Kinetics of Hydrogen Abstraction Reactions of Butene Isomers by OH

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Kinetics of Hydrogen Abstraction Reactions of Butene Isomers by OH Radical Hongyan Sun* and Chung K. Law Department of Mechanical and Aerospace Engineering, Princeton UniVersity, Princeton, New Jersey 08544, United States ReceiVed: July 7, 2010; ReVised Manuscript ReceiVed: September 13, 2010

The rate coefficients of H-abstraction reactions of butene isomers by the OH radical were determined by both canonical variational transition-state theory and transition-state theory, with potential energy surfaces calculated at the CCSD(T)/6-311++G(d,p)//BH&HLYP/6-311G(d,p) level and CCSD(T)/6-311++G(d,p)//BH&HLYP/ cc-pVTZ level and quantum mechanical tunneling effect corrected by either the small-curvature tunneling method or the Eckart method. While 1-butene contains allylic, vinylic, and alkyl hydrogens that can be abstracted to form different butene radicals, results reveal that s-allylic H-abstraction channels have low and broad energy barriers, and they are the most dominant channels which can occur via direct and indirect H-abstraction channels. For the indirect H-abstraction s-allylic channel, the reaction can proceed via forming two van der Waals prereactive complexes with energies that are 2.7-2.8 kcal mol-1 lower than that of the entrance channel at 0 K. Assuming that neither mixing nor crossover occurs between different reaction pathways, the overall rate coefficient was calculated by summing the rate coefficients of the s-allyic, methyl, and vinyl H-abstraction paths and found to agree well with the experimentally measured OH disappearance rate. Furthermore, the rate coefficients of p-allylic H abstraction of cis-2-butene, trans-2-butene, and isobutene by the OH radical were also determined at 300-1500 K, with results analyzed and compared with available experimental data. 1. Introduction The hydrogen-abstraction reaction of alkenes by the hydroxyl radical is dominant at temperatures above 700 K due to the fewer and less efficient stabilizing collisions of the addition adducts which tend to decompose thermally and rapidly before further reaction.1,2 Huynh et al.3 recently studied the kinetics of enol formation from the reaction of OH with propene and found that allylic H-abstraction is more significant than addition reactions in the overall rate with a branching ratio that is more than 90% in the temperature range of 500-1500 K. More recently, Za´dor et al.4 reported that allyl radical formation in the reaction of propene + OH is the most dominant bimolecular channel above 800 K by determining the branching fractions for various bimolecular product channels at atmospheric pressure, and it turns out to be the most dominant channel at all temperatures under collisionless condition. These results indicate that allylic H-abstraction reactions by the OH radical are critical in the intermediate temperature regime for combustion of unsaturated hydrocarbon fuels due to the low energy barrier and large exothermicity. There were a number of theoretical and experimental studies on the elementary reactions of the OH radical with ethene and propene.1-8 Butene is then the next step toward understanding OH reactions with the unsaturated hydrocarbon homologue, and it is the smallest alkene with isomers. The H-abstraction reactions of isomeric butenes + OH generate methylallyl radicals that undergo unimolecular dissociation leading to the formation of butadienes, propyne, and allene, which in turn are involved in the formation of polycyclic aromatic hydrocarbons and soot. Furthermore, addition of the OH radical to the double bond in butene can lead to the formation of butenols, which * To whom correspondence should be addressed. Fax: (609) 258-6233. E-mail: [email protected].

