Reaction between i-C4H3 Radical and Acetylene (C2H2): Is Phenyl

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Reaction between i-C4H3 Radical and Acetylene (C2H2): Is Phenyl (C6H5) the Primary Product? Endong Wang, Junxia Ding, and Keli Han Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b00474 • Publication Date (Web): 04 Apr 2018 Downloaded from http://pubs.acs.org on April 4, 2018

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Reaction between i-C4H3 Radical and Acetylene (C2H2): Is Phenyl (C6H5) the Primary Product? Endong Wang,†‡ Junxia Ding*,† Keli Han†* †

State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, 457 Zhongshan Road, Dalian 116023 (China) ‡

University of Chinese Academy of Sciences, Beijing 100049 (China) *

[email protected]

*

[email protected]

ACS Paragon Plus Environment

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ABSTRACT

In this study, we examined the reaction between the resonant i-C4H3 radical and C2H2. A reaction network was constructed using CCSD(T)/CBS//M06-2X/6-311++G(d,p) dual level theory. Several undisclosed reaction channels were first examined. Their necessities were demonstrated by the branching ratios. The reaction network shows that hydrogen elimination reaction products, carbon-carbon bond-breaking reaction products, four-membered rings, or sixmembered rings may be possible products. To further examine which products are more preferred under different conditions, one combined master equation was solved by including all interconnected reaction channels with temperature in the range of 600 K and 2100 K at 100 K interval under three pressures, 30 torr, 1 atm and 10 atm. The branching ratio shows in particular that aromatic products, including phenyl and o-benzyne, are not the most preferable products under all the conditions studied. 3-Hexene-1,5-diyne and 1,1-diethynylethene etc. may also be produced under different temperatures at each pressure. This work also shows that carbon-carbon bond-breaking reaction products can be generated with an appreciable fraction under some conditions. Finally, important reaction channels and their modified Arrhenius parameters leading to the preferable products are given.

KEYWORD

aromatic ring formation, phenyl, i-C4H3 + C2H2, quantum chemistry, rate constant


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1 Introduction The formation of the first aromatic ring has attracted many researchers in the combustion field, because this process is believed to be vital to the growth of polycyclic aromatic hydrocarbons (PAHs) and is often regarded as the rate-limiting step to PAHs growth and soot formation.1 The most common aromatic rings considered include benzene or phenyl. Studies on the formation of these two aromatic rings in combustion environments have been extensively reported. Reactions of n-C4H3 + C2H2 and n-C4H5 + C2H2 were initially proposed to be the main reactions leading to phenyl/benzene given their fast reaction rate constants.2-6 However, these pathways were later dismissed because n-C4H3 and n-C4H5 may instantly isomerize to their icounterparts i-C4H3 and i-C4H5, based on thermochemistry calculations and formation chemistry analysis.7-9 In additions to the studies on the formation of benzene or phenyl, studies leading to 7-carbon or 8-carbon aromatic species have also been reported.10-19 Also, experimental and theoretical works have been devoted on detecting the combustion intermediates or exploring reaction routes.20-24 i-C4H3 is a frequently studied species in the combustion field. Klippenstein and Kaiser et al. have shown that i-C4H3 can be formed through abundant H radicals + abundant diacetylene or through reactions between dicarbon with ethylene.1, 7, 25 Hansen et al. identified i-C4H3 in several fuel flames, including allene, propyne, cyclopentene, and benzene flames, using synchrotronbased molecular-beam mass spectrometry together with ab initio-based Franck-Condon modeling.26 The structure of i-C4H3 and its formation enthalpy have been carefully examined.7, 27, 28

Its reactions with C2H3,29 , vinylacetylene and butatriene,30 and OH,31 have also been studied.

For its role in the formation of aromatic species, i-C4H3 is regarded as a building block,32 and is


