Atmospheric Reaction of Cl + Methacrolein: A Theoretical Study on the

Article pubs.acs.org/JPCA

Atmospheric Reaction of Cl + Methacrolein: A Theoretical Study on the Mechanism, and Pressure- and Temperature-Dependent Rate Constants Cuihong Sun,‡,† Baoen Xu,‡ and Shaowen Zhang*,† †

School of Chemistry, Beijing Institute of Technology, Beijing 100081, People’s Republic of China College of Chemical Engineering, Shijiazhuang University, Shijiazhuang 050035, People’s Republic of China

‡

S Supporting Information *

ABSTRACT: Methacrolein is a major degradation product of isoprene, the reaction of methacrolein with Cl atoms may play some roles in the degradation of isoprene where these species are relatively abundant. However, the energetics and kinetics of this reaction, which govern the reaction branching, are still not well understood so far. In the present study, twodimensional potential energy surfaces were constructed to analyze the minimum energy path of the barrierless addition process between Cl and the CC double bond of methacrolein, which reveals that the terminal addition intermediate is directly formed from the addition reaction. The terminal addition intermediate can further yield different products among which the reaction paths abstracting the aldehyde hydrogen atom and the methyl hydrogen atom are dominant reaction exits. The minimum reaction path for the direct aldehydic hydrogen atom abstraction is also obtained. The reaction kinetics was calculated by the variational transition state theory in conjunction with the master equation method. From the theoretical model we predicted that the overall rate constant of the Cl + methacrolein reaction at 297 K and atmospheric pressure is koverall = 2.3× 10−10 cm3 molecule−1 s−1, and the branching ratio of the aldehydic hydrogen abstraction is about 12%. The reaction is pressure dependent at P < 10 Torr with the high pressure limit at about 100 Torr. The calculated results could well account for the experimental observations. CH 2C(CH3)CHO + Cl + M → CH 2C(Cl)(CH3)CHO + M (R2)

1. INTRODUCTION The biogenic volatile organic compounds, especially isoprene can undergo photolysis or chemical degradation by many species such as OH, O3, NO3, and Cl atoms. As one of isoprene’s major oxidation products, methacrolein (MACR) is also highly reactive toward OH,1−14 O3,15−20 NO3,21−23 and Cl,24−28 and is mainly degraded by the reaction with OH radical in atmosphere. However, large amounts of reactive chlorine compounds (ClNO2), gaseous photolytic Cl atoms precursor, have been observed in continental regions far from marine and coastal regions.29 In addition, several experiment studies have shown that the rate coefficients for the reactions of Cl atoms with organic compounds in coastal areas at dawn are approximately an order of magnitude or more than those of OH.24,26,27,30 Hence, chlorine atoms obviously can contribute significantly to the oxidation of volatile organic compounds where these species are abundant and play some roles in the loss of biogenic volatile organic compound more than previously thought. The reaction of MACR with Cl may proceed via either the addition of Cl to one of the carbon atoms of the CC double bond (R1 and R2) or the abstraction of the aldehyde hydrogen atom (R3) and the methyl hydrogen atom (R4) by Cl:28

CH 2C(CH3)CHO + Cl → CH 2C(CH3)CO + HCl (R3) CH 2C(CH3)CHO + Cl → CH 2C(CH 2)CHO + HCl (R4)

Kaiser et al. suggested that (47 ± 8)% of the reaction of MACR with Cl proceeds via addition to the CC double bond (R1 and R2) with most of the addition occurring at the terminal carbon atom, and (24.5 ± 5)% occurs via abstraction of the aldehydic hydrogen atom (R3), (2.3 ± 0.8)% via abstraction of the methyl hydrogen atom (R4).28 Canosa-Mas et al. found that the branching ratio for the hydrogen abstraction is 0.18.25 At room temperature and atmospheric pressure, the overall rate constant of the Cl + MACR reaction measured by experiments ranged from 2.09 × 10−10 to (3.2 ± 0.5) × 10−10cm3 molecule−1 s−1.24−28 The overall rate constant measured by Canosa-Mas et al. was (3.2 ± 0.5) × 10−10 cm3 molecule−1 s−1 at the atmospheric pressure,24 and (3.3 ± 0.6) × 10−10 cm3 molecule−1 s−1 at the low pressure of 1.6 Torr,25 so they concluded that the reaction of MACR with Cl atoms is Received: January 28, 2014 Revised: April 28, 2014 Published: April 30, 2014

CH 2C(CH3)CHO + Cl + M → CH 2ClC(CH3)CHO + M (R1) © 2014 American Chemical Society

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dx.doi.org/10.1021/jp500993k | J. Phys. Chem. A 2014, 118, 3541−3551