are the common intermediates found in hydrocarbon flames.9 The reactions are also important in understanding the OHinitiated oxidation of butanols, where the unimolecular dissociation of the β-hydroxybutyl radicals at elevated temperatures leads to isomeric butenes + OH. While the addition reactions of butenes + OH are dominant at lower temperatures, the allylic H-abstraction reactions are not negligible at lower temperatures and they are dominant at higher temperatures. However, at temperatures above 400 K, only few quantitative measurements are available on the reactions of butenes with OH for a very limited temperature range. Specifically, Tully2 measured the absolute rate coefficients for the reactions of the OH radical with ethane and 1-butene over the temperature range of 650-901 K by using laser-induced fluorescence. Later, Smith10 measured the rate constants of OH reacting with l-butene, trans-2-butene, isobutene, and 2,3dimethyl-2-butene at 1225-1259 K by using laser pyrolysis/ laser fluorescence. Consequently, most rate parameters for the H-abstraction reactions in the kinetic mechanism of butene isomer oxidation were estimated by generic reactions.11,12 Recently, Huynh et al.13 studied the kinetics of the vinylic hydrogen-abstraction reaction between the OH radical and alkene (CdC) to form water and the alkenyl radical (CdC•) using the reaction class transition-state theory (RC-TST) combined with linear energy relationship and barrier height grouping approaches. However, the strongly bounded vinylic hydrogens play a much smaller role in H-abstraction reactions of alkenes + OH as compared to the weakly bounded allylic and methyl hydrogens, in which the detailed chemical kinetics remains to be studied further. The allylic H-abstraction reactions of butenes by the OH radical have low and broad classical barriers compared with those of vinylic and methyl H abstractions, which can cause a shift in the position of the dynamical bottleneck as well as the

10.1021/jp1062786  2010 American Chemical Society Published on Web 10/26/2010

Kinetics of Hydrogen Abstraction Reactions

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Figure 1. One of the transition-state structures for s-allylic H abstraction of 1-butene by OH radical optimized at the (a) BH&HLYP//6-311G(d,p) and (b) CCSD/6-31G(d) level.

recrossing effect. Therefore, the variational transition-state theory was applied based on the potential energy surfaces from ab initio and DFT studies to determine the rate coefficients of allylic H-abstraction reactions of the four butene isomers by the OH radical. Furthermore, the rate coefficients of methyl and vinylic H abstractions of 1-butene + OH were calculated by the canonical transition-state theory to determine the total H-abstraction rate coefficients. These rate parameters are useful to study the effects of molecular structure on the chemical reactivity of isomers and are also critical to the kinetic mechanisms involving oxidation of butenes, butanes, butanols, and other C4 hydrocarbons. 2. Computational Details 2.1. Electronic Structures. Since the accuracy in the calculation of rate coefficients depends greatly on the quality of the optimized geometry, it is necessary to select a suitable method to locate reliable transition-state geometries. For the allylic H-abstraction reactions of isomeric butenes by the OH radical, it was found that the density functional B3LYP method predicts a reactant-like transition state for the abstraction of p-allyl hydrogen, and it cannot locate a transition state for the abstraction of s-allyl hydrogen in 1-butene. The HF/6-31(d) geometry optimization of s-allyl H abstraction in 1-butene + OH predicts the abstracted allylic hydrogen midway between the allylic carbon and oxygen. Specifically, the cleaving allylic C-H bond length is 1.268-1.278 Å and the forming O-H bond length is 1.282-1.268 Å, while the imaginary frequency for the stretching O-H bond is rather large, ca. 3000 cm-1, as expected in lower level calculations. The MP2/6-31(d) geometry optimization predicts a transition-state geometry with the abstracted s-allylic hydrogen closer to the allylic carbon; specifically, the cleaving allylic C-H bond length is 1.203-1.212 Å, and the forming O-H bond length is 1.300-1.317 Å. It is known that the MP2 method is not reliable for unsaturated radicals with high-spin contamination,14 since the wave functions of the open-shell system are often contaminated by contributions from higher spin states (S + 1 and S + 2, etc.) that could lead to erroneous energies to affect the shape of a potential energy surface, which is especially significant for most unsaturated radicals.15 An effective way to reduce the spin contamination is the use of coupled-cluster theory because of its infinite order electron correction effects.16 It was found that the coupled cluster

