RRKM study of the reaction mechanism and product branching ratios of the reactions of ethynyl radical with 1,2-butadiene

Chemical Physics Letters 518 (2011) 29–37

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An ab initio/RRKM study of the reaction mechanism and product branching ratios of the reactions of ethynyl radical with 1,2-butadiene Adeel Jamal, Alexander M. Mebel ⇑ Department of Chemistry and Biochemistry, Florida International University, 11200 SW 8th Street, Miami, FL 33199, USA

a r t i c l e

i n f o

Article history: Received 2 October 2011 In final form 29 October 2011 Available online 6 November 2011

a b s t r a c t Ab initio/RRKM calculations have been performed to investigate the mechanism of the C2H + 1,2-butadiene reaction and to compute its product branching ratios under single-collision conditions. The reaction starts with barrierless C2H addition to various sites of H2C@C@CHCH3 producing different exothermic initial adducts. The chemically activated C6H7 adducts can then isomerize and decompose by splitting H or CH3. With the assumption of equal formation probabilities of all initial adducts, C6H6 (2-ethynyl-1,3butadiene) + H are predicted as the dominant products (91–84% at collision energies of 0–7 kcal/mol), whereas C5H4 (penta-1,4-diyne) + CH3 (7–12%) and ethynylallene + CH3 (2–3%) are minor products. Ó 2011 Elsevier B.V. All rights reserved.

1. Introduction Reactions of the ethynyl radical, C2H (X2R+) with unsaturated hydrocarbons have been a subject of numerous theoretical and experimental studies. These reactions are believed to play a key role in the formation and growth of hydrocarbon molecules in reduced planetary atmospheres, such as that of a Saturn’s moon Titan, in the interstellar medium (ISM) and possibly in combustion flames. The reactions may lead to larger, more complex hydrocarbons such as polyenes, -ynes, -enynes, as well as aromatic and polycyclic aromatic hydrocarbons (PAH) in carbon-rich environments [1–4]. The main source of the ethynyl radical in the planetary atmospheres and ISM is ultraviolet photodissociation of acetylene, C2H2, at wavelengths shorter than 217 nm [5–9]. Photochemical models of Titan’s atmosphere assume that the C2H reactions with unsaturated hydrocarbons proceed via a C2H-for-H replacement mechanism to increase the carbon chain length as follows [10–15]:

C2 H þ Cx Hy ! Cxþ2 Hyþ1 ! Cxþ2 Hy þ H

ð1Þ

Here, C2H addition leads to a two-carbon increase of the unsaturated hydrocarbon skeleton after H loss has occurred on the Cx+2Hy+1 potential energy surface (PES). Meanwhile, this reaction path may also compete with C2H-for-CH3 and C2H-for-C2H5 channels:

C2 H þ Cx Hy ! Cxþ2 Hyþ1 ! Cxþ1 Hy2 þ CH3

ð2Þ

C2 H þ Cx Hy ! Cxþ2 Hyþ1 ! Cx Hy4 þ C2 H5

ð3Þ

⇑ Corresponding author. Fax: +1 305 348 3772. E-mail address: mebela@fiu.edu (A.M. Mebel). 0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.10.064

