Quantum Chemical Prediction of Pathways and Rate Constants for ...

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Quantum Chemical Prediction of Pathways and Rate Constants for Reaction of Cyanomethylene Radical with NO Hui-Lung Chen* and Wan-Chun Chao Department of Chemistry and Institute of Applied Chemistry, Chinese Culture University, Taipei, 111, Taiwan

bS Supporting Information ABSTRACT: High-level ab initio calculations have been per formed to study the mechanism and kinetics of the reaction of the cyanomethylene radical (HCCN) with the NO. The species involved have been optimized at the B3LYP/6-311þþG(3df,2p) level, and their corresponding single-point energies are improved by the CCSD(T)/aug-cc-PVQZ//B3LYP/ 6-311þþG(3df,2p) approach. From the calculated potential energy surface, we have predicted the favorable pathways for the formation of several isomers of a HCCN-NO complex. Barrierless formation of HCN þ NCO (P1) is also possible. Formation of HCNO þ CN (P3) is endoergic but may become significant at high temperatures. To rationalize the scenario of our calculated results, we also employ the Fukui functions and hard-and-soft acid-and-base (HSAB) theory to seek possible clues. The predicted total rate coefficient, ktotal, at He pressure 760 Torr can be represented with the equation ktotal = 1.40 10-7 T-2.01 exp(3.15 kcal mol-1/RT) at T = 298-3000 K in units of cm3 molecule-1 s-1. The predicted total rate coefficients at some available conditions (He pressures of 6, 18, and 30 Torr in the temperature of 298 K) are in reasonable agreement with experimental observation. In addition, the rate constants for key individual product channels are provided in different temperature and pressure conditions.

1. INTRODUCTION Since its first discovery in 1964 by Bernheim et al.,1 the cyanomethylene radical (HCCN) has been of interest to several experimentalists2-12 and theoreticians13-25 in the last half-century. The ground electronic state of the HCCN radical was found to be triplet multiplicity. In the early work on this radical, the primary interest was on whether this molecule is linear or bent; thus, most investigations have focused on the HCC bending potential. Early experimental studies based on electron paramagnetic resonance (EPR) technique1 and matrix isolation infrared spectra2 demonstrated that HCCN is a linear triplet molecule in its ground electronic state. In 1990, Brown et al.5 observed the microwave spectra of many isotopically substituted HCCN species and experimentally determined an unusually short CH bond length (0.998 Å), which led to the conclusion that the HCCN may possess a quasi-linear structure. In addition, the evidence for quasi-linearity was further supported by McCarthy et al.,7 who made a millimeter and submillimeter wave measurement of pure rotational lines for HCCN radical in the ground and several excited vibrational levels. Theoretically, a series of ab initio calculations since the late 1970s suggest that the bent cyanomethylene radical possesses the lowest energy structure.13-25 Subsequent calculations continued to support the greater stability of the bent HCCN structure, and the barrier from bent construction to linearity will be decreased with increasing the accuracy of ab initio theory or with enlarging its r 2011 American Chemical Society

basis sets. In higher level CCSD(T) calculations, Seidl et al.16 and Kellogg et al.18 indicated that the linear structure of HCCN radical was predicted to lie only ca. 0.8 kcal/mol higher above the bent conformation. The production of nitrogen oxides (NOx) via the combustion of fossil fuels attracts great interest because these oxides are toxic pollutants in the atmosphere.26 Therefore, the mechanisms and rate parameters for reactions involving nitrogen compounds have been extensively investigated in relation to such air pollutants.27 Numerous authors have reported theoretical and experimental approaches to eliminate NO,28-36 many of which contain cyanogen species as an effective reagent to remove NO. Adamson et al.28 carried out the first time kinetic study of the HCCN radical with nitric oxide (NO) in 1997. They proposed some possible reaction channels and suggested that the hydrogen cyanide (HCN) and the fulminic acid (HCNO) were observed as two major products. They also predicted the rate constant for such reaction using pseudo-first-order methods yielding (3.5 ( 0.6) 10-11 cm3 molecule-1 s-1. However, the diversity and complexity of such reaction mechanism still could not be defined accurately. Hence, a detailed theoretical construction on the potential energy surface and the kinetic prediction of the Received: November 22, 2010 Revised: December 23, 2010 Published: January 21, 2011 1133

