Astrochemical Modeling of Propargyl Radical Chemistry in TMC-1

Recent detections of aromatic species in dark molecular clouds suggest that formation pathways may be efficient at very low temperatures and pressures, yet current astrochemical models are unable to account for their derived abundances, which can often deviate from model predictions by several orders of magnitude. The propargyl radical, a highly abundant species in the dark molecular cloud TMC-1, is an important aromatic precursor in combustion flames and possibly interstellar environments. We performed astrochemical modeling of TMC-1 using the three-phase gas-grain code NAUTILUS and an updated chemical network, focused on refining the chemistry of the propargyl radical and related species. The abundance of the propargyl radical has been increased by half an order of magnitude compared to the previous GOTHAM network. This brings it closer in line with observations, but it remains underestimated by 2 orders of magnitude compared to its observed value. Predicted abundances for the chemically related C4H3N isomers within an order of magnitude of observed values corroborate the high efficiency of CN addition to closed-shell hydrocarbons under dark molecular cloud conditions. The results of our modeling provide insight into the chemical processes of the propargyl radical in dark molecular clouds and highlight the importance of resonance-stabilized radicals in polycyclic aromatic hydrocarbon formation.


INTRODUCTION
Polycyclic aromatic hydrocarbons (PAHs) are the probable carriers of the unidentified infrared emission bands pervasive in our and other galaxies (Tielens 2008), as well as potentially some of the diffuse interstellar bands that can be observed in the infrared, visible, and ultraviolet (UV) spectra of the interstellar medium (ISM) (Duley 2006).Despite the ubiquity of these molecules in the ISM, their formation pathways remain ambiguous.One suggested formation route is through high-temperature growth processes in the circumstellar envelopes of evolved stars followed by injection into the ISM (Kaiser & Hansen 2021;Tielens 2008).However, in the diffuse ISM and photodissociation regions, carbonaceous material on dust grains and in the gas phase is exposed to UV photon irradiation and shocks (Berné et al. 2015).It has been assumed that small PAHs of less than 20−30 atoms often cannot internally redistribute energy Corresponding author: Alex N. Byrne lxbyrne@mit.edufrom the absorption of UV photons in such regions or reradiate it back out before they are destroyed, resulting in short lifetimes (Chabot et al. 2019).Recent observations of the Taurus Molecular Cloud (TMC-1) reported the detection of benzonitrile (McGuire et al. 2018), the first six-membered aromatic ring detected via radio astronomy, followed by detection of the small PAHs 1-and 2cyanonaphthalene, indene, and 2-cyanoindene (McGuire et al. 2021;Burkhardt et al. 2021b;Sita et al. 2022).While the discovery of aromatic molecules in dark molecular clouds appears to imply the existence of efficient low-temperature formation routes, current astrochemical models dramatically fail to reproduce their observed abundances.This gap in our understanding of aromatic chemistry highlights the need for further exploration of the formation and chemical evolution of these molecules.
Several theoretical and experimental studies have proposed gas-phase formation pathways to benzene (C 6 H 6 ) from small hydrocarbons (Jones et al. 2011;Caster et al. 2019;Hébrard et al. 2006).In combustion flames, benzene, as well as the phenyl radical, are suggested to be efficiently formed from the recombination of two propar-gyl radicals (CH 2 CCH) (Miller & Melius 1992) CH 2 CCH + CH 2 CCH −−→ C 6 H 6 /C 6 H 5 + H. (1) CH 2 CCH is a small, resonance-stabilized hydrocarbon radical (as shown in Figure 1) that can form in flames from the insertion of 1 CH 2 into the C-H bond of C 2 H 2 , where 1 CH 2 denotes an electronically excited methylene radical.(Miller & Melius 1992).Computational studies of the C 6 H 6 potential energy surface have shown that two propargyl radicals can barrierlessly combine and undergo decomposition to form o-benzyne (c-C 6 H 4 ) + H 2 or phenyl radical (C 6 H 5 ) + H, with the latter pathway expected to be the dominant bimolecular pathway (Miller & Klippenstein 2003a).Experimental studies at high temperatures have revealed the formation of obenzyne as well as the C 6 H 6 isomers benzene, fulvene, 1,5-hexadiyne, and 2-ethynyl-1,3-butadiene (Zhao et al. 2021).The product branching ratios were found to heavily depend on temperature and pressure, providing critical information about formation of aromatic species in combustion flames and in dense environments such as Titan's atmosphere (Zhao et al. 2021).In contrast, the C 6 H 5 + H channel is expected to prevail in cold and less dense environments such as TMC-1, whereas the c-C 6 H 4 channel is expected to be negligible.While previous astrochemical studies have placed an emphasis on benzene as the first aromatic ring formed en route to PAH formation (Jones et al. 2011;Caster et al. 2019), these studies of CH 2 CCH recombination indicate that the phenyl radical may be equally important.In order to better model and understand aromatic chemistry of interstellar environments, a greater emphasis must be placed on alternative formation pathways involving the C 6 H 5 , beginning with CH 2 CCH recombination.The detection of CH 2 CCH in TMC-1 at millimeter wavelengths has further spurred astrochemical interest in the molecule (Agúndez et al. 2021(Agúndez et al. , 2022).An observed abundance of 1.0×10 −8 with respect to molecular hydrogen makes this one of the most abundant radicals in TMC-1, with a CH 3 CCH/CH 2 CCH ratio about equal to one (Agúndez et al. 2022).In addition to the detection of CH 2 CCH, the authors performed an astrochemical modelling study of the radical and its closed-shell counterparts.They concluded that the major contributions to the production of CH 2 CCH include the neutralneutral reaction between ethylene (C 2 H 4 ) and atomic carbon in the gas phase, and the dissociative recombination (DR) reactions of 3carbon cations, where n = 4, 5, and 6.The major destruction pathways are through reactions with neutral atoms such as C, O, and N.While these models reproduce the observed abundance of the closed-shell species CH 3 CCH well, the modeled propargyl abundance is underestimated by over two orders of magnitude.The presence of low-temperature kinetic measurements for a number of relevant neutral-neutral reactions is a significant benefit toward understanding the chemistry of this radical under molecular cloud conditions (Slagle et al. 1991;Canosa et al. 1997;Chastaing et al. 1999Chastaing et al. , 2000;;Canosa et al. 2007), but the sizeable difference between observed and modeled abundances indicates that existing gasphase reactions may need to be re-evaluated.In particular, experimental studies of the reactions between CH 2 CCH and neutral atoms at low temperatures are rare.Moreover, a main limitation of the astrochemical model presented in Agúndez et al. (2021) is the lack of consideration for grain chemistry.Hickson et al. (2016) revealed that surface hydrogenation of 3-carbon hydrocarbons on interstellar grains is critical for the formation of CH 2 CCH and its closed shell counterparts.
The high abundance of CH 2 CCH despite its open-shell nature and its close connection to aromatic species highlights it as an important species in the chemical evolution of molecular clouds, yet previous astrochemical knowledge on this species was incomplete.Detailed kinetic studies at low temperature provide the most relevant information for modeling the chemistry of dark molecular clouds and other interstellar regions (Hébrard et al. 2009), but the sheer number of possible reactions and difficulty in replicating interstellar conditions makes this a formidable problem.In order to investigate the chemical evolution of CH 2 CCH in the ISM, we performed astrochemical modeling under dark cloud conditions with an updated and expanded chemical network.In Section 2, we describe the modeling code and physical conditions used as well as the modifications made to the chemical network.The results of the modeling efforts toward CH 2 CCH and related species are presented in Section 3. Finally, we discuss these results in Section 4 along with comparisons to previous works and future directions.