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treated as one of the reagents involved in reactions important for building the first aromatic ring.33, 34 C2H2 is also an important species contributing to the formation of aromatic rings.1 The reaction of i-C4H3 + C2H2 has also been examined as one of the reaction routes contributing to aromatic species35 and already was included in the currently used kinetic mechanism.36, 37 To the best of our knowledge, only few works related to the reaction of i-C4H3 + C2H2 have ever been reported.38-40 Walch first proposed a single reaction route leading to phenyl.38 Although the reaction network on the C6H5 potential energy surface has been extended later,39, 40 we believe that nonnegligible reaction channels are still currently missing. As a result, the corresponding reaction mechanisms may also be different from previous ones. Thus, it is required to re-examine the reaction between i-C4H3 and C2H2 to find the preferred products under different conditions. This paper is organized as follows. First, the details of the calculation methods are given followed by the description of a reaction network of i-C4H3 + C2H2. Next, numerical analysis results based on the constructed reaction network is presented. Finally, we give a summary of this work. 2 Theoretical methods Unless otherwise specified, the quantum chemistry calculations were carried out using the CCSD(T)/CBS//M06-2X/6-311++G(d,p) dual level method, in which the complete basis set (CBS) limit was extrapolated.41, 42Optimizations of the equilibrium structures were done at the M06-2X/6-311++G(d,p) level of theory, which has also been used in the work reporting the formation of benzene.42 All frequencies were confirmed by frequency analysis, and intrinsic reaction coordinate (IRC) calculations were performed to ensure that the transition states corresponded to the intended reactants/products. Once the minimums or transition states were found, single point energies were calculated at the CCSD(T)/ cc-pVDZ and CCSD(T)/cc-pVTZ,


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respectively. Next, following the formula below, E_SCF(∞) was calculated. Finally, the ZPE correction at the M06-2X/6-311++G(d,p) level of theory was considered.

E _ SCF ( ∞) =

E_SCF ( CCSD ( T ) /cc-pVDZ ) * exp (-α * N ) − E_SCF ( CCSD ( T ) /cc-pVTZ ) * exp (-α * M ) exp (-α * N ) − exp(-α * M )

In this formula, M equals to 2 and N equals to 3. And the other parameter α equals to 4.42. All electronic structure calculations were performed using the Gaussian09 package.43 The Rice Ramsperger Kassel Marcus master equation (RRKM-ME) theory method was used to calculate the temperature-dependent and pressure-dependent rate constants by solving one combined master equation incorporating all interconnected reaction channels. The exponential-down

model

with

a

temperature

dependent

energy

transfer

parameter

=∆Edown,ref(T/Tref)n was used, where ∆Edown,ref = 333 cm-1, Tref = 300 K, and n = 0.70. These parameters have been used in similar systems.42,

44

The Lennard-Jones collision

parameters used were (ε/cm-1, σ/Å) = (4.5, 230).42 The bath is Kr. Tunneling correction using the asymmetric Eckart method was applied. The Rigid-Rotor, Harmonic-Oscillator (RRHO) model was generally applied in the calculation. The vibrational modes corresponding to torsional vibrations were treated as 1-dimensional hindered rotors. The corresponding normal modes were visually examined with hindrance potentials computed at the B3LYP/6-311G(d,p) level of theory.44 MESS,45, 46 a master equation system solver program for complex-forming reactions via solution of the one-dimensional master equation, was used. MESS has been widely used for the calculation of various reactions in the combustion field.47-53 In calculating the rate constants for barrierless reactions, geometries were obtained during the flexible scan and frequency calculations were performed at the M06-2X/6-311++G(d,p) level of theory. Then, the CCSD(T)/CBS corrected energies were calculated and used in the evaluation of the rate


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constants. As shown in Figure S1, reasonable agreements with other works were obtained.54 Temperatures in the range of 600-2100 K with 100 K interval and three pressures, 30 torr, 1atm, and 10atm, were selected to study the kinetic behavior of the system. 3 Results and discussions 3.1 Adducts of i-C4H3 and C2H2 and their reaction network As described by previous works,7,

28

i-C4H3 possesses two resonance-stabilized forms

based on the position of the unpaired electron. The two resonant forms are shown in Figure 1(a) and Figure 1(b). The reaction between i-C4H3 and C2H2 has previously been investigated by Walch38 and Lories et al.39, 55. Additionally, the phenyl dissociation channels leading to i-C4H3 and C2H2 have been studied by Mebel et al.40 Lories et al. only showed the results of the addition reaction leading to isomer c of Figure (c).38,

55

Adducts from other works will be discussed in the

description of the reaction network because this involves additional intermediates.38, 40 Due to the existence of resonant structures of i-C4H3, its reaction with C2H2 should have two distinct entrance channels, which lead to two different adducts as depicted in Figure 1 (c), and Figure 1 (d). Reactions can be initialized following these two entrance channels and a reaction network can thus be constructed as shown in Figure 2. In this reaction network, several new reaction channels were found.

(a)

(b)

(c)

(d)


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Figure 1 (a), (b): two i-C4H3 isomers showing possible resonant structures. (c), (d): i-C4H3 and C2H2 addition reaction adducts through the two distinct entrance channels.

