Quantum chemical mechanism on the depletion of C₃O by oxygen atoms: barrierless to produce CO

ABSTRACT

Accurate quantum chemical studies at the CCSD(T)/CBS//CCSD/cc-pVTZ level predicted the depletion reaction of C₃O by both singlet and triplet O-atoms to be barrierless, leading to the astrophysically very abundant CO plus triplet CCO. The barrierless nature of the reaction fully complied with the long conjecture, whereas the product differed significantly. Our kinetic calculations indicated that the reaction possesses significant negative temperature effect below 30 K. The calculations should be useful for understanding the astrophysical recycling for both the carbon and oxygen species.

1 INTRODUCTION

TMC-1 can be called the ‘accumulation area’ of carbon chain molecules in the Milky Way, including polycyclic aromatic hydrocarbon molecules (McGuire et al. 2021), C_nN (n = 3,5) (Friberg et al. 1980; Guélin, Neininger, & Cernicharo 1998), C_nS, (n = 2–4) (Kaifu et al. 1987; Saito et al. 1987; Cernicharo et al. 2021b), and C_nO (n = 2,3,5) (Matthews et al. 1984; Ohishi et al. 1991; Cernicharo et al. 2021a), etc. Carbon chain molecules with an oxygen end atom (C_nO) serve as important probe elements to determine the chemical composition of gases of molecular clouds and provide insights into the oxygen chemistry in the interstellar medium (ISM) (Jamieson, Mebel, & Kaiser 2006; Agúndez & Wakelam 2013; Loison et al. 2013; Vastel et al. 2014; Khadri & Hammami 2019; Khadri et al. 2022). More recently, in 2022, pentacarbon monoxide (C₅O) was recognized in TCM-1, which further sparked great interest in C_nO research (Cernicharo, et al. 2021b).

Tricarbon monoxide (C₃O), the first known interstellar carbon chain molecule, was first detected in TMC-1 in 1984 (Matthews, et al. 1984). In 1991, dicarbon monoxide (C₂O) was also identified in TMC-1. Furthermore, C₃O and C₂O were identified towards different astronomical sources, the carbon-rich star IRC+10216 (only C₃O was found), the low-mass protostar ELIAS 18, the pre-stellar core L1498 and L1544, etc (Ohishi, et al. 1991; Tenenbaum et al. 2006; Palumbo et al. 2008; Vastel, et al. 2014; Urso et al. 2019). Since the microwave spectrum of C₃O was first discovered in laboratory in 1983, its millimeter-wave spectrum and infrared absorption have been confirmed (Brown et al. 1983). As more and more evidences of C₃O and C₂O become available, numerous theoretical models that include detailed physical and chemical pathways have been developed to better understand their formation and destruction of them (Ekern & Vala 1997; Blanksby, Dua, & Bowie 1999; Trottier & Brooks 2004; Urso, et al. 2019). To date, the chemical reaction network involving carbon-chain species occurring in the gas phase has approximately 500 species connected by about 7000 reactions (Urso, et al. 2019). However, no reaction exists yet to directly connect C₃O and C₂O in the reported chemical network.

The depletion reaction of C₃O and O was one member of the chemical network, which aroused our particular interest. First, the oxygen (O) atom is Earth's most abundant element, and the third most abundant element after hydrogen (H) and helium (He) in the universe (Khadri & Hammami 2019). Secondly, the O atom is a highly reactive non-metal and an oxidizing agent that readily forms oxides with most elements as well as with other compounds (Harding & Wagner 1986; Schmoltner et al. 1989; Mebel et al. 1996; Xie, Ding, & Sun 2006). Thirdly, as early as 1984, it was reported that the fractional abundance (f) of O atom (f_o ∼ 5 × 10⁻⁵) is larger than that of ion (such as H₃⁺) (f_ion ∼ 3 × 10⁻⁸). So, the neutral species capable of reacting with C₃O is most likely the O atom, leading to the products C₃ + O₂ (i.e. O + C₃O → C₃ + O₂, model reaction 1) (Herbst, Smith, & Adams 1984; Herbst & Leung 1986). But, intuitively, model reaction 1 is thermodynamically infeasible because it is an endothermic reaction. Moreover, the detailed quantum chemical reaction mechanism of C₃O + O has not been reported, though model reaction 1 has continued to be accepted even very recently (Urso, et al. 2019).