METHODS
The astrochemical modeling code utilized is NAUTILUS, a three-phase gas-grain rate equation model (Ruaud et al. 2016).The gas phase, grain surface, and grain mantle are treated individually with their own parameters and chemical reactions.Additional physical processes of diffusion between grain surface and mantle, diffusion within grain surface and mantle, adsorption of gas-phase species onto the grain, and desorption of grain surface species into the gas phase are considered.
Additionally, the NAUTILUS model considers photodissociation and photodesorption by external UV photons and cosmic-ray induced UV photons, thermal evaporation, evaporation via cosmic-ray stochastic heating, and chemical desorption.We used the default 1% efficiency for the chemical desorption mechanism and peak grain temperature of 70 K for 1 × 10 −5 years for the cosmic ray heating mechanism.More information on these mechanisms and their implementations can be found in the NAUTILUS documentation (https://forge.oasu.ubordeaux.fr/LAB/astrochem-tools/pnautilus/-/blob/master/pnautilusdocumentation.pdf) as well as Ruaud et al. (2016) and the references therein.
The physical conditions chosen were those of a standard cold molecular cloud, namely a gas density of 2×10 4 cm −3 (Snell et al. 1982), a kinetic temperature of 10 K for both gas and dust (Pratap et al. 1997), a cosmic ray ionization rate of 1.3×10 −17 s −1 (Spitzer & Tomasko 1968), and a visual extinction of 10 mag (Rodríguez-Baras et al. 2021).The initial elemental abundances used, which are listed in Table 1 along with their references, were the low metal abundances of Graedel et al. (1982) with a few changes.In particular, the ratio of initial carbon abundance to initial oxygen abundance (C/O ratio) has been found to have a noticeable effect on the modeled chemistry, with long carbon chains being the most affected (Hincelin et al. 2011).It has been found that a C/O ratio of 1.1 due to a lowered initial abundance of atomic oxygen significantly improves the general agreement between modeled and observed abundances of carbon-chain molecules in TMC-1 (Xue et al. 2020;Loomis et al. 2021).Additionally, a depletion factor of 20 with respect to the solar abundance for sulfur has been used according to a recent study based on the GEMS survey (Fuente et al. 2023).
Based on kida.uva.2014(Wakelam et al. 2015), the chemical network was extended to include aromatic and carbon-chain networks in the GOTHAM (Green Bank Telescope Observations of TMC-1: Hunting for Aromatic Molecules) project (McGuire et al. 2018;Xue et al. 2020;McGuire et al. 2020;McCarthy et al. 2021;McGuire et al. 2021;Loomis et al. 2021).To compare and contrast, we present the model results of CH 2 CCH and its related species with both the default network used in previous GOTHAM analyses (without any of the changes new to this work, hereafter referred to as GOTHAM DR1) and a modified network, as detailed below 1

Formation Mechanisms of CH 2 CCH
To better represent the chemical evolution of CH 2 CCH and its closed shell counterparts in cold molecular clouds, an extensive literature search and analysis was performed to identify new reactions and to examine existing reactions.In general, low temperature and density laboratory kinetic studies provide the most accurate rate information for astrochemical models (Hébrard et al. 2009).In the absence of these, theoretical data and/or high-temperature experimental data are taken into account with caution when extrapolating high-temperature kinetic data to low temperatures such as 10 K.For example, rate constants estimated from high-temperature data could be inaccurate by multiple orders of magnitude if there is a U-shaped temperature dependence (Jiménez et al. 2016).Since previous astrochemical models underestimated the peak abundance of CH 2 CCH, a special focus was placed on the production mechanisms of this species.

Dissociative Recombination
DR reactions of molecular cations with electrons are essential to astrochemistry due to their high efficiency under low-temperature and low-density conditions (Geppert et al. 2004;Florescu-Mitchell & Mitchell 2006) DR reaction was investigated experimentally by Geppert et al. (2004), finding a large preference for the formation of CH 2 CCH.The branching ratios determined from this experiment were adopted here, along with an overall rate constant from Florescu-Mitchell & Mitchell (2006).Angelova et al. (2004) studied the DR reaction of C 3 H 5 + and found that products containing C 3 species

Ion-Neutral Reactions
In addition to DR reactions, reactions between ions and neutral molecules account for a significant portion of interstellar chemistry due to relatively large reaction rates, the absence of activation energies, and a variety of abundant interstellar ions (Friedman 1968).Rate constants for ion-molecule reactions can be estimated according to capture theories such as Equations 4 -6, the Su-Chesnavich formulae (Su & Chesnavich 1982;Woon & Herbst 2009).
These expressions are an empirical fit to classical trajectory calculations where k D is the ion-neutral rate constant, µ D is the dipole moment, α is the polarizability, k B is the Boltzmann constant, e is the charge of an electron, and µ is the reduced mass.The parameter x is a unitless value that determines which expression is used for calculation of a rate coefficient.When x ≥ 2, k D increases linearly with x and Equation 5 is used.When x < 2, the relationship between k D and x is quadratic and Equation 6 is used.If x = 0, the expression is reduced to the Langevin rate, the classical rate constant for the reaction between an ion and a non-polar neutral molecule.For many polar molecules, this value is greater than 2 over the temperature range of interest (10 − 300 K).For CH 2 CCH, however, x < 2 over this temperature range due to its small dipole moment of 0.150 D (Küpper et al. 2002).
In our reaction network, three neutral species, namely CNCH 2 CCH, CNCHCHCCH, and CNCHCCH, can generate CH 2 CCH via reaction with abundant cations.For CNCH 2 CCH and CNCHCHCCH, it was assumed that reactions with H + , H 3 + , He + , C + , HCO + , and H 3 O + all form CH 2 CCH.For CNCHCCH, only reactions with H + and H 3 + were considered to contribute to the formation of CH 2 CCH, as He + and C + do not contain hydrogen and reactions with HCO + and H 3 O + were assumed to produce l-C 3 H 2 instead.Ion-neutral rate coefficients were re-evaluated for each of these species using Equation 5 and the µ D and α values in Table 2.For species without experimental or calculated polarizabilities, the rate constant was estimated by adding a negative temperature dependence to the polarizabilityindependent term.The results of these calculations are listed in Table 6 in the Appendix.
In our network, CNCH 2 CCH and CNCHCHCCH can be formed directly or indirectly from reactions involving CH 2 CCH.In order to ensure that these ion-neutral reactions were not generating a loop of net-zero loss and arbitrarily inflating the abundance of CH 2 CCH, we tested the effect of these reactions on modeled abundances by varying only the products.These alternate products were taken from Quan & Herbst (2007).

Neutral-neutral reactions
While collisions between two neutral molecules may not be as efficient at low temperatures due to a lack of strong attractive forces and the possibility of energy  7 and 8 in the Appendix.

Destruction Mechanisms of CH 2 CCH
For a full chemical description of the CH 2 CCH and its counterparts, it is also necessary to investigate the relevant destruction mechanisms.As with the production mechanisms, an extensive literature search was performed with a priority toward low-temperature kinetic experiments.

Ion-neutral reactions
Analogous to many other polar neutral species discussed in Section 2.1.2,CH 2 CCH is assumed to be destroyed mainly by reacting upon collision with cations in dense molecular clouds.The reaction rates are welldescribed by the Su-Chesnavich formalism.In addition to abundant cations such as H 3 + and HCO + , a range of complex hydrocarbon cations such as C 2 H 2 + and C 3 H 4 + were also considered.These rates have been recalculated as required using Equation 6with the dipole and polarizability values from Table 2 and are summarized in Table 5 in the Appendix.