The elimination of H atoms or CH3 and C2H5 radicals may be preceded by isomerization processes on the Cx+2Hy+1 PESs leading sometimes to the formation of aromatic molecules. In recent years, our and other groups employed theoretical ab initio/RRKM calculations to systematically investigate PESs and possible products yields for a variety of ethynyl radical reactions with unsaturated hydrocarbons, including those with the simplest non-substituted alkynes, acetylene (C2H2) [16–18] and diacetylene (C4H2) [19], ethene (C2H4) [20,21] and larger -enes [20], allene and methylacetylene (C3H4) [22], vinylacetylene (C4H4) [23], C4H6 [24,25], benzene (C6H6) [26,27], phenylacetylene (C8H7) [28], and styrene (C8H9) [29]. The theoretical studies were carried out jointly or in parallel with crossed molecular beams [4,18,23,24,30,31] or Laval nozzle/photoionization experiments [32] and helped to provide an insight on the reaction mechanisms, to quantify product branching ratios, and eventually to improve the existing kinetic models of planetary atmospheres. In particular, we have studied the C2H reactions with three C4H6 isomers, 1,3-butadiene [24], 1butyne, and 2-butyne [25]. For the C2H reaction with 1,3-butadiene, a combined crossed molecular beams and ab initio/RRKM study showed the formation of benzene under single-collision conditions. According to the experimental results, the relative yield of benzene was 30 ± 10% at the collision energy of 10.8 kcal/mol, along with hexa-1,3-dien-5-yne as the other major product at 70 ± 10%. RRKM calculations indicated that the relative product yield of benzene is expected to increase to 40% for very low temperatures and zero-collision energies relevant to cold interstellar clouds. For the C2H + 1-butyne reaction, pulsed Laval nozzle experiments by Soorkia et al. over the temperature range of 74–295 K and the pressure of 4 Torr found the reaction to be fast, with nearly temperature-independent rate coefficients of 2.5  1010 cm3 molecule1 s1, close to the collision limit [32].

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The authors analyzed the reaction products via multiplexed photoionization mass spectrometry, and found the cyclic C6H6 isomers of dimethylenecyclobut-1-ene (DMCB) and fulvene to contribute nearly 50% to the total product yield of C6H6 + H, whereas the other C6H6 products included acyclic 2-ethynyl-1,3-butadiene, hexa-3,4diene-1-yne, and hexa-1,3-diyne. The authors also observed C5H4 (ethynylallene/methyldiacetylene) + CH3 product channels with the ratio of the two C5H4 isomers assigned as 4:1. On the contrary, our ab initio/RRKM study [25] found no formation of fulvene and DMCB and predicted 2-ethynyl-1,3-butadiene + H and ethynylallene + CH3 as the major products. Plausible reasons for this discrepancy could be a potential role of secondary reactions of 2-ethynyl-1,3-butadiene with H in the formation of fulvene and a possibility that the photoionization energy curve assigned to DMCB in experiment may have originated from 2-ethynyl-1,3butadiene, as its theoretical adiabatic ionization energy differs only by 0.15 eV from that of DMCB, with no experimental photoionization curve available for 2-ethynyl-1,3-butadiene thus far. For the C2H reaction with 2-butyne, no experimental measurements have been reported so far, but according to our theoretical calculations the dominant product is methyldiacetylene via CH3-loss (about 98%) with a trace amount of 1,1-ethynylmethylallene from H-loss. The present Letter reports on the ethynyl radical + 1,2-butadiene reaction and completes our investigation of the areas of the C6H7 PES accessed by C2H encounters with four stable C4H6 isomers. Although 1,2-butadiene is 13 kcal/mol less stable than the most favorable C4H6 isomer 1,3-butadiene [33], both 1,3- and 1,2-butadienes have been detected in combustion flames of hydrocarbon fuels [34,35]. In the ISM and probably in Titan’s atmosphere, the butadienes can be formed through the reaction sequence starting with the fast reaction of methylidyne radicals (CH) with ethane (C2H6) [36,37] producing propene (C3H6) + H. On Titan, CH itself can result from photodissociation of methane [38]. Next, C3H6 (H2C@CH–CH3) can rapidly react with another methylidyne radical via CH addition to the C@C double bond followed by the three-member ring opening and H loss from the CH3 group leading to 1,3-butadiene [39–41]. Alternatively, it is also conceivable that the CH + H2C@CH–CH3 reaction may proceed by CH insertion into the single C–CH3 bond followed by H elimination from the attacked CH carbon, which would result in 1,2-butadiene. To our best knowledge, the C2H + 1,2-butadiene reaction is yet to be studied experimentally. Based on the previous results for the other C4H6 isomers, we can expect the following product channels to be open:

C2 H þ 1; 2  butadiene ! C6 H7 !C6 H6 þ H !C5 H4 þ CH3 !C4 H2 þ C2 H5

ð4Þ ð5Þ ð6Þ

Reactions (4–6) may form various C6H7 intermediates and transition states via initial C2H addition to 1,2-butadiene followed by H migrations and cyclization/decyclization processes. These intermediates can eventually decompose leading to different isomers of the C6H6, C5H4, or C4H2 products via H, CH3, or C2H5 loss channels, respectively. Here, we present the results of ab initio calculations of the PES followed by RRKM computations of individual reaction rate constants and product branching ratios with the goal to understand the reaction mechanism and to predict the reaction outcome under single-collision conditions which are relevant to crossed molecular beam experiments as well as for very low pressure environments of Titan’s stratosphere and the ISM. 2. Computational methods Geometries of the reactants, products, intermediates, and transition states on the C6H7 PES have been optimized using the hybrid

density functional B3LYP level of theory [42,43] with the 6-311G(d,p) basis set. Vibrational frequencies and zero-point energies (ZPE) have also been calculated using the same B3LYP/6311G(d,p) method. Relative energies of various stationary points have been refined utilizing the coupled cluster CCSD(T) method [44,45] with Dunning’s correlation-consistent cc-pVTZ basis set [46]. For the reactants and products, CCSD(T) calculations were additionally performed with the cc-pVDZ and cc-pVQZ basis sets and then, the CCSD(T) total energies were extrapolated to the complete basis set (CBS) limit by fitting the following equation [47]:

Etot ðxÞ ¼ Etot ð1Þ þ BeCx

ð7Þ

where x is the cardinal number of the basis set (2, 3, and 4) and Etot(1) is the CCSD(T)/CBS total energy. It should be noted that the T1 diagnostic values in CCSD(T) calculations were within 0.01– 0.02 for all species on the PES indicating that their wavefunctions do not exhibit a strong multireference character and thus the CCSD(T) approach should be reliable for energy evaluation. We expect that our CCSD(T)/CBS//B3LYP/6-311G(d,p) + ZPE(B3LYP/6311G(d,p)) relative energies should be accurate within 2 kcal/mol. Also, the difference between CCSD(T)/CBS and CCSD(T)/cc-pVTZ relative energies did not exceed 1.3 kcal/mol and in most cases was in the 0.5–0.8 kcal/mol range. The GAUSSIAN 09 [48] and MOLPRO 2002 [49] programs were employed for the calculations. All optimized Cartesian coordinates, vibrational frequencies, moments of inertia, B3LYP/6-311G(d,p) total energies with ZPE corrections, and CCSD(T)/cc-pVTZ total energies are given in Table S1 in the Electronic Supplementary Material (ESM). CCSD(T)/cc-pVDZ, CCSD(T)/ cc-pVQZ, and CCSD(T)/CBS values are also given for the reactants and products. Energy-dependent rate constants for individual reaction steps were computed using microcannonical RRKM theory under single-collision conditions (zero-pressure limit), similar to our previous works [24,25]. The rate constants were calculated both for reversible isomerization steps of C6H7 intermediates and irreversible product formation using the CCSD(T)/cc-pVTZ (and CBS, where applicable) relative energies along with the B3LYP/6-311G(d,p) vibrational frequencies. The available internal energy E was taken as a sum of the energy of chemical activation in the C2H + 1,2-butadiene reaction and collision energy. The numbers and density of states were computed within harmonic approximation. Once k(E) were generated, they were utilized to write first-order kinetic equations according to the kinetic scheme incorporating all unimolecular reaction steps in the pertinent area of the C6H7 surface. These equations were then solved using steady-state approximation to give branching ratios of various products as functions of the collision energy. It should be noted that the rate constant for the initial bimolecular C2H addition reaction step was not considered here. This addition is barrierless and its rate constant is expected to be in the range of 1010 cm3 molecule1 s1 even at very low temperatures below 100 K, similar to the rate coefficients for other C2H reactions with unsaturated hydrocarbons [50], such as for example those with allene or ethylene. 3. Results and discussion Our ab initio calculations targeted all possible C6H7 intermediates and transition states connecting them, but here we present only the most favorable channels related to the C2H + 1,2-butadiene reaction. Ethynyl radical can attack various sites in 1,2-butadiene; C2H additions can occur to the terminal CH2 carbon (designated C1) resulting in a linear initial adduct, and to the central carbon atoms including the second allenic carbon C2 or the third sp2hybridized carbon C3, producing branched initial adducts. Furthermore, C2H additions can take place to one of the two C@C double