The Journal of Physical Chemistry A

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pressure-independent. However, Kaiser et al. studied the pressure dependence of the Cl + MACR reaction over the range of 1−950 Torr in N2 at 297 K and found that, at pressures of 10 Torr and below, there is a noticeable, but modest impact of pressure on the reaction, and at total pressure greater than 100 Torr, there is no discernible effect of pressure on the reaction. Kaiser et al. found that the high pressure limiting rate constant of the overall reaction is about 2.09 × 10−10cm3 molecule−1 s−1.28 Whether the reaction is pressure dependent or not remains a question in view of the above inconsistent results. Additionally, the temperature dependence of the rate constant has not been involved in all of the above experimental studies. More importantly, the experimental studies only speculated roughly the branching ratios of each channel by analyzing the product yields, and no elaborate mechanism on the reaction process was provided. Therefore, it is necessary to investigate the reaction path and the kinetics for the reaction of MACR with Cl. In the present work, we tried to obtain the integrated reaction mechanism by considering the possible reaction channel and locating the minimum energy paths (MEPs) at which the Cl atom adds to the CC double bond and abstracts the aldehydic hydrogen atom. Based on the higherlevel (denoted as HL) energy calculations,31 the canonical variational transition state theory (CVT)32−34 and the master equation (ME)35 method were employed to study the kinetics of the Cl + MACR reaction system under a pressure range of 1−760 Torr.

E HL = E[QCISD(T)/cc‐pVTZ] + (E[QCISD(T)/cc‐pVTZ] − E[QCISD(T)/cc‐pVDZ])*0.46286 + E[MP2(FC)/cc‐pVQZ] + (E[MP2(FC)/cc‐pVQZ] − E[MP2(FC)/cc − pVTZ])*0.69377 − E[MP2(FC)/cc‐pVTZ] − (E[MP2(FC)/cc‐pVTZ] − E[MP2(FC)/cc‐pVDZ])*0.46286

(1)

The HL method, which includes the extrapolation to the infinite basis set limit, is a dual-level theory and has been verified to predict accurate energies suitable for rate constants calculation.31 In order to circumvent the spin contamination problem and obtain the accurate MEP, we replaced the QCISD(T) and MP2(FC) methods in the above equation with ROCCSD(T) and ROMP2(FC) methods, respectively. All of the above calculations have been carried out by using the Gaussian 09 program package.39 2.2. Rate Constant Calculations. Both the addition channel and the aldehydic hydrogen abstraction channel proceed without well-defined transition states as will be discussed in later sections. To evaluate the rate constants of such reactions, one requires the variational treatment of the dividing surface where the traditional transition state theory (TST) rate constant is the minimum along the MEP. In the present study, we employed the CVT method for the thermal rate constants calculation. The CVT rate constant is given by kCVT(T ) = min[kGT(T , s)] s

kGT(T , s) = σ

2. COMPUTATIONAL METHODS

kBT QGT(T , s) −VMEP(s)/ kBT e h Q R (T )

(2)

(3)

GT

where k (T,s) is the generalized transition state theory rate constant at the dividing surface. QGT is the internal partition function of the generalized transition state. QR is the reactant partition function per unit volume. σ is the symmetry factor. kB and h are the Boltzman’s constant and Planck’s constant, respectively. Both the QGT and QR are approximated as the products of electronic, rotational, and vibrational partition functions. The relative translational partition function between the generalized transition state and the reactants is also included in QR. Translational and rotational partition functions were evaluated classically, whereas the vibrational partition functions were calculated quantum mechanically within the harmonic approximation. To address the temperature and pressure dependence of the rate constants for this reaction, it is necessary to employ the pressure and temperature dependent master equation method, which can be expressed in the total-energy resolved (i.e., onedimensional) form as

2.1. Electronic Structure Calculations. The hybrid meta density functional theory M06-2X recently developed by Truhlar and co-workers has shown its efficiency and accuracy in predicting properties for the main-group thermochemistry and kinetics.36 In this study, all the geometrical structures, including the structures of reactants and products, the structures of the intermediates and the complexes, the structures of the transition states, and the structures of the selected points at the MEPs, have been optimized by using the M06-2X method with the 6-31+G(d,p) basis set which was demonstrated to be an efficient basis set in predicting geometrical structures in most cases.37 However, the M062X/6-31+G(d,p) method fails to predict the reaction path of the methyl hydrogen atom abstraction from the addition intermediate, where the M06-2X/6-311+G(2df, 2pd) method was employ to recalculate the reaction path. Frequency calculations have been performed to identify all the stationary points as minima or transition state, i.e., equilibrium species possess all real frequencies while transition states possess one and only one imaginary frequency. The intrinsic reaction coordinate (IRC) method was also employed to confirm the validity of the transition state.38 To yield more accurate energetic information, a composite basis set extrapolation method (denoted as HL) has been carried out at all the geometries employed for further rate constants calculations.31 The HL method employs a combination of QCISD(T) and MP2(FC) methods, and can be expressed as

dni(E) = Zi dt

∫E

∞

Pi(E , E′)ni(E′) dE′ − Zini(E) − kjini(E) 0i

+ kijnj(E) − kdi(E)ni(E)δi1 + nR nmδi1KReqi kdi(E) ρi (E)e−E / kBT Q i(T )