On one hand, it is very curious how C₃O and C₂O are connected in the chemical reaction network in the interstellar space. On the other hand, the O atom is the most likely neutral species to react with C₃O and its reaction mechanism has remained to be understood. Thus, in this work, high-level quantum chemical calculations about the reaction mechanism of C₃O by O atoms were carried out for the first time. The detailed potential energy surface (PES) of the reactions of C₃O by singlet O (¹O) and triplet O (³O) atoms were constructed at the CCSD(T)/CBS//CCSD/cc-pVTZ level. The results show that the reactions of C₃O with ¹O (−0.14 kcal/mol) and ³O (−0.51 kcal/mol) have minute energy barriers, and the products are both the ground state C₂O and CO. Here, the first reaction connecting C₃O and C₂O directly was established, and the first mechanism investigating the reaction of C₃O with O atoms was theoretically predicted, which would greatly promote the development of carbon chemistry and oxygen chemistry in the ISM.

2 COMPUTATIONAL METHODS

2.1 Electronic structure and energy calculations

gaussian16 (Frisch, Trucks, & Schlegel 2016) and gaussian09 (Frisch, Trucks, & Schlegel 2013) program packages were used in this paper. The optimized geometries and harmonic frequencies of the reactants, products, isomers, and transition states were obtained at the CCSD/cc-pVTZ level (Pople et al. 1978). Connections of the transition states between designated local minima have been confirmed by intrinsic reaction coordinate (IRC) calculations at B3LYP/6–31G(d) (Fukui 1970; Parr 1980; Lee, Yang, & Parr 1988; Becke 1993). The specific coordinate information of structures was listed in the Section 3 of the ESI†. Initially, single-point calculations at CCSD(T)/CBS//CCSD/cc-pVTZ were performed by gaussian-16 using the CCSD/cc-pVTZ-optimized geometries and zero-point correction energy. The complete basis set (CBS) limit extrapolation was based on the aug-cc-pVTZ + aug-cc-pVQZ single-point energies (Kendall, Dunning Jr, & Harrison 1992; Halkier et al. 1998; Montgomery Jr et al., 1999, 2000; Woon & Dunning Jr 1993). It is worth noting that for the reaction processes with open-shell singlet character (the species with ‘u’ prefix), the broken symmetry strategy of Noodleman (Noodleman 1981; Noodleman & Davidson 1986; Ovchinnikov & Labanowski 1996; Adamo et al. 1999) was also used, i.e. UCCSD/cc-pVTZ, for the geometrical optimization with the ‘guess = (mix, always)’ keyword.

2.2 Kinetics calculations

The reaction rate constants for the reaction of ^3/1O + C₃O were performed by the Master Equation Solver for Multi-Energy Well Reactions (mesmer) 6.0 program (Glowacki et al. 2012). We used the Rice–Ramsperger–Kassel–Marcus theory to calculate the reaction rate constants for reactions with tight transition states (Robinson & Holbrook 1972; Holbrook et al. 1996). The required input parameters such as rotational constants, vibrational frequencies, and energies in the mesmer modelling were obtained at the CCSD/cc-pVTZ or CCSD(T)/CBS//CCSD/cc-pVTZ levels. For the barrierless entrance pathways (from ^3/1R1 to ^3/1C3), we used the inverse Laplace transformation (ILT) method (Glowacki et al. 2012). The temperature-independent capture rate constant was used to carry out the fitting calculation of the ILT method. The capture rate constants were calculated by the theory of dispersive long-range transition-states (Fu et al. 2021). For details, please refer to our previous published literature (Ma et al. 2021). N₂ was selected as the buffer gas. The single exponential down model was used to approximate the collisional energy transfer between active intermediates and N₂ (buffer gas) with ΔE_down = 50 cm⁻¹. The Lennard–Jones parameters of intermediates were estimated using the method of Gilbert and Smith and listed in the ESI†-Table S1 (Gilbert & Smith 1990).

3 RESULTS AND DISCUSSION

The structures of [C₃O, O] reactants, isomers, complexes, and products are shown in the Figs S1 and S2 in the ESI†. The schematic PESs of the ³O + C₃O and ¹O + C₃O reactions at CCSD(T)/CBS//CCSD/cc-pVTZ are presented in Figs 1 and 2, respectively. The most important singlet and triplet reaction pathways including the singlet–triplet intersystem crossing (ISCs) are given in Fig. 3. Fig. 4 shows the rate constants of ^3/1O + C₃O. The total energy of the reactant ³O + C₃O (³R1) is set as zero. Reactants are denoted by R, isomers by A, complexes by C, transition states by ts, and products by P.