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bonds, between C1 and C2 and between C2 and C3, forming threemembered cyclic intermediates. The overall potential energy maps for the terminal and central C2H additions are depicted in Figures 1 and 2, respectively. We will see that product branching ratios depend on the initial adduct that forms, and so we first address the results separately for each initial ethynyl radical addition channel, before summarizing the general picture. 3.1. Terminal addition to C1 The potential energy diagram for the most important channels following terminal addition of ethynyl radical to 1,2-butadiene is depicted in Figure 3. This barrierless addition to the C1 sp2-carbon of H2C@C@CHCH3 results in the initial intermediate INT 1 and is exothermic by 57.0 kcal/mol. Several products can be formed directly from INT 1, including penta-1,4-diyne by CH3-loss on the opposite terminal of INT 1 via TS 22 and a barrier of 35.4 kcal/mol as well as hexa-3,4-diene-1-yne and hexa-1,4-diyne by H eliminations via TSs 10 and 13 with barriers of 38.1 and 38.3 kcal/mol, respectively. The products, penta-1,4-diyne + CH3, hexa-3,4-diene-1-yne + H, and hexa-1,4-diyne + H, were found to be exothermic relative to the reactants by 31.2, 25.4, and 23.8 kcal/mol, respectively, at the CCSD(T)/CBS level of theory. Alternatively to the direct fragmentation, INT 1 can undergo several (de)cyclization and/or H migration steps leading to other intermediates on the C6H7 surface and

31

decompose after that. In particular, another favorable C6H6 product, 2-ethynyl-1,3-butadiene, exothermic by 39.1 kcal/mol, can be formed through a sequence of three reaction steps. These include ring closure, ring opening, and H-loss processes on the following overall pathway, C2H + 1,2-butadiene ? INT 1 ? INT 18 ? INT 7 ? 2-ethynyl-1,3-butadiene + H. INT 1 rearranges to the 3-membered-ring adduct INT 18 with a barrier of 24.2 kcal/mol via TS 49. This occurs by a cyclization of the added ethynyl moiety towards the C1@C2 bond of 1,2-butadiene, where the reverse process leading back to INT 1 has a barrier of 14.0 kcal/mol. Notably, INT 18 serves as the initial adduct of the central addition to the C@C bond between C1 and C2 and resides 46.8 kcal/mol below the C2H + 1,2-butadiene reactants. INT 18 can further ring-open to produce the branched adduct INT 7, which lies 81.4 kcal/mol below the reactants. This decyclization process occurs with a low barrier of 2.1 kcal/mol via TS 50, whereas the reverse process leading back to INT 18 has a barrier of 36.7 kcal/mol. INT 7 is also the initial adduct of the central C2H addition to the C2 atom in 1,2-butadiene. Finally, INT 7 can exhibit an Hloss from the CH3 terminal leading to the 2-ethynyl-1,3-butadiene product with a barrier of 46.6 kcal/mol via TS 40. The other reaction channels starting from INT 1 and depicted in Figure 1 most likely to be non-competitive because they involve H-migrations and cyclization/decyclizations processes which have too high of a barrier to result in products with any appreciable yields. We do not discuss these channels in detail, but only mention a pathway leading to the