method with the split valence basis set, CCSD/6-31G(d), predicts the cleaving s-allyl C-H bond length of 1.217 Å and the forming O-H bond length of 1.350 Å, with an imaginary frequency of 1672 cm-1 for the stretching O-H bond. The geometrical parameters obtained at the CCSD level in fact represent the accurate transition-state structure for the s-allyl H abstraction, recognizing nevertheless that calculations of the geometry and vibrational frequencies of the transition state for this five heavy atom system using the coupled cluster method is quite computationally time demanding. Alternatively, the BH&HLYP//6-311G(d,p) geometry optimization, which uses Becke’s half and half nonlocal exchange17 with the Lee-Yang-Parr (LYP)18 correlation functionals and the split valence basis set, was found to be able to capture the transition-state structure of the s-allylic H abstraction similar to that of the CCSD/6-31G(d) optimization. It predicts the cleaving s-allyl C-H bond length of 1.190 Å and forming O-H bond length of 1.369 Å, with an imaginary frequency of 1154 cm-1 for the stretching O-H bond. For s-allylic H abstraction in 1-butene + OH, one of the transition-state structures optimized at the BH&HLYP//6-311G(d,p) and CCSD/6-31G(d) levels are shown in Figure 1. It is seen that the structural difference at the two calculation levels is small: 0.01-0.03 Å in bond length, 0.1-1.4° in bond angle, and 0.1-1.9° in dihedral angle except for the dihedral involving O and H atoms from the OH radical in the transition region. This indicates that the BH&HLYP geometry optimization has sufficient accuracy to predict the transition-state properties for the H-abstraction reactions by the OH radical with computation time efficiency. It is noted that the BH&HLYP geometry optimization has been adopted to predict accurate TS structures for the H-abstraction reactions of alkane, alkene, and aldehyde by the OH radical.19,20 Consequently, the BH&HLYP//6-311G(d,p) method was applied to determine the geometries of the stationary points of the potential energy surface and also the minimum energy paths (MEP) of allylic H-abstraction reactions of isomeric butenes + OH. Geometry optimization was followed by vibrational frequency analysis to verify the stationary points for local minima (number of imaginary frequencies, NIMAG ) 0) or first-order saddle points (number of imaginary frequencies, NIMAG ) 1). Furthermore, Dunning’s correlation-consistent polarized valence triple-ζ basis set (cc-pVTZ)21 was also applied with the BH&HLYP method to calculate the geometries and

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vibrational frequencies for the stationary points of the potential energy surface of isomeric butenes with OH. To increase the accuracy of the computed potential energy surfaces, single-point energy calculations were applied using the CCSD(T) method with the split valence basis set which was augmented with diffuse and polarization functions, 6-311++G(d,p). It was found that the value of T1 diagnostic22,23 from the CCSD(T)/6311++G(d,p) calculations is less than 0.01 for stable species and less than 0.026 for radicals and transition states involved in the target reactions, indicating that the single-reference method is reliable for energies in chemical accuracy (within 1 kcal mol-1) for the reactions of butene + OH. All electronic structure calculations were performed by using the Gaussian03 program package.24 2.2. Rate Coefficients. The rate coefficients of allylic Habstraction reactions were calculated using the canonical variational transition-state theory (CVT).25 Briefly, the CVT thermal rate constants were determined by varying the location of the dividing surface along the reaction coordinate, s, to minimize the generalized transition-state rate constants, kGT(T,s). Thus, the CVT thermal rate constants, kCVT(T,s), at temperature T are given by

kCVT (T) ) min{kGT f f (T, s)} ) s

{

min κ(T)σ s

kBT QGT(T) {-∆V(s)/kBT} e h QR(T)

}

(1)

where the reaction coordinate s is the distance along the minimum energy path (MEP) from the saddle point and for each s a generalized transition state is defined perpendicular to the MEP and intersecting it at that s. Furthermore, QGT(T) is the partition function of the generalized transition state, QR(T) the reactant partition function per unit volume, σ the symmetry number, ∆V(s) the classical potential energy along the minimum energy reaction path with the zero of energy at the reactants, and κ(T) the transmission coefficient accounting for quantum mechanical tunneling effects, and kB and h are the Boltzmann and Planck constants, respectively. The partition functions, QGT(T) and QR(T), were calculated with the framework of the rigid-rotor-harmonic-oscillator approximation with correction for internal rotations. Specifically, the vibrational and rotational partition functions were calculated by standard statistical mechanics using the moments of inertia and frequencies determined at the BH&HLYP/6-311G(d,p) level. The BH&HLYP harmonic frequencies were scaled by a factor of 0.935 to calculate the vibrational partition functions. This scaling factor was determined by fitting the calculated frequencies vs experimental data for the four butene isomers,26,27 and it was found to be in agreement with those used by Izsa´k et al.8 and Guthmuller et al.28 at the same level of the theory. Furthermore, only the ground state was used to calculate the electronic partition function, except for the hydroxyl radical. This is because the spin-orbit interactions split the groundstate OH (2Π) into two doubly degenerate states, 2Π3/2 and 2 Π1/2, and the 2Π1/2 doublet state lies only 139.7 cm-1 above the 2Π3/2 doublet state;29 the low-lying state 2Π1/2 of the OH radical was included in the electronic partition function. All vibrations were treated as harmonic oscillators with the exception of a few low-frequency modes. The torsional motions on the single bonds between the heavy atoms were treated as hindered internal rotations, particularly for the torsional motion of the terminal methyl group, the torsional motion along the central C-C bond in 1-butene, and the OH group torsional