Neutral-neutral reactions
In addition to cations, CH 3 CCH and CH 2 CCH can be destroyed by reaction with atoms and small molecules at low temperatures.The reaction between CH 3 CCH and C has been studied at room temperature by Loison & Bergeat (2004) with a fast-flow reactor and resonance fluorescence and down to 15 K by Chastaing et al. (1999) with the CRESU apparatus.Loison & Bergeat (2004) observed a hydrogen production ratio of 85% corresponding to the H + C 4 H 3 product channel, with the remaining 15% most likely attributed to the H 2 + C 4 H 2 channel.These branching ratios, along with the 15 K reaction rate, were adopted into our chemical network.
For CH 2 CCH, reactions with H, O, N, and OH are of interest.Theoretical studies of the C 3 H 4 potential energy surface have shown the presence of activation barriers for the reactions As such, they are unlikely to be viable mechanisms under cold dense cloud conditions (Miller & Klippenstein 2003b).The radiative-association reaction however, is barrierless and feasible under interstellar conditions (Hébrard et al. 2013).As such, the rate and branching ratio for this reaction have been updated according to Loison et al. (2017).The CH 2 CCH + O reaction has been studied from 295 − 750 K using a heatable flow reactor and photoionization mass spectrometry, but did not show any temperature dependence in this range (Slagle et al. 1991).The branching ratios for the products have been assigned based on theoretical studies (Loison et al. 2017).Due to a lack of experimental or theoretical data, the rate and branching ratios for the reaction of CH 2 CCH with N has been estimated based on the N + C 2 H 3 reaction.(Loison et al. 2017).
For the CH 2 CCH + OH reaction, we use a temperatureindependent estimate from Hansen et al. (2009) for the overall rate, with assumed 50/50 branching ratios between the two product channels.These reactions have all been implemented in our updated chemical network and are listed with the rate coefficients in Tables 7 and  8 in the Appendix.
The self-recombination between propargyl radicals, Reaction 1, has been the subject of multiple kinetic studies at room temperature and above.Atkinson & Hudgens (1999), Fahr & Nayak (2000), and DeSain & Taatjes ( 2003) have all measured the rate constant of this reaction at room temperature and for pressures of 2.25 − 100 Torr, 50 Torr, and 16 Torr respectively.The results of these three experiments agree well upon a roomtemperature rate constant of ∼4.0×10 −11 cm 3 s −1 at the high pressure limit.There has not yet been any experimental low-temperature study of this propargyl recombination, however a theoretical study by Georgievskii et al. (2007) used variable reaction coordinate transition state theory (VRC-TST) to determine the temperature dependence of this reaction in the high-pressure limit.These calculations agree well with the aforementioned experiments and suggest a slight negative temperature dependence, leading to a rate constant that is only slightly larger (∼6.0×10 −11 cm 3 s −1 ) at 10 K. We adopt the experimental value of 4 × 10 −11 into our network as an estimate.The branching ratios under conditions relevant to TMC-1 are not known either, however, Miller & Klippenstein (2003a) and the neutral-neutral reactions et al. 2009;Loison et al. 2017;Canosa et al. 1997).This latter reaction also has a CH 3 CCH + H product channel that was already included in the network.For the radiative-association of CH 2 CCH with H, we assume 50/50 branching ratios for the C 3 H 4 due to the lack of low-temperature information, in line with (Loison et al. 2017).Destruction pathways of CH 2 CCH 2 include reaction with atomic carbon, as measured down to 15 K by Chastaing et al. (1999), reaction with CCH as measured down to 63 K by Carty et al. (2001), and reaction with CH as measured down to 77 K by Daugey et al. (2005).Additional ion-neutral destruction pathways have also been included (Loison et al. 2017).Some interstellar species are capable of isomerization with assistance from collisions with H and H 2 .However, the inter-conversion of the two C 3 H 4 species has barriers in both directions of a few kcal/mol, enough to make them negligible under TMC-1 conditions Narendrapurapu et al. (2011).

Reactions with CN radicals
Laboratory studies at low temperature and density suggest that the formation of CN-substituted hydrocarbons via reaction with CN radicals is efficient under dark molecular cloud conditions (Carty et al. 2001;Cooke et al. 2020).There are three isomers of C 4 H 3 N, propargyl cyanide (CNCH 2 CCH), cyanoallene (CH 2 CCHCN), and methylcyanoacetylene (CH 3 C 3 N) as shown in Figure 2, all of which have been detected in TMC-1 (Broten et al. 1984;Lovas et al. 2006;McGuire et al. 2020).In particular, McGuire et al. (2020) assumed CNCH 2 CCH to be formed as the major product from the reaction between CN and CH 3 CCH.However, Balucani et al. ( 2002) estimated a 50/50 branching ratio of CH 2 CCHCN/CH 3 C 3 N based on crossed molecular beam experiments and electronic structure calculations.Additionally, Abeysekera et al. (2015) investigated this reaction via chirped-pulse/uniform flow microwave spectroscopy and further confirmed that CH 3 C 3 N is the only C 4 H 3 N isomer formed, along with HC 3 N and CH 2 CCH, We, therefore, modified this reaction based on the branching ratios from Abeysekera et al. (2015) and the rate from Carty et al. (2001).
The reaction between CN and CH 2 CCH 2 can also form C 4 H 3 N isomers.Using the same procedure as the CN + CH 3 CCH reaction, Balucani et al. (2002) suggested that CH 2 CCHCN is the major product of this reaction, with CNCH 2 CCH being the minor product, This reaction was introduced to our network with the above branching ratios from Balucani et al. (2002) and the rate from Carty et al. (2001).As CH 2 CCHCN had previously not been included in our network, destruction pathways via reaction with abundant interstellar ions were included analogous to CNCH 2 CCH.The rates for these reactions were calculated using Equation 5and the dipole and polarizability in Table 2.As with CNCH 2 CCH, we tested alternate ion-neutral products from Quan & Herbst (2007) to avoid arbitrarily inflating the abundance of CH 2 CCH and related species.
There is limited information on the reaction between CN and CH 2 CCH.Although Cabezas et al. (2021) proposed 3-cyano propargyl radical (CH 2 C 3 N) as the main product, radical-radical reactions involving CN may not follow the pattern of CN addition, H elimination being the main product channel (Decker & Macdonald 2003).In contrast, the recombination channel seems to be more likely.A recent theoretical study found that radiative association reactions between radical species can proceed rapidly at low temperatures, such as that of TMC-1 (Tennis et al. 2021).As such, the reaction has been added, with CNCH 2 CCH assumed as the sole product and an estimated rate constant of 1.0 × 10 −10 cm 3 s −1 , in line with the calculated rate constants for the CH 3 + CH 3 O reaction (Tennis et al. 2021).It is likely that the CN-addition, H-elimination channel to form cyano propargyl radicals is in competition, however the cyano propargyl radicals are not of direct concern to this study.Instead we are more interested in determining whether the inclusion of this reaction can reproduce the observed abundance of CNCH 2 CCH.More experimental and theoretical work is necessary to confirm whether the closed-shell CNCH 2 CCH can form in this reaction.

Grain Chemistry
In addition to the various gas-phase chemistry, grainsurface processes, in particular, hydrogenation reactions, are also considered in cold interstellar regions.Even at 10 K, light H atoms can move efficiently on grain surfaces and reactions with activation barriers can occur through quantum mechanical tunneling.Hickson et al. (2016) and Loison et al. (2017) investigated the chemistry of C 3 H n species in cold dense clouds, including hydrogenation of these species on grain surfaces.These authors suggested that such hydrogenation processes can begin with C 3 and proceed all the way to C 3 H 8 , with the majority of these reactions having no activation barrier.Specifically, the hydrogenation reactions of were found to have no barrier (here 's-' denotes a grainsurface species).Likewise, using quantum chemical calculations Miller & Klippenstein (2003b) found the hy- to be barrierless for the two C 3 H 4 isomers, suggesting that these species can be efficiently formed on grain surfaces.These grain processes of the C 3 H n species were thus incorporated into our network according to Hickson et al. (2016) and Loison et al. (2017), and a full list can be found in Table 9 in the Appendix.
As well as grain surface reactions, desorption energies of relevant species were updated according to recent experimental and theoretical studies.Accurate desorption energies for species with efficient grain-surface formation pathways are vital for describing the release of these species into the gas phase.Recent temperatureprogrammed desorption (TPD) experiments on amorphous water ices reported a value of 4400 K for the desorption energy of CH 3 CCH on compact water ice (Behmard et al. 2019).In this study, we used this value for the desorption energy of CH 3 CCH in our model and assumed CH 2 CCH 2 has the same desorption energy as that of CH 3 CCH.Wakelam et al. (2017) estimated desorption energies for a variety of interstellar species on amorphous solid water using electronic structure calculations, including the CH 2 CCH radical (3300 K).Additionally, Villadsen et al. (2022) predicted binding energies of astrochemically-relevant molecules by applying Gaussian process regression to a training set of experimental TPD energies, finding generally good agreement between experiment and predictions.We incorporated their predicted value of 9520 K for the desorption energy of all three C 4 H 3 N isomers on water surfaces into our model.

