Kinetics of Hydrogen Abstraction and Addition Reactions of 3-Hexene

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Kinetics of Hydrogen Abstraction and Addition Reactions of 3-Hexene by #H Radicals Feiyu Yang, Fuquan Deng, Youshun Pan, Yingjia Zhang, Chenglong Tang, and Zuohua Huang J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b11499 • Publication Date (Web): 15 Feb 2017 Downloaded from http://pubs.acs.org on February 16, 2017

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The Journal of Physical Chemistry

Kinetics of Hydrogen Abstraction and Addition Reactions of 3-Hexene by ȮH Radicals Feiyu Yang, Fuquan Deng, Youshun Pan, Yingjia Zhang*, Chenglong Tang, Zuohua Huang* State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China Abstract: Rate coefficients of H-atom abstraction and H-atom addition reactions of 3-hexene by the hydroxyl radicals were determined using both conventional transition-state theory and canonical variational transition-state theory, with potential energy surface (PES) evaluated at the CCSD(T)/CBS//BHandHLYP/6-311G (d, p) level and quantum mechanical effect corrected by the compounded methods including one-dimensional Wigner method, multi-dimensional zero-curvature tunneling method and small-curvature tunneling method. Results reveal that accounting for approximate 70% of the overall H-atom abstractions occur in the allylic site via both direct and indirect channels. The indirect channel containing two Van der Waals pre-reactive complexes exhibits two times larger rate coefficient relative to the direct one. The OH-addition reaction also contains two Van der Waals complexes, and its submerged barrier results in a negative temperature coefficient behavior at low temperatures. In contrast, The OH-addition pathway dominates only at temperatures below 450 K whereas the H-atom abstraction reactions dominate overwhelmingly at temperature over 1000 K. All of the rate coefficients calculated with an uncertainty of a factor of 5 were fitted in a quasi-Arrhenius formula. Analyses on the PES, minimum reaction path and activation free Gibbs energy were also performed in this study. Keyword: 3-Hexene; H-atom abstraction; OH-addition; hydroxyl radical; Transition state; Rate coefficient *Corresponding author: Yingjia Zhang E-mail: [email protected] Zuohua Huang E-mail: [email protected]

1. Introduction With the efforts of worldwide researchers, the combustion of alkanes1-9 has been thoroughly investigated. However, well-understanding of oxidation and combustion for alkenes10-12 is still under way. It is well known that the fate of alkenes is of great importance in alkane combustion, particularly in rich flame where alkenes play an important role as the intermediates in the fuel oxidation and combustion and as a critical precursor of polycyclic aromatic hydrocarbons. Hydroxyl (ȮH), one of the top vital radicals involved in hydrocarbon combustion13, dominates the chain propagation, chain branching and even chain termination processes at different temperature regions. The reactions of alkenes with ȮH are therefore major reaction pathways under either atmospheric or typical combustion conditions. Limited research is available with respect to alkene + ȮH reaction systems at present. Tully14-15

ACS Paragon Plus Environment


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measured

the

global

rate

coefficients

of

ethene/propene/1-butene

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+

ȮH

using

a

laser

photolysis/laser-induced fluorescence technique. Together, they also explored the impact of deuteration on their measured results. However, the rate coefficients of individual elementary reactions were unavailable due to the limitation of research conditions. Recently, Huynh et al.16 studied the kinetics of enol formation from the reactions of propene + ȮH, and pointed out that H-atom abstraction was more important than OH-addition in terms of propene consumption due to the higher branching ratio of the former (more than 90%). Zádor et al.

17

predicted the detailed PES of the terminal addition, the central addition and the

H-atom abstraction of propene + ȮH, concluding that the channel resulting in allyl radicals predominates overwhelmingly. Szori et al.18 provided a detailed description of allylic H-atom abstraction for propene + ȮH system employing as many as 9 methods and they found that those reactions proceed through two channels, direct and indirect H-atom abstractions. With the occurrence of the reactant-complex, the indirect channel exhibits lower barrier and thus facilitates the reactions. Besides, within the 9 methods adopted, the BHandHLYP method behaves more accurate and more efficient. Sun and Law19 explored the kinetics of H-atom abstraction reactions of butane isomers by ȮH radicals. Similar to propene, both the direct and indirect allylic H-atom abstraction channels were identified and the latter appeared to be favorable. Among all of the H-atom abstractions, the allylic H-atom abstraction dominates overwhelmingly while the vinyl H-atom abstraction is least favored. Greenwald et al. examined the addition of ȮH radicals to ethylene20 and isoprene21 at high-temperature limit and as a function of pressure via transition state theory (TST) and master equation (ME) simulations. A two-transition-state model was proposed with simple reduction, the computed rate coefficient exhibited the reasonable agreement with experiments. To the best knowledge of the authors, current research mainly focuses on small alkene + ȮH reactions. However, the detail description of PES and detailed reaction path for larger alkene + ȮH reactions are limited. With this in mind, the aim of this study is to examine the 3-hexene + ȮH system via the high-level quantum mechanical calculations and sophisticated variational TST22, and to provide accurate rate constants of the title reactions for kinetic mechanism development of large alkenes, which can be eventually used to descript quantificationally the evolution of alkenes in alkane combustion.


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2. Theory 2.1 Electronic structures According to the mathematic expression of TST, rate coefficient exhibits an exponential dependence on energy, indicating that the energy accuracy has a significant influence on the uncertainty of rate coefficient. Therefore, a suitable selection of calculation method is crucial to locate reasonable TS and stationary geometries. Sun and Law19 found that for allylic H-atom abstraction reactions by ȮH radical, the widely applied density functional B3LYP23-25 method failed to locate the transition state for s-allyl H-atom abstraction and predicted a reactant-like TS for p-allyl H-atom abstraction. In this study, the HF/6-31G (d) geometry optimization of s-allyl H-atom abstraction predicts the length of the cleaving C-H bond and the forming H-O bond. The results show that the lengths of the cleaving C-H bond and the forming H-O bond are 1.268 Å and 1.285 Å, respectively, and the imaginary frequency for H-O bond stretching is as large as 2984 cm-1. The MP2/6-31G optimization predicts the s-allyl H-atom close to allylic. Specifically, the lengths of the cleaving C-H bond and the forming H-O bond are 1.231 Å and 1.307 Å, respectively, and a much smaller imaginary frequency of 2337 cm-1 is obtained. As proposed by Henry et al26. the second-order Møller-Plesset perturbation theory (MP2)27-28 is unreliable for the unsaturated radicals with high-spin contamination, since the wave function for open-shell system is no longer an Eigen-function of the total spin, thus some error are introduced into the calculation. A high spin contamination can affect the geometry and result in erroneous single point energy. Alternatively, the coupled-cluster theory can effectively avoid spin contamination due to its infinite order electron correction effects. However, optimization of the geometries and calculation of the vibrational frequencies for the 20-atom target system are computationally time demanding when the coupled-cluster method uses. 29-30 To accurately describe the electronic structure, the BHandHLYP/6-311G (d, p) level recommended by Sun and Law19 and Szori et al.

