Chinese Journal of Chemical Physics  2018, Vol. 31 Issue (6): 761-766

The article information

En-dong Wang, Guang-yue Li, Jun-xia Ding, Guo-zhong He
王恩栋, 李光跃, 丁俊霞, 何国钟
Unexpected Chemistry from the Homogeneous Thermal Decomposition of Acetylene: An ab initio Study
乙炔高温裂解的从头算动力学模拟
Chinese Journal of Chemical Physics, 2018, 31(6): 761-766
化学物理学报, 2018, 31(6): 761-766
http://dx.doi.org/10.1063/1674-0068/31/cjcp1802019

Article history

Received on: February 7, 2018
Accepted on: April 20, 2018
Unexpected Chemistry from the Homogeneous Thermal Decomposition of Acetylene: An ab initio Study
En-dong Wanga,b, Guang-yue Lic, Jun-xia Dinga, Guo-zhong Hea     
Dated: Received on February 7, 2018; Accepted on April 20, 2018
a. State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023, China;
b. University of the Chinese Academy of Sciences, Beijing 100049, China;
c. College of Chemical Engineering, North China University of Science and Technology, Tangshan 063009, China
*Author to whom correspondence should be addressed. Jun-xia Ding, E-mail:jxding@dicp.ac.cn
Abstract: The formation of the aromatic ring during the formation of polycyclic aromatic hydrocarbons (PAHs) remains controversial and the experimental evidence is still lacking. Moreover, the formation mechanism of benzene from acetylene in the gas phase has also puzzled organic chemists for decades. Here, ab initio molecular dynamics simulations and electronic structure calculations provide compelling evidence for an unexpected competitive reaction pathway in which the aromatic ring is formed through successive additions of vinylidene. Moreover, no collisions cause bond dissociation of the acetylene molecule during the formation of benzene in this work. This study reveals the key role for the vinylidene carbene and determines the lifetime of vinylidene.
Key words: ab initio calculations    Acetylene    Combustion    Aromatic ring    Carbenes    
Ⅰ. INTRODUCTION

Numerous reactions proceed rapidly and exothermically in combustion processes. Among them, reactions leading to PAHs have attracted considerable attentions because PAHs, which are by-products of the burning of fossil fuels, cause many environmental problems [1, 2]. Furthermore, reactions leading to aromatic compounds in the gas phase have long been of interest to organic chemists since Berthelot succeeded to synthesize benzene from acetylene in 1867 [3]. Thus, a clear understanding of the formation of PAHs is crucial to reduce the number of PAH-like compounds in the combustion emissions and will also benefit organic chemists.

The hydrogen abstraction/acetylene addition [4-7] mechanism has been considered a key route for the formation of PAHs by a number of researchers [7-12]. Notably, a common basis of these research indicates that an aromatic ring must be present to initialize the subsequent HACA reactions. However, differences emerge regarding how the ring is formed. In essence, the disagreements involve three types of reactions [3-15]. One type of formation reaction is the even-carbon-atom pathway, which involves addition reactions between C4 hydrocarbons and C2 hydrocarbons [5, 16-18] including

$ \begin{eqnarray} {\rm{CH}}\equiv {\rm{C}} - {\rm{CH}} = \dot{\rm{C}}{\rm{H}} +{\rm{C}}_2{\rm{H}}_2\to {\rm{phenyl}}\end{eqnarray} $ (1)
$ \begin{eqnarray} {\rm{C}}{\rm{H}}_2 = {\rm{CH}} - {\rm{CH}} = \dot{\rm{C}}{\rm{H}} +{\rm{C}}_2{\rm{H}}_2\to {\rm{benzene + H}} \end{eqnarray} $ (2)

Another type of formation reaction is the odd-carbon-atom pathway [19-21]:

$ 2{\rm{CH}} \equiv {\rm{C}} - \mathop {\rm{C}}\limits^. {{\rm{H}}_2}^ + \to {\rm{benzene}}\;{\rm{or}}\;{\rm{phenyl + H}} $ (3)