Figure 1. Potential energy map for the C2H + 1,2-butadiene reaction channels initiated by terminal addition to C1 forming INT 1 and central addition to the C1@C2 bond forming INT 18. Numbers show relative energies (in kcal/mol) of the reactants, intermediates, transition states, and products calculated at the CCSD(T)/cc-pVTZ//B3LYP/6– 311G(d,p) + ZPE(B3LYP/6–311G(d,p)) level of theory and at CCSD(T)/CBS (for the products, in parentheses).

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Figure 2. Potential energy map for the C2H + 1,2-butadiene reaction channels initiated by central additions to C2 and C3 and to the C1@C2 bond and C2@C3 bonds forming INT 7, INT 13, INT 18, and INT 12, respectively. Numbers show relative energies (in kcal/mol) of the reactants, intermediates, transition states, and products calculated at the CCSD(T)/cc-pVTZ//B3LYP/6-311G(d,p) + ZPE(B3LYP/6-311G(d,p)) level of theory and at CCSD(T)/CBS (for the products, in parentheses).

formation of the aromatic benzene molecule. A 1,3-H shift in INT1 leads to the intermediate INT3 via a barrier of 40.3 kcal/mol. INT 3 can subsequently dissociate to hexa-1,3-diene-5-yne by H elimination with a barrier of 45.0 kcal/mol, but also can cyclize to INT 21 via a barrier of 23.9 kcal/mol, which then undergoes an H shift to the hydrogen-less C atom in the ring followed by H elimination from the remaining CH2 group producing the most stable C6H6 isomer benzene, 102.4 kcal/mol lower in energy than the C2H + 1,2-butadiene reactants. Since INT 3 is the initial adduct in the C2H + 1,3-butadiene reaction, this channel has been described in detail in our previous work [24]. For C2H + 1,2-butadiene, this path is not likely

to be accessed because the INT 1 ? INT 3 rearrangement has a higher barrier than that for the CH3 loss in INT 1 producing penta-1,4-diyne as well as those on the INT 1 ? INT 18 ? INT 7 ? 2-ethynyl-1,3butadiene pathway and for the H losses leading to hexa-3,4-diene1-yne and hexa-1,4-diyne. 3.2. Central addition to C2 The potential energy diagram for the central addition of ethynyl radical to the C2 carbon of 1,2-butadiene is depicted in Figure 4. This barrierless addition results in INT 7 and is exothermic by

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Figure 3. Potential energy diagram for the most favorable channels in C2H + 1,2-butadiene reaction starting from INT 1 and INT 18.

81.4 kcal/mol relative to the reactants. The only significant product that can be formed directly from INT 7 is 2-ethynyl-1,3-butadiene, via an H loss and a barrier of 46.6 kcal/mol, with the overall C2H + 1,2-butadiene ? INT 7 ? 2-ethynyl-1,3-butadiene + H reaction being 39.1 kcal/mol exothermic. Alternatively, INT 7 can isomerize to INT 1 via INT 18 by migration of the C2H moiety over the C1@C2 bond, with highest barrier of 48.6 kcal/mol relative to INT 7. This pathway connects INT 7 with the area of the surface accessed by the terminal C2H addition to C1 and described in the previous section. The C2H group can also migrate over C2@C3 resulting in INT 13 via a cyclic intermediate INT 12, with the critical transition state lying 47.7 kcal/mol above INT 7. INT 13 is the initial adduct for the central addition to C3 and we consider its possible transformations in the next section. The other reaction channels from INT 7 shown in Figure 2 are less likely to compete. Those worth mentioning include INT 7 ? TS 23 (1,2-H shift) ? INT 8 ? TS 39 (H loss) ? 2-ethynyl-1,3-butadiene, with a critical barrier of 48.4 kcal/mol with respect to INT 7; INT 7 ? TS 23 (1,2-H shift) ? INT 8 ? TS 32 (1,4-H shift) ? TS 24 (C2H5 loss) ? diacetylene + ethyl radical, with