Sensitivity Analysis
In order to gauge the sensitivity of our modeling results to the rate constants of certain reactions, we have performed a sensitivity analysis on a select number of reactions involving CH 2 CCH, specifically CH 2 CCH reacting with H, C, O, N, CN, OH, and itself.The only formation pathway tested in this manner was Reaction 9, as the rate constants for other formation pathways of CH 2 CCH are well-constrained via low temperature kinetic measurements of capture theory.For each reaction, the rate constant was multiplied by values ranging from 0.01 to 100, with separate models performed for each modification.Additionally, the removal of each reaction from the network was tested.This technique allows us to determine the effects that different rate constants have on the modeled abundances of interstellar species, which is particularly useful for reactions that lack dedicated low-temperature studies.However, it is important to note that only one reaction is modified at a time, and thus we do not obtain information about how two reactions may be correlated.
Similarly, we have performed a sensitivity analysis on the effect of the C/O ratio on CH 2 CCH, CH 3 CCH, CH 2 CCH 2 .As stated previously, we assume a C/O ratio of 1.1 in our model in line with previous GOTHAM studies (Xue et al. 2020;Burkhardt et al. 2021a;Loomis et al. 2021;McCarthy et al. 2021;McGuire et al. 2021), as this ratio improves modeling results for a variety of carbonbearing species, especially the cyanopolyynes.Additionally, Hincelin et al. (2011) and Wakelam et al. (2006) both investigated the effect of C/O ratio on astrochemical models of TMC-1 and found better overall agreement to observations with a larger C/O ratio.However, some models of TMC-1 use a significantly lower C/O ratio of 0.7 (Ruaud et al. 2016;Loison et al. 2017), while other astronomical sources may have different chemical conditions and thus different C/O ratios.We have tested values of the C/O ratio ranging from 0.7 to 1.1 in increments of 1.1 by varying the initial abundance of elemental oxygen.

RESULTS
In order to consistently analyze the results of our models, we calculated best fit times by minimizing the mean absolute difference between the log observed abundances and the log modeled abundances for species of interest (CH 2 CCH, CH 3 CCH, CNCH 2 CCH, CH 3 C 3 N, and CH 2 CCHCN).This gives a best-fit time of 4.739 × 10 5 years.The cyanonaphthalene isomers were excluded from this calculation as the modeled abundances of these species are still ∼ 6 orders of magnitude below observations.This is in agreement with a best fit time of ∼ 5×10 5 years from previous GOTHAM modeling studies (Xue et al. 2020;Loomis et al. 2021).
The modeled column densities of select species at this best-fit time can be seen in Table 3, along with observed values and confidence levels.These latter values were calculated using the method introduced by Garrod et al. (2007) and are a metric of confidence that the bestfit abundance is in agreement with the observed abundance, assuming a log-normal distribution centered on the observed value with a standard deviation of one.We also calculated the mean confidence level excluding the cyanonaphthalene isomers, as the agreement for these species is very poor and would heavily skew the mean.
In astrochemical models of dark molecular clouds, it can also be assumed that some elements, typically carbon, sulfur, silicon, phosphorus, chlorine, and the metals, begin as cations in their initial state (Ruaud et al. 2016).If the initial elemental abundances as described in Table 1 are kept but the previously mentioned species are assumed to begin as cations, the resulting best-fit abundances increase slightly by factors of 1.21 or less.The relative contributions of production and destruction pathways are affected, such as Reaction 2 becoming less prevalent to the production of CH 2 CCH at early times.
The similarity in abundances at later times may be due to the efficient conversion of C + to C via electron capture and charge transfer.

C 3 H n Hydrocarbons
In Figure 3, the modeled abundances of CH 2 CCH, CH 3 CCH, and CH 2 CCH 2 are plotted as a function of time, as well as their observed column densities in TMC-1.Gratier et al. ( 2016) constrained the column density of CH 3 CCH as 1.15 × 10 14 cm −2 based on observations of the TMC-1 cyanopolyyne peak using the Nobeyama 45 m telescope.Agúndez et al. (2021) first detected CH 2 CCH at a wavelength of 8 mm with a column density of 8.7 × 10 13 cm −2 , and later used observations at 3 mm to revise the column density to 1.0 × 10 14 cm −2 (Agúndez et al. 2022).CH 2 CCH 2 has not been detected in TMC-1, and thus there is no observed value for this species.The observed column densities, as well as bestfit modeled column densities can be seen in Table 3.Our updated model gives best-fit abundances of CH 2 CCH and CH 2 CCH 2 that are ∼ 60 and ∼ 29 times lower than observations, respectively.Compared to the model results with the GOTHAM DR1 network, the modeled abundance of CH 2 CCH at 4.739 × 10 5 years has been increased by a factor of 2.65.The removal of Reactions 11 and 12 resulted in the largest increase to the modeled CH 2 CCH abundance, followed by the addition of the neutral-neutral Reactions 9 and 10.The modeled abundance of CH 3 CCH at this time has only been increased by a factor of 1.41 compared to the previous model results.The column densities of both CH 2 CCH and CH 3 CCH are still under-predicted by between 1 and 2 orders of magnitude, although the CH 3 CCH abundance is almost within the 1σ confidence interval.
In our updated model, the early-time production of CH 2 CCH is dominated by the reaction between atomic carbon and C 2 H 4 (Reaction 2), as shown in Figure 4. Grain-surface hydrogenation of both isomers of C 3 H 2 (Reactions 21 and 22) followed by chemical desorption also contributes significantly to CH 2 CCH formation due to the large abundance of atomic hydrogen and its high mobility on grains.After ∼ 10 4 years, the rates of other CH 2 CCH formation pathways become sizeable due to the build up of more complex hydrocarbons.In addition to the aforementioned reactions, the reaction between diatomic carbon and methane (Reaction 10) and the dissociative recombinations of C 5 H 5 + and C 3 H 5 + become significant sources of CH 2 CCH around 10 5 years.Despite a similar rate constant to the dissociative recombination of C 5 H 5 + , we find that the dissociative recombination of C 3 H 5 + is unable to efficiently form CH 2 CCH at all times.Likewise, the dissociative recombination of C 3 H 4 + has the greatest rate constant of these three reactions but still exhibits a lower rate than the dissociative recombination of C 5 H 5 + .This is due to an approximately 10-fold difference in abundance between C 5 H 5 + and the C 3 H n + cations.Similarly, the neutralneutral production pathways of CH 2 CCH generally outpace the dissociative recombination pathways, despite greater rate constants in the latter set of reactions, due to much larger modeled abundances of small neutral hydrocarbons.CH 2 CCH is primarily destroyed via reaction with O, C, and N at early times (before 10 5 years) and via reaction with H at later times (after 3 × 10 5 years).
For the first ∼ 10 3 years of the model, CH 3 CCH is primarily formed by the grain-surface reaction where energy from reaction exothermicity ejects a portion of the products into the gas phase.dances for CH 3 CCH and CH 2 CCH 2 .The rates of these reactions as a function of time can be seen in Figures 5  and 6.Destruction of both C 3 H 4 isomers occurs mainly through a combination of reaction with C, which dominates before 10 5 years, and reaction with H 3 + , which dominates shortly after 10 5 years.Between 10 5 and 10 6 years, reaction with CN radical significantly contributes to the destruction of CH  For more information on these reactions, including product channels, refer to Tables 4-9 in the Appendix.