Finally, the third type, which is discussed below, is the cyclization pathway [14]:

$ \begin{eqnarray} {\rm{CH}}_2 = {\rm{CH}} - {\rm{CH}} = {\rm{CH}} - {\rm{C}} \equiv {\rm{CH}} \to {\rm{benzene }} \end{eqnarray} $ (4)

Although several studies support reactions (1)-(3), evidence to dismiss these pathways also exists. For instance, there are uncertainties regarding the concentrations of $n$-C$_4$H$_3$ and $n$-C$_4$H$_5$ for the even-carbon-atom pathway [22]. Furthermore, for the odd-carbon-atom pathway, the experimental reactants include 1, 5-hexadiyne [21], allene [19], and Na+C$_3$H$_3$X [20] (X=Cl or Br). Thus, further investigation is required to clarify the formation of the aromatic ring. Moreover, although significant progress has been made in the development of scientific instruments, it remains difficult to monitor complex chemical reactions, such as the ultrafast reactions that occur during combustion process, and to detect short-lived intermediates in situ. To the best of our knowledge, this reason is primarily why the formation route for the aromatic ring in the HACA mechanism has not yet been directly observed experimentally. Ab initio molecular dynamics simulations are considered suitable to compensate for the lack of experimental data.

Though many studies regarding the formation of the aromatic ring have been reported, including the C$_3$H$_3$ radical path, C$_4$H$_4$ radical path described previously, the premier purpose of the present manuscript is to explore the reaction route via a more general way, i.e. through selecting the products with a larger concentration in the realistic combustion system as the reactants of the present work. Experimentally, acetylene, which has a high emission concentration in internal combustion engines [23-26], is believed to be a key precursor of PAHs [23, 26-32]. In addition, the acetylene to benzene reaction at high temperatures is itself an important total synthesis reaction in organic chemistry [14] and has been addressed by many studies, including the pioneering work [33-35] by Hopf et al. And a possible mechanism by which benzene is generated from acetylene has been proposed [14]. Thus, we select acetylene as the basis to investigate the formation of the aromatic ring using first principles plane-wave based Car-Parrinello molecular dynamics (CPMD) simulations [36]. The BLYP exchange-correlation function was used in the CPMD calculations. The ab initio method has been used in various systems [37-41]. Electronic structure calculations were performed using the composite method CBS-QB3. Other computational details are provided in supplementary materials.

Ⅱ. THEORETICAL METHODS

The BLYP exchange-correlation function was used in the CPMD calculations [42-44]. The ab initio molecular dynamics were performed using a time step of 4.5 a.u. and a fictitious electron mass of 600 a.u. The energy cutoff of the plane-wave basis set to expand the electronic wave functions was carefully chosen and was set to 90 Ry (see FIG. S1, Table S1, Table S2, and Table S3 in supplementary materials). Additionally, the Troullier-Martins norm-conserving pseudopotential [45] was used. The temperature of both the ions and electrons in the simulations was controlled using Nose-Hoover thermostats [46, 47, 48]. The ion temperature was set to 3000 K to accelerate the reactions [49]. We note that this temperature is within the experimental range [50]. The electronic degrees of freedom were coupled by a coupling frequency of 10000 cm$^{-1}$ [49], and the hydrogen mass was substituted by the deuterium mass [51, 52]. A total of 20 acetylene molecules were placed in a cubic box with a length of 16 Å, as depicted in FIG. S2. The density of the system is 0.21 g/cm$^3$ and is an order of magnitude higher than that reported in experiment [53] to reduce the computational cost because, even with the state of the art computational resources, the ab initio molecular dynamics in gas phase using the exact experimental conditions are hardly manageable for more than a few picoseconds. In addition, the carbene described herein is readily generated through the highly reversible reaction from each other [54, 55] and the C$_2$H$_2$ molecule is abundant [23-26]. Thus, to the best of our knowledge, the results shown here are credible. Periodic boundary conditions and an NVT ensemble were used in this work. Approximately 21.77 ps in this work are required to form a benzene ring, and data within this time period were collected and analyzed. In addition, unless otherwise specified, the geometry optimization and the Gibbs free energy calculations were performed using the composite method CBS-QB3. This method has been shown to be suitable for the calculation of C/H systems [44, 56-60]. All frequencies were confirmed by way of frequency analyses, and IRC calculations were performed for the transition states to ensure that they corresponded to the intended reactants/products. The molecular dynamics simulations were conducted using the cpmd-3.17.1 code [61], and all electronic structure calculations were performed using the Gaussian 09 software package [62].