dx.doi.org/10.1021/jp111136b | J. Phys. Chem. A 2011, 115, 1133–1142

The Journal of Physical Chemistry A

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HCCN þ NO reaction are very crucial. Here, we present the reaction mechanism of HCCN þ NO that provides an efficient route to remove NO. In addition, we carried out variational transition state theory (VTST) and Rice-Ramsperger-Kassel-Marcus (RRKM) Table 1. Electron Affinities (EA) and Single-Triplet Splitting Energies of HCCN Calculated at Various Levels of Theory and Some Experimental Data from the Literature EAa level of theory

S-T splittingb

(eV)

(eV)

MP2/6-31þþG(d,p)

1.987

MP2/6-311þþG(3df,2p)

2.336

B3LYP/6-31þþG(d,p)

1.967

0.700

B3LYP/6-311þþG(3df,2p) CCSD(T)/aug-cc-PVDZ //

2.002 1.841

0.682 0.511

1.969

0.513

2.004

0.507

2.003 ( 0.014c

0.481 ( 0.252d

B3LYP/6-311þþG(3df,2p) CCSD(T)/aug-cc-PVTZ // B3LYP/6-311þþG(3df,2p) CCSD(T)/aug-cc-PVQZ // B3LYP/6-311þþG(3df,2p) experiment a

-

0.516 ( 0.013c

Energy difference between anion HCCN and neutral HCCN. b Energy difference between the triplet and the singlet electronic states of HCCN. c Reference 21. d Reference 22.

calculations on the basis of the energies and structures predicted by a high-level molecular orbital method.

2. COMPUTATIONAL METHOD Ab initio molecular orbital calculations are carried out using the Gaussian 03 suite of programs.37 The geometrical structures of all relevant reactants, intermediates, transition states, and products for the HCCN þ NO reaction in the gas phase are optimized using the hybrid density functional B3LYP method with a 6-311þþG(3df,2p) basis set.38,39 Frequency calculations are performed at the same level to check whether the obtained stationary points are local minima or saddle points, and the reactants, intermediates, and products possess all real frequencies, whereas transition states have only one imaginary frequency. Zeropoint energy (ZPE) corrections are also considered at B3LYP/ 6-311þþG(3df,2p) level. Intrinsic reaction coordinates (IRC)40 calculations are performed at the same level of theory to actually establish the link between the transition state and the intermediates. To obtain more reliable energies, we perform single-point calculations employing a coupled-cluster technique with single and double excitations and evaluations by perturbation theory of triple contributions CCSD(T)41,42 on the basis of the geometries optimized at the B3LYP/6-311þþG(3df,2p) level. The highest level of theory attained in this work is thus denoted CCSD(T)/augcc-PVQZ//B3LYP/6-311þþG(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

Figure 1. Schematic diagram of proposed paths for the reaction of HCCN þ NO. 1134

dx.doi.org/10.1021/jp111136b |J. Phys. Chem. A 2011, 115, 1133–1142


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Figure 2. The optimized geometries of the relevant transition states on the potential energy surfaces of HCCN þ NO reactions calculated at the B3LYP/6-311þþG(3df,2p) level. Bond lengths are given in Å, and angles are in degrees. 1135



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

computed with the VTST and microcanonical RRKM theory43,44 using the VariFlex45 program.

