k3 a factor of 1.2 higher than those rate coefficients with considering the outer transition state. Over 200−600 K, the total rate coefficient is increased by factors of 2.7−1.04, hence reflecting significant effect from the outer transition states to the rate coefficients at the low temperatures. The contribution of the tunneling effect to the rate coefficients is shown in Figure 13, with the rate coefficients

4. CONCLUDING REMARKS The kinetics of hydrogen abstraction reactions of MMH by the OH radical were investigated by the second-order multireference perturbation theory and the microcanonical transition-state theory at the E/J resolved level, with the correction of internal rotor for the torsional modes and the correction of tunneling effect with asymmetric Eckart potentials. Due to the multireference character of the abstraction of amine hydrogen atoms, the geometries of stationary points of the potential energy surface for the H-abstraction reactions were optimized at the CASPT2/aug-cc-pVTZ level, and the energies of the stationary points were further refined at the QCISD(T)/CBS level via extrapolation of the QCISD(T)/cc-pVTZ and QCISD(T)/cc-pVQZ energies. By the intrinsic reaction coordinate (IRC) analysis, it was found that the abstraction of amine H atoms proceeds through two preactivated Hbonded reactant complexes via indirect abstraction pathways; consequently, the rate coefficients of MMH + OH for the Habstraction of the amine H atoms were determined using a twotransition-state model at the E and J resolved level. The result reveals that the abstraction of terminal amine hydrogen to form trans-CH3NHN•H radical is the most dominant channel among the different abstraction channels. Assuming that the rate coefficients are additive, the total rate coefficient of each abstraction channel quantitatively reproduces the measured rate constant over 200−650 K, with no adjustable parameters. Furthermore, the effects from various aspects such as internal rotors, outer transition state and outer transition-state rate constant, and quantum mechanical tunneling to the abstraction rate coefficients are demonstrated.

Figure 13. Comparison of the theoretical rate coefficients determined with (solid lines) and without (dashed lines) considering the tunneling effect for the H-abstractions of MMH + OH.

without considering the tunneling effect represented by dashed lines. It is seen that the tunneling effect for the abstraction of the central amine H atom (k1) and the terminal amine H atom to form trans-CH3NHN•H radical (k2) is not significant due to their smaller barrier heights and the relatively small imaginary frequencies 736.1 and 767.9 cm−1, respectively. However, the tunneling effect is significant for the abstraction of methyl H

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AUTHOR INFORMATION

Corresponding Author

*Fax: (609) 258-6233. E-mail: [email protected]. 5055



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Notes

(31) Ma, B.; Lii, J.-H.; Chen, K.; Allinger, N. L. J. Phys. Chem. 1996, 100, 11297. (32) Durig, J. R.; Gounev, T. K.; Zheng, C.; Choulakian, A.; Verma, V. N. J. Phys. Chem. A 2002, 106, 3395. (33) Durig, J. R.; Zheng, C. Vibr. Spectrosc. 2002, 30, 59. (34) Tsuboi, M.; Overend, J. J. Mol. Spectrosc. 1974, 52, 256. (35) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules; Van Nostrand Reinhold Co., 1979. (36) Stockman, P. A.; Bumgarner, R. E.; Suzuki, S.; Blake, G. A. J. Chem. Phys. 1992, 96, 2496. (37) Herbine, P.; Dyke, T. R. J. Chem. Phys. 1985, 83, 3768. (38) Chase, M. W. NIST-JANAF thermochemical tables; 4th ed.; American Chemical Society: Washington, DC, 1998. (39) Szori, M.; Fittschen, C.; Csizmadia, I. G.; Viskolcz, B. J. Chem. Theory Comput. 2006, 2, 1575. (40) Sun, H.; Law, C. K. J. Phys. Chem. A 2010, 114, 12088. (41) Pitzer, K. S.; Gwinn, W. D. J. Chem. Phys. 1942, 10, 428. (42) Klippenstein, S. J.; Wagner, A. F.; Dunbar, R. C.; Wardlaw, D. M.; Robertson, S. H.; Miller, J. A. VARIFLEX, 2.02m ed., 2010. (43) Sun, H.; Zhang, P.; Law, C. K. 7th US National Technical Meeting of the Combustion Institute, The Georgia Institute of Technology, Atlanta, GA, March 20−23, 2011. (44) Liu, H.-X.; Wang, Y.; Yang, L.; Liu, J.-Y.; Gao, H.; Li, Z.-S.; Sun, C.-C. J. Comput. Chem. 2009, 30, 2194.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge Dr. Stephen J. Klippenstein at Argonne National Laboratory for helpful comments and 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-AC02-05CH11231.

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Gas-Phase Kinetics Study of Reaction of OH Radical with CH3NHNH2

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