Rate constant using capture rate theory Georgievskii & Klippenstein (2005). Using the calculations of Peverati et al Peverati et al. (2016) for the C₄H₃⁺ + C₂H₂ reaction, and considering the exothermicity notably higher than for the C₄H₃⁺ + C₂H₂ reaction, we assume that the isomerization toward the cyclic isomer is favored. The exothermicity is given for l-C₆H₄ = C₂H₃C₄H.

Rate constant using capture rate theory Georgievskii & Klippenstein (2005). l-C₆H₆(CH₂CHCHCHCCH) is supposed to be produced in the C₂H + CH₂CHCHCH₂ reaction Jones et al. (2011). The TSs from l-C₆H₇⁺ to C₆H₇⁺ are located much below the exothermicity of the reaction as can be seen in Fig. A.2.1. As noted by Herbst et al Herbst et al. (2000), the typical time-scales for isomeric conversion is much shorter than for relaxation by one infrared photon emission. Thus, as relaxation occurs slowly, isomeric conversion leads to equilibrated isomeric abundances at each internal energy. The final balance is determined at or near the effective barriers to isomerization, which corresponds to the energy of the transition states favoring C₆H₇⁺. Some C₆H₇⁺ may dissociate into C₆H₇⁺ + H₂.

Considering M06-2X/AVTZ calculations shown in Fig. A.2.2 with cyclization in few steps with fairly low TS, and by comparison with the isoelectronic l-C₃H₃⁺ + C₃H₄ reaction, the formation of C₆H₅⁺ should be significant.

The first step is CH₂CH₂CHCCCH⁺ formation which self-isomerize into c-C₃H₅CCCH⁺. The TS from c-C₃H₅CCCH⁺ → c-C₄H₅CCH⁺ is located −187 kJ/mol below the entrance channel as shown in Fig. A.2.3. We use similar branching ratio than for C₄H₂⁺ + C₂H₄ Anicich et al. (2006) (with the fact that the more energy is put into the system, the more C₆H₅⁺ is disadvantaged when compared to C₃H₂⁺ + C₃H₄ using Anicich et al. 1984).

There are three isomers for C₃H₂⁺: c-C₃H₂⁺ (the most stable), HCCCH⁺ (+55 kJ/mol called l-C₃H₂⁺ but is in fact the t-C₃H₂⁺ using the nomenclature of the neutral) and H₂CCC⁺ (+196 kJ/mol not present in the network and is in fact the real l-C₃H₂⁺ using the nomenclature of the neutral). Experimentally, both c-C₃H₂⁺ and HCCCH+ isomers are produced and are not separated. They generally have similar reactivity, except with water Prodnuk et al. (1992), and we consider the same rate constants and branching ratios for both isomers.

Considering the M06-2X/AVTZ calculations shown in Fig. A.2.4 with cyclization in few steps with fairly low TS, we use similar branching ratio than for C₄H₂⁺ + C₂H₄ Anicich et al. (2006) (with the fact that the more energy is put into the system, the more C₆H₅⁺ is disadvantaged when compared to C₃H₂⁺ + C₃H₄ using Anicich et al. (1984)).

We performed new experiments at SOLEIL synchrotron using the CERISES setup (to be published) showing that l-C₃H₃⁺ is reactive with CH₃CCH as it is reactive with C₂H₂, C₂H₄, C₄H₂ . ..Anicich (2003). In Anicich et al. (1984) they cited old branching ratios : C₆H₅⁺ + H₂ (45%), C₄H₅⁺ + C₂H₂ (35%) and C₄H₃⁺ + C₂H₄ (20%).

We performed new experiments at SOLEIL synchrotron using the CERISES setup (to be published) showing that l-C₃H₃⁺ is reactive with CH₂CCH₂ as it is reactive with C₂H₂, C₂H₄, C₄H₂ ...Anicich (2003). In Anicich et al. (1984) they cited old branching ratios : C₆H₅⁺ + H₂ (38%), C₄H₅⁺ + C₂H₂ (37%) and C₄H₃⁺ + C₂H₄ (25%).

There is probably no barrier compared to the reactions of C₃H₄⁺ with C₂H₂ and C₂H₄. We consider similar rate and branching ratio than for the C₄H₂⁺ + C₂H reaction Anicich et al. (2006) (with the fact that the more energy is put into the system, the more C₆H₅⁺ is disadvantaged when compared to C₃H₂⁺ + C₃H₄ using Anicich et al. (1984)). Moreover, the production of c-C₃H₂CH₂⁺ requires few steps and is likely favoured.

