Theoretical Study on Reaction Mechanisms and Kinetics of

Mar 11, 2010 - Department of Chemistry and Institute of Applied Chemistry, Chinese Culture UniVersity, Taipei, 111, Taiwan. ReceiVed: NoVember 3, 2009...
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J. Phys. Chem. A 2010, 114, 4655–4663

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Theoretical Study on Reaction Mechanisms and Kinetics of Cyanomidyl Radical with NO Ruei-Ching Jian, Chiitang Tsai, Ling-Chieh Hsu, and Hui-Lung Chen* Department of Chemistry and Institute of Applied Chemistry, Chinese Culture UniVersity, Taipei, 111, Taiwan ReceiVed: NoVember 3, 2009; ReVised Manuscript ReceiVed: January 5, 2010

The mechanisms and kinetics of the reaction of the cyanomidyl radical (HNCN) with the NO have been investigated by the high-level ab initio molecular orbital method in conjunction with VTST and RRKM theory. The species involved have been optimized at the B3LYP/6-311++G(3df,2p) level and their single-point energies are refined by the CCSD(T)/aug-cc-PVQZ//B3LYP/6-311++G(3df,2p) method. Our calculated results indicate that the favorable pathways for the formation of several isomers of an HNCN-NO complex. Formations of HNC + N2O (P1) and HNCO + N2 (P2) are also possible, although these two pathways involve little activation energy. Employing the Fukui functions and HSAB theory, we are able to rationalize the scenario of the calculated outcome. The predicted total rate constants, ktotal, at a 760 Torr Ar pressure can be represented by the equations ktotal ) 4.39 × 108 T-7.30 exp(-1.76 kcal mol-1/RT) at T ) 298-1000 K and 1.01 × 10-32 T5.32 exp(11.27 kcal mol-1/RT) at T ) 1050-3000 K, respectively, in units of cm3 molecule-1 s-1. In addition, the rate constants for key individual product channels are provided in a table for different temperature and pressure conditions. These results are recommended for combustion modeling applications. 1. Introduction The cyanomidyl radical (HNCN) and other HCN2 structural isomers have been proposed as intermediates in the CH + N2 reaction, which is important reaction in hydrocarbon combustion because of its possible role in the formation of “prompt” NO.1-5 In addition, the HNCN radical is a reactive transient species that plays an important role in a variety of chemical environments, including interstellar chemistry and primordial reactions leading to the synthesis of amino acids from simple inorganic compounds. In 1963, the HNCN radical was first identified spectroscopically by Herzberg and Warsop.6 In 1993, the laserinduced fluorescence (LIF) spectrum of jet-cooled HNCN was observed and discussed by Wu et al.,7 and they yielded more accurate spectroscopic constants and probed the significant transition of B2A′′′ r X2A′′′. In 1997, Yamamoto et al8 reported the microwave spectrum of the HNCN radical, and they found the rotational spectral lines are observed in the millimeter-wave and submillimeter-wave regions. Clifford et al.9 used negative ion photoelectron spectroscopy to measure the electron affinities of HNCN radical (EA ) 2.622 ( 0.005). In 2001, Bise et al10 investigated the photodissociation spectroscopy and dynamics of the HNCN free radical by fast beam photofragment translational spectroscopy. On the other hand, theoretical calculations of the equilibrium structure and vibrational frequencies for the ground state HNCN radical were first performed by Tao et al.11 in 1994, and then more recently by Puzzarini et al.12 in 2005. Besides, Berman et al.13 performed the calculation on the decomposition reaction of HNNC molecule, and they reported that the HNNC can convert to HNCN with energy barrier of ca. 39.6 kcal/mol. This radical may be a key intermediate in the combustion of sulfur-containing fuels and may play an important role in the RAPRENOx (rapid reduction of nitrogen oxides) process.14,15 There have been numerous reports on theoretical and experimental approaches to eliminate NO,16-24 many of which contain * To whom correspondence should be addressed. E-mail: chl3@ faculty.pccu.edu.tw. Fax: +886-2-28614212.