3. RESULTS AND DISCUSSION As shown in Table 1, we first present data for the electron affinities (EA) and singlet-triplet splitting energies of HCCN radical calculated at varied levels of theory with pertinent experimental data from the literature. The electron affinity (EA) predicted by the hybrid density functional B3LYP method with a 6-311þþG(3df,2p) basis set is 2.002 eV, which is in good agreement with experimental value (2.003 ( 0.014 eV),21 whereas the calculated B3LYP energy for singlet-triplet splitting energy of HCCN radical, 0.682 eV, substantially overestimates the experimental values (0.516 ( 0.01321 and 0.481 ( 0.252 eV,22 respectively). For this reason, we perform a single-point energy calculation at the level CCSD(T)/aug-cc-PVQZ on the basis of the geometry obtained from B3LYP/6-311þþG(3df,2p) and obtain a satisfactory result, 0.507 eV, which is much closer to the experimental values. In addition, we employ the same method to predict the ionization energy of NO and the electron affinities of NCO and CN (NO, NCO, and CN molecules are important reactants and products in the title reaction), and the results; IE(NO) = 9.20 eV, EA(NCO) = 3.62 eV, and EA(CN) = 3.90 eV; are all in satisfactory agreement with the experimental data (9.263 ( 0.01,46 3.609 ( 0.005,47 and 3.862 ( 0.004 eV,47

respectively). In this regard, we choose CCSD(T)/aug-ccPVQZ//B3LYP/6-311þþG(3df,2p) as the method for an energetic calculation of all possible processes in the reaction system of HCCN þ NO. As depicted in Figure 1, we categorized the examined reaction into seven paths, A;G, corresponding to seven possible product formation channels. The intermediates are correspondingly numbered as IM1-IM11; seven possible channel products, HCN þ NCO, HCN þ CNO, HCNO þ CN, HCC þ N2O, HCCO þ N2, HC(C)O þ N2, and HCON þ CN, are labeled in the same order of P1-P7. TS1-TS15, TSiso1-TSiso3 denote the transition-state species connecting two intermediates located at local minima. The geometries of the relevant reactants, intermediates, and products optimized at the B3LYP/ 6-311þþG(3df,2p) level are shown in Figure S1 (Supporting Information) and Figure 2, respectively. The potential energy surfaces (PESs) calculated at the CCSD(T)/aug-cc-PVQZ// B3LYP/6-311þþG(3df,2p) level are shown in Figure 3. All the calculated energetics for the reactants, intermediates, transition states, and products are tabulated in Tables 2 and 3. Among them, the zero-point energy (ZPE) corrections are included, and energies with respect to the reactants (HCCN þ NO) calculated at the CCSD(T) level are denoted as CRE. As shown in Table 2, the predicted heats of reaction for production of HCN þ NCO (P1), HCNO þ CN (P3), and HCCO þ N2 (P5) are -74.30, 1136



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Table 2. Zero-Point Vibration Energies (ZPE, Hartree), Total Energies (TE, Hartree), and Relative Energies (RE, kcal/mol) of Reactants, Intermediates, and Products Calculated at the B3LYP/6-311þþG(3df,2p) (BTE) and CCSD(T)/aug-cc-PVQZ// B3LYP/6-311þþG(3df,2p) (CTE, CRE) Levels for the Reaction of HCCN þ NO ZPEa

BET þ ZPEb

CTE þ ZPEb

CREc

R(HCCN þ NO)

0.021844

-261.386636

-260.961620

0.00

IM1

0.031533

-261.480765

-261.056934

-59.81

IM2

0.031071

-261.481392

-261.057042

-59.88

IM3

0.029648

-261.410538

-260.982548

-13.13

IM4 IM5

0.029814 0.029069

-261.399908 -261.402335

-260.971098 -260.979072

-5.95 -10.95

IM6

0.028827

-261.402481

-260.978286

-10.46

IM7

0.030579

-261.413511

-260.997588

-22.57 -18.47

IM8

0.032459

-261.405579

-260.991049

IM9

0.029186

-261.368720

-260.952916

5.46

IM10

0.032404

-261.419607

-261.004726

-27.05

experimentd

IM11

0.029485

-261.465019

-261.036991

-47.30

P1(HCN þ NCO) P2(HCN þ CNO)