CN-Substituted Species
Considering the strong chemical link between pure hydrocarbons and their CN-substituted derivatives in TMC-1, we are interested in how the updated chemical network affects the formation of C 4 H 3 N isomers.The modeled abundances of these species as a function of  The decrease in the modeled abundance of CNCH 2 CCH stems from the change in its formation pathways, particularly the removal of Reaction 18 as a formation route to this species.The addition of new production routes in Reaction 20 and Reaction 19 are able to nearly reproduce the GOTHAM DR-1 abundance, despite CNCH 2 CCH being only a minor product of the latter reaction.Before 3×10 5 years, the formation of CNCH 2 CCH is dominated by Reaction 20, and following this time Reaction 19 becomes the dominant formation pathway.As mentioned in Section 2, we tested models with alternate products for CNCH 2 CCH and CH 2 CCHCN ion-neutral pathways to determine their effects on the abundances of species considered here.
When alternate product channels were used, the peak abundance of the directly affected species, CH 2 CCH, decreased by a factor less than 1.15.Likewise, the peak abundances of the C 3 H 4 and C 4 H 3 N isomers changed by factors of less than 1.2.Considering the almost negligible differences in results, the products of these ion-neutral reactions do not seem to significantly affect the species of interest.

Aromatic Species
In addition to the previously mentioned species, we also examined C 6 H 5 and the two cyanonaphthalene isomers to determine the effect of the propargyl recombination reaction on the formation of these species.These abundances were plotted as a function of time in Figure 8, and the best-fit modeled abundances can be seen in Table 3.The astrochemical model still severely underpredicts the column densities of 1-and 2-cyanonaphthalene (C 10 H 7 CN, C 10 CNH 7 ), although the modeled abundancse of the cyanonaphthalenes have been increased by about a factor of 1.7 at the best-fit time for both isomers.The two C 10 H 7 CN isomers are primarily produced from reaction between naphthalene (C 10 H 8 ) and CN, while C 10 H 8 's main production pathway is the reaction between C 6 H 5 and CH 2 CHC 2 H.The reaction of CN with benzene to form C 6 H 5 CN is barrierless and efficient at low temperatures, and the analogous reaction with C 10 H 8 to form C 10 H 7 CN is expected to be as well (Cooke et al. 2020;McGuire et al. 2021).Thus it is the formation of C 10 H 8 that limits production of C 10 H 7 CN.Our addition of CH 2 CCH 2 as a species and its reaction with CH to form CH 2 CHC 2 H leads to an increase in C 10 H 8 , and an increase in C 10 H 7 CN as a result.The modeled abundance of C 6 H 5 has not been changed by the addition of CH 2 CCH recombination (Reaction 14), except for at early times.At these times a significant increase in C 6 H 5 abundance is observed, but this difference is made up for by a time of 100 years.To understand why, we must look at the other production mechanisms for C 6 H 5 included in our network.These are dissociation of benzene via cosmic ray induced photons or external photons and hydrogen abstraction from benzene via OH and H. Activation barriers to hydrogen abstraction and a large visual extinction make dissociation by cosmic ray induced photons the major mechanism.At early times, the modeled benzene abundance is over 10 orders of magnitude lower than the modeled propargyl abundance.However, the benzene abundance quickly increases, and this difference becomes only six orders of magnitude at 50 years.At this point, the unimolecular decomposition becomes fast enough to outpace the bimolecular recombination of CH 2 CCH.Although CH 2 CCH abundance has been increased at most times, the resulting rate is not large enough to exceed the rate for C 6 H 6 dissociation.This can be seen in Figure 9, where the modeled abundance of the phenyl radical is significantly increased in our new model compared to GOTHAM DR1 at early times but the GOTHAM DR1 abundance makes up the difference by approximately 100 years.

Sensitivity Studies of Key Reactions and C/O Ratio
In addition to the astrochemical modeling performed using the updated chemical network, we have also performed sensitivity studies on this chemical network to investigate the importance of several reactions to the chemistry of CH 2 CCH.The results of these studies on Reaction 20 can be seen in Figure 10.When the rate constant for this reaction is increased by one order of magnitude to a value of 1.0 × 10 −9 cm 3 s −1 , the best-fit abundance of CNCH 2 CCH increases by a factor of almost 5, essentially reproducing the observed value.The best-fit abundance continues to increase beyond the observed value as the rate constant is further raised.If this reaction is removed from the network entirely, the best-fit abundance of CNCH 2 CCH only decreases by a factor of 1.7 compared to the presented network.In contrast, there is no noticeable change in the modeled abundance of CH 2 CCH, even when this rate constant is increased by two orders of magnitude or removed from the network entirely.
This procedure has been repeated for the reactions of CH 2 CCH with C, H, N, O, OH, and CH 2 CCH, as well as for the reaction CCH + CH 3 −−→ CH 2 CCH + H. Column density (cm 2 ) As noted by Agúndez et al. (2021) in their initial detection, CH 2 CCH is one of the most abundant radicals detected in TMC-1, with a derived column density only slightly below that of the closed-shell CH 3 CCH.As the authors remark, this radical is an example of a resonance-stabilized radical, and as such the delocalization of the unpaired electron is expected to lower its reactivity compared to radicals without resonance.In addition to the detection, the authors use astrochemi-cal modeling to investigate the major formation and destruction mechanisms of CH 2 CCH and its closed-shell relatives.They achieve a peak modeled abundance of ∼ 1 × 10 −10 with respect to H 2 similar to our model, but at an earlier time of 2 × 10 5 years.They also obtain much larger modeled abundances of CH 3 CCH and CH 2 CCH 2 on the order of 10 −8 at a time of ∼ 5 × 10 5 years, close to the TMC-1 observed value for CH 3 CCH.
In terms of production pathways, our models agree that Reaction 2 is the dominant pathway toward forming CH 2 CCH.The kinetics of this reaction were measured twice from 295 K to 15 K by Chastaing et al. (1999) and Chastaing et al. (2001) using the CRESU technique and two different product detection techniques.In both cases, the data was fit via a non-linear least-squares fit to a modified Arrhenius form, yielding a temperature-dependent rate constant of k(T ) = 3.1 × 10 −10 (T /298 K) −0.07 cm 3 molecule −1 s −1 from the first set of measurements and k(T ) = 3.0 ± 0.4 × 10 −10 (T /298 K) −0.11±0.07cm 3 molecule −1 s −1 from a fit combining both sets of measurements.The strong agreement between the two sets of measurements and relatively low errors in fit parameters and individual rate constant measurements suggest this reaction is fast at 10 K with a rate constant near 4 × 10 −10 cm 3 molecule −1 s −1 .The KIDA database and our model presently use the temperature dependent fit from Chastaing et al. (1999), while Agúndez et al. (2021) use a slightly smaller, temperature-independent value of 3.1 × 10 −10 cm 3 molecule −1 s −1 .A number of experimental and theoretical studies (Le et al. 2001;Bergeat & Loison 2001;Geppert et al. 2003;Chin et al. 2012;Mandal et al. 2018) indicate that CH 2 CCH + H is the only major product channel, resulting from more than 90% of reactions.
However, Agúndez et al. (2021) also observe that CH 3 CCH and CH 2 CCH 2 are primarily formed from the dissociative recombinations of C 3 H n + cations.In our model, the dissociative recombination of C 3 H 5 + is inefficient compared to gas-phase and grain-surface hydrogenations of CH 2 CCH, and C 3 H n + cations larger than C 3 H 5 + are not included in the network.This suggests significant differences in chemical networks, particularly regarding the chemistry of C 3 H n species.Inclusion of larger neutral and cationic C 3 H n species and a thorough investigation of their formation paths in cold molecular clouds would benefit modeling of CH 2 CCH and the C 3 H 4 isomers.
The model of Agúndez et al. (2021) agrees with our model that the major destruction mechanisms of CH 2 CCH are with atoms such as C, N, and O, although they do not consider the radiative association of CH 2 CCH with H.The authors propose that CH 2 CCH could be reproduced by the model if reaction with O and N atoms are removed, or alternatively if the initial C/O ratio is above one.Despite an initial C/O ratio of 1.1, we obtain a similar maximum abundance of CH 2 CCH to their initial model.Additionally, our sensitivity analysis of CH 2 CCH reactions shows that the maximum abundance of CH 2 CCH is not significantly affected by the removal of any individual reaction except for CH 2 CCH + H.This barrierless reaction is estimated to be fairly efficient at low temperature based on a semi-empirical approach involving reaction exothermicity and molecule size, however there is significant uncertainty in the rate constant (Hébrard et al. 2013).We find that CH 2 CCH, CH 3 CCH, and CH 2 CCH 2 abundances are all sensitive to this rate constant, as this reaction is a major destruction mechanism for the first species and production mechanism for the latter two.A decrease in the rate constant would lead to a significantly larger modeled abundance for CH 2 CCH, which could then be compounded by removal of the CH 2 CCH + O and CH 2 CCH + N reactions.However, such a scenario could result in significant decreases to the modeled abundances of CH 3 CCH and CH 2 CCH 2 .Potential energy surface calculations on the CH 2 CCH + O and CH 2 CCH + N reactions, as well as an experimental measurement of the CH 2 CCH + H radiative association rate constant and branching ratios, would significantly improve our understanding of propargyl radical chemistry in cold molecular clouds.
Neither our model nor the model of Agúndez et al. (2021) considers the reaction between CCH and CH 3 to be a major formation reaction for CH 2 CCH.In our model, the rate for this reaction is slow compared to many other CH 2 CCH production mechanisms at most times.It isn't until ∼ 10 6 years, after the expected age of TMC-1, that this rate becomes large enough for the reaction to significant to CH 2 CCH formation.Both reactants experience significant increases in modeled abundance, over an order of magnitude for CH 3 and slightly less for CCH, from 10 5 years to 10 6 years.As the major destruction pathways for these species are with C, N, and O atoms, these increases in abundance may be due to the drop in neutral atom abundances during this time period.The rate constant for this reaction was estimated to be 1 × 10 −10 molecule −1 s −1 as an approximate value for a radical-radical association followed by H elimination, but without any experimental or theoretical studies there is significant uncertainty in this value.Our sensitivity analysis of the rate constant for this reaction reveals that an increase in this rate constant could result in a moderate increase to modeled CH 2 CCH abundance, but not until after 6 × 10 5 years.
Decreasing this rate constant or removing this reaction only leads to a slight decrease in CH 2 CCH abundance after this time, and a negligible decrease before then.