cyanogen species as an effective reagent to remove NO. Our purpose of this study is to find the possible reactants which may react with NO to form the stable product such as N2, which is not harmful to our environment and possibly with lower energy barriers. To the best of our knowledge, however, no theoretical study regarding the HNCN + NO reaction mechanism was available. Here, we present the novel reaction mechanism of HNCN + NO that provides an efficient route to remove NO. Besides, the rate constants and branching ratios for the primary reaction channels in the temperature range of 298-3000 K have been predicted for combustion modeling applications. 2. Computational Method The optimized geometries of the reactants, intermediates, transition states, and products for the HNCN + NO reaction in the gas phase are calculated at the B3LYP/6-311++G(3df,2p) level25,26 by using the Gaussian 03 suite of programs.27 The calculated equilibrium structures (local minima and saddle points) are characterized with calculations of harmonic vibrational wavenumbers (one imaginary frequency for a transition state and all positive frequencies for a minimum) at the same level of theory with calculations of intrinsic reaction coordinates (IRC)28 to establish the link between transition structure and the intermediates. To obtain reliable energies, we perform singlepoint calculations employing a coupled-cluster technique with single and double excitations and evaluations by perturbation theory of triple contributions CCSD(T)29,30 based on the geometries optimized at the B3LYP/6-311++G(3df,2p) level. The highest level of theory attained in this work is thus denoted CCSD(T)/aug-cc-PVQZ//B3LYP/6-311++G(3df,2p). Unless otherwise specified, the CCSD(T) single-point energies are used in the following discussion. The rate constants for the key product channels are computed with the variational transitionstate theory (VTST) and microcanonical Rice-RamspergerKassel-Marcus (RRKM) theory31-34 using the VariFlex35 program.

10.1021/jp9104823  2010 American Chemical Society Published on Web 03/11/2010

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TABLE 1: The Geometries (Bond Lengths and Angles), Electron Affinities (EA) of the HNCN Molecule Calculated at Various Levels of Theory and Some Experimental Data from the Literature level of theory MP2/6-31++G(d,p) MP2/6-311++G(3df,2p) B3LYP/6-31++G(d,p) B3LYP/6-311++G(3df,2p) CCSD(T)/6-311++G(3df,2p)//B3LYP/6-311++G(3df,2p) CCSD(T)/aug-cc-PVTZ// B3LYP/6-311++G(3df,2p) CCSD(T)/aug-cc-PVQZ// B3LYP/6-311++G(3df,2p) experiment a

N-C-Na (Å)

N-H (Å)

∠CNH (deg)

2.47 2.45 2.48 2.46

1.02 1.02 1.02 1.02

111.2 111.9 112.8 113.6

2.470 ( 0.002c

1.034 ( 0.020c

116.5 ( 2.7c

EAb /eV 2.94 3.21 2.53 2.55 2.55 2.60 2.62 2.622 ( 0.005d

The sum of the heavy atom distances. b Energy difference between the anion HNCN- and neutral HNCN. c Reference 6. d Reference 9.

SCHEME 1: Schematic Diagram of Proposed Paths for the Reaction HNCN + NO

3. Results and Discussion 3.1. Computational Condition Tests. In Table 1, we present data for the electron affinities (EA) and geometrical parameters of HNCN radical calculated at various levels of theory with pertinent experimental data from the literature. The N-C-N and N-H bond lengths as well as the ∠CNH bond angle predicted by the hybrid density functional B3LYP method with a modest 6-311++G(3df,2p) basis set are 2.46 Å, 1.02 Å, and 113.6°, which are in satisfactory agreement with experimental values (2.470 ( 0.002 Å, 1.034 ( 0.020 Å, and 116.5 ( 2.7°, respectively),6 whereas the calculated B3LYP energy for the electron affinity of HNCN, 2.55 eV, substantially underestimates the experimental value (2.622 ( 0.005, shown in Table 1).9 However, at the CCSD(T)/aug-cc-PVQZ// B3LYP/6311++G(3df,2p) level the predicted value of 2.62 eV is much closer to the experimental one. For this reason, we therefore choose CCSD(T)/aug-cc-PVQZ//B3LYP/6-311++G(3df,2p) as the method for an energetic calculation of all feasible processes in the reaction system HNCN + NO. 3.2. Potential Energy Surface for the HNCN + NO Reaction. As depicted in Scheme 1, we classified the examined reaction into eight paths, A-H, corresponding to eight possible product channels. The intermediates are correspondingly num-

bered as IM1-IM8, and the products in these eight channels, HNC + N2O, HNCO + N2, HCNO + N2, HNC + c-N2O, NCO + HNN, CNO + HNN, CN + HNNO, and HNC + NON, are labeled in the same order of P1-P8. TS1-TS10, TSiso1, and TSiso2 denote the transition state species connecting two intermediates located at local minima. The computed geometric structures of the relevant reactants, intermediates, products, and the transition states at the B3LYP/6-311++G(3df,2p) level are drawn in Figures 1 and 2, respectively. The profiles of the potential energy surface (PES) calculated at the CCSD(T)/ aug-cc-PVQZ//B3LYP/6-311++G(3df,2p) level are shown in Figure 3. All the calculated energetics for the reactants, intermediates, transition states and products are listed in Table 2. Among which, the zero-point energy (ZPE) correction is considered, and the energies with respect to the reactant (HNCN + NO) calculated at the CCSD(T) level are denoted as CRE. As shown in Table 2, the heats of reaction for the productions of HNC + N2O (P1), HNCO + N2 (P2), and HCNO + N2 (P3) are predicted to be -32.36, -126.09, and -57.30 kcal/mol, respectively; they are in excellent agreement with the experimental values, -31.99 ( 0.73, -126.41 ( 0.37, and -57.81 ( 0.69 kcal/mol. The experimental values are derived from the