0.026340 0.024224

-261.500669 -261.402229

-261.080022 -260.981559

-74.30 -12.51

-75.66 ( 3.34

P3(HCNO þ CN)

0.024248

-261.361755

-260.944733

10.60

7.94 ( 4.54

P4(HCC þ N2O)

0.023783

-261.345564

-260.931581

18.85

P5(HCCO þ N2)

0.024348

-261.528371

-261.110871

-93.66

P6(HC(C)O þ N2)

0.024350

-261.439165

-261.027749

-41.50

P7(HCON þ CN)

0.021057

-261.207386

-260.790768

107.21

-95.06 ( 4.34

a

Zero-point energy (au) at the level B3LYP/6-311þþG(3df,2p). b The unit of energy is hartree. c Relative energy (kcal/mol) with respect to the reactants. d References 22 and 48.

10.60, and -93.66 kcal/mol, respectively; they agree satisfactorily with experimental values -75.66 ( 3.34, 7.94 ( 4.54, and -95.06 ( 4.34 kcal/mol. The experimental values are derived from the given experimental heats of formation: HCCN (115.6 ( 5.0 kcal/mol),22 NO (21.46 ( 0.04 kcal/mol),48a HCN (30.9 ( 0.7 kcal/mol),48b NCO (30.5 ( 1.0 kcal/mol),48c CN (104.1 ( 0.5 kcal/mol),48d and HCCO (42.0 ( 0.7 kcal/mol).48e In addition, the heat of formation of HCNO (40.9 kcal/mol) was rigorously calculated using the ab initio approach by Schuurman et al.48f As shown in Figure 1, our calculated results have shown that there are two possible orientations exist for C-N, N-N, and C-O bond addition, and these six separated adducts, IM1-IM6, lead to completely different follow-up reaction mechanisms and different product formations. First of all, with regard to C-N bond combination, our calculated results for channels A-C are RfIM1fTS5fIM7fTS11fP1, RfIM1f TS6fIM8fTS12fP2, and RfIM2fP3, respectively. All these courses involve first the formation of an adduct HC(NO)CN, which has two isomers, cis-HC(NO)CN (IM1) and trans-HC(NO)CN (IM2). Even though the trans-isomer is somewhat more stable than the cis-isomer by 0.07 kcal/mol, they might interchange promptly on conquering a small energy barrier of ca. 13.6 kcal/mol (TSiso1). For channel A, the initial step involves the barrierless entrance to the adduct isomer IM1 with an exothermicity of 59.81 kcal/mol. The cis-isomer (IM1) can form a cyclic intermediate (IM7) via a very tight four center transition state (see TS5 in Figure 2) whose energy is 15.99 kcal/mol below the reactants. In TS5, the forming C-O bond, 1.687 Å, is 0.275 Å longer than that in IM7. It may then go further by passing a barrier (TS11, -5.85 kcal/mol) to open the ring by breaking two C-C and N-O bonds concurrently and to form the products of