18

was employed in this work. This method using Becke’s half and half

nonlocal exchange24 with the Lee-Yang-Parr (LYP)25 correlation functional and the split valence basis set, has been proved to be able to reproduce the stationary and TS geometries acquired at CCSD/6-31G (d) of theory with small discrepancy (e.g. ~2% for bond length). The BHandHLYP/6-311G (d, p) optimization predicts the s-allyl H-atom even closer to the allylic C atom compared to that predicted by the MP2/6-31G optimization. Specifically, the lengths of the cleaving C-H bond and the forming H-O bond are 1.216 Å and



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1.300 Å, respectively. As expected, a smaller imaginary frequency for H-O bond stretching of 1516 cm-1 was acquired. Note that the BHandHLYP method has also been widely adopted to accurately predict the TS structures of reactions between alkane, alkene, aldehyde and ȮH radical31-32. As a consequence, the BHandHLYP/6-311G (d, p) method was selected to optimize the geometries of stationary point (reactant, product, reactant complex and product complex) and first-order saddle point (TS with only one imaginary frequency) as well as to predict thePES and minimum energy path (MEP). Moreover, to increase the accuracy of PES, the single point-energy calculations were also conducted using the CCSD(T) method with the correlation-consistent, polarized-valence, double-ζ (cc-pVDZ) and triple-ζ (cc-pVTZ) basis set of Dunning33. The CCSD(T) level of energies were extrapolated to complete the basis set limit (CBS)34 using the following expressions: (X ) (∞) ESCF = ESCF + A exp(−α X )

(1) (∞) ESCF =

(3) (2) eα 3 ESCF − eα 2 ESCF

eα

3

− eα

2

(2) where and

( X) ESCF is the SCF (self-consistent field) energy calculated with the basis set with cardinal number X

( ) ESCF is the CBS limit energy, and A and α are constants. When two-point extrapolation are conducted ∞

with X = 2 and 3, α = 4.42 and the value of A is not necessary because it can be canceled during deriving ( ) ESCF . Computational results show that the T1 diagnostic29-30 values are quite small (< 0.01 for stable ∞

species and < 0.025 for radicals and TS), indicating that the single-reference method is reliable. In this work, all of the electronic structure calculations were performed using the Gaussian 09 program35 package.

2.2 Calculation of rate coefficients The rate coefficients involved in the title reaction were calculated applying both conventional TST22 and canonical variational transition-state theory (CVT)22, 36. The CVT locates the dividing surface along the reaction coordinate s to minimize the generalized transition-state rate coefficient22. The generalized transition-state is defined as the geometry perpendicular to the MEP and intersecting it at that s. The CVT thermal rate coefficient at temperature T can be thus expressed as


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k CVT = min{k GT (T , s)} = min{κ (T ) s

s

σ QGT (T , s) exp[−βVMEP (s)]} β h Q R (T )

(3)

where reaction coordinate s stands for the distance from the saddle point along the MEP. While

QGT (T, s)

term is the partition function of the generalized TS,

the reactants, σ

is the symmetry number,

VMEP(s)

QR (T )

term is the partition function of

term is the potential energy at point s on the MEP

relative to overall zero of energy. κ (T ) term denotes the transmission coefficient for quantum mechanical tunneling correction, and β and h are the Boltzmann factor and Planck constant, respectively. Considering that OH addition reaction is pressure dependent, the rate coefficients at different pressures were obtained by solving ME. The partition functions for reactants and generalized TS are calculated from the statistic mechanics theory on the basis of the rigid-rotor-harmonic-oscillator (RRHO) approximation with internal rotation corrections37. The vibrational frequencies and moments of inertia obtained at BHandHLYP/6-311G (d, p) level are employed to determine the vibrational and rotational partition functions. A frequency scaling factor of 0.93519 was used to compensate the difference with experimentally observed vibrational frequencies. All of the frequencies were treated as harmonic oscillators except partial low-frequency torsional modes, specifically, the torsional motions of ȮH, methyl and ethyl groups. These low-frequency torsional modes were treated as hindered internal rotations using the segmented reference Pitzer-Gwinn (SRPG) method38. This method decomposes the partition function into the contributions from each well. For each well, the partition function consists of the contributions from left of the minima and right of the minima. The SRPG partition function can be thus determined by

Q

SRPG tor

=∑ j

Q HO (ω j ) j Q

CHO j

(ω j )

Q SRC j

(4)

where

 (φ j − φ jL )  (φ jR − φ j ) L L β β β QSRC = exp( − U ) Q exp( − W / 2) I ( W / 2) + exp(−βWjR / 2)I 0 (βWjR / 2)  j j FR , j j 0 j 2π  2π  (5), in which j denotes the jth well. Q F R , j term stands for the free rotor partition function.


Uj

term is the


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minimum energy of the jth well centered at φ left and right barrier heights located at

j

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relative to the global minima energy.

WjL and W jR are the

φ jL and φ jR , respectively. QCHO (ω j ) and QHO j j (ω j )

terms are the

classical and quantum mechanical partition functions, respectively.

2.3 Quantum mechanical effect Quantum mechanical effects along reaction coordinate play crucial roles at low temperature, especially for light particle (for instance, a proton) transferring between donor and acceptor. Chemical processes involving low and narrow barrier height, H-atom abstraction reactions, for example, may lead to a significant tunneling effect. In addition to the tunneling effect, there also exists non-classical reflection, which suggests that even when energy is higher than the quantum threshold energy (the lowest energy at which it is possible to have tunneling), the transmission coefficient is lower than unity. Generally, the quantum effect is incorporated through the multiplicative factor, transmission coefficient κ (T ) . In this work, κ (T ) was computed using the one-dimensional Wigner correction39, the multi-dimensional zero-curvature tunneling method (ZCT)40-41 and small-curvature tunneling (SCT)42-44 methods, respectively. The Wigner correction takes the form

κ W (T ) = 1 + where

h

1 hω † β 24

2

(6)

is the reduced Planck constant and ω † is the imaginary frequency at the saddle point. This

correction is valid under severe restrictions and is justifiable at high temperature where it is near unity. While the assumptions are not satisfied and it is usually inaccurate when it differs appreciably from unity. Both the ZCT and SCT methods observe the semi-classical adiabatic ground-state assumption (SAG)45 and the

κ SAG (T )

takes the form

∞

κ SAG (T ) =

β ∫ dE exp( − β E )P SAG ( E ) 0

(7)

exp( − β VaAG )

where V aA G is the barrier height of the ground-state adiabatic potential and

PSAG (E)

is the quantum

probability. The ZCT method takes MEP as tunneling path without considering the coupling of the motion along the reaction coordinate and the modes perpendicular to it. While the SCT method, is also named the basis of the centrifugal-dominant small-curvature semi-classical ground-state (CD-SCSAG) method,


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including corner-cutting tunneling46. Corner-cutting means that the tunneling path is shorter than the MEP and the coupling of the motions along and perpendicular to the reaction coordinate is considered. The more sophisticated SCT has been proved to be more accurate in describing quantum effects. Note that the generalized transition-state locates at the peak of the activation Gibbs free energy for CVT and at saddle point for TST. However, the multi-dimensional transmission coefficient is calculated on the adiabatic ground-state PES; to correct this discrepancy, the multiplicative factor

κ †/CAG (T ) 45, 47

is applied and

the notation † can be TST or CVT.

{

κ TST / CAG (T ) = exp β V aG ( s*TST ) − V aAG 

}

{

κ CVT / CAG (T ) = exp β V aG ( s*CVT (T )) − V aAG 

(8)

}

(9)

Apparently, this factor must be lower than or equal to unity. All the rate coefficient calculation and tunneling corrections were performed applying the PolyRate program48 package.