Figure 2 Reaction network following the two distinct entrance channels. The dash arrows represent dissociation reactions while the solid arrows represent isomerization reactions. Figure 2 shows that various reactions can be initialized from the adduct IM1 and IM11. To easily target the isomers, labels are given in Figure 2 based on isomers’ positions in the reaction network. Generally, the label given in the circle ranks from left to right. The numbers also given in the circles are their relative energies. The zero energy corresponds to the sum of the energy of i-C4H3 radical and C2H2. The numbers in italic beside the arrows are the relative energies of the transition states. We use the word ‘barrierless’ to indicate a reaction without a tight transition state. The circles with lightblue background indicate intermediates generated via the H-swing reaction or trans-cis conversion reaction, starting from the two i-C4H3 and C2H2


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adducts. These isomers interconvert with relatively low barriers. The circles with a lightgray background indicate bimolecular products. Circles with a red background indicate potentially important ring intermediates that initialize the subsequent ring expansion reactions. Walch et al. have reported that the reaction between i-C4H3 and C2H2 would generate IM2 in Figure 2 instead of IM1.38, 40 Similar to Lories et al.,39 we did not find a transition state (TS) leading to IM2. This result may be caused by the 6-31G(d) basis set used by Walch is not able to properly describe the interaction between the triple bond of i-C4H3 and the double bond of acetylene.39 We further confirmed the absence of this transition state through calculations at the B2PLYPD3/6311++G(d,p), B2PLYPD3/cc-pVTZ, B3LYP/6-311++G(d,p), B3LYP/cc-pVTZ, and B3LYP/ccpV5Z level of theory. Once IM1 is formed, IM2, IM3, and IM5 can be formed through H-swing reactions or isomerization reactions with low barrier heights. These four intermediates with highly similar structural characteristics can dissociate to B10. Other studies only included the reaction IM2-B10 or IM3-B10 in their reaction networks.39,

40

However, it would be more

unbiased to include all four of these dissociation channels because they have comparable barrier heights. In the reported reaction of i-C4H5+C2H2, the authors also found that the direct Helimination reaction from the initial adducts may contribute considerably to the equilibrium products under some conditions.56 IM1 and IM2 can also form another common product, IM4, through an intra-molecular H-transfer reaction. IM4 then produces B6, butatriene and ethynyl. Butatriene is calculated to be the most stable isomer, only higher than vinylacetylene by approximately 7 kcal/mol according to the latest C4H4 potential energy surface calculated at the CCSD(T)-F12b/cc-pVQZ-F12//M06-2X/MG3S level of theory.57 IM3 can cyclize to a fourmembered ring IM7. The formation of IM7 has been reported previously by Lories et al.39 However, the authors stopped exploring the subsequent reactions beyond IM7. Actually, IM7


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can be converted by a ring-opening reaction into the linear product IM17, which can then dissociate to the bimolecular product B41 (3-Hexene-1,5-diyne and H radical) via a barrierless reaction or can cyclize to the five-membered ring IM27 or six-membered ring IM40. IM40 can eliminate H to form B45 (p-benzyne and H radical) or can produce the IM46 phenyl through the H-shift reaction. Note that the reaction between B41 and B45 is necessarily added because it represents a reaction channel of aromatic ring formation/reaction between the existing intermediates of the present reaction network. The formed five-membered ring IM27 can further form IM46 phenyl through two ring expansion reaction routes initialized with IM27-IM34 and IM27-IM35. Then, the generated IM46 can lose one of the H atoms, forming B47 (o-benzyne and H radical). In addition to the cyclization reaction leading to the four-membered ring IM7, IM3 can also convert to the five-membered ring IM21. Others have reported that IM21 is generated through reaction of IM2-IM21.40 However, we did not find the corresponding transition state of this reaction. The existence of the transition state of the reaction IM3-IM21 was also confirmed by calculation at the B2PLYPD3/cc-pVTZ and B3LYP/cc-pVTZ level of theory. IM21 can further expand the ring to form IM46 phenyl via two H-shift reaction products, i.e., IM27 and IM28. In addition, direct cyclization reactions can proceed from IM21 following the two rotational directions of the methylene group in IM21. m-Benzyne can be formed in one of the cyclization reactions. o-Benzyne can also be formed through the dissociation reaction from IM44 in another cyclization reaction channel. IM5, produced directly from IM1 or from IM3, can cyclize to the four-membered ring IM9, which can then lose H, forming bimolecular product B30 through a barrierless reaction. In addition, we also examined the H-shift reaction channel from IM5. To the best of our knowledge, this part of the reaction channel has not been examined before either. The formed IM8 from IM5, on the one hand, can dissociate to diacetylene and