motion around the partially formed O-H bond in the transition states. These torsional motions correspond to low-frequency modes and were treated as hindered internal rotations using the polynomial expression proposed by Ayala and Schlegel30 to compute the partition functions of hindered internal rotors as

n QHR(T) ) Πi)1

(

uie-ui/2

)(

8π3kBT

)

1/2

× 1 - e-ui h2σ2 1 + p2 exp[-Vi /2kBT] × exp[-Vi /2kBT]Jo(iVi /2kBT) 1 + p1 exp[-Vi /2kBT] (2) Iγ,i

where ui is defined as hVi/kBT, νi the ith vibrational frequency associated with the hindered rotation, Ir,i and Vi the reduced moment of inertia and barrier height of the ith rotor, respectively, and σ its periodicity. For a hindered rotor with a periodic potential, Vi is approximated as 8π2ν2i Ir,i/σ2. Furthermore, p1 and p2 are polynomial functions of the inverse partition function of the free rotor and the function (Vi/kBT)1/2 and J0 the Bessel function. 2.3. Tunneling Effect. Quantum mechanical tunneling is critical for chemical processes occurring with small and narrow reaction barriers, and the transmission coefficient κ(T) is known to be important at low temperatures. For methyl and vinyl H-abstraction reactions in the reactions of 1-butene + OH, the rate coefficients were calculated by the conventional TST formula with correction of the tunneling effect by the Eckart method.31 This method approximates the potential by a onedimensional function that is fitted to reproduce the zero-point energy corrected barrier, the enthalpy of reaction at 0 K, and the curvature of the potential curve at the transition state. For allylic H-abstraction reactions of isomeric butenes by the OH radical, small curvature tunneling (SCT)32 within the framework of variational transition-state theory was applied to correct the quantum mechanical effect on the motion along the reaction coordinate. Depending on the curvature of the reaction path, the SCT method is more sophisticated and has been shown to be accurate in the description of the temperature-dependent transmission coefficient κ(T),33,34 which was computed as the ratio of the Boltzmann-weighted multidimensional semiclassical transmission probability, to the Boltzmann-weighted classical transmission probability using the small-curvature method (SCT)

∫0∞ P(E)e-E/k T dE ∞ e-E/k T dE ∫E*(T) B

k(T) )

(3)

B

This method requires substantial calculation to establish the force constant matrix (Hessian) and the energy gradient of selected points along the minimum energy path. The thermal rate coefficients in the temperature range of 300-1500 K were calculated using TheRate program.35 3. Results and Discussion 3.1. Stationary Points of the Potential Energy Surface. For 1-butene, there are two rotational conformers, skew (C1) and syn (Cs) forms,36,37 which have the conformation of the C-H and C-C bonds eclipsing the CdC double bond, respectively. Furthermore, the skew conformer was observed by Kondo et al.36 to have approximately 0.15 kcal mol-1 lower energy. Recently, Wu et al.38 found by electron momentum spectroscopy

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Figure 2. Energy diagram for the H-abstraction reactions of 1-butene + OH calculated at the CCSD(T)/6-311++G(d,p)//BH&HLYP//6-311G(d,p) level at 0 K. The dashed lines are s-allylic H-abstraction channels of syn-1-butene + OH.