3. Results and discussion 3.1 Stationary points and transition-states of the PES Since the C=C bond locates at the middle of carbon chain, there are two isomers of 3-hexene, cis-3-hexene and trans-3-hexene with two ethyl groups located at the same and the different sides of the C=C bond. Trans-3-hexene has a looser carbon chain structure and possesses around 5.5 kcal/mol (evaluated at BHandHLYP/6-311G level) lower energy than that of cis-3-hexene, revealing that the trans-3-hexene presents more stable and has usually been therefore chosen as representative of 3-hexene; the terminology 3-hexene in present work refers to trans-3-hexene as well. For 3-hexene, since the two allylic C-C and C-H bonds can individually eclipse C=C double bond, there are 4 rotational conformers (syn-syn form, syn-skew form, same-side skew form and different-side skew form) as shown in Table 1. Syn-syn conformer has an energy of 1.15 kcal/mol relative to the most stable same-side skew conformer. However, the syn-skew conformer with a relative energy of 0.56 kcal/mol accounts for the largest proportion of 4/9. Thus, in this work, the stationary points and TS geometry searching and energy calculations are performed on the basis of the syn-skew conformer. Nevertheless, these rotational conformers and their corresponding TSs are not distinguishable at high temperature. Therefore, the results derived from one of them can reasonably be applied to the rest



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conformers. The hydroxyl radical can either abstract H atom from alkyl, allylic and vinylic sites forming different hexenyl radicals and H2O or undergo addition reaction forming 1-ethyl-2-hydroxyl-butanyl (PA) adduct. Table 2 presents the MEP energies and zero-point corrected energies calculated at BHandHLYP/6-311G (d, p) and CCSD(T)/CBS level, respectively. The more accurate CCSD(T) method predicts average 1.07 kcal/mol lower energy than the BHandHLYP method, and the maximum difference is 5.22 kcal/mol. Figure 1 illustrates the PES of H-atom abstraction and OH-addition reactions predicted at CCSD(T)/CBS level. While Figure 2 shows the optimized electronic structures of TSs and Van der Waals complexes, including the length of the cleaving C-H bond, the length of the forming H-O bond, the length of C-C bond and the distances between other atoms. As depicted in Figure 1, the H-atom abstraction from allylic-C site can take place through both indirect and direct channels. For the indirect channel, 3-hexene proceeds through the reactant-complex RC2 with an energy of 1.72 lower than the entrance channel to the transition state TS2Ind and then forms the Van der Waals product-complex PC2 with a relative energy of -33.91 kcal/mol before the formation of 1-methyl-2-pentenyl (P2). The overall reaction exothermicity is -31.76 kcal/mol. For the direct channel, alternatively, 3-hexene directly surmounts a barrier height of 3.90 kcal/mol (TS2Dir) and then enter the Van der Waals product-complex well to form the product. Note that, as presented in Figure 2, the cleaving C-H bond and forming H-O bond are 1.209 Å and 1.363 Å for TS2Dir and 1.213 Å and 1.307 Å for TS2Ind, respectively, suggesting that the roaming H atom locates closer to the allylic-C for TS2Dir and closer to hydroxyl oxygen for TS2Ind. In addition, the ȮH fragment orientations in TS2Dir and TS2Ind are almost opposite; for instance, the C=C-O-H (the second C is the one involved in bond cleaving and the Ḣ atom denotes the hydroxyl hydrogen) dihedral angle is around 78° for TS2Dir and -75° for TS2Ind. The RC2 shows a symmetric electronic structure with the O-H bond perpendicular to the C=C double bond and the distances between the hydroxyl-H and the two vinylic-C atoms are identically equal to 2.464 Å. Note that similar reactant-complex structures can be found for propene + ȮH18 and 1-butene + ȮH19. It is worth mentioning that Szori et al.24 performed the calculation in allylic H-atom abstraction for propene + ȮH at QCISD (T)/6-311+G (3df, 2p)//CCSD/6-31G (d) level and, similarly, an indirect TS with an energy of 0.3 kcal/mol and a direct TS with an energy of 5.7 kcal/mol were located. The indirect channel with a Van der Waals well of -7.1 kcal/mol and a 5.4 kcal/mol lower barrier height relative to the direct-channel TS is chemically in priority. Moreover, Sun and Law19 calculated the allylic H-atom


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abstraction reaction for 1-butene + ȮH at CCSD (T)/6-311++G (d, p)//BHandHLYP/6-311G (d, p) level, and the 1-butene also exhibits two reaction channels, the indirect and the direct H-atom abstractions. 1-butene can directly enter a -32.10 kcal/mole product-complex well through a 1.22 kcal/mol direct transition-state. Alternatively, the 1-butene can enter a -2.96 kcal/mol reactant-complex well and surmount the 0.84 kcal/mol indirect transition-state before entering the product-complex well. In propene + ȮH system, the indirect channel with 0.38 kcal/mol lower barrier height than the direct channel is energetically more favorable. Interestingly, for the 3-hexene + ȮH system, the TS2Ind shows 0.03 kcal/mol higher energy than the TS2Dir, suggesting that the reactant-complex is rather stable and hinders the formation of product-complex, which is contrary to the case of propene and 1-butene. As can be seen that the energy of TSDir - TSInd decreases from propene to 3-hexene (propene: 5.4 kcal/mol; 1-butene: 0.38 kcal/mol; 3-hexene: -0.03 kcal/mol). The different phenomenon of 3-hexene could result from the longer paraffin carbon chain. In addition to allylic H-atom abstraction, as illustrated in Figure 1, H-atom abstraction reaction can take place on methyl-C and vinyl-C sites as well. For the methyl site H-atom abstraction, 3-hexene proceeds through TS1 with a barrier height of 4.52 kcal/mol forming 3-hexenyl (P1) and H2O with an overall exothermicity of 15.47 kcal/mol. For the vinyl site H-atom abstraction, 3-hexene proceeds through TS3 with a barrier height of 4.76 kcal/mol and releases 8.65 kcal/mol heat before producing 1-ethyl-1-butenyl (P3). Generally, the bond dissociation energies (BDEs) of vinyl, methyl and allylic C-H bonds from NIST49, are roughly 111, 100 and 88 kcal/mol. Therefore, the strong vinyl C-H bond contributes to the higher energy barrier of Rxn3 (abbreviation from Table 2, same for below) and the weak allylic C-H bond leads to the lower barrier of Rxn2IND and Rxn2DIR. Benefiting from the lower transition-state energy and larger exothermicity, Rxn2IDR and Rxn2IND are kinetically and thermodynamically more favorable than Rxn1 and Rxn3. 3-hexene, as an unsaturated hydrocarbon, can not only proceed H-atom abstraction reaction but also ȮH addition reaction. Due to the symmetrical electronic structure of 3-hexene, only one adduct 1-ethyl-2-hydroxyl-butanyl (PA) can be obtained. As mentioned previously, 3-hexene and ȮH might interact to form reactant-complex before overcoming a transition-state barrier. As shown in Figure 3(a), the H-atom abstraction and ȮH addition channels share a common reactant-complex before reaching their transition-states individually. However, for some systems, the H-atom abstraction channel possesses a separate reactant-complex with hydroxyl hydrogen atom closer to C=C bond and the ȮH addition channel possesses another reactant-complex with oxygen atom closer to C=C bond, as illustrated in Figure 3(b).



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Two reactant-complexes are located for 3-hexene, the reactant-complex of H-atom abstraction (RC2) and the reactant-complex of ȮH addition (RCA), as depicted in Figure 2. The addition channel has a slightly deeper Van der Waals well of -2.46 kcal/mol compared to that of H-atom abstraction, whose well depth is -1.72 kcal/mol. This discrepancy might result from the different ȮH location and orientation. As can be noted from Figure 2, with the distances between the hydroxyl hydrogen and the two vinyl carbons of 2.443 Å and 2.449 Å, respectively, RCA shows a more compact geometry structure compared with RC2. 3-hexene proceeds through a transition-state (TSA), with an energy of only 0.21 kcal/mol lower than that of the entrance channel to RCA and then forms 1-ethyl-2-hydroxyl-butanyl. For TSA, the distance between vinyl carbon and oxygen atom is predicted to be 2.098 Å and because of the cleaving of the π-bond, the overall reaction exothermicity is found to be as large as 26.60 kcal/mol.