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Figure 1. The optimized geometries of the relevant reactants, intermediates, and products on the potential energy surfaces of HNCN + NO reactions, calculated at the B3LYP/6-311++G(3df,2p) level. Bond lengths are given in angstroms and angles in degrees.

known experimental heats of formation, HNCN (77.25 ( 0.69 kcal/mol),10 NO (21.46 kcal/mol),36a HNCO (-27.7 ( 1.1 kcal/ mol),36b HNC (46.4 kcal/mol),36c and N2O (20.32 kcal/mol).36a In addition, the heat of formation of HCNO (40.9 kcal/mol) was rigorously calculated using state-of-the-art ab initio electronic structure theory by Schuurman et al.36d The further calculations are performed to extrapolate the CCSD(T) results to the complete basis set limit. By fitting results obtained from basis sets with different n, aug-cc-PVnZ, an extrapolation to nf∞ can be achieved. For this purpose, the “cardinal number”

X is introduced, where X ) 2, 3, 4, 5 for n ) D, T, Q, 5, respectively. For the extrapolations to the complete basis set limit, we use the two-parameter exponential model,37 E ) a + bX-3, to fit the data points (two-point basis set extrapolation using aug-cc-PVTZ and aug-cc-PVQZ). As shown in Table S1, the result is quite consistent, the discrepancy between CCSD(T)/ aug-cc-PVQZ and CBS limit is less than 1.2 kcal/mol. As shown in Figure 3, it is found that there exist four possible orientations for N-N bond addition, and these four separated adducts, IM1, IM2, IM3, and IM4, lead to completely different

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Figure 2. The optimized geometries of the relevant transition states on the potential energy surfaces of HNCN + NO reactions, calculated at the B3LYP/6-311++G(3df,2p) level. Bond lengths are given in angstroms and angles in degrees.

follow-up reaction mechanisms and different product formations. First, with regard to N-Nt coordination (Nt denotes the N atom in the terminal position of HNCN), our calculated results for channels A-D are RfIM1fTS2fP1, RfIM1fTS3fIM6f TS9fP2, RfIM1fTS4fIM7fTS10fP3, and RfIM2f TS5fP4, respectively. All these processes involve first the formation of an adduct HNCNNO, which has two isomers, cisHNCNNO (IM1) and trans-HNCNNO (IM2). Although the trans-isomer is more stable than the cis-isomer by 3.05 kcal/ mol, they might interconvert readily on overcoming a small energy barrier of 0.36 kcal/mol (TSiso1). For channel A, the

first step is barrierless formation of IM1, with an exothermicity of 17.86 kcal/mol. It may go through a dissociative transition state, TS2, lying 8.64 kcal/mol above the reactants, and forming the products of HNC + N2O (P1), with an overall exothermicity of 32.36 kcal/mol. However, for channel B, the IM1 adduct will proceed another pathway, via TS3 (Ea ) -3.62 kcal/mol, with respect to the reactants), to form four-membered ring intermediate, IM6, and then go further by passing a barrier (TS9, 7.15 kcal/mol) to open the ring by breaking two C-N and O-N bonds simultaneously and form the products of HNCO + N2 (P2), with an overall exothermicity of 126.09 kcal/mol. On the

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Figure 3. Calculated profiles on the potential-energy surface for possible paths in the reaction HNCN + NO at the level of CCSD(T)/aug-ccPVQZ//B3LYP/6-311++G(3df,2p); the labels in the figure represent the same species as those in Figures 1 and 2.

other hand, P3 (HCNO + N2) and P4 (HNC + c-N2O) products, could also be formed via the channels C and D, and the highest barrier in the former pathway is 17.38 kcal/mol (TS10), while the latter is 41.52 kcal/mol (TS5). The cyclic conformer of c-N2O is around 62.7 kcal/mol less stable than the linear counterpart. Obviously, these two pathways (C and D) are not favorable as compared to the pathways forming products P1 and P2 since they need higher activated barriers to achieve the reactions. Second, with regard to N-N coordination our calculated results for channels E to G are RfIM3fTS6fP5,RfIM3f TS7fIM8fP6, and RfIM4fP7, respectively. Similarly, these pathways involve the formation of another adduct HN(NO)CN, which also has two isomers, cis-HN(NO)CN (IM3) and trans-HN(NO)CN (IM4). As we can see, the relative energy difference between cis- and trans-isomers is not obvious (less than 0.4 kcal/mol), but the activation energy required for the interconversion is quite high (TSiso2, 88.53 kcal/mol). To seek possible clues, the ∠NNO (θ) angle that would correspond to the cis-trans isomerization reaction coordinate (IM3 f IM4) is scanned over 120° in 5° steps. At each step, the ∠NNO angle is frozen and the remaining degrees of freedom are optimized. Plot of total energy versus ∠NNO (θ) angle for the IM3 f IM4 isomerization is shown in Figure S4 in the Supporting Information. As seen from this figure, the total energy of the system significantly increases as the ∠NNO angle approaches to 180°. The highest value of the rotation around the N-O bond is located at a structure which contains linear moiety of “NdNdO”, indicating that a huge supplement of thermal energy would be needed to twist its two double bonds. For channel E,