the highest barrier of 56.4 relatively INT 7, and INT 7 ? TS 26 (1,3-H shift) ? INT 11 ? TS 43 (CH3 loss) ? methyldiacetylene + CH3, where the highest in energy transition state resides 57.4 kcal/mol above INT 7. 3.3. Central addition to C3 The potential energy diagram of the central addition of ethynyl radical to the C3 carbon of 1,2-butadiene is illustrated in Figure 5. In this case, the barrierless addition produces INT 13 and is 56.3 kcal/mol exothermic. From INT 13, ethynylallene can be formed by the CH3 loss with a barrier of 32.3 kcal/mol via TS 45. Ethynylallene + CH3 are 35.5 kcal/mol exothermic with respect to the reactants. However, a more probable dissociation mechanism of INT 13 involves its initial isomerization to INT 7 (via INT 12) followed by an H loss leading to 2-ethynyl-1,3-butadiene, C2H + 1,2butadiene ? INT 13 ? INT 12 ? INT 7 ? 2-ethynyl-1,3-butadiene. The highest barrier on this pathway (relative to INT 13) is found for the first step, with the corresponding transition state TS 31

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Figure 4. Potential energy diagram for the most favorable channels in C2H + 1,2-butadiene reaction starting from INT 7 and INT 12.

residing only 22.6 kcal/mol above INT 13. The H loss channels from INT 13 producing 3-ethynyl-1,2-butadiene (1,1-ethynylmethylallene) and 3-ethynyl-1-butyne exhibit prohibitively high barriers of 37.6 and 40.5 kcal/mol, respectively (Figure 2) and are unlikely to contribute.

INT 18, the isomerization of INT 12 to INT 7 is more favorable and thus we can expect the 2-ethynyl-1,3-butadiene + H products to dominate following the C2H addition to C2@C3. Figures 4 and 5 include the PES of the central addition to the C1@C2 bond and C2@C3 bonds, respectively, along with the most favorable pathways and products.

3.4. Central additions to the C1@C2 and C2@C3 bonds 3.5. Product branching ratios This barrierless C2H addition to C1@C2 results in the 3-membered cyclic intermediate INT 18 and is exothermic by 46.8 kcal/ mol. This intermediate cannot directly decompose and would rather decyclize to INT 7 or INT 1 via 2.1 and 14.0 kcal/mol barriers, and enter the areas of the PES accessed by the ethynyl additions to C2 and C1, respectively, described in the previous sections. Clearly, the rearrangement to INT 7 is preferable and therefore, the 2-ethynyl-1,3-butadiene + H products are expected to be dominate. The ethynyl addition to C2@C3 is also predicted to occur without a barrier and to form INT 12, 46.3 kcal/mol below C2H + 1,2-butadiene. INT 12 can ring-open to INT 7 or INT 13 overcoming respective barriers of 4.1 and 12.6 kcal/mol. As for

In this section, we move from the qualitative discussion of the reaction mechanism to a quantitative consideration of product branching ratios obtained from kinetic calculations based on RRKM rate constants. All calculated rate constants are collected in Table S2 in the ESM. The calculations were carried out at collision energies of 0–7 kcal/mol assuming one of the adducts, INT 1, INT 7, INT 12, INT 13, or INT 18, to be the only initial intermediate that forms. The resulting branching ratios with different initial adducts are given in Table S3 in the ESM. We then considered 20% concentrations of each initial adduct to evaluate the formation of products when all five possible initial adducts are accessed with equal probabilities.

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Figure 5. Potential energy diagram for the most favorable channels in C2H + 1,2-butadiene reaction starting from INT 13.