3.2 MEP and adiabatic ground-state energy According to transition-state theory, bond cleaving and forming proceed along the minimum energy path (MEP) due to lowest energy expense. Intrinsic reaction coordinate (IRC) calculation offers how electronic energy (VMEP) evolves with the signed reaction coordinate s, which is defined as the mass-scaled distance (amu1/2·Bohr) from the saddle point, with s < 0 referring to reactants side and s > 0 referring to products side. Besides, the adiabatic ground-state potential energy (VaG), which equals the sum of VMEP and the ZPE, is of significant importance as well. Gaussian 09 package35 can perform IRC calculation to obtain VMEP but the VaG calculation must be conducted point by point, which is tedious. Fortunately, GaussRate 2009-A package50 incorporates both VMEP and VaG calculation by calling Polyrate 2010-A and Gaussian 09 software35. For H-atom abstraction reactions, reasonable potential energy evolution can be followed applying the Euler steepest-descents (ESD) algorithm, in which repeated steps of length, ∆s, are taken in the direction of negative normalized gradient. The whole process is then repeated for the other direction of leaving the saddle point, thus providing the entire reaction path. The ESD algorithm is a first-order method and for an accurate evolution of the MEP, the step size has to be small due to the error is proportional to (∆s)2. However, the ESD algorithm fails to follow the energy evolving trend and even fluctuation occurs when applied to ȮH addition reaction, as depicted in Figure 4. To obtain reasonable predictions, the Page-McIver method51 was recommended and applied in this work, in which second-order algorithm is employed to describe the steepest descent path. The reaction path and the adiabatic ground-state potential


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energy evaluated at BhandHLYP/6-311G (d, p) level for H-atom abstraction and ȮH addition reactions of 3-hexene + ȮH system are illustrated in Figure 5. The VMEP and VaG values of 50 points were computed at each direction of the saddle point with an interval of ∆s = 0.02 amu1/2·Bohr. Extra 382 points are computed for ȮH addition reaction at s < 0 side. As can be seen, the H-atom abstraction reactions from non-allylic sites exhibit similar VMEP and VaG evolutions. Yet the potential energy of H-atom abstraction from methyl-C (Rxn1) site is slightly higher than from the vinyl-C site (Rxn3) and this results from the different orientations towards which ȮH radical approaches to 3-hexene molecule. Both the Rxn1 and Rxn3 possess a well at the reactant side of the VaG curve. For Rxn1, the appearance of the reactant-well shifts the maximum value from near the saddle point to the left side of the reactant-well. While for Rxn3, the stronger attractive force (due to the small s value, this attractive force exists among fragments instead of molecules so it is not Van der Waals force) near vinyl-C side contributes to a deeper reactant-well. Despite of the deeper reactant-well, the curve still peaks near the saddle point with its s slightly larger than zero, which is different from Rxn1. At the product side, a shallow product-well occurs at s = ~0.5 amu1/2·Bohr for Rxn3, while only a well-like curve, which exhibits sharp variation in slope but fails to generate a local minima, occurs in Rxn1 at similar coordinate. Similar to the reactants side, the attractive force between the products of Rxn3 is stronger than that of Rxn1. As can be concluded that the 3-hexene + ȮH system demonstrates stronger attractive force at the “shoulder” position and weaker force at the “head” position. Note that since the depths of those wells are smaller than 1 kcal/mol, the influence of those wells on rate coefficient is negligible. Regarding relatively lower BDE of allylic C-H bonds, the average energy level decreases dramatically when H-atom abstraction from allylic-C sites are concerned. Due to similar geometry structures, the Rxn2DIR and Rxn2IND share almost identical MEPs which are ~2 kcal/mol lower than those of Rxn1 and Rxn3. Besides, the VaG curves of Rxn2DIR and Rxn2IND are flatter than those of Rxn1 and Rxn3 at the reactant-side, which could cause a weaker tunneling effect on allylic H-atom abstraction. Note that although a shallow product-well and 3 well-like curves are labeled in Figure 5(c) and 5(d), those intermediates are not the reactant-complex and/or product-complex exhibited in Figure 1. In fact, the real Van der Waals complexes are beyond the s region scanned. For bimolecular reactions, the reactants locates at s = +∞ and thus the location of the reactant-complex can be distant from the saddle point. Therefore, sometimes it is really time consuming to search the reactant-complex from the saddle point, and the same happens to product-complex.



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When ȮH addition reaction is concerned, the energy level declines further. As can be seen in Figure 5(f), the energy level of electrophilic ȮH addition reaction is apparently lower than those of H-atom abstraction reactions. It suggests that 3-hexene exhibits stronger repulsion when ȮH approaching to hydrogen atom, yet smaller repulsion when ȮH approaching to carbon atom. Unlike the reactions analyzed above, the energy of ȮH addition is much flat near the saddle point with the maximum VMEP lower than zero and the maximum VaG lower than that of the reactants (red dash line). As a consequence, this reaction might possess some characteristics of barrier-less reactions and the rate coefficient might exhibit negative temperature dependence, particularly at low temperature. Moreover, extra 382 points are computed at reactant side and the lower limit of reaction coordinate reaches s= -8.64 amu1/2·Bohr. However only two attractive force wells occur and the reactant-complex is still beyond the scanned region.

3.3 Activation Gibbs free energy change From the perspective of TST, saddle point is regarded as the TS due to its maximum electronic energy. The associated conventional rate constant is usually treated as the upper limit of real rate constant. To acquire more reasonable results, the CVT method involving the impact of not only energy but also entropy was applied. And the geometry where the generalized rate constant reaches its minimum and the corresponding activation Gibbs free energy change (∆G) reaches its maximum is chosen as the generalized TS. The Gibbs free energy change can be expressed as

 Q GT (T , s )  ∆ G (T , s ) = RT  β VMEP ( s ) − ln R  Q (T ) K o  

(10)

where Ko is the activation equilibrium constant. Apparently, the variational rate constant has to be smaller than the conventional one. Figure 6 illustrates ∆G as a function of reaction coordinate for Rxn3 at 294 – 2000 K. Results indicate that ∆G is almost proportional to temperature. The smax (peak of ∆G) values are larger than zero for low and high temperatures, meaning that all the generalized TSs locate at the product side of saddle point. Similarly, the smax is almost proportional to temperature as well. Figure 7 shows the smax evolution with temperature for H-atom abstraction and ȮH addition reactions. Obviously, the generalized TS of H-atom abstraction reactions is much close to the saddle point, especially for Rxn2IND. The smax of ȮH addition reaction exhibits a wide span of ~0.25 amu1/2·Angstrom, while the smax span of H-atom abstraction reactions are


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smaller than 0.05 amu1/2·Angstrom. This could be due to the flat MEP curve of ȮH addition reaction and the steep MEP curve of H-atom abstraction reactions. Large span corresponds to significant variational effect, and the rate coefficient of TST can be a reasonable approximation of CVT rate coefficient when the span is small.