Ⅲ. RESULTS AND DISCUSSION

Unexpectedly, no molecular collisions during the simulated time period induced C-H bond or C-C bond dissociation in acetylene. Instead, the collisions only caused geometric distortions and translations of the acetylene molecules (see supplementary materials for further discussion). This mechanism is plausible given the weak steric hindrance of deformation and the small-molecule-aided accessible translation of acetylene. The reaction begins with an isomerization of acetylene and the vinylidene carbene, which is consistent with previous reports [63-65]. Given the prominent role of the vinylidene carbene in the newly proposed pathway (see below), the lifetime of this carbene was also determined (FIG. S7(a) and (b)). The results showed that the most vinylidene carbenes survived for more than 100 fs. The shortest lifetime was 38.97 fs and the longest lifetime was 1009.26 fs which is constent with another study [55]. Notably, based on the notion that whether the two migrated H atoms are identical during the formation and reaction of vinylidene, the isomerization of the vinylidene carbene to acetylene was found to have two distinct mechanisms: an H-exchange mechanism (FIG. S7(c)) and a non-H-exchange mechanism (FIG. S7(d)). In addition, the conversion between acetylene and vinylidene carbene is so highly reversible from each other [55] that makes the carbene seem to have lived for 3.5 μs in the CEI experiment [54].

We now focus on the formation of the benzene molecule. A brief route is depicted in Scheme 1. Although CPMD simulations can provide an accurate trajectory for the reaction pathway, additional Gibbs free energy changes were calculated at 298.15 K, 1 atm to provide a precise energy diagram for quantitatively evaluating the competitiveness of the reaction pathway. The results are depicted in FIG. 1.

Scheme 1 A brief scheme of the newly proposed reaction pathway.
FIG. 1 Gibbs free energy diagram for the formation of benzene through successive vinylidene additions. The Gibbs free energy was calculated at 298.15 K, 1 atm. Optimized geometries of all intermediates and transition states are also shown. See FIG. S8 for enlarged images of the intermediates and transition states.

First, the carbon atom with two unpaired electrons in the vinylidene carbene, which isomerized from acetylene, attacks one acetylene molecule to form methylenecyclopropene (abbreviated as IM3 hereafter). IM3 is then attacked by the vinylidene carbene to eventually form benzene (a video of selected key snapshots is provided for clarity). As seen in FIG. 1, acetylene isomerizes to form vinylidene (IM2) through TS1. This process, along with the calculation of rate constants, has been widely discussed and interested readers can refer elsewhere [66-73]. Though the calculation of rate constants is not the focus of the present manuscript, it is noteworthy to clarify that one should also consider the concentrations of the reactants besides the rate constants to evaluate the contribution of one reaction route. As a high-energy carbene, vinylidene with the two lone electrons readily pairs with two p-orbital electrons from the two C atoms in acetylene to form IM3 through transition state TS3 with a barrier of 12.68 kcal/mol. And an acetylene $\pi$-bond must be broken for this reaction to proceed. In FIG. 1, IM3 and IM3$'$ are identical structures, but their relative energies differ based on their respective pathways. IM3 could react with another vinylidene carbene through a 18.37 kcal/mol barrier at transition state TS4 to give IM4, a six C-based ring with its two meta-position C atoms bonded together. FIG. S5 (supplementary materials) indicates that IM4 is formed ahead of the H migration to form IM5, which proceeds through TS5 via a 3.65 kcal/mol barrier. Next, the IM5 intermediate proceeds through the meta-position C-C bond dissociation and another intra-molecular H-atom migration with respective barriers of 8.25 and 0.31 kcal/mol to finally generate benzene. In summary, reaction (5) proceeds through roughly four steps: formation of a 5-member ring, hydrogen migration, ring expansion, and another H migration.