HCN þ NCO (P1) with an overall exothermicity of 74.30 kcal/mol. However, for channel B, the IM1 adduct will proceed another pathway, via TS6 (E a = -14.81 kcal/mol with respect to the reactants), to form a five-membered ring intermediate, IM8. It will then simultaneously break two C-C and N-O bonds to produce HCN þ CNO (P2, -12.51 kcal/mol) via a five-membered-ring transition-state TS12 lying 36.80 kcal/mol above IM8 (or 18.33 kcal/ mol above the reactants). For channel C, after the formation of trans-HC(NO)CN (IM2), it can then directly produce the final products HCNO þ CN (P3) via a direct dissociation process with pertinent endothermicity of 10.60 kcal/mol. Second, with regard to N-N bond formation, our calculated results for channels D-Fa are RfTS1fIM3fTS7fP4, RfTS2fIM4fTS8fIM9fTS13fP5, and RfTS2f IM4fTS9fIM10fTS14fIM11fTS15fP6, respectively. Similarly, these pathways involve the formation of another adduct HCCN(NO), which also has two isomers, transHCCN(NO) (IM3) and cis-HCCN(NO) (IM4). The relative energy difference between cis- and trans-isomers is around 7.2 kcal/mol, and the activation energy required for the interconversion is a little high (TSiso2, 16.44 kcal/mol). The highest barrier in channel D is 26.20 kcal/mol (TS7), while the latter two channels (E and Fa) are 20.13 kcal/mol equally through TS2. Third, for C-O bond conjunction cases, P6 (HC(C)O þ N2) and P7 (HCON þ CN) products could also be formed via the channels Fb and G. The highest barrier in the former pathway (Fb: RfTS3fIM5fTS10fIM10f TS14fIM11fTS15fP6) is 12.97 kcal/mol (via TS3), while the latter channel (G: RfTS4fIM6fP7) should overcome a huge energetic dissociation process and should be highly endothermic by 107.21 kcal/mol. 1137



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On the basis of the above comparison, our calculated results indicate that both channels A and C are two major possible channels of the title reaction (HCCN þ NO); channel A, Rf IM1fTS5fIM7fTS11fP1, can be expected as the most dominant channel. Our theoretical prediction also agrees satisfactorily with the experimental observation by Adamson et al.28 in which they stated that the hydrogen cyanide (HCN) was a major product of HCCN þ NO reaction, and fulminic acid (HCNO) formation was attributed to secondary contribution. They also suggested that the HCNO could not be a primary product at room temperature because of the endoergicity of the process. From the aforesaid outcomes, it is found that the HCCN þ NO reaction may form two predominant adducts, IM1 and IM2, which are energetically more stable than the reactants by 59.81 and 59.88 kcal/mol, respectively. In addition, the formation of other subordinate adducts;IM3, IM4, IM5, and IM6;are also possible even though these procedures involve some energy barrier and heat absorption. Obviously, the former two adducts

possess much higher stability than the others. To explore this specific phenomenon, we calculate the Fukui functions49,50 and apply the theory of hard-and-soft acid-and-base (HSAB) to seek the possible clues. The extrapolation of the usual behavior soft likes soft and hard likes hard locally, together with the concept of 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.51-57 Gazquez and Mendez58 also stated that the largest value of the Fukui function is generically associated with the most reactive site. In our calculation for N electrons in a system, independent calculations

Table 3. Zero-Point Vibration Energies (ZPE, Hartree), Total Energies (TE, Hartree), and Relative Energies (RE, kcal/mol) of All Transition States Calculated at the B3LYP/ 6-311þþG(3df,2p) (BTE) and CCSD(T)/aug-cc-PVQZ// B3LYP/6-311þþG(3df,2p) (CTE, CRE) Levels for the Reaction of HCCN þ NO ZPEa

BET þ ZPEb

CTE þ ZPEb

CREc

TS1

0.024463

-261.373282

-260.929159

20.37

TS2

0.024819

-261.368888

-260.929546

20.13

TS3

0.025945

-261.368130

-260.940948

12.97

TS4

0.025672

-261.366932

-260.939438

13.92

TS5

0.028858

-261.406690

-260.987107

-15.99

TS6 TS7

0.030743 0.026562

-261.402414 -261.340885

-260.985217 -260.919870

-14.81 26.20

TS8

0.027160

-261.355890

-260.936188

15.96

TS9

0.028802

-261.361577

-260.937079

15.40

TS10

0.029491

-261.361430

-260.946493

9.49

TS11

0.027469

-261.388747

-260.970938

-5.85

TS12

0.027260

-261.361171

-260.932410

18.33

TS13

0.026235

-261.354839

-260.936024

16.06

TS14 TS15

0.029939 0.025150

-261.416394 -261.429294

-260.998072 -261.015141

-22.87 -33.59

TSiso1

0.029922

-261.463077

-261.035340

-46.26

TSiso2

0.028222

-261.366544

-260.935425

16.44

TSiso3

0.027951

-261.377337

-260.950913

6.72

a

Zero-point energy (au) at the level B3LYP/6-311þþG(3df,2p). b The unit of energy is hartree. c Relative energy (kcal/mol) with respect to the reactants.