3.4 Rate coefficients 3.4.1 Quantum mechanical effects The broad shape of PES in the allylic H-atom abstraction and OH-addition channels suggests that the CVT would be suitable to accurately determinate the rate coefficients. Besides, the relative high and narrow barriers in methyl and vinyl H-atom abstraction channels suggests that the quantum mechanical tunneling effect could dramatically impact the rate coefficients particularly at low temperature. Therefore, the CVT incorporated with the one-dimensional Wigner tunneling, the zero curvature tunneling (ZCT) and small curvature tunneling (SCT) was employed; meanwhile the TST was applied as well to observe the variational effect. Figure 8 illustrates the rate coefficients and pressure dependence obtained in unit of

cm3 ⋅ molecule-1 ⋅ s -1 and according to the similar methods of Sun and Law19, the uncertainty should be a factor of 5. Note that the reaction-degeneracies defined as the number of equivalent reaction channels are 6,4,4,2 and 2 for reaction Rxn1, Rxn2DIR, Rxn2IND, Rxn3 and RxnAdd respectively. For the reactions processing through non-allylic H-atom abstraction channels, kTST and kCVT are comparable due to the high and narrow barrier. However, the kTST is generally considered as the upper limit of rate coefficient so the kCVT must be reasonably lower than kTST. The difference between kTST and kCVT value suggests how far the generalized TS shifts from the saddle point, namely the variational effect. For non-allylic H-atom abstraction, Rxn1 exhibits more significant variational effect compared to Rxn3. As analyzed above, this can be resulted from the reactant-well of Rxn1, which shifts the maximum to the left side of it. On the contrary, the maximum point of Rxn3 remains unshifted. For both Rxn1 and Rxn3, the tunneling effect is significant and the rate coefficients increase by a factor of 8 at 300 K under the correction of SCT. The ZCT transmission coefficient is lower than SCT, because the ZCT uses reaction path for tunneling and its effective mass simplifies to the reduced mass. On the contrary, the SCT couples the reaction coordinate with the motions perpendicular to it and tunnels through corner-cutting path. The



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ZCT method has the drawback that tunneling is usually seriously underestimated; however the transmission coefficient of SCT is reasonably larger and more accurate. It is noteworthy that the Wigner tunneling which only takes into account imaginary frequency exhibits comparable value to that evaluated with SCT method. This might be coincidental due to the Wigner method is generally trends to be coarse and lack of accuracy. For allylic H-atom abstraction channels, though the PES is broader and flatter than non-allylic channels, the variational effect is, however, weaker. Specifically, the kTST and kCVT almost share the identical value from 300 to 2000 K, which can be reasonably interpreted by Figure 7, in which the maximum displacement of smax for Rxn2DIR and Rxn2IND is lower than 0.03 amu1/2·Angstrom. When tunneling is considered, the rate coefficients even drop at low and intermediate temperature especially when ZCT is applied. Figure 9 displays the correction factors of Rxn2DIR and the meanings of abbreviations are detailed in its caption. Whereas the non-classical reflection occurs in VaAG≤E≤2VaAG -E0 (VaAG denotes the maximum VaG and E0 denotes the quantum threshold energy) can reduces the rate coefficients, with more significant tunneling effect, the overall quantum mechanical effect tends to enhance the reaction. Therefore κ ZCT and κ SCT are larger than unity. Nevertheless, due to the displacement between transition-state and VaAG, the adiabatic ground-state correction contributes a relatively small correction factor. Thus the overall correction value is lower than unity and give rise to the unusual decline in rate coefficient when quantum mechanical effects are considered. Since the ȮH addition reaction exhibits the loosest TS and the strongest varivational effect, apparent difference between kTST and kCVT occurs. Moreover, since the VaAG value is smaller than E0, the submerged barrier makes rate coefficient exhibit negative temperature dependence at lower temperature, which is different from the H-atom abstraction reactions. Although the reactant-complex of the ȮH addition reaction distinguish this ȮH addition reaction from the typical barrier-less association reaction, the software still regards this reaction as a barrier-less reaction and takes no quantum effects along the reaction coordinate into account. However, given the large mass of ȮH radical and the flat barrier, the quantum mechanical effect should be negligible.

3.4.2 Competition and branching ratio Generally different reaction categories exhibit different competitive capability at specific temperature and the dominated-reaction varies with temperature; and typically 3-Hexene + ȮH system is not an


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exception. To explore the competition among the H-atom abstraction channels, as well as between the H-atom abstraction and the ȮH addition channels, the calculated CVT rate coefficients with SCT correction (kCVT/SCT) are illustrated in Figure 10. Meanwhile, the branching ratios are illustrated in Figure 11. The ȮH addition reaction dominates the system overwhelmingly at temperature lower than 600 K while for higher temperature region, the H-atom abstraction reactions are predominant, especially for those proceeding at allylic sites. The branching ratio of ȮH addition reaction reaches 80% at 450K and the branching ratio of H-atom abstraction reaction reaches 80% at 1000K. Within 450-1000K the competitiveness of both reaction categories are comparable. Although abstracting hydrogen from methyl carbon exhibits higher barrier than from vinyl carbon, the rate coefficients of those two reactions are comparable. As presented in Figure 1, the products of H-atom abstraction from methyl site are more stable than that from the vinyl site. As a result, Rxn1 is kinetically and thermodynamically more preferential than Rxn3 due to the larger rate coefficient of Rxn1. The allylic H-atom abstraction reactions exhibit around ten time higher rate coefficients than non-allylic H-atom abstraction reactions, because of the obviously lower barrier. It is noteworthy that the indirect channel proceeding at allyic site exhibits around two times higher rate coefficient than the direct channel. Although the barrier of the indirect channel is even slightly higher than the direct channel, the reactant-complex can readily facilitate the H-atom abstraction and increases the rate coefficient. Accounting for a portion of around 70%, the allylic channels overwhelmingly dominate the H-atom abstraction reactions. Figure 12 compares the rate coefficients evaluated at CCSD(T) and BHandH3LYP level. With more accurate energies applied, the rate coefficients at temperature larger than 600 K almost keep unchanged. For lower temperature region, the non-allylic H-atom abstraction and addition rate coefficients vary by a factor of two while the allylic H-abstraction reaction rate coefficients decrease by a factor of ten. Therefore, the rate coefficients acquired at BHandH3LYP can be reasonable approximations of the accurate values for the non-allylic H-atom abstraction and the OH addition reactions. Simultaneously, the quasi-Arrhenius parameters of those reactions are presented in Table 3 for chemical reaction mechanism constructions. Figure 13 compares the rate coefficients of 3-hexene with those of 1-butene and ethylene. As can be noted that most reactions of the same category almost stay in the same magnitude which means our computation are physically valid. For the non-allylic H-abstraction reactions, the rate coefficients are comparable, while the rate coefficients of the allylic H-abstraction are close to the OH addition reactions at high temperature. The difference increases with the decrease in temperature, resulting from more



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significant tunneling effect of small mass molecules. It could also be concluded that the appearance of saturated carbon-chain reduced the rate of not only allylic H-atom abstraction but also the ȮH addition reaction.

4. Concluding remarks The H-atom abstraction and addition reactions of 3-hexene by ȮH radical was initially investigated using sophisticated quantum mechanical method and variational TST. The stationary points and TSs were optimized at BHandHLYP/6-311G (d, p) level and more accurate energies were evaluated at CCSD(T)/CBS level. The evolution of minimum reaction paths, adiabatic ground-state energy surface and activation Gibbs free energy changes were described in details. Rate coefficient calculations were performed using TST and canonical TS theory with quantum effect consideration of Wigner correction, zero curvature correction and small curvature correction. The rate coefficients were obtained with an uncertainty factor of 5. The 3-hexene + ȮH system is dominated by addition reaction when temperature is under 450K and dominated by H-atom abstraction reactions at over 1000K. At intermediate temperature region, both addition and H-atom abstraction reactions play significant roles. Allylic H-atom abstraction overwhelmingly dominates the overall H-atom abstraction with a branching ratio larger than 70%. Thanks to the reactant-complex, the indirect allylic H-atom abstraction channel exhibits around two times larger rate coefficient compared to the direct one in spite of its slightly higher barrier. Similarly, the ȮH addition reaction also possesses a reactant Van der Waals well and its submerged barrier makes contribution to the obvious negative temperature dependence at low temperature region. The comparison of rate coefficients computed with conventional and canonical variational TST indicates that the addition reaction exhibits strongest variational effect while allylic H-atom abstraction reactions exhibit the least. Due to the narrower barriers, non-allylic H-atom abstraction reactions demonstrate significant tunneling effect. The rate coefficients were fitted in the of quasi-Arrhenius formula and can be applied directly when constructing detailed chemical reaction mechanisms concerning 3-hexene. Further investigations can be focused on the pressure dependence of the ȮH reactions and other reactions of this PES.