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vinyl radical or can isomerize to IM12, which can then convert to IM15 through a cyclization reaction. H-swing reaction of IM15-IM19 can proceed, which is followed by the H-elimination reaction, producing m-benzyne via IM18. Another reaction channel starting with IM19 involves successive H-transfer reactions producing IM28 via IM20. Alternatively, the five-membered ring IM15 can further convert to form six-membered IM44 via IM26 and IM33 through ring expansion reaction. As mentioned above, IM44 can isomerize to IM46 phenyl or loss one of the H atoms to produce o-benzyne. In addition to the ring expansion reaction of IM28-IM39-IM46, a ring-opening reaction can also proceed forming IM36 starting with IM28, where IM36 can further dissociate to n-C4H3 and C2H2. We now focus on another entrance channel that produces IM11 from i-C4H3 and C2H2. Similar to the above entrance channel that leads to IM1, there are also four intermediates IM11, IM14, IM16, and IM24 connected through trans-cis conversion reactions or H-swing reactions. All of these four isomers can dissociate to the bimolecular product B31. Similar to the reaction of IM1-IM4, IM11, IM14, and IM24 can form IM32, IM23, and IM32 through H-shift reactions and can then dissociate to B38. IM16 is also an important intermediate, because it can either cyclize to the four-membered ring IM22, which then can lose H to form B30 or can produce the aforementioned five-membered ring IM21 or six-membered ring IM44. According to Figure 2, hydrogen elimination reaction products, carbon-carbon bond-breaking reaction products, fourmembered rings, or six-membered rings may be possible products. However, we cannot determine the preferred equilibrium products only based on the reaction network. Thus, further numerical analysis to determine the favorable products under different conditions is required. 3.2 Branching ratios at different temperatures and pressures


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Temperatures in the range of 600 K to 2100 K at 100 K intervals and three pressures: 30 torr, 1 atm and 10 atm were selected to calculate the branching ratios of stabilized intermediates and bimolecular molecules. These conditions were chosen to model combustion systems covering internal engine and premixed flames.58-60 The branching ratios are shown in Figure 3. In this figure, stabilized intermediates with lower energies and higher formation reaction rate constants are shown. This also applies to the bimolecular products. We can see in Figure 3 that the products vary with temperatures under each pressure. The peak ratios of stabilized intermediates IM17, IM21 move to higher temperatures gradually when increasing pressures. The generations of the other two intermediates IM27 and IM46 seem to be less important compared to IM17 and IM21. All the ratios of bimolecular products have the negative-pressure dependence. At lower temperature range, the distinct C6H5 intermediates are preferable, whereas the bimolecular products are more favored at higher temperature range. According to Figure 3, the production of the aromatic products, IM46 and B47, is limited. The ratio of IM46 gradually decreases to zero at different temperatures. Whereas the generation of B47 (o-benzyne+H) only show appreciable ratio at lower temperatures.

Figure 3 Branching ratios based on the reaction network at 30 torr, 1 atm, 10 atm within 6002100 K.


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Based on the reaction net, most reaction channels leading to the products of Figure 3 are plain. The results are shown below in Figure 4. Specifically, we would like to focus more on the production of on B47, i.e. o-benzyne+H. As shown in Figure 5, at lower temperatures of 30 torr, the production of B47 seems to come from P1-IM44-IM47 only (P1: i-C4H3+C2H2). When temperature increases, both the reaction channels of P1-IM44-B47 and P1-IM46-B47 become important. However, at higher pressures of this work, the generation of B47 seems to come from the reaction channel of P1-IM44-B47 exclusively within the temperatures studied.

(a)

(b)


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(c)

(d)

(f)


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Figure 4 Major reaction channels leading to the products shown in Figure 3. (a) i-C4H3+C2H2IM1(IM2,

IM3,

IM5)-B10,

IM11(IM14,IM16,IM24)-B31,

(b) (d)

i-C4H3+C2H2-IM1-IM5-IM8-B13,

(c)

i-C4H3+C2H2-

i-C4H3+C2H2-IM1-IM2-IM3-IM7-IM17-B41,

(e)

i-

C4H3+C2H2-IM1-IM2-IM3-IM21-IM37-IM44(-IM47)-IM46-IM47. The zero energy corresponds to the sum of i-C4H3 and C2H2 radical.

Figure 5 Rate constants leading to B47 (o-benzyne+H). 3.3 Arrhenius equation parameters In this section, the modified Arrhenius parameters of reactions leading to the reaction channels shown in Figure 3 are listed in Table 1.