There is probably no barrier compared to the reactions of C₃H₅⁺ with C₂H₂ and C₂H₄. Since the hydrogen atoms are distributed across all the carbons, cyclization into C₆H₇⁺ requires few steps and is probably favored. We assume similar rate and branching ratio that the isoelectronic l-C₃H₃⁺ + CH₂CCH₂ reaction favoring th c-C₃H₂CH₃⁺ production.

the most stable isomer for C₄H₄⁺ is c-C₃H₂CH₂⁺ (then CH₂CCCH₂⁺: +47 kJ/mol, CH₂CHCCH⁺: +58 kJ/mol (used for the exothermicities of the reactions) c-C₄H₄⁺: +59 kJ/mol). The various C₄H₄⁺ isomers have not the same reactivity

The most stable isomer for C₅H₃⁺ is c-C₃H₂CCH⁺ rather than H₂C₅H⁺ (+83 kJ/mol). We have little information about the nature of the isomers studied in the few experiments that have been conducted but C₅H₃⁺, produced from l-C₃H₃⁺ + C₄H₂, is reactive with C₄H₂ Ozturk et al. (1989). In astrochemical models, there ar several effective sources of C₅H₃⁺: c,t,l-C₅H₂ + H₃⁺/HCO⁺, c,l-C₃H₂⁺ + C₂H₂, CH₃C₄H + He⁺ .... Both c-C₃H₂CCH andH₂C₅H are likely to be produced.

The exit channels on the triplet surface are not very exothermic which should favor intersystem crossing toward the singlet surface. The rate constant has bee measured at room temperature and low pressure. C₇H₅ has been clearly identified in crossed molecular beam experiment without branching ratio determination Hahndorf et al. (2002); Kaiser et al. (1999). The most favorable bimolecular products seems to be c-C₅H₄CCH + H according to da Silva (2014).

There is no barrier at level M06-2X/AVTZ (Fig. A.1.1) for the addition of C₃ to C₃H₅(CH₂CHCH₂ most stable isomer Stranges et al. (2008), yielding the adduct CH₂CHCH₂CCC (similar to the absence of barrier for the C₃ to C₃H₃ reaction Mebel et al. (2023). This adduct can evolve either by direct loss of hydrogen to yield a linear isomer of C₆H₄ or, more favorably, to yield C₆H₄ (cyclic) + H (Fig. A.1.2). The rates proposed are approximate and will require further calculations (an experiments).

No barrier in the entrance valley according to Castiñeira Reis et al. (2024) leading to CH₂CCCHCCH₂ and CH₂CCCH₂CCH. The pathway from CH₂CCCHCCH to C₆H₅ involve various TS as high as −93 kJ/mol below the l-C₃H₂ + C₃H₃ entrance level Castiñeira Reis et al. (2024), so some C₆H₄ may be produced.

Georgievskii et al. (2007); Miller & Klippenstein (2003); Vuitton et al. (2019); Hrodmarsson et al. (2024). We neglect the C₆H₆ formation (various isomers) at very low pressure.

Rate derived from Berteloite et al. (2010), the experimental values being valid in the 39-300K range. The isomerization toward benzyne likely involve high TS using Castiñeira Reis et al. (2024) (even if CH₂CH₂C₄H isomer was not considered in Castiñeira Reis et al. (2024).

The pathway for C₂H₃C₄H → C₆H₄ involves 3 TS located as high as 367 kJ/mol above the C₂H₃C₄H energy Castiñeira Reis et al. (2024). Moreover, he pathway for the various C₆H₅ isomers toward the cyclic one involve TS as low as 370 kJ/mol above the l-C₆H₅ energy so isomerization of C₆H₅ before C-H dissociation i possible.

Rate constant from Hamberg et al. (2011), branching ratio guessed by comparison with C₆H₆ photodissociation.

Global rate from Hamberg et al. (2011) with the preserved cycle.

Same rate as C₆H₆⁺ + e⁻. Large uncertainties, C₆H₆ + C₂H and C₆H₆ + C₂H₂ may also be produced.

Same rate as C₆H₆⁺ + e⁻.