C 4 H 3 N Isomers and CH 2 CCH 2 Abundance Constraint
In cold molecular clouds, CN radical is thought to react efficiently with many unsaturated hydrocarbons via a CN-addition H-elimination pathway (Balucani et al. 2000;Carty et al. 2001;Cooke et al. 2020).The ability of our model to reproduce the observed column densities of CH 2 CCHCN and CNCH 2 CCH within a factor of 5 further demonstrates the importance of this mechanism in forming interstellar CN-derivatives.The column density of CH 3 C 3 N is also reproduced by our model within a factor of 5, however the major mechanism for this species is the dissociative recombination of H 3 C 4 NH + .In addition to a 10% branching ratio from the Reaction 19, we assumed a radiative association reaction between CH 2 CCH and CN to produce CNCH 2 CCH with a rate constant of 1.0 × 10 −10 cm −2 .Our sensitivity analysis of this reaction reveals that an order of magnitude increase in this rate constant could reproduce the observed CNCH 2 CCH, however such a large rate constant is unreasonable for an association reaction between two neutral species.Conversely, lowering this rate constant or removing the reaction entirely only slightly lowers the best-fit abundance, resulting in a value still within an order of magnitude compared to observations.As the major formation route to CNCH 2 CCH and CH 2 CCHCN is through CH 2 CCH 2 , it is possible that a deficiency in modeled CH 2 CCH 2 is responsible for the deficiencies in these two C 4 H 3 N isomers.Quan & Herbst (2007) have performed astrochemical modeling on CH 2 CCHCN and CH 3 C 3 N, testing the effects of different CH 3 CCH/C 3 H 4 ratios on abundances at 10 5 years.Using branching ratios of 50/50 CH 2 CCHCN/CH 3 C 3 N for CN + CH 3 CCH and 90/10 CH 2 CCHCN/CNCH 2 CCH for CN + CH 2 CCH 2 , the authors find the best agreement with observations when the CH 3 CCH abundance is 35% of the total C 3 H 4 abundance.More recent branching ratio measurements for CN + CH 3 CCH suggest that CH 2 CCHCN is not formed significantly at low temperature (Abeysekera et al. 2015), and the detection of CNCH 2 CCH allows for the inclusion of the third C 3 H 4 N isomer in the analysis.More recently, Marcelino et al. (2021) examined all three C 4 H 3 N isomers using astrochemical modeling, testing both sets of experimental branching ratios for CN + CH 3 CCH.The authors obtain very similar results to our own model, finding good agreement with observations for all three species.As in our study, they find that the dissociative recombination of H 3 C 4 NH + is mainly responsible for the formation of CH 3 C 3 N.They also find that the choice in branching ratios for CN + CH 3 CCH does not notably affect the resulting modeled abundances.
Since CH 2 CCH 2 is a symmetric hydrocarbon and does not possess a permanent dipole moment, it is not possible to detect this species via radio astronomy.However, a rough estimate to its TMC-1 abundance can be made using our modeled CH/CN ratio and the observed abundance of CH 2 CCHCN.Taking the ratio of CH 2 CCH 2 to CH 2 CCHCN at our best-fit time, 6.1, and multiplying it by the observed column density of CH 2 CCHCN, we obtain an extrapolated CH 2 CCH 2 column density of 1.64 × 10 13 cm −2 .This value is almost an order of magnitude lower than the observed column density of CH 3 CCH and would suggest a difference in interstellar chemistry between these species that is not present in our model, although it is within the one σ uncertainty of the observed CH 3 CCH column density.It is important to note that modeled CH/CN ratios are sensitive to the model parameters used, such as the rate constant for the CN-addition H-elimination pathway Sita et al. (2022), as well as the time of choice.Although the CN + CH 2 CCH 2 rate constant has been measured at low temperature (Carty et al. 2001), the branching ratios have not.Additionally, CH/CN ratios could be significantly different in other interstellar regions with different physical and chemical conditions.Thus this method of column density approximation is only a rough estimate based on certain modeling parameters and our time of best fit.A detailed analysis of CH/CN ratios in TMC-1, as well as a more constrained column density for CH 3 CCH, would be beneficial toward understanding the relationship between these two isomers and their CN-substituted derivatives.