A notable mechanism in Ref.[14], as indicated in FIG. 2(a), argues that vinylidene (B) could insert into the C-H bond of acetylene to form vinylacetylene (C). Then, the H atom on the terminal carbon atom of (C) migrates to form (D). The carbon atom with two free electrons in (D) could then insert into the C-H bond of another acetylene to give hexa-1, 3-dien-5-yne (E), followed by the isomerization of (E) to form benzene. This route represents a competing pathway to that of our newly proposed mechanism. The key step in the two mechanisms involves whether the vinylidene carbene reacts with acetylene to form methylenecyclopropene (i.e., from IM2 to IM3 in FIG. 1) or is inserted into the C-H bond of acetylene to form vinylacetylene (i.e., from (B) to (C) in FIG. 2(a). To clarify the competitiveness of the two steps in each mechanism, additional calculations were performed. For the reaction from (B) to (C) depicted in FIG. 2(a), a transition structure TS9 (FIG. 2(b)) is found. The energy barrier of TS9 is 29.29 kcal/mol, whereas the barrier of the competing step in the newly proposed mechanism is 12.68 kcal/mol, which suggests that the newly proposed pathway is more advantageous than that proposed in Ref.[14]. Additionally, we note that the vinylacetylene carbene cation could isomerize to methylenecyclopropene following exposure to light [74]. Kiefer et al. also reported pathways through the IM3 structure, but a cycle opening of IM3, which might make this route less favor because a C=C=C linear bend structure is generated due to the ring opening, is involved in their following route [75, 76].

FIG. 2 (a) Acetylene to benzene reaction pathway as described in chapter 5 of Ref.[14]. (b) Comparison of the key reaction steps in the two mechanisms. The Gibbs free energy was calculated at 298.15 K, 1 atm.

As stated previously, no collisions to induce bond dissociation in acetylene were observed. A single C-H bond dissociation must absorb approximately 131.30 kcal/mol, and approximately 230.60 kcal/mol is required to break a C$\equiv$C bond [77]. Thus, the first vinylidene reaction with acetylene, which possesses an energy barrier of 12.68 kcal/mol, is preferred. We note that 43.72 kcal/mol in forming vinylidene carbene is the highest energy barrier of the entire pathway. It has also been argued [63-65] that the pyrolysis of acetylene actually begins with its isomerization and that multiple re-crossings between acetylene and vinylidene are realistic because of the coupling between kinetic energy and the vibrational mode [55]. The multiple re-crossings are consistent with Coulomb explosion imaging (CEI) experiment [54], in which experiment Levin et al. reported that half the molecules were roughly "still" vinylidene at 3.5 μs after the birth of this carbene. Another reaction that might be considered is the addition of a second vinylidene rather than an acetylene molecule. Based on the PES, we see that the energy barriers of adding an acetylene molecule and vinylidene carbene are 31.34 and 18.37 kcal/mol, respectively. Thus, the second vinylidene is preferred. Additionally, reactions involving carbenes are typically faster than those involving closed-shell species. The new route is also supported by results showing that acetylene has a higher emission concentration and is widely believed to be an important contributor to the formation of soot [3, 27-29, 31, 32]. Thus, the successive vinylidene addition pathway may be more important in the formation of benzene compared to previously described pathways.