3.1. Mechanism of ³O + C₃O reaction via triplet PES

On the triplet PES for ³O + C₃O (Fig. 1), three initial attack channels of ³O on C₃O are considered: (1) ³O attacking the C1 atom through the transition state ts³C3/³A1 (−0.51) to form ³A1 (−84.86), (2) ³O attacking C2 atom through ts³C3/³A2 (4.61) to form ³A2 (−64.97), (3) ³O attacking the C3 atom through ts³C3/³A4 (56.89) to form ³A4 (58.40). The values in parentheses are relative energies in kcal mol⁻¹ with respect to ³R1, ³O + C₃O (0.00). At the CCSD(T)/CBS//CCSD/cc-pVTZ level, the barriers of channels 1, 2, and 3 are −0.51 via ts³C3/³A1, 4.61 via ts³C3/³A2, and 56.89 kcal mol⁻¹ via ts³C3/³A4, respectively. Surely, the formation of ³A1 in channel 3 is of little practical interest due to the high product energy. At the entrance to channel 1, there is a barrier of 0.49 kcal mol⁻¹ from ³C3 to ³A1. Notably, the associated transition state lies by a submerged barrier, i.e. ts³C3/³A1 lies by 0.51 kcal mol⁻¹ below the reactant ³R1. This is the rate-determining step (with the lowest barrier) in the three reaction channels. Besides, among the three channels, channel 1 has the lowest energy intermediate ³A1 with an exothermic value of −84.86 kcal mol⁻¹. Therefore, channel 1 associated with the low-lying isomer OCCCO, ³A1 is the most competitive both kinetically and thermodynamically, and it is the channel with the most interest to us in the following discussions.

From the isomer OCCCO, ³A1, formed with a large exothermicity of 84.86 kcal mol⁻¹, there are two possible reaction pathways: (A) O migration to ³A3 (−25.66) via ts³A1/³A3 (−7.39), and finally decomposition into ³P2, CO₂ + ³C₂ (−35.02) via ts³A3/³C2 (−16.11); (B) CO removal to ³P1, CO + ³CCO (−75.97), via ts³A1/³C1 (−69.80). Surely, channel B is more favourable than channel A, since ts³A1/³C1 (−69.80) in channel B is lower by 62.41 kcal mol⁻¹ than ts³A1/³A3 (−7.39) in channel A, and the most relevant pathway on the triplet PES for the reaction ³O + C₃O can be summarized here: ³Path 1, ³O + C₃O (³R1)→OCCCO(³A1)→ CO + ³CCO (³P1)

In short, the rate-determining step is the entrance O-addition channel to the terminal C1 atom (channel 1). If the reaction proceeds completely via the triplet PES, the dominant product should be ³P1, CO + ³CCO (channel A).

3.2. Mechanism of ¹O + C₃O reaction via singlet PES

On the singlet PES for the ¹O + C₃O reaction (Fig. 2), one initial attack channel of ¹O on C₃O was identified that O addition to the terminal C1 atom via uts¹C3/¹A1 (with the barrier of −0.14 kcal mol⁻¹) forming OCCCO (A1) (−160.23). The values in parentheses are relative energies in kcal mol⁻¹ concerning ³R1, ³O + C₃O (0.00). There are three transformation channels starting from ¹A1: (1) forming u¹CCO + CO; (2) generating cyclo-CCO(c-CCO) + CO; (3) producing CO₂ + ¹C₂. These pathways from reactant ¹R1 are schematically written as:

• ¹Path 1, u¹O + C₃O (¹R1)→OCCCO (¹A1)→ u¹CCO + CO (u¹P1)

• ¹Path 2, ¹R1→¹A1→¹A2→c-¹CCO + CO (¹P2)

• ¹Path 3, ¹R1→¹A1→¹A2→¹A3→CO₂ + ¹C₂ (¹P3)

All the involved transition states and intermediates of the three above-mentioned processes lie energetically lower than ¹R1, u¹O + C₃O. Thus, all three processes can occur barrierlessly. ¹Path 1 is the most competitive pathway leading to the product u¹P1, u¹CCO + CO associated with lower barrier (via uts¹A1/u¹C1) and smaller endothermic value.