that the syn-skew relative Gibbs free energy is 0.47 ( 0.20 kcal/mol and the relative distributions at 298 K are 69% and 31%. This suggests that equilibrium between the two conformers plays a role in chemical reactions at low temperatures, and the two conformers of 1-butene probably need to be considered in the allylic H-abstraction mechanism at temperatures at which equilibrium between the two conformers exists. Recently, Viskolcz et al.7,8 studied the H-abstraction reaction of propene by the OH radical by using various DFT and ab initio methods and found the p-allylic H abstraction follows two reaction paths: a direct abstraction path and an indirect path via a pre-active van der Waals complex. This p-allylic H-abstraction mechanism can be used as a prototype to characterize the p-allylic and s-allylic H abstractions in the reactions of butene isomers + OH. 1-Butene contains s-allylic, p-vinylic, s-vinylic, and alkyl hydrogens, which can be abstracted to form different butene radicals. Figure 2 presents the potential energy diagram of various H-abstraction reactions in 1-butene + OH calculated at the CCSD(T)/6-311++G(d,p)//BH&HLYP/6-311G(d,p) level, where the energies are the zero-point-corrected energies relative to that of the skew conformer of 1-butene at 0 K. The optimized electronic structures of the transition states and van der Waals complexes involved in the H abstractions of 1-butene + OH are shown in Figure 3, where the carbon-carbon bond length, cleaving C-H bond length, forming O-H bond length, and interaction distances between the hydroxyl H and the sp2 carbon and between the hydroxyl O and various H atoms are illustrated. For the transition states TS1-TS3 of s-allylic abstraction, the allylic carbon atom is connected to four different groups, i. e., a methyl group, a vinyl group, a H atom, and a forming water molecule. Therefore a 2-fold degeneracy of optical isomerism of the allylic carbon atom was considered for the reaction path degeneracy. In addition, a 2-fold degeneracy of optical isomerism of the vinyl carbon atoms was also considered for the TS5-TS7 of the vinyl H-abstraction.

As shown in Figure 2, two van der Waals reactant complexes (RC1 and RC2) and two van der Waals product complexes (PC1 and PC2) were found in the potential energy surface of allylic H-abstraction reactions of 1-butene + OH. Specifically, RC1 and RC2 are the complexes of the OH radical interacting with the skew and syn forms of 1-butene, and they are rotational conformers. PC1 and PC2 are the complexes of the H2O molecule interacting with two isomers of the methylallyl radical, respectively. As discussed above, the skew and syn conformers of 1-butene exist in the equilibrium at room temperature, so the s-allylic H-abstraction reaction may occur via the following mechanism at 0 K. The skew form of 1-butene (abbreviated as skew-1-butene, so on with the syn form) proceeds through the reactant-complex RC1 with an energy of 2.83 kcal mol-1 lower than that of the entrance channel to the transition state TS1 and then forms the van der Waals product-complex PC1 with a relative energy of -31.81 kcal mol-1 before the formation of skew-1-methylallyl radical. The overall reaction exothermicity is found to be -30.39 kcal mol-1. For syn-1-butene, it proceeds through the RC2 with an energy of 2.69 kcal mol-1 lower than that of the entrance channel, to the transition state TS2, and then form the van der Waals product complex PC2 with a relative energy of -32.10 kcal mol-1 before formation of the syn-1-methylallyl radical. In addition, it was found that syn-1butene undergoes direct allylic H abstraction via TS3 with an energy barrier of 1.22 kcal mol-1. Since TS3 is an OH rotamer of TS2 in the reaction of syn-1-butene + OH, it forms the product-complex PC2 before producing the syn-1-methylallyl radical. For the direct path of skew-1-butene, a transition state with the configuration of the OH fragment not oriented to the CdC double bond in the skew-1-butene backbone was not located, and it is not clear that such a direct path exists in the s-allylic abstraction of 1-butene + OH. Nevertheless, we note that the transition states TS1, TS2, and TS3 are the rotational conformers, and they are not distinguishable at higher temperatures.

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Figure 3. BH&HLYP/6-311G(d,p)-optimized transition-state and van der Waals complex structures in different H-abstraction reactions of 1-butene + OH.