Ⅳ. CONCLUSION

This report presents compelling evidence of a viable pathway by which the aromatic ring forms under high temperature conditions. According to the ab initio calculations, benzene can be formed through successive vinylidene additions. No collisions involving acetylene were found to induce C-H bond or C-C bond dissociation. These findings are in direct contrast to previous results suggesting that the formation of benzene molecule occurs through reactions between a C$_4$H$_x$ radical and a C$_2$H$_y$ radical, which are formed through acetylene collisional reactions or between C3 radicals. The reaction pathway presented herein is energetically preferable than the pathway described in [14]. Considering the abundance of acetylene, the conversion between acetylene and vinylidene carbene is highly reversible from each other [55], the experimental result that half molecules are "still" vinylidene after 3.5 μs in CEI experiment [54], and the faster reaction of the carbenes involved in the reactions, successive vinylidene additions may contribute significantly to the formation of benzene under certain conditions. In addition, most of the vinylidene carbenes in the present simulation were found to survive for more than 100 fs. Consequently, we expect this mechanism to be helpful in clarifying the formation of aromatic compounds. At last, these theoretical results await direct comparison from experiments, which hopefully could be provided by time-resolved coulomb explosion imaging experiments [78].

Supplementary materials

Further discussions on the effects brought by molecular collisions and definitions of lifetime of vinylidene are provided in the supporting materials. We provide also additional information about validations of CPMD calculations, enlarged images and optimized coordinates of intermediates involved in the newly proposed reaction route.

Changes made by molecular collisions

Unexpectedly, no molecular collisions to induce C-H bond or C-C bond dissociation were observed within the simulated time period. Details of the collisions that caused geometric transformations are discussed in this section. To illustrate the molecular collisions, the centroid distance between one randomly chosen acetylene molecule and other acetylene molecules were calculated (Figure S3). Among these distances, those below 4.0 Å were recognized to represent a close approach between two molecules. A total of 144 close approaching acetylene molecules occurred within the simulated time. However, none of these interactions led to bond dissociation reactions. Figure S6 depicts changes of the C-C-H angle to represent collision-induced molecular deformations and changes to the H-H distance of two molecules to represent the molecular distance within the selected time period. After RH-H reached its minimum (i.e., two acetylene molecules approached closest) RH-H increased gradually, indicating that the two molecules began to depart. At this point, both the differentiation of the C-C-H angle (θ1, θ2) over time and the amplitude of the C-C-H angle (θ2) tended to increase for the next several cycles. The larger differentiation of angle θ1 and angle θ2 over time suggests a faster rotation of the respective H-atom whereas the broader amplitude of θ2 indicates the molecular deformation of mol2. We note that the two C-H bonds did not break. This implies that the molecular collision only caused the transfer of energy between the molecules rather than inducing chemical reactions. This scenario is plausible because acetylene, a linear molecule with just four atoms, possesses weak steric hindrance for deformation, and it is thus readily accessible to transfer the energy through translations and deformations.

Lifetime of vinylidene and the isomerization of vinylidene to acetylene

Vinylidene was found to exist in this work and was also found to play a key role in the formation of benzene. It is valuable to clarify the lifetime of vinylidene in terms of experimental limits of detection, especially because a relatively long lifetime is constructive for the reaction pathway presented herein. To depict the lifetime explicitly, a criterion was defined as illustrated in Figure S7(a) involving two time points. The first time point was when an angle is formed by 70° between an isomerized-H atom, a newly linked C atom and a previously linked C atom in acetylene. This time point indicates the formation of vinylidene. The second time point was when the angle of 70° was formed between an isomerized-H atom, a now-linked-C atom and the other C atom. Vinylidene was considered not to exist at this time point. The angle of 70° was carefully chosen by checking the respective C-C-H angle in non-isomerized acetylene and an isomerized acetylene (see Figure S4). Based on this scheme, counts of the existence of vinylidene over time and their respective lifetimes were recorded, as shown in Figure S7(b). A total of 11 vinylidene molecules appeared during the simulation. Note that only those isomerized to acetylene were counted, and most vinylidene molecules survived for more than 100 fs. The shortest lifetime was 38.97 fs whereas the longest lifetime was 1009.26 fs. Notably, the reaction from vinylidene to acetylene was found to have two distinct mechanisms: an H-exchange mechanism (Figure S7(c)) and a non-H-exchange mechanism (Figure S7(d)). Essentially, the mechanism is named based on whether the two H atoms that isomerize are identical during the formation/reaction of vinylidene. Assuming that the first H atom isomerized, the mechanism is termed the H-exchange mechanism if the reaction from vinylidene to acetylene is led by the migration of the second H atom bound to the C atom to which the first H atom was originally bonded. In the same way, the mechanism is termed a non-H-exchange mechanism if the first H atom migrated back to form a covalent bond with its original C atom. Among all 11 vinylidene molecules that isomerized to acetylene, 4 became acetylene through the non-H-exchange mechanism and 7 became acetylene through the H-exchange mechanism.