Np

−

∑ kpi(E)ni(E)δi1 p

(4)

where i, j = 1, 2 correspond to the terminal and central addition intermediates of the Cl atom with CC double bond, respectively; R corresponds to the reactants of Cl + MACR; ni(E) is the number density of the intermediate i at energy E, nR 3542



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and nm are the number densities of the two reactants MACR and Cl, respectively, δi1 is the Kronecker delta function with value 1 emphasizing that only the intermediate for i = 1 (the terminal addition intermediate) can be formed directly from the reactants and can decompose to a variety of products by different channels with number Np (Np = 2 in the present study representing the Cl atom abstraction of the aldehyde hydrogen atom and the methyl hydrogen atom in the terminal addition intermediate); E0i is the ground-state energy of intermediate i; Zi is the collision number per unit time, and Pi(E,E′) is the collision probability that intermediate i with the energy between E′ and E′ + dE will be transferred to the energy between E and E + dE; Keq Ri is the equilibrium constant between R and intermediate i; kji(E) and kij(E) are the microcanonical rate constants of isomerization from i to j and j to i, respectively; kdi(E) and kpi(E) are the microcanonical rate constants for dissociation from intermediate i to reactants and products p, respectively. ρi(E) is the density of states at energy E of intermediate i; Qi(T) is the partition function at temperature T of intermediate i. The collision number Zi was calculated using the LennardJones parameters of the intermediates with the bath gas N2; the Lennard-Jones parameters of the addition intermediates are approximately assumed to be σ = 6.0 Å and ε/kb = 450 K, the same as those in ref 40 for the MACR−OH reaction system. The L-J parameters of N2 are taken from ref 41. The collision probability Pi(E,E′) is approximated by a single-exponential down function with the average transfer energy ⟨ΔEd⟩ = 200 cm−1. In this study, the master equation was solved by an ordinary differential equation (ODE) solver to evolve directly the number population of the species with time.42−44 The populations of species as functions of time can be obtained directly and the first-order rate constants can be extracted from the reactant population using the “exponential decay” approach. For detailed description of the master equation, see refs 35, 44, and 45. All the rate constants calculation were carried out using the VKLab program package.46

Figure 1. Optimized geometries of the antiperiplanar (ap) and synperiplanar (sp) conformers of MACR at the M06-2X/6-31+G(d,p) level of theory. Bond lengths are given in Å.

abstraction, the Cl atom abstracts the aldehyde-H, the methyl-H, or the methylene-H atoms; (3) group abstraction, the Cl atom abstracts the −CH3 or the −HCO group. In order to acquire the comprehensive reaction mechanism on which the kinetics calculation is based, we tried to calculate all of the above possible paths. In fact, not all the above-mentioned reaction paths exist; the finally located reaction paths are depicted in Figure 2, and the corresponding energetics are shown in Figure 3, which are discussed in detail in the following sections. The Cartesian coordinates, the vibrational frequencies, and the absolute energies at each method/basis set combination for all species are shown in the Supporting Information. 3.1.1. The Addition Reaction to the CC Double Bond. Since MACR has Cs symmetry, the Cl atom can symmetrically add to the double bond at both sides of the MACR molecular plane, so only one side of the addition reaction is discussed here. Figure 3 shows that the Cl atom barrierlessly adds to the CC double bond to form the terminal addition intermediate IMadd‑t, and IMadd‑t will successively undergo complicated unimolecular reactions to produce various products. Since the PES of the addition reaction of the Cl atom to the CC double bond is important for further kinetics study, it will be described in detail later in this section, and we first discuss the unimolecular reactions of IMadd‑t from top to bottom as shown in Figure 2. First, IM add‑t can isomerize to the central addition intermediate IMadd‑c, which is about 11.7 kcal mol−1 less stable than IMadd‑t, through the transition state TSadd‑t/c with the barrier height of 18.1 kcal mol−1. However, no further reaction was found from the central addition intermediate IMadd‑c, indicating that the concentration of IMadd‑c is small in the reaction system since the reacting species either deposit in IMadd‑t or form other products from IMadd‑t, which is consistent with experimental results.28 Second, the Cl atom in IMadd‑t can abstract the methyl-H atom H2 (the hydrogen atom numbering is shown in IMadd‑t in Figure 2). The energy of the transition state TSabsH−CH3 is about 26.4 and 0.9 kcal mol−1 higher than that of IMadd‑t and R, respectively. It should be noticed that in the structure of TSabsH−CH3, the Cl atom is close to the hydrogen atom and far from the terminal carbon atom of the CC bond. IRC calculations indicate that the reaction path can be divided into two parts: the first part is characterized by the Cl atom shift from the terminal carbon to the methyl-H atom H2 on the IRC between IMadd‑t and TSabsH−CH3, and the second part is characterized by the H2 abstraction by the Cl atom on the IRC between TSabsH−CH3 and the complex ComabsH−CH3. We should point out that the M06-2X/6-311+G(2df, 2pd) method, instead of the M06-2X/6-31+G(d, p) method, is adopted to