For the allylic H-abstraction channels, it is seen in Figure 2 that the energy barrier of TS1 (with the 1-butene backbone in the skew form) is 0.85 kcal mol-1 lower than that of TS2 (with the 1-butene backbone in the syn form). It was also found that this is the case for the methyl and three vinyl H-abstraction channels, i.e., the zero-point energy corrected barriers for forming the syn radicals at 0 K are 0.3-1.8 kcal mol-1 higher than those of forming the skew radicals, as shown in Table 1. To simplify, only the lowest energy conformation (skew form) is shown in Figure 2 for the transition states and radical products in the methyl and vinyl H-abstraction reactions. In particular, for the methyl H-abstraction channel, it was found that the lowest energy structure, TS4, has a characteristic that the OH fragment is orientated to the CdC double bond to form a sixmembered ring transition state. Furthermore, for electrostatic interaction, it has an interatomic distance of 2.76 Å between

the hydroxyl H and the s-vinyl C atoms (see Figure 3). Because of this six-membered ring transition-state structure, it only has an energy barrier of 2.27 kcal mol-1 to form the trans-3-buten1-yl radical with an exothermicity of -14.65 kcal mol-1. It is noted that the van der Waals complexes also exist on the potential energy surface of the methyl and vinyl H-abstraction channels, and one of the van der Waals product-complexes PC3 in the methyl H-abstraction channel is shown in Figure 3. For the s-vinyl H-abstraction channel, a six-membered ring transition state TS5 that consists of three C atoms, the O atom, and a methyl H and a vinyl H atom is also observed (see Figure 3). In TS5, the interatomic distance between the hydroxyl O atom and the methyl H atom is 2.81 Å, and it has an energy barrier of 3.90 kcal mol-1 to form the trans-1-buten-2-yl radical with an exothermicity of -8.42 kcal mol-1. For the p-vinyl H abstraction, there are two different transition states, TS6 and

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TABLE 1: Calculated Relative Energies of the Transition State by Different Methodsa BH&HLYP/ 6-311G(d,p)

CCSD(T)/ 6-311++G(d,p)

transition state

energy

energy including ZPE

energy

energy including ZPE

TS1 (skew-CdCC•C + H2O) TS2 (syn-CdCC•C + H2O) TS3 (syn-CdCC•C + H2O) TS4 (skew-CdCCC• + H2O) TS4′ (syn-CdCCC• + H2O) TS5 (skew-CdC•CC + H2O) TS5′ (syn-CdC•CC + H2O) TS6 (skew-C•)CCC + H2O) TS6′ (syn-C•)CCC + H2O) TS7 (skew-C•)CCC + H2O) TS7′ (syn-C•)CCC + H2O) TS8 (cis-CC)CC• + H2O) TS9 (cis-CC)CC• + H2O) TS10 (trans-CC)CC• + H2O) TS11 (trans-CC)CC• + H2O) TS12 (CdC(C)C• + H2O)b TS13 (CdC(C)C• + H2O)b

3.76

1.95

1.80

-0.01

3.70

2.04

1.85

0.84

4.11

2.34

2.35

1.22

6.60

5.03

3.84

2.27

6.99

5.48

4.91

3.40

7.91

6.08

5.74

3.90

8.69

6.77

6.12

4.20

9.89

8.07

7.84

6.01

11.53

9.65

9.67

7.80

10.85

8.81

8.08

6.04

11.09

9.13

8.52

6.55

4.96

3.33

3.30

1.67

4.81

3.21

2.90

1.30

5.08

3.41

3.55

1.89

4.86

3.22

3.14

1.50

5.16

3.57

3.59

2.00

4.92

3.33

3.25

1.73

a Unit is in kcal mol-1. The energies of transition states TS1-TS7 are relative to the energies of 1-butene (skew) + OH at 0 K. The energies of transition states TS8-TS13 are relative to the sum of the corresponding reactant energy at 0 K. b The energies were calculated based on the geometries optimized at the BH&HLYP/cc-PVTZ level.

TS7, corresponding to the abstraction of two p-vinyl H atoms at different positions. Although the two p-vinyl H-abstraction channels have similar energy barriers, they correspond to two very different transition-state structures, TS6 and TS7. Specifically, TS6 has a six-membered ring transition-state structure that consists of three C atoms, the O atom, and an allylic H and a vinyl H atom (see Figure 3) with an interatomic distance between the allylic H atom and the O atom being 2.624 Å for electrostatic interaction. Furthermore, it has an energy barrier of 6.01 kcal mol-1 to form the trans-1-buten-1-yl radical product with an exothermicity of -5.44 kcal mol-1. For the formation of the cis-1-buten-1-yl radical channel, TS7 has an energy barrier of 6.04 kcal mol-1 with an exothermicity of -4.99 kcal mol-1. We note that the above notations for cis and trans in the radical products stand for the orientation of the H atom on the terminal sp2 carbon. Due to the different TS structures for the abstraction of p-vinyl H atoms at two positions, it is expected that the kinetic rate coefficients of the two channels vary at higher temperatures corresponding to different entropy changes. Overall, the allylic H-abstraction channels are dominant due to their low energy barriers and a large exothermicity.