5. Supplementary information Vibrational frequencies, moments of inertia and geometries optimized at the BHandHLYP/6-311G(d, p) level are presented in the supplementary data. This material is available free of charge via the Internet at


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http://pubs.acs.org.

6. Acknowledgment The authors acknowledge the financial support of the National Natural Science Foundation of China under Grant No. 91541115, 91441203 and 91541107, the National Basic Research Program under Grant No. 2013CB228406, and the Science Challenge Project under Grant No. JCKY2016212A501.

7. References and Notes (1) Babushok, V.; Tsang, W., Inhibitor Rankings for Alkane Combustion. Combust. Flame 2000, 123, 488-506. (2) Bufferand, H.; Tosatto, L.; La Mantia, B.; Smooke, M. D.; Gomez, A., Experimental and Computational Study of Methane Counterflow Diffusion Flames Perturbed by Trace Amounts of Either Jet Fuel or a 6-Component Surrogate under Non-Sooting Conditions. Combust. Flame 2009, 156, 1594-1603. (3) Curran, H. J.; Gaffuri, P.; Pitz, W. J.; Westbrook, C. K., A Comprehensive Modeling Study of Iso-Octane Oxidation. Combust. Flame 2002, 129, 253-280. (4) Gallagher, S. M.; Curran, H. J.; Metcalfe, W. K.; Healy, D.; Simmie, J. M.; Bourque, G., A Rapid Compression Machine Study of the Oxidation of Propane in the Negative Temperature Coefficient Regime. Combust. Flame 2008, 153, 316-333. (5) Herbinet, O., et al., Experimental and Modeling Investigation of the Low-Temperature Oxidation of N-Heptane. Combust. Flame 2012, 159, 3455-3471. (6) Jahangirian, S.; Dooley, S.; Haas, F. M.; Dryer, F. L., A Detailed Experimental and Kinetic Modeling Study of N-Decane Oxidation at Elevated Pressures. Combust. Flame 2012, 159, 30-43. (7) Ji, C.; Dames, E.; Wang, Y. L.; Wang, H.; Egolfopoulos, F. N., Propagation and Extinction of Premixed C5– C12 N-Alkane Flames. Combust. Flame 2010, 157, 277-287. (8) Kelley, A. P.; Smallbone, A. J.; Zhu, D. L.; Law, C. K., Laminar Flame Speeds of C5 to C8 N-Alkanes at Elevated Pressures: Experimental Determination, Fuel Similarity, and Stretch Sensitivity. Proc. Combust. Inst. 2011, 33, 963-970. (9) Liu, N.; Ji, C.; Egolfopoulos, F. N., Ignition of Non-Premixed C3–C12 N-Alkane Flames. Combust. Flame 2012, 159, 465-475. (10) Yang, F.; Deng, F.; Pan, Y.; Tian, Z.; Zhang, Y.; Huang, Z., Ab Initio Kinetics for Isomerization Reaction of Normal-Chain Hexadiene Isomers. Chem. Phys. Lett. 2016, 663, 66-73. (11) Yang, F.; Deng, F.; Zhang, P.; Hu, E.; Cheng, Y.; Huang, Z., Comparative Study on Ignition Characteristics of 1-Hexene and 2-Hexene Behind Reflected Shock Waves. Energy & Fuels 2016, 30, 5130-5137. (12) Yang, F.; Deng, F.; Zhang, P.; Tian, Z.; Tang, C.; Huang, Z., Experimental and Kinetic Modeling Study on Trans-3-Hexene Ignition Behind Reflected Shock Waves. Energy & Fuels 2016, 30, 706-716. (13) Hong, Z.; Davidson, D. F.; Barbour, E. A.; Hanson, R. K., A New Shock Tube Study of the H + O2 → OH + O Reaction Rate Using Tunable Diode Laser Absorption of H2O near 2.5 Μm. Proc. Combust. Inst. 2011, 33, 309-316. (14) Tully, F. P., Hydrogen-Atom Abstraction from Alkenes by OH, Ethene and 1-Butene. Chem. Phys. Lett. 1988, 143, 510-514. (15) Tully, F. P.; Goldsmith, J. E. M., Kinetic Study of the Hydroxyl Radical-Propene Reaction. Chem. Phys. Lett. 1985, 116, 345-352. (16) Huynh, L. K.; Zhang, H. R.; Zhang, S.; Eddings, E.; Sarofim, A.; Law, M. E.; Westmoreland, P. R.; Truong,



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T. N., Kinetics of Enol Formation from Reaction of OH with Propene. The Journal of Physical Chemistry A 2009, 113, 3177-3185. (17) Zádor, J.; Jasper, A. W.; Miller, J. A., The Reaction between Propene and Hydroxyl. PCCP 2009, 11, 11040-11053. (18) Szori, M.; Fittschen, C.; Csizmadia, I. G.; Viskolcz, B., Allylic H-Abstraction Mechanism: The Potential Energy Surface of the Reaction of Propene with OH Radical. J. Chem. Theory Comput. 2006, 2, 1575-1586. (19) Sun, H.; Law, C. K., Kinetics of Hydrogen Abstraction Reactions of Butene Isomers by OH Radical. The Journal of Physical Chemistry A 2010, 114, 12088-12098. (20) Greenwald, E. E.; North, S. W.; Georgievskii, Y.; Klippenstein, S. J., A Two Transition State Model for Radical−Molecule Reactions: A Case Study of the Addition of OH to C2H4. The Journal of Physical Chemistry A 2005, 109, 6031-6044. (21) Greenwald, E. E.; North, S. W.; Georgievskii, Y.; Klippenstein, S. J., A Two Transition State Model for Radical−Molecule Reactions: Applications to Isomeric Branching in the OH−Isoprene Reaction. The Journal of Physical Chemistry A 2007, 111, 5582-5592. (22) Truhlar, D. G.; Isaacson, A. D.; Garrett, B. C., Generalized Transition State Theory. CRC Press: Boca Raton, FL: 1985; Vol. 4, pp 65-137. (23) Becke, A. D., Density‐Functional Thermochemistry. I. The Effect of the Exchange‐Only Gradient Correction. The Journal of Chemical Physics 1992, 96, 2155-2160. (24) Becke, A. D., Density‐Functional Thermochemistry. Iii. The Role of Exact Exchange. The Journal of Chemical Physics 1993, 98, 5648-5652. (25) Lee, C.; Yang, W.; Parr, R. G., Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Physical Review B 1988, 37, 785-789. (26) Henry, D. J.; Parkinson, C. J.; Radom, L., An Assessment of the Performance of High-Level Theoretical Procedures in the Computation of the Heats of Formation of Small Open-Shell Molecules. The Journal of Physical Chemistry A 2002, 106, 7927-7936. (27) Head-Gordon, M.; Pople, J. A.; Frisch, M. J., MP2 Energy Evaluation by Direct Methods. Chem. Phys. Lett. 1988, 153, 503-506. (28) Møller, C.; Plesset, M. S., Note on an Approximation Treatment for Many-Electron Systems. Physical Review 1934, 46, 618-622. (29) Lee, T. J.; Taylor, P. R., A Diagnostic for Determining the Quality of Single-Reference Electron Correlation Methods. Int. J. Quantum Chem. 1989, 36, 199-207. (30) Lee, T. J.; Rendell, A. P.; Taylor, P. R., Comparison of the Quadratic Configuration Interaction and Coupled-Cluster Approaches to Electron Correlation Including the Effect of Triple Excitations. The Journal of Physical Chemistry 1990, 94, 5463-5468. (31) Vega-Rodriguez, A.; Alvarez-Idaboy, J. R., Quantum Chemistry and TST Study of the Mechanisms and Branching Ratios for the Reactions of OH with Unsaturated Aldehydes. PCCP 2009, 11, 7649-7658. (32) Huynh, L. K.; Ratkiewicz, A.; Truong, T. N., Kinetics of the Hydrogen Abstraction OH + Alkane → H2O + Alkyl Reaction Class: An Application of the Reaction Class Transition State Theory. The Journal of Physical Chemistry A 2006, 110, 473-484. (33) Jasper, A. W.; Klippenstein, S. J.; Harding, L. B.; Ruscic, B., Kinetics of the Reaction of Methyl Radical with Hydroxyl Radical and Methanol Decomposition. The Journal of Physical Chemistry A 2007, 111, 3932-3950. (34) Martin, J. M. L.; Uzan, O., Basis Set Convergence in Second-Row Compounds. The Importance of Core Polarization Functions. Chem. Phys. Lett. 1998, 282, 16-24.