3. RESULTS AND DISCUSSION 3.1. Reaction Mechanism. There exist two distinct conformers for MACR as a result of the internal rotation around the C−C single bond joining the vinyl and the aldehyde moieties of the molecule. The conformers are called synperiplanar (sp) or antiperiplanar (ap) depending on whether the CO and CC double bonds appear on the same or opposite side with respect to the C−C single bond. The optimized geometries of the two conformers have the Cs symmetry as shown in Figure 1. The energy of ap conformer is lower than that of the sp conformer by 3.5 kcal mol−1 at the HL level of theory, which is in consistent with the theoretical results performed by Ochando-Pardo et al., who obtained the ap:sp ratio of 99.6:0.4,8 and experimental results (97.5:2.5 and 100:0 at room temperature) also showed that the ap conformer of MACR has significant weight in its reactivity.47 So only the ap conformer was taken into account for the mechanism and kinetics study of the Cl + MACR reaction, just like researchers did with the OH + MACR reaction.8,9 From the geometric structure of MACR shown in Figure 1, we can see that the Cl atom may react with MACR by the following possible paths: (1) addition, the Cl atom adds to the CC or the CO double bonds; (2) hydrogen atom 3543



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Figure 2. Calculated mechanism and optimized structures of the complexes, intermediates, transition states, and products of the Cl + MACR reaction system.

11.4 kcal mol−1 higher in energy than IMadd‑t and R, to form the complex ComabsH−CH2 and the products PabsH−CH2. The abstraction of H4 is very interesting, and we did find a transition state for the abstraction of H4; however, when the IRC was followed from this transition state, it is found that the IRC connects to the complex and the hydrogen (H4) abstraction products on one side as expected, and that on the other side of the IRC the H4 atom moves back to the carbon atom and the Cl atom gradually moves to the aldehyde-H atom H5 and then abstracts H5. These results indicate that the MEP for abstracting H4 may cross with the MEP for abstracting H5, and the latter is a barrierless reaction whose MEP is much lower than that of the former so that the Cl atom will overwhelmingly abstract the aldehyde-H atom, and the reaction of abstracting H4 is rare. Fourth, the Cl atom in IMadd‑t can abstract the aldehyde-H atom H5. This reaction proceeds through the transition state TSabsH−CHO with the energies of 24.4 and −1.1 kcal mol−1 relative to those of IMadd‑t and R, respectively. The IRC calculation shows that the reaction is characterized by the Cl

optimize the transition state and to calculate the IRC for this reaction because the M06-2X/6-31+G(d, p) method predicted wrong results in which two transition states with one intermediate between were optimized. The details of the IRCs calculated at the two levels of theory are presented in the Supporting Information. We have also made efforts to investigate the direct methyl-H atom abstraction as the Cl atom approaches asymptotically to the methyl-H atom from infinite distance. It is found that the geometry of transition state for the abstraction of the methyl-H atom H2′ is symmetrical to that of TSabsH−CH3 for the abstraction of the methyl-H atom H2. The abstraction of the methyl-H atom H1 results in a second order transition state which connects the two symmetrically identical transition states for the abstraction of the methyl-H atom H2 and H2′. Thus, it is inferred that the methyl-H atoms could only be abstracted from the intermediate IMadd‑t. Third, the Cl atom in IMadd‑t can abstract the methylene-H atoms H3 and H4. The abstraction of H3 will proceed through the transition state TSabsH−CH2, which is respectively 36.9 and 3544



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All of the above four reaction paths start from the intermediate IMadd‑t. In particular, the energies of transition states TSabsH−CHO and TSabsH−CH3 are close to that of the reactants R. Thus, as the intermediate IMadd‑t is generated barrierlessly from the reactants, the internal energy of IMadd‑t makes it possible for the successive unimolecular reactions to take place. Finally, we managed to find out the characteristics of the barrierless reaction path for the Cl atom adding to the CC double bond. For the barrierless reactions without well-defined transition states, one has to locate the approximate MEPs in order to elucidate the reaction mechanism and provide the essential information on the variational transition states for further kinetics calculations, which is similar to the variational approach applied to the barrierless reactions by Lin et al.48,49 The MEP was obtained by treating the forming bond as the reaction coordinate, fixing the distance of the two approaching atoms while optimizing the remaining geometrical parameters of the reaction system. In order to have an insight into the interaction between the Cl atom and the CC double bond of MACR during the addition process, we selected several planes (σp) which are parallel to the MACR molecular skeleton plane and scanned the two-dimensional PES by moving the Cl atom within a given range on every σp plane. The Cl atom was limited in a rectangle of X by Y just above the CC double bond, X is sampled in increment of 0.1 Å from −2.0 to 2.0 Å, and Y is sampled in increment of 0.1 Å from 0 to 1.5 Å. The projected coordinates

