Detection of Interstellar HC₄NC and an Investigation of Isocyanopolyyne Chemistry under TMC-1 Conditions

Understanding the formation and destruction routes of molecules in astronomical environments remains one of the challenging issues in modern astrochemistry. Increasingly sensitive astronomical observations can reveal detailed information about the chemical inventories present in interstellar sources. Laboratory experiments and astrochemical modeling can then work in tandem to uncover the chemical mechanisms underlying these molecular inventories. However, there are still deficiencies in our understanding of the chemistry of interstellar sources. For example, in spite of proposed formation routes through grain chemistry, gas-phase formation routes cannot be ruled out as a viable pathway for the formation of large astronomical molecules (Balucani et al. 2015; Acharyya & Herbst 2017; Coutens et al. 2017, and references therein). The question remains as to how to better model the chemistry present in these astronomical environments and make the models more predictive. In turn, these robust models could then suggest further chemical species to be investigated both in the laboratory and through astronomical observations.

Structural isomers are a promising class of molecules for improving the accuracy of models. Structural isomers contain the same constituent atoms but are arranged in different elemental configurations (Xue et al. 2019). One of the most well studied isomeric pairs in astronomical environments is that of hydrogen cyanide (HCN) and isocyanide (HNC) (Schilke et al. 1992; Turner et al. 1997; Hirota et al. 1998; Herbst et al. 2000; Tennekes et al. 2006; Graninger et al. 2015). At 100 K, under thermal equilibrium conditions, the relative abundance ratio between HNC and HCN is ∼10⁻³⁰ (Brown 1977). However, it is well known that under dark cloud conditions, such as those found in the Taurus Molecular Cloud 1 (TMC-1), the abundance ratio approaches ∼1 (Irvine & Schloerb 1984), indicating that thermodynamic equilibrium certainly does not apply to the two species in these regions (Brown et al. 1989). Instead, measured column densities toward these sources are dominated by the kinetics of chemical reactions in the gas phase; these measurements give observational constraints on the chemical formation and destruction networks (Graninger et al. 2014). As such, measuring the relative abundance ratios for pairs of chemical isomers, and incorporating isomer-specific chemistry into chemical networks, can be a powerful tool to improving the predictive power of these models. Here, we focus on exploiting the cyanide and isocyanide pairs of isomers.

The family of astronomically detected cyanides includes HCN, methyl cyanide (CH₃CN), vinyl cyanide (CH₂CHCN), ethyl cyanide (CH₃CH₂CN), and other species including isocyanogen (CNCN), E-cyanomethanimine (E-HNCHCN), glycolonitrile (HOCH₂CN) and many others (McGuire 2018; Zeng et al. 2019, and references therein). Some of these species are found in high abundance and are readily detectable in a variety of interstellar environments (Miao & Snyder 1997; Araya et al. 2005; López et al. 2014; Hung et al. 2019). In contrast to the numerous detection of cyanides in astronomical environments, there have been very few confirmed detection of isocyanides, such as methyl isocyanide (CH₃NC) (Remijan et al. 2005; Gratier et al. 2013). Most recently, the Protostellar Interferometric Line Survey observed CH₃NC in a solar-type star, IRAS 16293-2422, for the first time toward a source of this type (Calcutt et al. 2018). Despite that, there have been no successful detections of CH₂CHCH₂NC (Haykal et al. 2013) or CH₃CH₂NC (Remijan et al. 2005; Margulès et al. 2018).

Alongside CH₃CN, one of the most frequently observed families of cyanide species, especially in cold sources, are the cyanopolyynes (HC_2nCN) (Broten et al. 1978; Little et al. 1978; Bell et al. 1998). Yet, despite their relative ubiquity, the only isocyanide version that has been successfully detected is HCCNC (Kawaguchi et al. 1992), the isomer of HC₃N. Remijan et al. (2005) first searched for isocyanodiacetylene (HC₄NC), the isomer of HC₅N, toward Sagittarius B2(N). To the best of our knowledge, this has been the only attempt to detect this molecule in astronomical environments, setting an upper limit on the abundance ratio to HC₅N as 0.03. In this work, we report the first astronomical detection of HC₄NC using the data available from the GOTHAM (Green Bank Telescope Observations of TMC-1: Hunting for Aromatic Molecules) observational program of TMC-1 (McGuire et al. 2020a). The detection of HC₄NC along with new observations of HCCNC and an upper limit to the abundance of HC₆NC, have been used to better constrain the gas-phase formation models of both cyanopolyynes and isocyanopolyynes (HC_2nNC) under TMC-1 conditions. The interplay between –CN and –NC formation chemistry can also provide insights into the physical conditions and history of the sources where these species are detected, therefore making new mechanistic insights into –CN versus –NC chemistry particularly relevant for both new and continuing problems such as the HCN/HNC abundance ratio (e.g., Hacar et al. 2020).