FIG. S1 Single-point energies of 20 acetylene molecules in a cubic box with a length of 16.00 Å using different energy cutoffs
Table S1 Energy differences of vinylidene and acetylene using different cutoffs
Table S2 Accuracy of the bond lengths of the optimized vinylidene and acetylene structures.
Table S3 Harmonic Frequencies (cm-1) of C2D2 calculated using CPMD and those from some references
FIG. S2 Initial configuration used in the first-principles molecular dynamics simulations
FIG. S3 Centroid distance between one picked molecule and other molecules as a function of time. For clarity, only those below 4.0 Å are listed here.
FIG. S4 (a) Distribution of C-C-H angles for non-isomerized acetylene molecules. A sampling of 200, 000 (time steps) * 14 (number of non-isomerized acetylene molecules) was collected. The C-C-H angle as a function of time during the isomerization and the respective C-H bond lengths are listed in (b). From these two figures, we find that a C-C-H angle of 70° is a safe criterion to measure the extent of the reaction because this angle could only be approached during isomerization.
FIG. S5 Bond lengths r1, r2 and r3 as a function of time. Bond length r2 and bond length r3 in TS4 and TS5 were calculated to be 2.135 and 1.347. From Figure S4, it is clear that r2 approaches its transition state ahead of r3. Additionally, if r3 approached its transition state first, the main reaction route would proceed through TS8. That is, another acetylene would be added rather than a vinylidene radical, which possesses a higher energy barrier (Figure 1).
FIG. S6 Changes of angles of C-C-H of two collided molecules over time. The geometry in the figure corresponds the one when the two molecules approach closest. The tick labels at the bottom are calculated and rounded through the corresponding steps multiply timestep.
FIG. S7 (a) Scheme to define the lifetime of vinylidene. (b) Lifetime of vinylidene that isomerises back to acetylene is plotted as a function of time. Two mechanisms of isomerisation between vinylidene radical and acetylene are identified, i.e. H-exchange mechanism and non-H-exchange mechanism. Time evolution of typical bond length in the two mechanisms is listed in (c) and (d).
FIG. S8 Images of intermediates and transition states corresponding to the potential energy diagram given in the main text.
Table S4 Optimized geometries (Ǻ) using the composite method CBS-QB3 in XYZ format.

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Ⅴ. ACKNOWLEDGEMENTS

This work was supported by the National Natural Science Foundation of China (No.21403221 and No.91441106)

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乙炔高温裂解的从头算动力学模拟
王恩栋a,b, 李光跃c, 丁俊霞a, 何国钟a     
a. 中国科学院大连化学物理研究所,分子反应动力学国家重点实验室,大连 116023;
b. 中国科学院大学,北京 100049;
c. 华北理工大学,唐山 063009
摘要: 本文采用了从头算动力学结合量化计算来研究乙炔的热裂解,发现了一条通过连续乙烯基卡宾加成生成苯环的机理,并和与这条路径相竞争的路径进行了对比.此外,还得到了乙烯基卡宾的寿命.
关键词: 从头算动力学模拟    乙炔    燃烧    芳香环    乙烯基卡宾