Figure 3. Potential energy diagram of the Cl + MACR reaction system at the HL level of theory, the total energy of the reactants Cl + MACR is set as zero for reference, and the relative energies are given in kcal mol−1.

atom shift before the transition state and by the hydrogen abstraction after the transition state. A complex ComabsH−CHO is formed between the two products. The IRC paths for the Cl atom abstracting the H atom of −CH2 and the H atom of −CHO are also provided in the Supporting Information.

Figure 4. PESs and the contour plots of the PESs for the interaction of MACR with Cl. For each PES and contour plot the Cl atom is restricted to a plane (σp) parallel to the MACR molecular skeleton plane, with the symbol D denoting the distance of the σp from the MACR molecular skeleton plane. 3545



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Figure 5. (a) Assignation of the two-dimensional coordinate grids of the Cl atom addition to the CC double bond. The line mp is the midperpendicular of the CC double bond, the hollow circle denotes the Cl atom which is located in the plane σv, the solid circle denotes the Cl atom which is located out of the plane σv, rC‑X denotes the horizontal distance of the Cl atom from the terminal C atom along the CC double bond of MACR, and rCl‑X denotes the vertical distance of the Cl atom from the CC bond. Distances are given in Å. (b) The potential energy surface of Cl addition to the CC double bond at the M06-2X/6-31+G(d,p) level of theory, the arrowed line indicates the MEP of the addition channel, and the total energy of the reactants Cl + MACR is set as zero for reference. The relative energies are given in kcal mol−1.

the CC double bond, and the plane is defined as σv for convenience. A two-dimensional coordinate grid that represents the relative position of the Cl atom with respect to the CC double bond of MACR was established in the σv plane as depicted in Figure 5a. The horizontal distance of the Cl atom from the terminal C atom along the CC double bond of MACR was defined as an axis labeled rC‑X; the vertical distance of the Cl atom from the CC bond was defined as the other axis labeled rCl‑X, and the two-dimensional grid was established by setting rC‑X from −0.2 Å to 1.6 Å with spacing of 0.2 Å, rCl‑X from 2.2 to 4.0 Å with spacing of 0.2 Å. We calculated the energies of the reaction system at each grid point by fixing the coordinate rCl‑X and rC‑X in plane σv while fully optimizing the other geometrical parameters, and constructed the twodimensional PES for the addition channel at the M06-2X/631+G(d,p) level of theory, which is portrayed in Figure 5b. From Figure 5b we can see that the energy of the reaction system decreases as the Cl atom approaches the CC double bond; and as expected, the addition channel is indeed a barrierless process. From the two-dimensional PES, the MEP of the Cl atom adding to the CC double is located and marked by the arrowed line in Figure 5b. Obviously, as the Cl atom approaches the CC double bond, the MEP is about at the midperpendicular of the CC double bond as rCl-X is longer than 3.0 Å, and then the MEP declines gradually toward the terminal carbon atom, which implies that the only MEP of the Cl atom adding to the CC double bond will lead to the terminal addition intermediate. Figure 5b also shows that there exist a significant barrier between the terminal addition intermediate and central addition intermediate when rCl-X is about 2.2 Å, which has been discussed earlier. The above MEP was located with the constraint that the Cl atom approaches to the CC double bond in the plane (σv) that is perpendicular to the MACR molecular skeleton plane. In order to obtain a more reliable reaction path, the MEP was reoptimized by relaxing the restricted conditions on the coordination of the Cl atom. That is, the Cl atom was not limited in the σv plane; furthermore, rC‑X was set as a variable so that the Cl atom can move freely in the horizontal direction.