Table 1 Modified Arrhenius parameters for rate constants in k = AT n exp( reaction

A

n

E0

− E0 * 4.184 ) RT T range, K

p = 30 torr i-C4H3 + C2H2 → B10

6.66E-16

1.03

15840.39

i-C4H3 + C2H2 → B13

1.85E-03

-2.82

23549.48

i-C4H3 + C2H2 → B31

1.47E-16

1.23

21042.00

i-C4H3 + C2H2 → B41

6.72E-01

-3.57

22096.20

i-C4H3 + C2H2 → B47

2.71E+19

-9.53

30716.12

600 - 2100


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i-C4H3 + C2H2 → IM17

1.00E+44

-17.48

31319.79

i-C4H3 + C2H2 → IM21

2.54E+44

-17.96

28963.04

i-C4H3 + C2H2 → IM27

2.39E+44

-17.97

31385.46

i-C4H3 + C2H2 → IM46

1.26E+44

-17.57

31573.57

p = 1 atm i-C4H3 + C2H2 → B10

2.95E-09

-0.74

23341.42

i-C4H3 + C2H2 → B13

3.93E+03

-4.48

31174.50

i-C4H3 + C2H2 → B31

6.98E-13

0.26

25119.60

i-C4H3 + C2H2 → B41

1.95E+08

-5.76

33496.39

i-C4H3 + C2H2 → B47

9.91E+19

-9.53

36906.75

i-C4H3 + C2H2 → IM17

9.56E+43

-16.92

36134.65

i-C4H3 + C2H2 → IM21

4.02E+44

-17.45

33203.89

i-C4H3 + C2H2 → IM27

4.57E+44

-17.57

35547.53

i-C4H3 + C2H2 → IM46

1.96E+44

-17.17

35834.48

600 - 2100

p = 10 atm i-C4H3 + C2H2 → B10

6.07E-02

-2.64

32948.94

i-C4H3 + C2H2 → B13

2.97E+17

-8.13

48586.12

i-C4H3 + C2H2 → B31

2.50E-01

-2.81

38287.41

i-C4H3 + C2H2 → B41

1.03E+20

-8.78

50581.65

i-C4H3 + C2H2 → B47

9.18E+20

-9.57

45501.47

i-C4H3 + C2H2 → IM17

7.02E+43

-16.46

40882.26

i-C4H3 + C2H2 → IM21

5.58E+43

-16.86

35152.91

i-C4H3 + C2H2 → IM27

1.31E+44

-17.06

38332.16

i-C4H3 + C2H2 → IM46

3.05E+36

-14.82

31505.81

600 - 2100

Units of A and E0 is cm3 molecules-1s-1 and J/mol. R = 8.314 J/(mol∗K). Conclusions In this study, the reaction between i-C4H3 and C2H2 was examined. A reaction network was constructed based on the results of high level CCSD(T)/CBS//M06-2X/6-311++G(d,p) calculations. Several important reaction channels were first uncovered. The reaction network showed that hydrogen elimination reaction products, carbon-carbon bond-breaking reaction


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products, four-membered rings, or six-membered rings may be possible products. However, we cannot conclude which products are more likely to be formed under different conditions based on a single reaction network, because the Gibbs free energy barrier height together with the reaction rate constants may change when altering the system conditions. Thus, kinetic calculation at different temperatures and pressures was carried out to further determine the branching ratios. A combined master equation including all interconnected reaction channels was solved with temperatures in the range of 600 K to 2100 K at 100 K interval and three pressures: 30 torr, 1 atm and 10 atm. The results suggested that the peak ratios of IM17 and IM21 move to the higher temperature range gradually when increasing pressures. The bimolecular products are not important at lower temperatures and become more and more important when increasing temperatures. This conclusion is similar to that of a study involving the reaction i-C4H5+C2H2, in which the authors illustrated that the direct H-elimination reaction products of the initial adducts become more and more prominent at higher temperatures.56 And the ratios of bimolecular products decrease when increasing pressures. Aromatic products including benzyl and o-benzyne are not the most important products under all the conditions studied. In addition, the preferable reactions channels leading to the important products under the conditions studied are given together with their modified Arrhenius equation parameters. In summary, the reaction between i-C4H3 and C2H2 was studied carefully. An extended reaction network was constructed, the branching ratios under different conditions were determined, and the reaction channels leading to them were analyzed. At last, the modified Arrhenius equation parameters of these reaction channels were given. ASSOCIATED CONTENT Supporting Material


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This material is available free of charge via the Internet. AUTHOR INFORMATION Corresponding Author: [email protected], [email protected] ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (No. 21403221 and 91441106). References 1.

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Graphical Abstracts


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Reaction between i-C4H3 Radical and Acetylene (C2H2): Is Phenyl

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