Figure 4. Predicted rate constants of (a) kM1, kM2, kP1, and kP3 and (b) the total rate constants (ktotal = kM1 þ kM2 þ kP1 þ kP3) at He pressure of 760 Torr in the temperature range of 298-3000 K.

Table 4. Condensed Fukui Functions for H, CH,a C, and N atoms in HCCN, and N and O atoms in NO, and Global and Local Softnesses of the Molecules Calculated at the Level CCSD(T)/aug-cc-PVQZ//B3LYP/6-311þþG(3df,2p) f0b

local softness (s0)d

molecule

H

C Ha

C

N

HCCN

0.021

0.753

0.316

0.541

NO

0.610

O

global softness Sc

H

CHa

C

N

3.182

0.067

2.397

1.005

1.722

0.390

2.517

1.535

O

0.982

CH signifies the carbon atom near the hydrogen atom. b Atomic charges according to a natural population analysis. c S = 1/(IE - EA) with ionization energy IE and electron affinity EA; the energy unit is hartree. d s0 = f 0 3 S. a

1138



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Table 5. Predicted Total Rate Constantsa for HCCN þ NO Reaction at the He Pressures of 6, 18, and 30 Torr at a Temperature of 298 K and Corresponding Experimental Data from the Literature total pressures

predicted by RRKM theory

experimentb

6 Torr

1.49 10-11

4.0 10-11

-11

3.3 10-11

18 Torr 30 Torr a

Figure 5. Predicted branching ratios for the principal reaction channels of HCCN þ NO reactions at 760 Torr He pressure in the temperature range of 298-3000 K.

are made for the corresponding (N - 1), N, and (N þ 1) electron systems with the same geometry. A natural population analysis yields qk(N - 1), qk(N), and qk(N þ 1) for the predicted possible sites of reaction of HCCN and NO molecules, and the Fukui function is calculated as a difference of population between N and N þ 1 or N and N - 1 electron systems. We will choose the f 0 value for comparison as this title reaction is more representative of a radical system.50 On the basis of our calculated data in Table 4, it is found that the largest Fukui function (f 0, 0.753) is on the CH (the subscript H symbol signifies the carbon atom near the hydrogen atom) atom in the HCCN molecule and that of the other reactant NO is on the N atom (0.610), which accounts for the formation of the complexes, IM1 and IM2, being more favorable than other complexes (such as IM3, IM4, IM5, and IM6). Applying the HSAB theory, we find also that the largest values for the local softness s0 for both reactants are on the CH atom of HCCN and on the N atom of NO (2.397 and 1.535, respectively), which also accounts for the effective formation of the adducts IM1 and IM2. Moreover, we also carried out a kinetic study employing variational TST and RRKM theory.43,44 We have employed the Variflex code45 to deal with all low-lying reaction channels (as shown in the following scheme) including isomerization processes by solving the T- and P-dependent master equation.