3.3. Possibility of intersystem crossing

For such a reaction system that involves singlet and triplet species, it is desirable to discuss the possibility of intersystem crossing, as shown in Fig. 3. There are mainly two triplet–singlet crossing processes. At the entrance addition process, ³O + C₃O (³R1)→³A1 and u¹O + C₃O (¹R1) →¹A1, the first triplet–singlet crossing seems to appear. ¹R1, u¹O + C₃O (11.87) was higher than ³R1 (0.00), while ¹A1 (−160.23) was lower than ³A1(−84.86). The second crossing occurs at the processes of ³A1→³C1 and ¹A1→u¹C1. For these two processes, at the CCSD(T)/CBS//CCSD/cc-pVTZ level, the triplet isomer ³A1 (−84.86) lies by 75.37 kcal mol⁻¹ higher than singlet ¹A1 (−160.23) while the transition state ts³A1/³C1 (−69.80) lies by 1.54 kcal mol⁻¹ lower than uts¹A1/u¹C1 (−68.26). Moreover, the triplet complex ³C1 (−76.79) and dissociation limit ³CCO + CO (³P1) (−75.97) are lower than the singlet complex u¹C1 (−72.41) and dissociation product u¹CCO + CO (u¹P1) (−69.43), respectively. Therefore, the triplet→singlet (³C3→¹A1) and singlet→triplet (¹A1→³C1) intersystem crossing might take place for the two processes via ISC1 and ISC2, respectively. The two intersystem crossings alter the reaction mechanism, proceeding via the lowest intermediate ¹A1 (carbon suboxide, C₃O₂) and generating the lowest product ³P1. The predominant pathway for the ³R1, ³O + C₃O and ¹R1, u¹O + C₃O reaction can be expressed by ³ISCPath, ³O + C₃O (³R1)→³C3→ISC1→ ¹A1→ISC2→³C1→³CCO + CO (³P1)

• ¹ISCPath, u¹O + C₃O (¹R1)→¹C3→¹A1→ISC2→³C1→ ³CCO + CO (³P1)

Interestingly, both the reactions of singlet and triplet O atoms with C₃O lead to the lowest-lying product ³P1, ³CCO + CO.

3.4. Kinetics for the reaction of ^3/1O + C₃O

Based on the favourable reaction pathways in PES of triplet (³O + C₃O (³R1)→³C3→OCCCO (³A1)→CO + ³CCO (³P1)) and singlet state (¹O + C₃O (¹R1)→¹C3→OCCCO(¹A1)→CO + ¹CCO (¹P1)), the mesmer modelling was employed to investigate the reaction rate constants (ranging from 5–300 K, P = 10 Torr) (Figs 4 a and b) for the entrance of ^3/1O + C₃O reaction (^3/1R1→^3/1A1). Note that the rather low pressure in space would allow the little cage effect, because of which the recombination of the generated fragments u¹CCO and CO in u¹P1 resulting from the ^3/1R1 (^3/1O + C₃O) reaction should be unlikely and is omitted here. The used very low pressures and temperatures allowed us to evaluate the reaction rate constants under conditions relevant to interstellar environments, which is usually difficult to tackle in laboratory. The detailed rate constant values are listed in the Tables S2 and S3 in the ESI†. At 10 K, our calculated rate constant for the triplet reaction was 4.35 × 10⁻¹° cm³ mol⁻¹ s⁻¹, which is basically in agreement with the estimated value 10⁻¹¹ cm³ mol⁻¹ s⁻¹ reported in 1984 (Herbst, Smith, & Adams 1984). As shown in Figs 4a and b, within the temperature range of 5–30 K, the reaction showed a negative temperature effect decreasing from 9.14 × 10⁻¹⁰ to 2.64 × 10⁻¹° cm³ mol⁻¹ s⁻¹ (³O + C₃O) and 1.43 × 10⁻⁹ to 2.43 × 10⁻¹° cm³ mol⁻¹ s⁻¹ (¹O + C₃O), respectively. Because our activated complex well is shallow, the negative temperature interval is narrow. Furthermore, since even the lowest-lying ¹A1 still remains uncertain in interstellar space (Ciaravella et al. 2016), it should be of great interest to see whether or not any C₃O₂ isomers could be sufficiently stabilized during the atomic O reactions with C₃O. We calculated the time-dependent fractional yields for the rate-determining step of ^3/1O + C₃O (^3/1R1→^3/1P1) at 298 K and 760 Torr (see Fig. S3 in the ESI†). Besides, we used the conventional transition state theory (Fernández-Ramos et al. 2007) to calculate the ratio of rate constants (K_d/K_r) of the decomposition (^3/1A1→^3/1P1) and returning (^3/1A1→^3/1R1)of ^3/1A1 (see Table S4 in the ESI†) at very low temperatures. For ^3/1A1, the ratios are |${{\rm{e}}}^{2.099\, \times {{10}}^{24}}$| (⁠|${{\rm{e}}}^{2.099\, \times {{10}}^{23}}$|⁠) and |${{\rm{e}}}^{2.051\, \times {{10}}^{24}}$| (⁠|${{\rm{e}}}^{2.422\, \times {{10}}^{23}}$|⁠) at 10 (100) K, respectively. These results show that the decomposition of ^3/1A1 to ^3/1P1 has the overwhelming kinetic competition over the returning of ^3/1A1 to ^3/1R1, resulting in the almost no stabilization of ^3/1A1 for the very exothermic reaction ^3/1R1 (^3/1O + C₃O). For the ^3/1O + C₃O reaction, formation of the C₃O₂ isomers other than A1 have the even much lower kinetic competition. Thus, considering the rather low number density of gas molecules in space, we believe that no C₃O₂ isomers can act as thermodynamic sinks for the ^3/1O + C₃O reactions, which instead can most favourably lead to the fragments P1. In all, the A1 intermediate cannot be stabilized from the ^3/1R1 (^3/1O + C₃O) reaction channel.