Regarding the other butene isomers, the optimized geometries show that cis-2-butene, trans-2-butene, and isobutene have C2V, C2h, and C2V symmetry, respectively. For the allylic H-abstraction reactions, three p-allyl radicals, cis-2-buten-2-yl (cis-C•H2CHd CHCH3), trans-2-buten-2-yl (trans-C•H2CHdCHCH3), and 2methylallyl (CH2dC(CH3)C•H2) are formed. Since these allylic H-abstraction reactions produce the p-allylic radical, the abstraction mechanisms of these isomers at low temperatures may follow that of propene + OH, i.e., which involves the indirect path via a van der Waals prereactive complex and the direct H-abstraction path.7 For direct and indirect allylic H-abstraction paths, three pairs of rotamers corresponding to the transition states for the p-allylic H abstractions of three butene isomers with OH were found (TS8-TS13), as shown in Figure 4. Furthermore, for cis-2-butene + OH, it was found that the zeropoint energy corrected forward barriers at 0 K are 1.30 (via TS9) and 1.67 kcal mol-1 (via TS8) for indirect and direct allylic H-abstraction paths. For trans-2-butene + OH, the barriers are 1.50 (via TS11) and 1.89 kcal mol-1 (via TS10) for the indirect and direct allylic H-abstraction paths, respectively. For isobutene + OH, it has barriers of 1.77 (via TS13) and 2.07 kcal mol-1 (via TS12) for the indirect and direct allylic H-abstraction reactions, respectively. It is noted that these p-allylic abstractions have energy barriers of 1-2 kcal mol-1 higher than that of forming the s-allylic radical in 1-butene + OH, as seen in Table 1. Regarding the structural parameters in different types of transition states in the isomeric butenes + OH, it is seen in Figure 4 that the transition states of H abstraction producing the p-allylic radicals proceeds via an early TS, with the cleaving C-H bonds stretched from 1.195 to 1.208 Å and an O-H bond formed from 1.328 to 1.357 Å. However, the transition states of H abstraction producing the s-allylic radicals occurs even earlier, with the cleaving C-H bonds stretched from 1.190 to 1.193 Å and an O-H bond formed from 1.359 to 1.369 Å (see Figure 3). These results are consistent with those from the CCSD(T)/6-31(d) optimization (see Figure 1). Regarding the methyl and vinyl H abstractions, the normal transition states were observed with an attracted hydrogen being midway between the corresponding carbon and oxygen, i.e., the cleaving C-H bond length is 1.241-1.267 Å and the forming O-H bond length is 1.198-1.254 Å. Furthermore, the calculated imaginary frequencies of these transition states were found to be in the range of 1150-1980 cm-1. These geometrical and frequency parameters support reasonable accuracy of the BH&HLYP/6311G(d,p) method for the H-abstraction reactions of butene isomers by the OH radical studied herein. The vibrational frequencies and moments of inertia optimized at the BH&HLYP/ 6-311G(d,p) level for the species involved in the reactions of OH with isomeric butenes are provided in Supporting Information Table S1. 3.2. Minimum Energy Paths of Allylic H Abstraction. Intrinsic reaction coordinate calculations (IRC) were performed at the BH&HLYP/6-311G(d,p) level to obtain the minimum energy path (MEP). The calculations were carried out by starting from the fully optimized saddle-point geometries and then moving downhill along the reactant and product channels in mass-weighted Cartesian coordinates. Two hundred points were calculated in each direction at a gradient step size of 0.01 bohr. The reaction coordinate s is defined as the signed distance from the saddle point, with s < 0 referring to the reactants side and s > 0 to the products side. Force constants, harmonic vibrational frequencies, and normal-mode vectors for the 3N - 7 degrees of freedom that are orthogonal to the reaction path were