Implications for PAH formation
C 6 H 5 is an aromatic resonance-stabilized radical and a key precursor to formation of PAHs in cold molecular clouds.The Hydrogen Abstraction-Vinylacetylene Addition (HAVA) mechanism, which begins with the addition of C 6 H 5 to vinylacetylene followed by rearrangement and hydrogen loss, is one viable low-temperature formation pathway to C 10 H 8 and larger PAHs (Parker et al. 2012;Kaiser & Hansen 2021).This mechanism is the major generator of C 10 H 8 in our chemical network.Likewise, indene can be formed via reactions of C 6 H 5 with small hydrocarbons, although these reactions are so far limited to high-temperature (Doddipatla et al. 2021;Kaiser & Hansen 2021).An understanding of the production of the C 6 H 5 in TMC-1 is critical for describ-ing the formation of C 10 H 8 , indene, and other PAHs in cold molecular clouds.A major motivation of modeling CH 2 CCH was to assess its role as an interstellar aromatic precursor, however addition of the CH 2 CCH recombination reaction resulted in no significant change to C 6 H 5 abundance after 100 years.Based on the sensitivity analysis of this reaction, increasing this rate constant by an order of magnitude does not appreciably change the best-fit abundance of C 6 H 5 , nor would this increase agree with the temperature-dependence calculated by Georgievskii et al. (2007).Thus the abundance of CH 2 CCH appears to be the limiting factor.As the CH 2 CCH recombination reaction is second order in CH 2 CCH abundance, an underproduction of CH 2 CCH by almost two orders of magnitude would lead to a recombination rate that is lowered by almost four orders of magnitude.Continuing to improve our understanding of propargyl radical chemistry is necessary to assess the role of this species in PAH formation.Additionally, a detection of C 6 H 5 in TMC-1 and a derived column density would allow us to better gauge our knowledge of interstellar aromatic chemistry.
Additional reactions of resonance-stabilized radicals, including CH 2 CCH, may be important to the formation of aromatic species in dark molecular clouds.In combustion flames, CH 2 CCH is thought to react with allyl radicals followed by isomerization to benzene (Miller et al. 2010).
The authors calculated the potential energy surface for this system and found it to be a barrierless addition with two exothermic, bimolecular exit channels corresponding to two isomers of the hydrofulvenyl radical (C 5 H 5 CH 2 ).They also predicted the rate constant for this reaction to be on the order of 10 ).Fulvenallene has been detected recently in TMC-1, with the reaction between cyclopentadiene and the ethynyl radical proposed as a possible formation pathway (Cernicharo et al. 2022).Further investigation of these larger resonancestabilized radicals under dark molecular cloud conditions will greatly benefit the understanding of PAH formation in these regions.

CONCLUSIONS
We performed astrochemical modeling on the propargyl radical, CH 2 CCH, and related species using the NAUTILUS code and an updated chemical network.We also incorporate two new species, CH 2 CCH 2 and CH 2 CCHCN, into the network.We find that the predicted abundance of CH 2 CCH is improved by about an order of magnitude, but is still almost two orders of magnitude below the observed value.The C 4 H 3 N isomers are found to be formed primarily from CH 3 CCH, CH 2 CCH 2 , and CH 2 CCH.We obtain predicted abundances for these C 4 H 3 N isomers within one order of magnitude of the observed values, suggesting that our chemical model is able to account for the major formation mechanisms of these species.We do not observe any significant improvements for aromatic species, but CH 2 CCH remains a potential precursor to aromatic species in dark molecular clouds.Further studies of interstellar C 3 H n and resonance-stabilized radical chemistry under conditions relevant to dark molecular clouds would provide key information for improved astrochemical modeling of the species presented here.

B. ION-MOLECULE REACTIONS
Table 5 lists the updated rate coefficients (k) for the reactions of CH 2 CCH with interstellar cations while table 6 lists those of four species chemically related to CH 2 CCH with abundant interstellar cations.The rate coefficients were calculated using the Su-Chesnavich equations and the dipole and polarizability from Table 2.In the case of multiple product channels for one reaction, the branching ratios are assumed to be an even split among all product channels.In actuality this is likely not the case, however these branching ratios do not have a notable effect on our model as these reactions primarily act as destruction mechanisms.    1 The rate constants for reactions with formula 4 are calculated using the ion-polar formula 1, k = αβ 0.62 + 0.4767γ 300 T

1/2
, where α is the branching ratio, β = 2πe α µ is the Langevin rate in units of cm 3 s −1 , and γ = x = µD √ 2αkBT is a unitless correction term based on the dipole moment and polarizability of the neutral species.
2 Reactions with formula 3 are calculated using the modified Arrhenius formula, k = α (T /300) β e −γ/T .Here, α is in units of cm 3 s −1 and is calculated as a portion of the Langevin rate multiplied by the dipole-correction term x, α = 0.47672 × 2πe α µ x. β is unitless temperature-dependence term and γ is the activation energy in K.
C. NEUTRAL-NEUTRAL REACTIONS Tables 7 and 8 contain new and updated rate coefficients for neutral-neutral gas-phase reactions involving CH 2 CCH 2 , CH 3 CCH, and CH 2 CCH.Table 9 contains new and updated rate information for grain reactions pertaining to C 3 H n species.   1 An asterisk preceding a reaction denotes that the reaction has been added to the network rather than modified.
2 The rates of the listed neutral-neutral reactions are computed using the modified Arrhenius equation: k = α (T /300) β e −γ/T , where α is a temperature-independent prefactor, β is a unitless temperature-dependence parameter, and γ is the activation energy in K.
3 Since the molecule HCCCHO is currently not included in our network, we substitute C3O + H + H2 as the products for this reaction.These do not lead directly back to CH2CCH, avoiding a net zero change in abundance.  In addition to these reactions forming grain products, the model also accounts for chemical desorption of 1% to form gas-phase products.
2 The rate of reaction between two grain species i and j is calculated using the equation: , where α is the branching ratio and κij is a parameter that depends on the activation barrier.For more information, refer to  For more information on these reactions, including product channels, refer to Tables 4-9.
Figures 15 and 16 display the sensitivity analysis results not shown in the manuscript.For each reaction, the rate constant was multiplied by a number of factors and a model performed for each factor.

Figure 3 .
Figure 3. Modeled abundances and column densities of propargyl radical (green), methylacetylene (red), and allene (purple) as a function of time.The dotted lines represent the observed column densities in TMC-1, with the shaded areas signifying an error of 1 σ.The dashed lines represent modeled abundances obtained from GOTHAM DR1, and the solid lines are the modeled abundances with the updated model presented in this work.

Figure 4 .
Figure4.Reaction rates for key CH2CCH formation pathways as a function of time.Each color represents a different reaction, with the reactants given in the legend ('s-' denotes a grain species).For more information on these reactions, including product channels, refer to Tables 4-9 in the Appendix.

Figure 5 .
Figure5.Reaction rates for key CH3CCH formation pathways as a function of time.Each color represents a different reaction, with the reactants given in the legend ('s-' denotes a grain species, and CRP denotes a cosmic-ray induced photon).For more information on these reactions, including product channels, refer to Tables 4-9 in the Appendix.

Figure 7 .
Figure 7. Modeled abundances and column densities of propargyl cyanide (blue), methylcyanoacetylene (yellow), and cyanoallene (brown) as a function of time.The dotted lines represent the observed column densities in TMC-1, with the shaded areas signifying an error of 1 σ.The dashed lines represent modeled abundances from GOTHAM DR1, and the solid lines are the modeled abundances with the updated model presented in this work.

Figure 8 .
Figure8.Modeled abundances and column densities of 1cyanonaphthalene (C10H7CN, maroon), 2-cyanonaphthalene (C10CNH7, pink) and C6H5 (gray) as a function of time.The dotted lines represent the observed column densities in TMC-1, with the shaded areas signifying an error of 1 σ.The dashed lines represent modeled abundances from GOTHAM DR1, and the solid lines are the modeled abundances with the updated model presented in this work.As the formation pathways and observed TMC-1 abundances of the two cyanonaphthalene isomers are very similar, the plotted curves for one isomer are overlapping with those of the other.