the initial reaction of HNCN + NO takes place by a barrierless addition to form IM3, a long-lived intermediate with an exothermicity of 28.33 kcal/mol. Subsequently, IM3 will then undergo a dissociative transition state, TS6, lying 12.32 kcal/ mol above the reactants, and forming the products of NCO + HNN (P5), with an overall exothermicity of 8.06 kcal/mol. However, for channel F, the rearrangement of the initial adduct cis-HN(NO)CN (IM3) could form another intermediate IM8 via a higher energetic transition state (TS7, 31.37 kcal/mol). Scission of the N...O bond occurs at this stage through a direct dissociation process, to form products of CNO + HNN (P6), with highly endothermic by 54.32 kcal/mol. On the other hand, for channel G after the formation of trans-HN(NO)CN (IM4), it can then directly produce the final products CN + HNNO (P7) via variational transition state with huge endothermicity of 57.40 kcal/mol. Further, there is still one unlikely occurring pathway having exceptional large energy barrier in taking the oxygen atom of NO to bind to a nitrogen atom of HNCN in forming HNCNON adduct (IM5) with barrier height of 9.51 kcal/mol (TS1). The IM5 might pass through a dissociative transition state (TS8), with an enormous energy barrier of 97.02 kcal/mol, forming the products of HNC + NON (P8), 79.10 kcal/mol higher than the reactants. The preference for the formation of HN(NO)CN and/or HNCNNO rather than HNCNON is explicable with the Fukui function described in a following section. Consequently, as shown in Figure 3, our calculated results indicate that both channels A and B are two major possible channels of the title

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TABLE 2: Zero-Point Vibration Energies (ZPE, hartree), Total Energies (TE, hartree), and Relative Energies (RE, kcal/mol) of Reactant, Intermediates, Transition States and Products, Calculated at the B3LYP/6-311++G(3df,2p) (BTE), and CCSD(T)/ aug-cc-PVQZ//B3LYP/6-311++G(3df,2p) (CTE, CRE) Levels for the Reaction of HNCN+ NO R (HNCN + NO) IM1 IM2 IM3 IM4 IM5 IM6 IM7 IM8 TS1 TS2 TS3 TS4 TS5 TS6 TS7 TS8 TS9 TS10 TSiso1 TSiso2 P1 (HNC + N2O) P2 (HNCO + N2) P3 (HCNO + N2) P4 (HNC + c-N2O) P5 (NCO + HNN) P6 (CNO + HNN) P7 (CN + HNNO) P8 (HNC + NON)

ZPEa

BTE + ZPEb

CTE + ZPEb

CREc

0.024113 0.028970 0.029116 0.030835 0.030652 0.028355 0.031541 0.031251 0.028782 0.027905 0.026806 0.028822 0.030383 0.024227 0.029768 0.029259 0.023369 0.028617 0.028410 0.029136 0.028950 0.026835 0.026899 0.024917 0.022597 0.023223 0.022066 0.025118 0.025201

-278.101854 -278.128619 -278.134880 -278.139133 -278.138937 -278.085979 -278.119079 -278.069554 -278.043036 -278.077437 -278.084511 -278.100917 -278.070322 -278.022973 -278.070346 -278.040844 -277.905090 -278.112736 -278.061466 -278.127947 -278.008655 -278.144733 -278.292010 -278.183810 -278.035493 -278.118252 -278.018853 -277.997473 -277.961223

-277.668020 -277.696489 -277.701341 -277.713172 -277.712540 -277.653912 -277.699953 -277.649458 -277.618099 -277.652868 -277.654248 -277.673784 -277.649286 -277.601854 -277.648389 -277.618030 -277.513404 -277.688562 -277.640315 -277.695909 -277.571461 -277.719582 -277.868953 -277.759341 -277.619750 -277.680872 -277.581455 -277.576542 -277.541963

0.00 -17.86 -20.91 -28.33 -27.94 8.85 -20.04 11.65 31.33 9.51 8.64 -3.62 11.76 41.52 12.32 31.37 97.02 -12.89 17.38 -17.50 60.59 -32.36 -126.09 -57.30 30.29 -8.06 54.32 57.40 79.10

experimentd

-31.99 ( 0.73 -126.41 ( 0.37 -57.81 ( 0.69

a Zero-point energy (au) at the level B3LYP/6-311++G(3df,2p). b The unit of energy is hartree. c Relative energy (kcal/mol) with respect to the reactants. d Derived from ref 36.