of the terminal carbon atom and the central carbon atom on the rectangle of the σp plane are (0.0, 0.0) and (0.0 1.34), respectively, i.e., X and Y axes are vertical and parallel to the CC double bond, respectively. The PESs and the contour plots of the PESs are illustrated in Figure 4. The distances (denoted as D) between the selected planes (σp) and the MACR molecular skeleton plane are 5.0 Å, 4.0 Å, 3.0 and 2.6 Å, respectively. Obviously, the PES is flat at D = 5.0 Å with the relative energies less than 0.1 kcal mol−1 on the whole PES, indicating the Cl atom can move freely at this distance; the PES gets steeper as the Cl atom approaches closer to the CC double bond, with the largest relative energies being about 0.7, 4.5, and 13 kcal mol−1 on each whole PES at D = 4.0, 3.0, and 2.6 Å, respectively. The contour plots of the PESs clearly show that the minimum of the PESs are nearly located above the CC double bond, and gradually shift from the center of the CC bond to the terminal carbon atom as the Cl atom approaches the CC bond with Y = 0.7, 0.5, and 0.2 Å respectively at D = 4.0, 3.0, and 2.6 Å. From these results it may be concluded that no complex exists between the Cl atom and the CC double bond and that the MEP of the Cl atom adding to the CC double bond will lead to the terminal carbon addition intermediate IMadd‑t. However, it should be pointed out that the reactive system does not exactly follow the MEP, but vibrate around it. Although there is not a bifurcating transition state50,51 by which IMadd‑c and IMadd‑t are formed simultaneously, the central carbon addition intermediate IMadd‑c could also be formed with less possibility. As aforementioned for the addition reaction of the Cl atom to the CC double bond, no transition state was located between the reactants and the CC addition intermediates, and there exists only a transition state between the two intermediates. To depict the energetic landscape of the Cl atom approaching the CC double bond of MACR, we also constructed another two-dimensional potential energy surface (PES). In view of that, the Cl atom adds to π orbital of the C C double bond in the direction vertical to the molecular plane of MACR, the PES calculations were done in the plane perpendicular to the molecular skeleton of MACR and contains 3546



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We varied the distance between Cl and the CC double bond (rCl‑X) from 4.0 to2.2 Å, with an interval of 0.2 Å, and other geometric parameters were fully optimized without constrains for each selected point. The reoptimized MEP is plotted in Figure 5a by hollow circles and solid circles, which respectively represent that the Cl atom at the MEP is located in or out of the paper plane (σv). Apparently, it is similar to the MEP in Figure 5b obtained from the two-dimensional PES. The Cl atom is always near the midperpendicular (line mp) of the C C double bond at the range of 4.0 Å > rCl‑X > 3.0 Å, then it approaches the terminal C atom drastically when rCl‑X < 3.0 Å. In addition, the Cl atom deviates slightly from the σv plane as rCl‑X changes from 4.0 to2.2 Å with spacing of 0.2 Å, and the corresponding angles of the Cl atom deviating from the σv plane are −23.9, −20.3, 11.3, 5.5, 4.6, 3.5, 3.4, 2.6, 1.4, and −0.3 degree, respectively, where the negative and positive values respectively represent that the Cl atom is located in or out of the paper plane (σv). The MEPs calculated at the M06-2X/631+G(d,p) and HL level of theory for the addition process are portrayed in Figure 6. It can be easily found that the MEP of

Figure 7. Minimum energy path of the aldehydic hydrogen abstraction channel. The total energy of the reactants Cl + MACR is set as zero for reference.

double bond addition channel (Figure 6) and the direct aldehydic hydrogen abstraction channel (Figure 7), we can find that the energy of the addition channel is always lower than that of the aldehydic hydrogen abstraction channel at the same distance of rCl‑X and rH−Cl. 3.1.3. Methyl Group Abstraction. The Cl atom directly abstracts the methyl group via the transition state TSabs‑CH3 forming the methyl group abstraction products as shown in Figure 2 and Figure 3. The energy of TSabs‑CH3 is about 41.2 kcal mol−1 higher than that of the reactants; thus, this reaction is very difficult to happen due to its higher reaction barrier than the CC double bond addition channel and the direct aldehyde-H abstraction channel. 3.1.4. Addition Reaction to the CO Double Bond and the Abstraction of the Aldehyde Group. The Cl atom interacts with the O atom of the CO double bond and the hydrogen atoms of the methyl group forming the complex Comadd‑CHO. From Comadd‑CHO, the Cl atom moves to the C atom via the transition state TSadd‑CHO to form the intermediate IMadd‑CHO, which further decomposes to the products Pabs‑CHO via transition state TSabs‑CHO by the rupture of the C−C single bond joining the vinyl and the aldehyde. As shown in Figure 3, the energies of Comadd‑CHO, TSadd‑CHO, IMadd‑CHO, and TSabs‑CHO are about −3.5, 6.8, 1.7, and 16.6 kcal mol−1 higher than that of the reactants, indicating that this channel is also unimportant compared to the CC double bond addition channel and the direct aldehyde-H abstraction channel. From the above results it is can be seen that the addition reaction of the CC double bond and the aldehyde-H abstraction reaction are more favorable thermodynamically because the energies of the intermediate, transition states and products involved in these channels are lower than that of the reactants, and that the methyl-H abstraction reaction is also possible to proceed because the energy barrier height of this path is not very high. This is in agreement with the experimental observations of Kaiser et al.28 So we will focus on the addition reaction of the CC double bond, the aldehyde-H and methyl-H abstraction reactions in the following kinetic calculation. 3.2. Rate Constant Calculations. The Cl atom adds to the terminal carbon atom of the CC double bond or abstracts directly the aldehydic hydrogen atom without a well-defined