In our kinetic predictions, the reverse dissociation of the energized intermediates IM1 and IM2 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 tabulated in Table S1 (Supporting Information). In the scheme above, * indicates an activated molecule and M is the third body (He in this

2.69 10 3.48 10 3

-11

-1 -1 b

Rate constants are in units of cm molecule

3.6 10-11

s . Reference 28.

work). The Lennard-Jones (LJ) parameters employed for the HCCN þ NO reaction are as follows: for He,59 σ = 2.55 Å and ε/k = 10.0 K; for HCCN-NO, σ = 3.90 Å and ε/k = 205.0 K, which are approximated to be the same as that of NCO-NO system.29 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 HCCN þ NO f IM1 and IM2, 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.43,44,60 The barrierless association minimum energy path is approximately presented by the Morse potential function, V(R) = De{1 - exp[-β(R - R0)]}2. Among which, De is the bond energy excluding zero-point energy, and R0 is the equilibrium value of R. The three parameters of this Morse potential function are R0 = 1.289 Å, β = 4.022 Å-1, and De = 65.89 kcal/mol for formation IM1 and R0 = 1.288 Å, β = 4.040 Å-1, and De = 65.67 kcal/mol for formation IM2. Also, 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 transitional mode 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 down value (the mean energy transferred per collision) of 150 cm-1 for He. In principle, the different down values should be determined by comparing the experimental pressure-dependent rate constants with the calculated values using the exponential down model in the solution of the master equation. Since there is no experimental value available for this system, our selected value of down for He, 150 cm-1, is approximately taken from the published computational works.61-63 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. In the RRKM calculations, we neglect the paths for P2 and P4-P7 formations since their energy barriers are much greater than our proposed predominant channels. The predicted values for kM1, kM2, kP1, and kP3 are shown in Figure 4a, and the total rate constants (ktotal = kM1 þ kM2 þ kP1 þ kP3) at He pressure of 760 Torr in the temperature range 298-3000 K are shown in Figure 4b. The values of kM1 and kM2 decrease gradually with increasing temperature. The values of kP3 have strong positive temperature dependence over the entire range of temperature, whereas kP1 appears to be nearly independent of temperature. The branching ratios for the four principal reaction channels (RIM1, RIM2, RP1, and RP3) at He pressure of 760 Torr in the temperature range of 298-3000 K are shown in Figure 5. 1139



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Table 6. Predicted Rate Expressionsa of kM1, kM2, kP1, and kP3 at the He Pressures of 5 Torr, 100 Torr, 380 Torr, 760 Torr, 10 atm, 50 atm, and 100 atm in the Temperature Range of 298-3000 K reaction kM1

kM2

kP1

kP3

P

A

ktotal = 1.40 10-7 T-2.01 exp(3.15 kcal mol-1/RT) at T = 298-3000 K, in units of cm3 molecule-1 s-1. At present, no comparison can be made for the experimental data when the pressures and temperatures are higher than 30 Torr and 298 K. As our main interest in the present work is to evaluate the rate coefficients at higher pressures and temperatures relevant to combustion, this critical reaction might be employed for future applications in modeling combustion kinetics.