TABLE 3: Condensed Fukui Functions for H, N, C and Nta Atoms in HNCN, and N and O atoms in NO, and Global and Local Softnesses of the Molecules Calculated at the level B3LYP/6-311++G(3df,2p) f

0b

local softness (s0)d

molecule

H

N

C

Nt

HNCN NO

0.054

0.481 0.628

0.022

0.488

c

O

Global softness S

H

N

C

N-t

0.101

0.901 1.949

0.041

0.914

0.372

1.874 3.104

O 1.155

N atom in the terminal position of HNCN molecule. Atomic charges according to a natural population analysis. S ) 1/(IE - EA), with ionization energy IE and electron affinity EA; the energy unit is hartree. d s0 ) f 0S. a

b

reaction (HNCN + NO), and the channel B, RfIM1f TS3fIM6fTS9fP2, which is also the thermochemically most favorable. 3.3. Fukui Function Analysis. From the aforementioned results, it is found that the HNCN + NO reaction may form the four primary adducts, IM1, IM2, IM3, and IM4, which are energetically more stable than the reactants by 17.86, 20.91, 28.33, and 27.94 kcal/mol, respectively. Besides, the formation of secondary adduct, IM5, is also possible, although this procedure involves an energy barrier and absorption of heat (ca. 8.9 kcal/mol). Obviously, the former four adducts, IM1, IM2, IM3, and IM4, possess much higher stability than that of the IM5. To investigate this phenomenon, we calculate the Fukui functions38,39 and applied the theory of hard-and-soft acid-andbase (HSAB) to seek the possible explanation. The extrapolation of the general behavior “soft likes soft” and “hard likes hard” locally, together with the idea that the larger the value of the Fukui function, the greater the reactivity, is also a very useful approach to explain the chemical reactivity of many chemical systems.40-46 Clearly, the determination of the specific sites at which the interaction between two chemical species is going to occur is of fundamental importance to the determination of the

c

path and the products of a given reaction. Ga´zquez et al.47 also stated that the largest value of the Fukui function is, in general, associated with the most reactive site. In our calculation for N electrons in a system, independent calculations are made for the corresponding (N - 1), N, and (N + 1) electron systems with the same geometry. A natural population analysis yields qk(N - 1), qk(N), and qk(N +1) for the predicted possible sites of reaction of HNCN and NO molecules, and the Fukui function is calculated as a difference of population between N and N + 1 or N and N - 1 electron systems. We choose the f 0 value for comparison since HNCN + NO reaction is more characteristic of a radical system.39 According to our calculated data in Table 3, it is found that the largest Fukui function (f 0, ca. 0.49) is on the N (and/or Nt) atom in the HNCN radical, and that of the other reactant NO is on the N atom (ca. 0.63), which accounts for the formation of the complexes, IM1, IM2, IM3, and IM4, being more effective than other complexes (such as IM5). In addition, applying the HSAB theory, we find also that the largest values for the local softness s0 for both reactants are on the N (and/or Nt) atom of HNCN and the N atom of NO (ca. 0.91 and 1.95), which also accounts for the favorable formation of the adducts of IM1, IM2, IM3, and IM4. In contrast, the Fukui

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function calculated to be smallest, f 0 ) 0.372, and the local softness, s0 ) 1.155, of the O atom in NO, indicating an unfavorable addition through its O-terminus site is thus readily explained. 3.4. Rate Constant Calculation. Variational TST and RRKM calculations have been carried out for this reaction with the VariFlex code35 including the more favorable reaction channels are shown as follows.

In our kinetic calculations, the reverse dissociation of the energized intermediates IM1-IM4 back to the reactants is included. The energies used in the calculation are plotted in Figure 3, and the vibrational frequencies and moments of inertia are listed in Table S2 (Supporting Information). In above scheme, * indicates an activated molecule and M is the third body (Ar in this work). The Lennard-Jones (LJ) parameters employed for the HNCN + NO reaction are as follows: for Ar,48 σ ) 3.47 Å, ε/k ) 114.0 K and for HNCN-NO, σ ) 3.90 Å, ε/k ) 205.0 K, which are approximated to be the same as those of NCO-NO system.17 For the variational rate constant calculations by the VariFlex code, a statistical treatment of the transitional-mode contributions to the transition-state partition functions is performed variationally. On account of the absences of well-defined transition states for the initial association processes HNCN + NO f IM1, IM2, IM3, and IM4, the potential functions were computed variationally as a function of the bond length along the reaction coordinate R, which was evaluated according to the variable reaction coordinate flexible transition state theory.31-34,49 The Morse potential function V(R) ) De{1 - exp[-β (R - R0)]}2, was employed to approximate the minimum energy path in our rate constant calculation. In the above equation, R is the reaction coordinate (i.e., the distance between the two bonding atoms), De is the bond energy excluding zero-point energy, and R0 is the equilibrium value of R. The three parameters of this Morse potential are R0 ) 1.500 Å, β ) 1.107 Å-1, and De ) 20.91 kcal/mol for formation IM1, R0 ) 1.502 Å, β ) 1.117 Å-1, and De ) 24.05 kcal/mol for formation IM2, R0 ) 1.410 Å, β ) 1.367 Å-1, and De ) 32.55 kcal/mol for formation IM3, and R0 ) 1.393 Å, β ) 1.262 Å-1, and De ) 32.04 kcal/mol for formation IM4, respectively. In addition, an energy grain size of 1.00 cm-1 is used for the convolution of the conserved mode vibrations, and a grain size of 80.00 cm-1 is used for the generation of the transitionalmode numbers of states. The estimate of the transitional-mode contribution to the transition-state number of states for a given energy is evaluated via Monte Carlo integration with 10 000 configuration numbers. The energy-transfer process is computed on the basis of the exponential down model with a 〈∆E〉down value (the mean energy transferred per collision) of 400 cm-1 for Ar. In principle, the different 〈∆E〉down values should be determined by comparing the experimental pressure-dependent rate constants with the calculated values using the exponentialdown model in the solution of the master equation. Since there is no experimental value available for this system, our selected