Figure 6. Minimum energy path of the addition channel. The total energy of the reactants Cl + MACR is set as zero for reference.

the terminal addition process calculated at the M06-2X/631+G(d,p) level of theory is below that calculated at the HL level of theory by about 0.5 kcal mol−1 at rCl‑X = 4.0 Å to about 3 kcal mol−1 at rCl‑X = 2.2 Å. 3.1.2. Direct Aldehyde-H Abstraction. Apart from the aldehyde-H abstraction reaction from the IMadd‑t intermediate, the Cl atom can abstract directly the aldehyde-H from MACR to form the complex ComabsH−CHO, as shown in Figures 2 and 3. The MEP for the direct aldehydic hydrogen abstraction channel was calculated by varying the forming H−Cl bond distance point by point from 4.0 to2.0 Å, with an interval of 0.2 Å. Other geometric parameters were fully optimized without constrains for each selected point. The MEP of the aldehydic hydrogen abstraction channel calculated at the M06-2X/631+G(d,p) level of theory differs largely from that calculated at the HL level of theory, as shown in Figure 7. The MEP obtained at the M06-2X/6-31+G(d,p) level of theory is smooth and barrierless, while the MEP obtained at the HL level of theory exhibits a small peak at the point of rH−Cl = 2.8 Å, although its energy is still below that of the reactants. Thus, the HL method is necessary to acquire reliable MEPs for further kinetics calculations. By comparing the MEPs of the CC 3547



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Figure 8. (a) The variation of TST rate constants at 298 K in the addition channel. (b) The variation of TST rate constants at 298 K in the direct aldehydic hydrogen abstraction channel.

Figure 9. (a) The plots of the temperature dependence of the rate constants at 760 Torr for the direct aldehyde hydrogen abstraction channel and the addition channel. (b) The branching ratio of the products at different temperatures.

kME‑add calculated by the CVT theory for the addition channel and the direct aldehydic hydrogen abstraction channel, and by the ME method for the addition channel, respectively. It can be seen that both kCVT‑add and kME‑add decrease with the increase of temperature, and almost coincide in the temperature range T < 300 K, whereas kME‑add has a sudden fall-off in the temperature range 300 K < T < 350 K and remains unchanged as T > 350 K. The reason for this phenomena is that kCVT‑add is the elementary reaction rate constant only for the entrance addition reaction, but kME‑add is the apparent rate constant for the reactions involved in the master equation. At temperatures T < 300 K, the entrance addition reaction is the rate-determining step, which results in the very close rate constants between kCVT‑add and kME‑add; in fact, kME‑add is slightly lower than kCVT‑add due to the dissociation reaction of IMadd‑t back to the reactants. At temperatures T > 350 K, the exit channels for the aldehydeH abstraction and the methyl-H abstraction become the ratedetermining step, kME‑add is controlled by the elementary rate constant of these steps, and the reactants and the intermediates IMadd‑t and IMadd‑c maintain the thermal equilibrium at this temperature range. In the temperature range 300 K < T < 350 K, the rate-determining step shifts gradually from the entrance addition reaction to the aldehyde-H and the methyl-H abstraction reactions, which results in the fall-off of kME‑add. Obviously, kME‑add, instead of the kCVT‑add, is the correct apparent rate constant for the addition reaction system. kCVT‑abs

transition state. According to the CVT method discussed in the Computational Methods section, we evaluated the rate constants for such reactions by minimizing the traditional transition state rate constant along the MEPs based on the M06-2X/6-31+G(d,p) optimized geometries with energies refined by the HL method. The calculated TST rate constant curves along the MEPs at 298 K for the addition channel and the direct aldehydic hydrogen abstraction channel are plotted in Figure 8a,b, respectively, and the corresponding structure of the minima on the TST curve is taken as the approximate variational transition state. For the addition channel, the rate constant minima (kadd, CVT = 2.15 × 10−10 cm3 molecule−1 s−1) appears at the point where the distance between the Cl atom and the CC double bond is 3.8 Å; for the direct aldehydic hydrogen abstraction channel, the rate constant minima (kabs, CVT = 1.64 × 10−11 cm3 molecule−1 s−1) appears at the point where the distance between the Cl atom and the H atom is 2.8 Å, and this point is exactly at the peak of the MEP. To evaluate the pressure and temperature-dependent rate constants and the branching ratios of the products, we carried out the master equation calculation for the reaction system involving the reactants, the intermediates IMadd‑t and IMadd‑c; and only the two low-lying energy reaction paths starting from IMadd‑t for the aldehyde-H abstraction and the methyl-H abstraction are adopted as reaction exits. Figure 9a shows the temperature-dependent rate constants kCVT‑add, kCVT‑abs and 3548