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Sun and Law

Figure 4. BH&HLYP/6-311G(d,p)-optimized transition-state structures in p-allylic H-abstraction reactions of 2-butene and isobutene by OH radical.

computed at the BH&HLYP/6-311G(d,p) level at selected points along the IRC to construct the minimum energy paths for the allylic H-abstraction reactions. To obtain an accurate potential energy curve, more points in the saddle point zone -0.5 < s < 1.0 were selected for the calculation of the Hessian and energy gradients. It was found that the single-point energy of the saddle point calculated at the CCSD(T)/6-311++G(d,p) level is ca. 0.46 hartree higher than that of the BH&HLYP/6-311G(d,p) level, and this difference remains the same for each allylic H-abstraction reaction involved in this study. Consequently, the BH&HLYP/6-311G(d,p) energies along the MEP for each channel were corrected by the single-point energy difference between the two levels of theory at the saddle point of each individual channel, such that the energy maximum corresponding to the saddle point is not shifted from original calculations in order to avoid the problem of numerical defect that is mistaken for any variational effect.39 Figure 5 presents the classical potential energies (VMEP), the local zero-point energies (Eint), and the ground-state vibrationally adiabatic potential energies (VaG) along the reaction coordinate for indirect and direct s-allylic H abstractions of 1-butene + OH via TS1, TS2, and TS3. It is seen that the potential energy curves of VMEP and VaG along the transition-state region are rather flat; however, the Eint curves in the right corner show a substantial drop near the saddle point, characterizing where the H-abstraction reaction occurs. Furthermore, the Eint of the syn conformer is higher than that of the skew conformer, as expressed by the dotted curves in Figure 5, and each channel is

Figure 5. Potential energies and local zero-point energies along the mass-weighted reaction coordinates in the s-allylic H abstractions of 1-butene + OH via TS1 (black solid line), TS2 (black dotted line), and TS3 (red dotted line).

unique, showing two maxima within the range of -0.5 < s < 1. The harmonic vibrational frequencies of the generalized normal modes along the mass-weighted reaction coordinate calculated

Kinetics of Hydrogen Abstraction Reactions

J. Phys. Chem. A, Vol. 114, No. 45, 2010 12095 the following scheme k1

k2

1-butene + OH y\z prereactive complex 98 products k-1

Figure 6. Generalized vibrational frequencies along the mass-weighted reaction coordinates in the s-allylic H abstraction of 1-butene + OH via TS1.

in the s-allylic H abstraction of 1-butene + OH via TS1 are shown in Figure 6. These frequencies were correlated by maximizing the overlap between the normal modes of consecutive Hessian grid points. As discussed above, the Eint curve significantly drops in the range of -0.5 < s < 1, which is ascribed to the significant drops of the stretching frequencies for cleaving the C-H bond and forming the O-H bond in this s range, as seen in Figure 6. Furthermore, the low frequencies are increased in this s range, resulting in the reduced contribution to the vibrational partition function of the transition state. Since the potential energies VMEP and VaG decrease significantly after the saddle point region, the variational transition states were found to be located in the reaction coordinates before the first barrier of the Eint curve, within which the deepest drops of the Eint curves were observed. The VMEP, Eint, and VaG curves along the reaction coordinate for indirect and direct p-allylic H abstractions of cis-2-butene, trans-2-butene, and isobutene by the OH radical are presented in Figures S1 and S2 in the Supporting Information. In these two figures, the scale of Eint is expressed in the right axis of ordinates to exhibit the facile change of the Eint curve for each reaction channel. It is seen that the potential energy curves of VMEP and VaG for the p-allylic H abstractions of 2-butene and isobutene by the OH radical within the transition-state region are flat, and each Eint exhibits a unique curvature that falls into two groups: the indirect p-allylic H-abstraction channel and the direct p-allylic H-abstraction channel. For the local zero-point energy Eint curves, they all have a substantial drop after the reaction coordinates of s > -0.5 and show two submerged barriers within the range of -0.5 < s cis-2-butene > trans-2-butene > isobutene.

potential energy surfaces along the reaction coordinates are rather flat, and each local zero-point energy curve is unique and shows a substantial drop near the saddle point with submerged two barriers in the reaction coordinates of -0.5 < s