Figure 4. Predicted rate constants of (a) kM1, kM2, kM3, kM4, kP1 and kP2 and (b) the total rate constants (ktotal ) kM1 + kM2 + kM3 + kM4 + kP1 + kP2) at Ar pressures of 760 Torr in the temperature range of 298-3000 K.

value of 〈∆E〉down for Ar, 400 cm-1, is approximately taken from the published computational work.50,51 To achieve convergence in the integration over the energy range, an energy grain size of 120 cm-1 is used. The total angular momentum J covered the range from 1 to 250 in steps of 10 for the E, J-resolved calculation. Miller et al.52 used a particularly simple and instructive example (ethyl radical with oxygen) to compare the difference between 1-D (E-resolved) and 2-D (E, J-resolved) values for rate constants, and they pointed out that the angular momentum conservation is usually not an important factor for bimolecular reactions producing bimolecular products. A more detailed description on this subject can also refer to their relevant studies.53,54 In the RRKM calculations, we neglect the pathways of P3-P8 formation since their energy barriers are much higher than TS2 and TS3 in which they are the rate-controlling steps of our proposed two predominant channels. In addition, for the prediction of kP2 values we ignore the contribution by TS9 since it is below the reactants around 12.9 kcal/mol; our predicted kP2 should be the maximum values. The predicted values for kM1, kM2, kM3, kM4, kP1, and kP2 and the total rate constants (ktotal ) kM1 + kM2 + kM3 + kM4 + kP1 + kP2) at Ar pressures of 760 Torr in the temperature range of 298-3000 K are shown in Figure 4a,b, respectively. It can be seen that the values of kM1, kM2, kM3, and kM4 substantially decrease when the temperature increases from 750 to 3000 K.

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Jian et al. TABLE 4: The Predicted Rate Expressionsa of kM1, kM2, kM3, kM4, kP1 and kP2 at the Ar Pressures of 10 Torr, 50 Torr, 380 Torr, 760 Torr, 10 atm, 50 atm and 100 atm in the Temperature Range of 298-3000 K reaction kM1

kM2

Figure 5. Predicted branching ratios for the primary reaction channels of HNCN + NO reactions at 760 Torr Ar pressure in the temperature range of 298-3000 K.

The values of kP1 have positive temperature dependence in the whole temperature range, while kP2 appears to be nearly independent of temperature. The branching ratios for the six primary reaction channels (RM1, RM2, RM3, RM4, RP1, and RP2) at Ar pressure of 760 Torr in the temperature range of 298-3000 K are shown in Figure 5. The results indicate that in the temperature range of 298-750 K the deactivation of IM3 is dominant (RM3 accounts for 0.44-0.36). The results imply that at low temperatures IM3 can be stably formed from HNCN + NO, which need to be experimentally confirmed. However, in the higher temperature range (760-1950 K) the branching ratio for RP2 (0.36-0.93) which forms HNCO + N2 (P2) becomes the most significant product. Besides, it is found also that the formation of HNC + N2O (P1) turns more competitive when the temperature goes higher than 1950 K. Figure S5 displays different 〈∆E〉down tests for the total rate constants as a function of pressure (Torr) at four varied temperatures (298, 500, 750, and 1000 K). Both the 300 and 400 cm-1 values for total rate constants are shown on the plot. At lower temperature range (298, 500, and 750 K), the 400 cm-1 result for the total rate constants is about 20% larger than the 300 cm-1 result; the difference becomes even smaller as the temperature increases to 1000 K. We summarize the rate expressions (kM1, kM2, kM3, kM4, kP1 and kP2) at seven specific pressures between 10 Torr and 100 atm in the temperature range of 298-3000 K, which are listed in Table 4. As we can see, in this temperature range, the values of kM1, kM2, kM3, and kM4 have strong pressure dependence; however, it has the pressure independence for the values of kP1 and kP2. The predicted total rate constants, ktotal, at a 760 Torr Ar pressure can be represented as ktotal ) 4.39 × 108 T-7.30 exp(-1.76 kcal mol-1/RT) at T ) 298-1000 K and 1.01 × 10-32 T5.32 exp(11.27 kcal mol-1/RT) at T ) 1050-3000 K, respectively, in units of cm3 molecule-1 s-1. At present, no comparison can be made for the calculated and experimental data. For this newly identified, potentially important, prompt NO precursor reaction, our results are recommended for hightemperature combustion modeling applications. 4. Conclusion Using the high-level CCSD(T) method, we have calculated the energetically accessible reaction routes for the HNCN + NO reaction. Both the reaction mechanisms and the kinetic