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4. CONCLUSIONS The complicated reaction mechanism of Cl + MACR reaction has been investigated. Besides the reaction mechanism, the kinetics of the reaction between the Cl atom and the MACR molecules depends largely on the minimum energy paths of the entrance channels about which scientists known very little. In this study we managed to locate the MEP for the addition process of the Cl atom to the CC double bond by constructing the two-dimensional potential energy surfaces which are parallel and vertical to the MACR molecular skeleton plane. The MEP for the direct aldehydic hydrogen abstraction was also determined. Based on these MEPs, the thermal rate constants for the direct aldehydic hydrogen abstraction and the entrance of the addition channel were calculated with the canonical variational transition state theory, and the ME simulation was further performed to predict the pressure and temperature dependent apparent rate constants for the addition channel; the temperature-dependent branching ratios for the products has been predicted by combining the ME and CVT calculation results. The main conclusions are summarized as follows: (1) Four entrance channels were located for the Cl atom to react with MACR, namely, the addition channel to the terminal carbon of the CC double bond, the direct aldehyde-H abstraction channel, the addition to the carbon atom of the CO double bond, and the abstraction of the methyl group, among which the first two channels are kinetically important due to their lowlying energetics. (2) The addition of the Cl atom to the terminal carbon atom of the CC double bond is a barrierless process and the direct aldehydic hydrogen abstraction by the Cl atom is predicted having a little energy barrier. The Cl atom in the terminal addition intermediate can further abstract the aldehyde-H, the methyl-H and the methylene-H atoms, while the first two reactions are dominant exit channels. (3) Combining the CVT and the ME calculation results, the overall rate constant of the title reaction at 298 K and 760 Torr is predicted to be koverall, CVT = 2.3 × 10−10 cm3 molecule−1 s−1, and the branching ratios of the terminal addition intermediate of the CC double bond, the aldehyde-H abstraction products and the methyl-H abstraction products are about 86%, 12% and 2%, respectively, which is coincident with the reported experimental results. The terminal addition intermediate of the CC double bond and the aldehyde-H abstraction products are the main products at T < 300 K and T > 350 K, respectively. (4) The solution of the master equation has shown the dependence of the rate constants on the pressure and temperature. At temperatures T < 300 K, the pressure dependence is obvious when the pressure is below 10 Torr, and the high pressure limit is about 100 Torr.

increases slightly with the increase of temperature, and is much smaller than kME‑add in the whole temperature range. So the overall rate constant at 760 Torr and 297 K is simply the sum of the addition process and the direct aldehyde-H abstraction process with koverall, CVT = 2.3 × 10−10 cm3 molecule−1 s−1, which is in agreement with the values determined by experiments (2.09 × 10−10 ∼ 3.2 × 10−10 cm3 molecule−1 s−1).24−28 The branching ratios of the products at different temperatures are shown in Figure 9b, with the contribution of the direct aldehyde-H process involved. At 297 K and 760 Torr, the branching ratios of the terminal addition intermediate of the CC double bond, the aldehyde-H abstraction products, and the methyl-H abstraction products are about 86%, 12% and 2%, respectively, and the central addition intermediate of the CC double bond is close to zero, which is coincident with the results of most of the addition reaction occurs at the terminal carbon atom.28 The branching ratios of the aldehyde-H abstraction products is slightly lower compared to the experimental data of about 0.1825 and (24.5 ± 5)%,28 whereas the branching ratios of the methyl-H abstraction products are in good agreement with the experimental data of (2.3 ± 0.8)%.28 From Figure 9b we can see that the terminal addition intermediate of the CC double is dominant over the hydrogen abstraction products at T < 300 K, while the branching ratios of the aldehyde-H and the methyl-H abstraction products increase with the increase of the temperature with the results of about 73% and 27% for the aldehyde-H and the methyl-H abstraction products at T > 350 K, respectively; the reason for this phenomena is the same as the variation of kME‑add with temperature aforementioned. The corresponding data for the rate constants and the branching ratios in Figure 9a,b are shown in the Supporting Information. The rate constant for the addition process was predicted in the 200−300 K temperature range and 1−760 Torr pressure range, which is shown in Figure 10 (the rate constants data are

Figure 10. Rate constants for the addition process versus pressures at different temperatures in the N2 bath gas.

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ASSOCIATED CONTENT

S Supporting Information *

shown in the Supporting Information). As shown in Figure 10, the rate constant increases significantly with the pressure increasing from 1 to 10 Torr, and there is no discernible pressure dependence when P > 100 Torr. This finding is in good agreement with the experiment observations of Kaiser et al.28

The Cartesian coordinates and vibrational frequencies of all species; the absolute energies (a.u.) at each method/basis set combination for all species (Table S1); tables of the rate constant data and the branching ratio data used to create Figures 9 and 10 (Table S2, Table S3, and Table S4); the IRC 3549



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paths for the Cl atom abstracting the H atom of −CHO, the H atom of −CH3, and the H atom of −CH2 (Figure S1, Figure S2, and Figure S3). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (No. 21173022).

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REFERENCES

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