The results of this equal probability product branching ratios are presented in Table 1. For the case of terminal addition leading to the formation of INT 1, the two major products include the H-loss product 2-ethynyl-1,3butadiene and the CH3-loss product penta-1,4-diyne + CH3. The calculated branching ratios of these products at zero collision energy are 67% and 32%, respectively. The trend with increasing collision energy is a decrease in the formation of 2-ethynyl-1,3-butadiene + H and an increase in the formation of penta-1,4-diyne + CH3. At the collision energy of 7 kcal/mol, the yield of 2-ethynyl-1,3butadiene + H drops to 44% while that of penta-1,4-diyne + CH3 increases to 54%. For the cases of central addition to C2 leading to the formation of INT 7, central addition to C2@C3 leading to INT 12, and central addition to C1@C2 leading to INT 18, the dominant product is 2-ethynyl-1,3-butadiene + H. At the collision energies in the range of 0–7 kcal/mol, the formation of 2-ethynyl-1,3-butadiene + H shows a slightly decreasing trend. Starting with INT 7, INT 12, and INT 18, the branching ratios of 2-ethynyl-1,3-butadiene + H are 99.2–98.7%, 98.9–97.8%, and 98.5–96.8% in the given collision energy range. The central addition to C3 leading to INT 13 also has 2-ethynyl-1,3-butadiene + H as the major product, however, a significant minor product, ethynylallene + CH3, is also present. In the

0–7 kcal/mol collision energy range, 2-ethynyl-1,3-butadiene + H exhibits branching ratios of 90.6–81.5%, whereas the CH3-loss product ethynylallene has branching ratios of 8.2–15.4%. Finally, assuming equal probabilities of 20% for the formation of each of the initial adducts INT 1, INT 7, INT 12, INT 13, and INT 18, we find that the two most important products to be formed are 2ethynyl-1,3-butadiene + H (90.8–83.7%) and penta-1,4-diyne + CH3 (7.0–11.9%). The yield of 2-ethynyl-1,3-butadiene + H showed a decrease in the 0–7 kcal collision energy range, while that for penta-1,4-diyne + CH3 increases. A third possible minor product is expected to be ethynylallene + CH3 (1.8–3.4%) and trace amounts of some other products, such as diacetylene + C2H5, 3-ethynyl-1-butyne + H, hexa-1,4-diyne + H, hexa-3,4-diene-1-yne + H, and 1,1ethynylmethylallene, may be also present.

4. Conclusion Ab initio/RRKM calculations of the mechanism and product branching ratios of the reaction of ethynyl radical with 1,2-butadiene show that the reaction can proceed by C2H addition occurring without a barrier to various sites of H2C@C@CHCH3. The addition

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Table 1 Product branching ratios (in%) in the C2H + 1,2-butadiene reaction calculated at collision energies of 0–7.0 kcal/mol assuming equal formation probabilities (20%) of all initial adducts. Product

2-Ethynyl-1,3-butadiene + H Penta-1,4-diyne + CH3 Ethynylallene + CH3 Hexa-1,4-diyne + H 3-Ethynyl-1-butyne + H Diacetlyne + C2H5 Hexa-3,4-diene-1-yne + H 1,1-Ethynylmethylallene + H Hexa-1,3-diyne + H Hexa-1,2,3,4-tetraene + H Benzene + H Hexa-4,5-diene-1-yne + H Hexa-1,3-diene-5-yne + H Hexa-1,2-diene-4-yne + H

Collision energy (kcal/mol) 0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