kM3

kM4

kP1

kP2

P

A

10 Torr 50 Torr 380 Torr 760 Torr 10 atm 50 atm 100 atm 10 Torr 50 Torr 380 Torr 760 Torr 10 atm 50 atm 100 atm 10 Torr 50 Torr 380 Torr 760 Torr 10 atm 50 atm 100 atm 10 Torr 50 Torr 380 Torr 760 Torr 10 atm 50 atm 100 atm 10 Torr 50 Torr 380 Torr 760 Torr 10 atm 50 atm 100 atm 10 Torr 50 Torr 380 Torr 760 Torr 10 atm 50 atm 100 atm

8.67 × 10 1.35 × 1030 1.31 × 1033 6.36 × 1033 6.51 × 1035 2.39 × 1037 1.42 × 1038 2.06 × 1037 1.35 × 1038 2.16 × 1039 6.31 × 1039 3.87 × 1041 1.34 × 1043 7.56 × 1043 8.31 × 1048 6.44 × 1049 1.27 × 1051 3.96 × 1051 2.76 × 1053 8.18 × 1054 3.69 × 1055 1.37 × 1048 1.13 × 1049 2.03 × 1050 6.13 × 1050 3.81 × 1052 1.06 × 1054 4.74 × 1054 4.32 × 10-21 4.32 × 10-21 4.32 × 10-21 4.32 × 10-21 4.32 × 10-21 4.32 × 10-21 4.32 × 10-21 2.66 × 10-19 2.66 × 10-19 2.66 × 10-19 2.66 × 10-19 2.66 × 10-19 2.66 × 10-19 2.66 × 10-19 26

n

B

-15.34 -15.96 -16.47 -16.56 -16.82 -17.06 -17.18 -18.05 -18.08 -18.17 -18.22 -18.43 -18.66 -18.78 -21.15 -21.20 -21.31 -21.36 -21.58 -21.78 -21.88 -20.95 -21.00 -21.10 -21.15 -21.36 -21.56 -21.65 2.34 2.34 2.34 2.34 2.34 2.34 2.34 1.42 1.42 1.42 1.42 1.42 1.42 1.42

-3.62 -4.49 -5.57 -5.83 -6.61 -7.35 -7.75 -7.73 -7.84 -8.11 -8.26 -8.98 -9.75 -10.18 -12.63 -12.84 -13.28 -13.49 -14.47 -15.44 -15.93 -12.35 -12.60 -13.00 -13.19 -14.09 -15.00 -15.47 -7.53 -7.53 -7.53 -7.53 -7.53 -7.53 -7.53 3.55 3.55 3.55 3.55 3.55 3.55 3.55

a Rate constants are represented by k ) ATn exp(B kcal mol-1/ RT) in units of cm3 molecule-1 s-1.

characteristics have been revealed on the basis of the sound ab initio data. The total and individual rate constants for the primary channels of the aforementioned reactions in the temperature range of 298-3000 K are predicted. The four association adducts, IM1, IM2, IM3, and IM4, are dominant in the lowtemperature range (T ) 298-750 K); over 750 K, formation of HNCO + N2 (P2) becomes dominant and the production of HNC + N2O (P1) becomes competitive while the temperature goes higher than 1950 K. Our predicted total and individual rate constants and product branching ratios for this critical reaction may be employed for combustion kinetic modeling applications. Acknowledgment. H.-L.C. would like to acknowledge the National Science Council, Republic of China, under Grant NSC 98-2113-M-034-002-MY2 for the financial support and the financial support by Chinese Culture University. In addition, we are deeply indebted to Professor M. C. Lin (from NCTU, Taiwan, and Emory University, USA) for persistent encouragement and instruction.