n

B

5 Torr

1.23 10

63

-24.56

-19.56

100 Torr

5.04 1063

-24.27

-20.44

380 Torr

1.42 1064

-24.21

-20.98

760 Torr

2.25 1064

-24.17

-21.29

10 atm

4.88 1064

-23.94

-22.33

50 atm

2.05 1064

-23.61

-22.95

100 atm 5 Torr

8.37 1063 5.33 1062

-23.40 -24.39

-23.15 -19.58

100 Torr

1.26 1064

-24.39

-20.57

380 Torr

4.24 1064

-24.36

-21.12

760 Torr

7.06 1064

-24.33

-21.42

10 atm

1.63 1065

-24.11

-22.47

50 atm

7.15 1064

-23.78

-23.10

100 atm

2.96 1064

-23.58

-23.30

5 Torr 100 Torr

1.22 10-15 2.70 10-14

0.37 0.01

3.23 2.08

380 Torr

1.78 10-13

-0.22

1.35

760 Torr

5.25 10-13

-0.34

0.91

10 atm

2.78 10-11

-0.81

-0.83

50 atm

4.22 10-10

-1.12

-2.24

’ ASSOCIATED CONTENT

bS

-9

100 atm

1.12 10

-1.22

-2.86

5 Torr

7.06 10-22

2.08

-8.26

100 Torr 380 Torr

7.06 10-22 7.06 10-22

2.08 2.08

-8.26 -8.26

760 Torr

7.06 10-22

2.08

-8.26

10 atm

7.06 10-22

2.08

-8.26

50 atm

7.42 10-22

2.07

-8.28

100 atm

8.83 10-22

2.05

-8.33

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

4. CONCLUSION We have presented in this work a direct theoretical study on the reaction mechanisms and kinetics for the HCCN þ NO reaction using the high-level CCSD(T) approach. The total and individual rate constants for the primary channels of the aforementioned reactions in the temperature range of 2983000 K are predicted. Kinetics results show that the reaction of HCCN with NO producing cis-HC(NO)CN (IM1) and trans-HC(NO)CN (IM2) adducts are dominant below 1200 K; over 1200 K, formation of HCN þ NCO (P1) becomes predominant and the production of HCNO þ CN (P3) becomes competitive. The equations for the individual and total rate constants are given; the predicted total and individual rate constants and product branching ratios for this critical reaction may be employed for combustion kinetic modeling applications.

Supporting Information. Table S1: Frequencies and moments of inertia for the species involved in the reaction of HCCN þ NO calculated at the B3LYP/6-311þþG(3df,2p) level. Figure S1: Optimized geometries of the relevant reactants, intermediates, and products on potential energy surfaces of HCCN þ NO reactions calculated at the B3LYP/6-311þþG(3df,2p) level. This material is available free of charge via the Internet at http://pubs.acs.org.

a

’ AUTHOR INFORMATION Corresponding Author

The predicted results indicate that, in the temperature range of 298-1200 K, the deactivation of IM1 and IM2 are dominant (RM1 and RIM2 both account for 0.50-0.33). The results imply that, at low temperatures, IM1 and IM2 can be steadily formed from HCCN þ NO and will then start to dissociate as the temperature goes higher than 1200 K. However, in the higher temperature range (1200-1950 K), the branching ratio for RP1 (0.33-0.99) which forms HCN þ NCO (P1) becomes the most significant product. Besides, it is found also that the formation of HCNO þ CN (P3) turns to a certain extent competitive as the temperature goes higher than 1950 K. Compared with the previous experimental values (as shown in Table 5), the total rate constants predicted here at different pressures (6, 18, and 30 Torr) for the title reaction are consistent with the experimental observation by Adamson et al.,28 although there is a little discrepancy at the lower pressure. In Table 6, we summarize the rate expressions (kM1, kM2, kP1, and kP3) at seven specific pressures between 5 Torr and 100 atm in the temperature range 298-3000 K. In this range, the values of kM1, kM2, and kP1 depend strongly on pressure, but the values of kP3 are independent of pressure. The predicted total rate coefficient, ktotal, at He pressure 760 Torr can be represented with an equation:

*E-mail: [email protected]. Tel: þ886-2-28610511 ext 25313. Fax: þ886-2-28614212.

’ ACKNOWLEDGMENT H.-L. Chen would like to acknowledge the (1) National Science Council, Republic of China, under Grant Number NSC 98-2113-M-034-002-MY2 for the financial support, (2) the financial support by Chinese Culture University, and (3) National Center for High-performance Computing, Taiwan, for the use of computer time. In addition, we are deeply indebted to Professor M. C. Lin (from NCTU, Taiwan, and Emory University, United States) for persistent encouragement and instruction. ’ REFERENCES (1) Bernheim, R. A.; Kempf, R. J.; Humer, P. W.; Skell, P. S. J. Chem. Phys. 1964, 41, 1156. (2) Wasserman, E.; Yager, W. A.; Kuck, V. J. Chem. Phys. Lett. 1970, 7, 409. (3) Dendramis, A.; Leroi, G. E. J. Chem. Phys. 1977, 66, 4334. (4) Saito, S.; Endo, Y.; Hirota, E. J. Chem. Phys. 1984, 80, 1427. 1140


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