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(35) Gaussian 09, R. E., M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson et al., Gaussian, Inc., Wallingford CT, 2009. (36) Fernández-Ramos, A.; Miller, J. A.; Klippenstein, S. J.; Truhlar, D. G., Modeling the Kinetics of Bimolecular Reactions. Chem. Rev. 2006, 106, 4518-4584. (37) Ayala, P. Y.; Schlegel, H. B., Identification and Treatment of Internal Rotation in Normal Mode Vibrational Analysis. The Journal of Chemical Physics 1998, 108, 2314-2325. (38) Ellingson, B. A.; Lynch, V. A.; Mielke, S. L.; Truhlar, D. G., Statistical Thermodynamics of Bond Torsional Modes: Tests of Separable, Almost-Separable, and Improved Pitzer–Gwinn Approximations. The Journal of Chemical Physics 2006, 125, 084305. (39) Davis Jr, J. C., Statistical Mechanics (Rapp, Donald). J. Chem. Educ 1974, 51, A345. (40) Daudel, R.; Pullman, B., The World of Quantum Chemistry: Proceedings; Reidel, 1974. (41) Kuppermann, A.; Truhlar, D. G., Exact Tunneling Calculations. J. Am. Chem. Soc. 1971, 93, 1840-1851. (42) Lu, D.-h., et al., Polyrate 4: A New Version of a Computer Program for the Calculation of Chemical Reaction Rates for Polyatomics. Comput. Phys. Commun. 1992, 71, 235-262. (43) Melius, C. F.; Blint, R. J., The Potential Energy Surface of the Ho2 Molecular System. Chem. Phys. Lett. 1979, 64, 183-189. (44) Schatz, G. C.; Elgersma, H., A Quasi-Classical Trajectory Study of Product Vibrational Distributions in the Oh + H2 → H2o + H Reaction. Chem. Phys. Lett. 1980, 73, 21-25. (45) Fernandez-Ramos, A.; Ellingson, B. A.; Garrett, B. C.; Truhlar, D. G., Variational Transition State Theory with Multidimensional Tunneling. Rev. Comput. Chem. 2007, 23, 125. (46) Kim, Y.; Truhlar, D. G.; Kreevoy, M. M., An Experimentally Based Family of Potential Energy Surfaces for Hydride Transfer between Nad+ Analogs. J. Am. Chem. Soc. 1991, 113, 7837-7847. (47) Garrett, B. C.; Truhlar, D. G.; Grev, R. S.; Magnuson, A. W., Improved Treatment of Threshold Contributions in Variational Transition-State Theory. The Journal of Physical Chemistry 1980, 84, 1730-1748. (48) Steckler, R.; Chuang, Y.; Coitino, E.; Hu, W.; Liu, Y.; Lynch, G.; Nguyen, K.; Jackels, C.; Gu, M.; Rossi, I., Polyrate, Version 7.0. University of Minnesota, Minneapolis 1996, 33. (49) Linstrom, P. J.; Mallard, W., Nist Chemistry Webbook; Nist Standard Reference Database No. 69. 2001. (50) Zheng, J.; Zhang, S.; Corchado, J.; Chuang, Y.; Coitino, E.; Ellingson, B.; Truhlar, D., Gaussrate, Version 2009-A. University of Minnesota: Minneapolis, MN 2010. (51) Page, M.; McIver, J. W., On Evaluating the Reaction Path Hamiltonian. The Journal of Chemical Physics 1988, 88, 922-935.



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Table 1. The comparison of structures, energies and proportions of the four conformers of 3-hexene optimized at BHandHLYP/6-311G level. Conformer

Structure

Energy (kcal/mol)

Proportion

Syn-syn

1.15

1/9

Syn-skew

0.56

4/9

0

2/9

0.01

2/9

Same-side skew Different-side skew

Table 2. Calculated relative energies of species involved in 3-hexene + OH reactions at BHANDHLYP and CCSD(T) level. The unit is kcal/mol and the nomenclatures are self-explanatory.

Rxn1 Rxn3 RxnAdd

Rxn2IND

Rxn2DIR

Species

BH&HLYP/ 6-311g(d, p)

CCSD(T)/ cc-PVDZ

CCSD(T)/ cc-PVTZ

CCSD(T)/ CBS

CCSD(T)/ CBS+ZPE

TS1 P1+H2O TS3 P3+H2O RCA TSA PA RC2 TS2IND PC2 P2+H2O TS2DIR PC2 P2+H2O

7.8 -8.87 7.39 -3.49 -4.77 -2.55 -28.51 -5.74 4.62 -33.14 -27.65 4.54 -33.14 -27.65

8.64 -8.76 7.46 -3.50 -4.64 -0.85 -29.05 -7.46 3.87 -32.17 -25.37 4.00 -32.17 -25.37

7.02 -12.78 6.76 -7.14 -4.05 -1.73 -29.94 -4.19 5.35 -33.32 -29.52 5.35 -33.32 -29.52

6.49 -14.09 6.54 -8.33 -3.85 -2.02 -30.22 -3.13 5.83 -33.70 -30.87 5.79 -33.70 -30.87

4.52 -15.47 4.76 -8.65 -2.46 -0.21 -26.60 -1.72 3.93 -33.19 -31.76 3.90 -33.19 -31.76

Table 3. The quasi-Arrhenius parameters of 3-Hexene + OH reactions. The unit of rate coefficient is cm3• molecule-1•s-1 and of pressure is atm. Reactions Rxn1

A

n

Ea (kcal)

1.39E-19

2.59

3.27

Rxn3

2.4E-21

3.14

3.36

Rxn2IND

1.35E-20

2.99

2.79

Rxn2DIR

9.42E-21

2.98

2.74

RxnAdd

2.06E-19

2.15

-1.40

0.001

3.79E-22

2.25

-2.58

0.01

9.99E-22

2.24

-2.55

0.1

2.6E-21

2.24

-2.51


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1

7.21E-21

2.22

-2.43

10

2.31E-20

2.18

-2.27

100

9.09E-20

2.10

-1.96

1000

2.14E-19

2.08

-1.61

Figure 1. Energy diagram for the abstraction and addition reactions of 3-hexene + OH calculated at CCSD(T)/CBS level at 0 K. The dash lines denote the s-allylic H-atom abstraction channels and the dot line denotes the addition reaction.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2. BHANDHLYP/6-311G (d, p)-optimized structures of transition states, reactant complexes and product complexes involved in 3-hexene + ȮH radical reactions.