Reaction Mechanisms and Kinetics of HNCN with NO Supporting Information Available: Table S1: Relative energies of reactant, intermediates, transition states and products, calculated at various levels of theory. Table S2: Frequencies and moments of inertia for the species involved in the reaction of HNCN + NO, calculated at the B3LYP/6-311++G(3df,2p) level. Figures S1 to S3: IRC calculations for specific transition states, calculated by B3LYP/6-311++G(3df,2p) level. Figure S4: Rotational potential of ∠NNO of the transition state for the IM3 f IM4 isomerization, calculated by B3LYP/6311++G(3df,2p) level. Figure S5: Different 〈∆E〉down tests for the total rate constants as a function of pressure at varied temperatures. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Miller, J. A.; Bowman, C. T. Prog. Energy Combust. Sci. 1989, 15, 287. (2) Miller, J. A.; Walch, S. P. Int. J. Chem. Kinet. 1997, 29, 253. (3) Berman, M. R.; Lin, M. C. J. Phys. Chem. 1983, 87, 3933. (4) Medhurst, L. J.; Garland, N. L.; Nelson, H. H. J. Phys. Chem. 1993, 97, 12275. (5) Dean, A. J.; Hanson, R. K.; C. T. Bowman, C. T. In Proceedings of the 23rd Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1990; p 259. (6) Herzberg, G.; Warsop, P. A. Can. J. Phys. 1963, 41, 286. (7) Wu, M.; Hall, G.; Sears, T. J. J. Chem. Soc., Faraday Trans. 1993, 89, 615. (8) Yamamoto, S.; Saito, S. J. Chem. Phys. 1994, 101, 10350. (9) Clifford, E. P.; Wenthold, P. G.; Lineberger, W. C.; Petersson, G.; Ellison, G. B. J. Phys. Chem. A 1997, 101, 4338. (10) Bise, R. T.; Hoops, A. A.; Neumark, D. M. J. Chem. Phys. 2001, 114, 9000. (11) Tao, F.-M.; Klemperer, W.; Thaddeus, P. J. Chem. Phys. 1994, 100, 3691. (12) Puzzarini, C.; Gambi, A. J. Chem. Phys. 2005, 122, 064316. (13) Berman, M. R.; Tsuchiya, T.; Gregusova, A.; Perera, S. A.; Bartlett, R. J. J. Phys. Chem. A 2007, 111, 6894. (14) Miller, J. A.; Bowman, C. T. Int. J. Chem. Kinet. 1991, 23, 289. (15) Baren, R. E.; Hershberger, J. F. J. Phys. Chem. A 1999, 103, 11340. (16) Adamson, J. D.; DeSain, J. D.; Curl, R. F.; Glass, G. P. J. Phys. Chem. A 1997, 101, 864. (17) Zhu, R. S.; Lin, M. C. J. Phys. Chem. A 2000, 104, 10807. (18) (a) Rim, K. T.; Hershberger, J. F. J. Phys. Chem. A 1998, 102, 4592. (b) Rim, K. T.; Hershberger, J. F. J. Phys. Chem. A 1998, 102, 5898. (c) Baren, R. E.; Hershberger, J. F. J. Phys. Chem. A 2002, 106, 11093. (d) Thweatt, W. D.; Erickson, M. A.; Hershberger, J. F. J. Phys. Chem. A 2004, 108, 74. (e) Meyer, J. P.; Hershberger, J. F. J. Phys. Chem. A 2005, 109, 4772. (19) Liu, P. J.; Pan, X. M.; Zhao, M.; Sun, H.; Wu, Z. M.; Wang, R. S. Chem. J. Chin. UniV. 2004, 25, 685. (20) Chen, H.-T.; Ho, J.-J. J. Phys. Chem. A 2005, 109, 2564. (21) Huang, C. L.; Tseng, S. Y.; Wang, T. Y.; Wang, N. S.; Xu, Z. F.; Lin, M. C. J. Chem. Phys. 2005, 122, 184321. (22) (a) Wei, Z. G.; Huang, X. R.; Sun, Y. B.; Sun, C. C. Chem. J. Chin. UniV. 2004, 25, 2112. (b) Wei, Z. G.; Li, Q. S.; Zhang, S. W.; Sun, Y. B.; Sun, C. C. J. Mol. Struct. (Theochem) 2005, 722, 139. (23) Jin, L.; Ding, Y. H.; Wang, J.; Sun, C. C. J. Comput. Chem. 2006, 27, 883. (24) (a) Chen, H.-L.; Ho, J.-J. J. Mol. Struct. (Theochem) 2006, 772, 93. (b) Chen, H.-L.; Wu, C.-W.; Ho, J.-J. J. Phys. Chem. A 2006, 110, 8893. (c) Chen, H.-L.; Li, H.-J.; Ho, J.-J. Chem. Phys. Lett. 2007, 442, 35. (d) Chen, H.-L.; Zhu, R. S.; Chen, H.-T.; Li, H.-J.; Ju, S.-P. J. Phys. Chem. A 2008, 112, 5495. (25) (a) Becke, A. D. J. Chem. Phys. 1992, 96, 2155. (b) Becke, A. D. J. Chem. Phys. 1992, 97, 9173. (c) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.

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