90.80 6.98 1.78 0.10 0.06 0.12 0.04 0.02 0.00 0.00 0.00 0.00 0.00 0.00

89.76 7.72 1.98 0.12 0.08 0.16 0.06 0.04 0.00 0.00 0.00 0.00 0.00 0.00

88.76 8.46 2.18 0.14 0.10 0.18 0.06 0.04 0.00 0.00 0.00 0.00 0.00 0.00

87.68 9.24 2.4 0.16 0.14 0.18 0.06 0.04 0.00 0.00 0.00 0.00 0.00 0.00

86.68 9.90 2.68 0.18 0.16 0.18 0.08 0.06 0.00 0.00 0.00 0.00 0.00 0.00

85.62 10.62 2.9 0.20 0.22 0.18 0.08 0.06 0.00 0.00 0.00 0.00 0.00 0.00

84.64 11.26 3.14 0.24 0.26 0.18 0.08 0.08 0.00 0.00 0.00 0.00 0.00 0.00

83.68 11.86 3.38 0.26 0.32 0.18 0.10 0.08 0.00 0.00 0.00 0.00 0.00 0.00

produces different initial adducts exothermic by 46–81 kcal/mol, where the terminal addition to C1 forms INT 1 and central additions to C2, C3 and as well as to the C1@C2 and C2@C3 bonds produce INT 7, INT 13, INT 18, INT 12, respectively, with INT 7 being the most thermodynamically favorable among these adducts. The kinetically preferable isomerization/decomposition channels for these chemically activated C6H7 intermediates include the following:

INT1 ! INT18 ! INT7 ! 2  ethynyl  1; 3  butadiene þ H

2-ethynyl-1,3-butadiene + H together with ethynylallene + CH3 and penta-1,4-diyne + CH3, respectively. At higher temperature – higher pressure conditions, the primary C6H6 and C5H4 products may be rapidly converted to their more thermodynamically favorable isomers via secondary reactions involving H-assisted isomerization. However, under low temperature – nearly single-collision reaction conditions existing in the ISM or in Titan’s stratosphere, the predicted isomeric product specificity of the C2H + C4H6 reactions may play a siginificant role in the growth chemistry of larger hydrocarbon molecules.

ð8Þ INT1 ! penta  1; 4  diyne þ CH3

ð9Þ

INT7 ! 2  ethynyl  1; 3  butadiene þ H

ð10Þ

INT12 ! INT7 ! 2  ethynyl  1; 3  butadiene þ H

ð11Þ

INT13 ! INT12 ! INT7 ! 2  ethynyl  1; 3  butadiene þ H ð12Þ INT13 ! ethynylallene þ CH3

ð13Þ

INT18 ! INT7 ! 2  ethynyl  1; 3  butadiene þ H

ð14Þ

Acknowledgements This work was funded by the Collaborative Research in Chemistry (CRC) Program of the National Science Foundation (Award No. CHE-0627854). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2011.10.064. References

The 2-ethynyl-1,3-butadiene + H products are generally favorable, but the overall branching ratios are somewhat sensitive to the initial adduct. The terminal addition to C1 is preferable for the formation of penta-1,4-diyne + CH3, whereas the addition to C3 enhances the yield of ethynylallene + CH3. Assuming equal formation probabilities for all five initial adducts, the calculations indicate that 2-ethynyl-1,3-butadiene + H are expected to be the dominant products in the C2H + 1,2-butadiene reaction (91–84% at collision energies of 0–7 kcal/mol), with penta-1,4-diyne + CH3 (7–12%) and ethynylallene + CH3 (2–3%) being relatively minor products. While completing our systematic studies of C2H reactions with C4H6 isomers, we can also conclude that the primary reaction outcome under single collision conditions strongly depends on the reacting C4H6 isomers because different local areas of the global C6H7 PES are accessed. For instance, only the C2H reaction with 1,3-butadiene can form the most stable and aromatic C6H6 isomer benzene, together with hexa-1,3-diene-5-yne (1-ethynyl-1,3-butadiene) [24]. Alternatively, the reaction with 2-butyne is predicted to produce methyldiacetylene + CH3 [25], whereas the reactions with 1-butyne [25] and 1,2-butadiene are calculated to mostly form

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