Figure 9 .
Figure 9. Modeled abundances and column densities of the phenyl radical from 1 to 10 4 years.The dashed line represents modeled abundances from GOTHAM DR1 and the solid line is the modeled abundances of the updated model presented in this work.

Figure 14 .
Figure14.Reaction rates for key destruction pathways of (a) CH2CCH, (b) CH3CCH, and (c) CH2CCH2 as a function of time.For more information on these reactions, including product channels, refer to Tables4-9.

Figure 15 .
Figure 15.Modeled abundances and column densities of CH2CCH for different values of the (a) CH2CCH + C, (b) CH2CCH + N, (c) CH2CCH + O, (d) CH2CCH + OH, (e) CH2CCH + CN, and (f) CCH + CH3 rate constants.The dashed lines are networks where this rate constant has been modified by the factors in the legend.The base network (presented in this paper) is shown for comparison as a solid line, as well as a network where this reaction is removed entirely.The color gradient corresponds with the magnitude of the factor of change.

Figure 16 .Figure 17 .
Figure 16.Modeled abundances and column densities of (a) CH2CCH and (b) C6H5 for different values of the CH2CCH + CH2CCH rate constant.The dashed lines are networks where this rate constant has been modified by the factors in the legend.The base network (presented in this paper) is shown for comparison as a solid line, as well as a network where this reaction is removed entirely.The color gradient corresponds with the magnitude of the factor of change.
. In our current chemical model, we considered four different species that produce CH 2 CCH via disso-

Table 1 .
Initial atomic/molecular abundances with reference to hydrogen CCH with branching ratios of 50% and 65% respectively based on enthalpies of reaction.A full list of changes to dissociative recombination reactions implemented in our updated model is shown in Table4in the Appendix.

Table 2 .
Polarizabilities and Dipole Moments for Updated Ion-Neutral Reactions Of the two linear closed-shell isomers of C 3 H 4 , CH 3 CCH and CH 2 CCH 2 , only the former species was previously considered in the chemical network.As with CH 3 CCH, CH 2 CCH 2 is a closed-shell counterpart of CH 2 CCH, and thus these species are likely linked chemically.Our model has been updated to produce CH 2 CCH 2 through three reaction paths, including the DR reaction At 10 4 years and later, CH 3 CCH is predominantly formed from Reactions 13 and 23.Similarly, Reactions 16 and 23 constitute the main formation pathways of CH 2 CCH 2 at all times.Despite the low rate constant, the gas-phase radiative association between H and CH 2 CCH is able to efficiently form both C 3 H 4 isomers due to the large abundance of H and increased abundance of CH 2 CCH.Likewise, the analogous grain-surface hydrogenations are able to form large amounts of C 3 H 4 in both the gas phase and on grain surfaces, resulting in high grain-surface abun-

Table 3 .
Modeled and observed column densities for select speciesMoleculeBest-Fit 1 (cm −2 ) Observed 2 (cm −2 ) Confidence Level 3 Modeled column density at the best-fit time of 4.739 × 10 5 years. 2 Species with no value in this column have not been detected in TMC-1.3CalculatedaccordingtoGarrodetal. (2007).Species with no value in this column have not been detected in TMC-1.4Thecyanonaphthalene isomers (C10H7CN and C10CNH7) were not included in this calculation.
3 CCH and CH 2 CCH 2 .The rates of key destruction mechanisms for CH 2 CCH, CH 3 CCH, and CH 2 CCH 2 as a function of time are displayed in Figure 14 in the Appendix.
Reaction rates for key CH2CCH2 formation pathways as a function of time.Each color represents a different reaction, with the reactants given in the legend ('s-' denotes a grain species).For more information on these reactions, including product channels, refer to Tables 4-9 in the Appendix.
Figure 10.Modeled abundances and column densities of CNCH2CCH for different values of the CN + CH2CCH rate constant.The dashed lines are networks where this rate constant has been modified by the factors in the legend.The base network (presented in this paper) is shown for comparison as a solid line, as well as a network where this reaction is removed entirely.The color gradient corresponds with the magnitude of the factor of change.As with the other previous figures, a dotted horizontal line is plotted representing the observed abundance of CNCH2CCH in TMC-1, with the shaded region signifying an error of 1 σ.Figure 13.Modeled abundances and column densities of CH2CCH2 for different values of the CH2CCH + H rate constant.The dashed lines are networks where this rate constant has been modified by the factors in the legend.The base network (presented in this paper) is shown for comparison as a solid line, as well as a network where this reaction is removed entirely.The color gradient corresponds with the magnitude of the factor of change.
years) of CH 2 CCH, CH 3 CCH, and CH 2 CCH 2 significantly decrease, with smaller decreases in early-time (∼ 1 − 2 × 10 5 years) abundances.In particular, Morozov & Mebel (2020)emperature, independent of the pressure.Moreover, calculations on the C 6 H 5 + CH 2 CCH potential energy surface have been performed byMorozov & Mebel (2020), resulting in two barrierless sites for addition of CH 2 CCH to C 6 H 5 . The ion of CH 2 CCH via its CH 2 terminal yields 3-phenyl-1propyne (C 6 H 5 CH 2 CCH), which can decompose via Hloss directly to form C 6 H 5 CHCCH or after isomerization to form the indenyl radical (C 9 H 7 )CH 2 CCH + C 6 H 5 −−→ C 6 H 5 CH 2 CCH C 6 H 5 CH 2 CCH −−→ C 6 H 5 CHCCH + H CCH via its CH terminal results in phenylallene (C 6 H 5 CHCCH 2 ), which can also isomerize to C 9 H 7 or immediately decompose to form two monocyclic H-loss productsCH 2 CCH + C 6 H 5 −−→ C 6 H 5 CHCCH 2 C 6 H 5 CHCCH 2 −−→ C 6 H 5 CCCH 2 + H −−→ C 6 H 5 CCCH 2 +H CCH and the benzyl radical (C 7 H 7 ) may be yet another key process to PAH formation in dark molecular clouds.A recent theoretical study (Krasnoukhov et al. 2022) on the C 7 H 7 + CH 2 CCH potential energy surface has shown that CH 2 CCH can add to the -CH 2 group of C 7 H 7 without barrier, leading to a variety of exothermic bimolecular exit channels.Possible products consist of bicyclic aromatic species such as methyleneindanyl radicals (C 9 H 7 CH 2 ), methyleneindenes (C 9 H 6 CH 2 ), Hnaphthalenyl (C 10 H 9 ), and naphthalene (C 10 H 8 ).In the high temperature environments of asymptotic branch stars, C 7 H 7 is formed from H-abstraction of toluene (C 7 H 8 ), which itself is formed from benzene or C 6 H 5 (Krasnoukhov et al. 2022).It is currently not known whether C 7 H 8 or C 7 H 7 can be formed efficiently under dark molecular cloud conditions.Likewise, putational studies of fulvenallene (C 7 H 6 ) and the corresponding fulvenallenyl radical (C 7 H 5 ) in combustion environments suggest that the C 7 H 5 radical can be formed from H-abstraction of C 7 H 6 and further react to form PAHs, such as naphthalene via reaction with CH 2 CCH (da Silva & Bozzelli 2009

Table 6 .
Ion-Molecule Reactions of CN-substituted species

Table 8 .
Related Neutral-Neutral Reactions Continued

Table 9 .
Related Neutral-Neutral Reactions on Grains Ruaud et al. (2016) D. DESTRUCTION RATES OF CH 2 CCH, CH 3 CCH, AND CH 2 CCH 2 Figure 14 displays the rates of reaction for the major destruction mechanisms of CH 2 CCH, CH 3 CCH, and CH 2 CCH as a function of time.