But one should note that the generation and stabilization degree of a structure usually depend on the suitable reaction routes and conditions. The reaction of u¹CCO with the residual CO molecules coming from the substrate [e.g. CO ice (DeVine et al. 2022)] instead of the O + C₃O reaction might be feasible, leading to the formation and stabilization of ¹A1. As depicted in Fig. 3, the reaction u¹P1 (u¹CCO + CO)→ ¹C1→¹A1 has the overall zero barrier height, whereas its triplet counterpart ³P1  ³CCO + CO possesses a considerable barrier height of 6.17 kcal mol⁻¹ via ts³A1/³C1.

4 IMPLICATION

Up to now, in the reported reaction network (about 7000 carbon-chain reactions connecting among 500 species), there is no reaction directly linking C₃O and C₂O. The model reaction of C₃O and O to generate C₃ and O₂ was reported early in 1984 and has been applied so far. Here, the first quantum chemical calculation on the detailed reaction mechanism of C₃O and O was reported. Surprisingly, the products of the reaction of C₃O and O are the triplet C₂O and CO, which present the first reaction to directly connect C₃O and C₂O. In addition, due to the harsh critical conditions of interstellar space (low temperature around 10–100 K), it might be difficult to study the reaction under this condition in the laboratory. Thus, the theoretical mechanism and the kinetic calculations over the temperature range (5–300 K) presented here for the reaction between the O atoms and C₃O should help understand the carbon chain chemistry in interstellar or laboratory. Our study not only quantitatively confirmed the high efficiency for depletion of C₃O by oxygen atoms to produce CO, but also showed the negative temperature effect at very low temperature (below 30 K), which would indicate the increased importance with lowered temperature for ^3/1O + C₃O reactions. The work might be useful for future molecular dynamic (MD) modelling for the ^3/1O + C₃O reactions. Note that density functional theory (DFT)-based molecular dynamics (MD) might be inapplicable due to the failure of locating entrance O-attack transition states at DFT levels. For the ^3/1O + C₃O reactions, MD calculations based on coupled cluster method (denoted as CC-MD) are desirable despite being very costly.

5 CONCLUSIONS

We have made the first detailed PES study of the astrophysically important reactions of oxygen atoms (³O and ¹O) with tricarbon monoxide (C₃O). The results are summarized below:

1. For the ³R1, ³O + C₃O reaction via the triplet PES, the dominant pathway is

³Path 1, ³R1 (³O + C₃O)→³C3→³A1→³C1→³P1 (³CCO + CO) (dominant)

2. For the ¹R1, u¹O + C₃O reaction via the singlet PES, the most important fragmentation pathway is

¹Path 1, ¹R1 (u¹O + C₃O)→¹A1→u¹C1→u¹P1 (u¹CCO + CO)

3. With consideration of the intersystem crossing processes, ³R1→¹A1, ¹A1→³C1 and ¹R1→¹A1, ¹A1→³C1, both ¹R1, ¹O + C₃O, and ³R1, ³O + C₃O, reactions lead to the lowest lying product ³P1, ³CCO + CO, via the respective pathways

• ³ISCPath, ³R1 (³O + C₃O)→³C3→ISC1→¹A1→ISC2→ ³C1→ ³P1 (³CCO + CO),

• ¹ISCPath, ¹R1 (u¹O + C₃O)→¹C3→¹A1→ISC2→³C1→³P1 (³CCO + CO).

ACKNOWLEDGEMENTS

This work was funded by the National Natural Science Foundation of China (no. 22073069, 21773082, 22176022, and 22206020), the National Pre-research Program of Hebei GEO University in 2023 (QN2022006), and the China Postdoctoral Science Foundation (2022M720640). The reviewer's invaluable comments and suggestions are greatly acknowledged. We wish to thank Prof. Struan H. Robertson for helping us better understand and use mesmer during this work.

DATA AVAILABILITY

All the data and results presented in this work have been included in the supporting information. All other necessary information will be shared upon reasonable request to the authors.

CONFLICT OF INTEREST

The authors declare that they have no conflict of interest.

References