Page 22 of 28

Page 23 of 28

Figure 3. Model PESs involving addition as well as H-atom abstraction. (a) Two reaction channels with one reactant-complex; (b) Two reaction channels involving two separate reactant-complexes. 30

VMEP (kcal/mol)

VaG ESD algorithm

10

VaG Page-McIver algorithm

90

0 80

VaG (kcal/mol)

100

20

-10 VMEP ESD algorithm

-20

70

VMEP Page-McIver algorithm

-4

-2

0

2

4

Reaction coordinate s (amu1/2Bohr)

Figure 4. Comparison of searching MEP and adiabatic ground-state potential energy curve with ESD and Page-McIver algorithm for ȮH addition reaction. 8

(a) Rxn1

Max

112

(b) Rxn3

8

Max

110

108 106

0

104

V

G a

108

106 0

102

VMEP

-4

Well 4

VaG

104

VMEP

100

Well-like curve

Well 98

-1.0

-0.5

0.0

0.5 1/2

Reaction coordinate s (amu Bohr)

1.0

102

-4 -1.0

-0.5

0.0

0.5 1/2



1.0

VaG (kcal/mol)

Well

VMEP (kcal/mol)

4

VaG (kcal/mol)

110

VMEP (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



110

6

108

4

102 -4

100

Well -1.0

-0.5

0.0

0.5

102

-4 99

-6

98

VMEP

-8

-2

VaG

-8

96

-10

94

-12

1.0

VMEP Well-like curve -1.0

-0.5

1/2

0.5

93

1.0


(f) All Rxns

105

110

15

(e) RxnAdd

-4

103

Well 102

105

10

5

100

0

95

G

104

VaG (kcal/mol)

VMEP

VMEP (kcal/mol)

Max

VaG

-5

Rxn1 Rxn2IND

-5 -8

0.0

1/2


-3

96

-6

-4

-2

Va (kcal/mol)

Va

G

108

105

Well-like curve

0

VMEP (kcal/mol)

104

VaG (kcal/mol)

VMEP (kcal/mol)

Well-like curve

(d) Rxn2IND

2

106 0

Max

VaG (kcal/mol)

(c) Rxn2DIR

Max

4

VMEP (kcal/mol)

0

-1.0


Rxn3 RxnAdd Rxn2DIR solid: VaG, dash: VMEP

-0.5

0.0

90

0.5

1.0


Figure 5. MEP potential energy and the adiabatic ground-state potential energy evaluated at BHANDHLYP/6-311G (d, p) level for H-atom abstraction and ȮH addition reactions of 3-hexene + ȮH. Red dash line denotes the VaG value of the reactants. 250 s positions for maximum ∆G at different T Solid: ∆G at different T Rxn3

2000

1500 150 1000 100

Temperature (K)

at 2000 K

200

∆G (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 28

500 50 at 294 K

0

0 -0.2

-0.1

0.0

0.1

0.2

0.3

0.4

Reaction coordinate s (amu1/2Angstrom)

Figure 6. Activation Gibbs free energy change for Rxn3 at 294-2000 K and the reaction coordinates where the activation Gibbs free energy change peaks (smax).


Page 25 of 28

0.4 Rxn1 Rxn2DIR Rxn2IND Rxn3 RxnAdd

0.06

0.3

0.04 0.2 0.02

0.1

0.00

0

500

1000

1500

s for addition (amu1/2Angstrom)

s for H-abstraction (amu1/2Angstrom)

0.08

2000

Temperature (K)

Figure 7. Relationship between temperature and reaction coordinates where the activation Gibbs free energy change peaks (smax). 1E-10

1E-12 1E-13 1E-14 1E-15 1E-16

-1 -1

1E-11

3

(a) Rxn1 TST CVT TST/W CVT/ZCT CVT/SCT

Rate coefficient (cm molecule s )

3

-1 -1


1E-10

1E-17

(b) Rxn3 TST CVT TST/W CVT/SCT CVT/ZCT

1E-11 1E-12 1E-13 1E-14 1E-15 1E-16 1E-17

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.5

1.0

1.5

-1

2.0

2.5

3.0

3.5

-1

1000/T (K )

1000/T (K )

-1 -1

(c) Rxn2DIR TST CVT CVT/ZCT CVT/SCT

3

1E-11

1E-12

1E-13

Rate coefficient (cm3molecule-1s-1)

1E-10


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(d) Rxn2IND TST CVT CVT/ZCT CVT/SCT

1E-10

1E-11

1E-12

1E-13

1E-14

1E-14 0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.5

1.0

-1

1000/T (K )


1.5

2.0

1000/T (K-1)

2.5

3.0

3.5

4E-12

2E-12


(e) RxnAdd TST CVT

6E-12

Page 26 of 28

(f) RxnAdd 0.001atm 0.01atm 0.1atm

1E-11

1atm 10atm 100atm 1000atm

1E-12

1E-13

1E-14

0 0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.5

1.0

1000/T (K-1)

1.5

2.0

2.5

3.0

3.5

1000/T

Figure 8. TST and CVT rate coefficients with Wigner, ZCT and SCT tunneling corrections of H-atom abstraction and ȮH addition reactions for 3-hexene +ȮH.

Rxn2DIR CVT/CAG ZCT-notunn SCT-notunn ZCT SCT CVT/CAG/ZCT CVT/CAG/SCT

2.0

Correction factor

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



1.5

1.0

0.5

400

800

1200

1600

2000

Temperature (K)

Figure 9. Correction factors for Rxn2DIR. CVT/CAG denote classical adiabatic ground-state correction. ZCT-notunn and SCT-notunn denote non-classical reflection effects. ZCT and SCT denote the quantum mechanical effects including both tunneling and non-classical reflection. CVT/CAG/ZCT denotes classical adiabatic ground-state and ZCT quantum effect correction. CVT/CAG/SCT denotes classical adiabatic ground-state and SCT quantum effect correction.


Page 27 of 28

1E-11

1E-12

3

-1 -1


1E-10

1E-13

Rxn1 Rxn2 Rxn3 Rxn2DIR Rxn2IND RxnAdd H-abs

1E-14

1E-15

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1000/T (K-1)

Figure 10. CVT/SCT rate coefficients of H-atom abstraction and ȮH addition reactions for 3-hexene +ȮH.

1.0

0.8

Branching ratio

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Rxn1 Rxn2 Rxn3 Rxn2DIR Rxn2IND RxnAdd H-abs

0.6

0.4

0.2

0.0 0.5

1.0

1.5

2.0

2.5

3.0

3.5

-1

1000/T (K )

Figure 11. Branching ratios of H-atom abstraction and ȮH addition reactions for 3-hexene +ȮH.




1E-10

1E-11

1E-12

1E-13

Rxn1 Rxn2DIR 1E-14 Rxn2IND Rxn3 RxnAdd 1E-15 Solid: CCSD Open: BHandH3LYP 1E-16

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-1

1000/T (K )

Figure 12. Comparison of the CVT/SCT rate coefficients of H-atom abstraction and ȮH addition reactions for 3-hexene +ȮH calculated at CCSD(T) and BHandH3LYP level.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 28

1E-10

1E-11

1E-12

1E-13

C2H4 Add 1-C4H8 Rxn1 1-C4H8 Rxn2 1-C4H8 Rxn3

1E-14

3-C6H12 Add 3-C6H12 Rxn1 3-C6H12 Rxn2 3-C6H12 Rxn3

1E-15 0.5

1.0

1.5

2.0

2.5

3.0

3.5

1000/T (K-1)

Figure 13. Comparison of rate coefficients of 3-hexene, 1-butene and ethylene + ȮH system.


Kinetics of Hydrogen Abstraction and Addition Reactions of 3-Hexene

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