In Section 2, we describe the molecular properties of HC₄NC. Section 3 presents the detection of HC₄NC with the GOTHAM observations and the observational analyses. The results of the analyses are used to constrain the new chemical formation network developed to account for the formation of HC₄NC in Section 4. Finally, in Section 5, we summarize our results and describe the next steps in refining the chemical network and searches for larger isocyanopolyynes toward other astronomical sources.

The HC₄NC molecule has a linear equilibrium structure (Gronowski & Kołos 2006). For this work, transition frequencies of HC₄NC were taken from the CDMS catalog (Müller et al. 2005); the entry was based on Fourier transform microwave (FTMW) spectroscopy data and ab initio calculations reported by Botschwina et al. (1998).

In addition to the molecular structure, Botschwina et al. (1998) also provided estimates of the electric dipole moment. However, the authors did not report the dipole polarizability, which is required for estimating reaction rate coefficients, as will be discussed in Section 4. To this end, we carried out new calculations with the CFOUR (Coupled-Cluster techniques for Computational Chemistry) suite of electronic structure programs (Stanton et al. 2017), employing the coupled-cluster method with single, double, and perturbative triple excitations (CCSD(T)) under the frozen-core approximation, paired with a Dunning's correlation-consistent quadruple-ζ (cc-pVQZ) basis set. At this level of theory, we obtain an equilibrium dipole moment of 3.24 D in agreement with the value of 3.25 D obtained by Botschwina et al. (1998) employing a smaller Dunning's triple-ζ (cc-pVTZ) basis set. The small difference between the cc-pVTZ and cc-pVQZ values suggests that the one-electron properties have effectively converged with respect to basis set, thereby lending confidence in our calculations. With the same method and the cc-pVQZ basis set, we obtain a value of 10.3501 ų for the average dipole polarizability listed in Table 1.

The capabilities of the Green Bank Telescope (GBT) have expanded the molecular census in TMC-1 and, thereby, increased the known molecular inventory in the interstellar medium (McGuire et al. 2017, 2018). The GBT observations of the GOTHAM project targeted the TMC-1 cyanopolyyne peak (CP) centered at α_J2000 = 04^h41^m425, δ_J2000 = 25°41'268, where the column densities of the carbon-chain species peak. The GOTHAM spectral line survey covers the GBT X-, K- and Ka-bands with total 13.1 GHz frequency coverage from 7.906 to 29.827 GHz. The beam size varies between ∼90'' at 8 GHz and ∼26'' at 29 GHz. At a uniform $0.05\,\mathrm{km}\,{{\rm{s}}}^{-1}$ velocity resolution, the rms noise ranges from ∼2 to 20 $\mathrm{mK}$ across the data set. Detailed information concerning the GOTHAM observations and the data calibration can be found in McGuire et al. (2020a).

As presented in Figure 1, we identified three emission features above the noise level of the observations assigned to HC₄NC with the GOTHAM survey. Each feature comprises three hyperfine components of the rotational transition. Table 2 summarizes the spectroscopic properties of the nine transitions. The HC₄NC lines show a good match between the observed frequencies and the calculated frequencies from the CDMS database assuming a systematic local standard of rest velocity (V_lsr) of $5.8\ \mathrm{km}\,{{\rm{s}}}^{-1}$.

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Table 2.  Spectroscopic Properties of the Identified HC₄NC Lines

Transitions		Frequency	Eup	${\mathrm{log}}_{10}\tfrac{{A}_{{ul}}}{{{\rm{s}}}^{-1}}$	${S}_{{ij}}{\mu }^{2}$
$J^{\prime} \ \to J^{\prime\prime}$	$F^{\prime} \ \to F^{\prime\prime}$	(MHz)	(K)		(D2)
$8\ \to 7$	$9\ \to 8$	22418.8438(10)	4.84	−6.1859	94.43
	$8\ \to 7$	22418.8461(10)	4.84	−6.1927	83.18
	$7\ \to 6$	22418.8498(10)	4.84	−6.1936	73.24
$9\ \to 8$	$10\ \to 9$	25221.1790(16)	6.05	−6.0295	105.07
	$9\ \to 8$	25221.1808(17)	6.05	−6.0350	93.88
	$8\ \to 7$	25221.1837(17)	6.05	−6.0356	83.88
$10\ \to 9$	$11\ \to 10$	28023.5067(25)	7.40	−5.8899	115.69
	$10\ \to 9$	28023.5082(26)	7.40	−5.8943	104.57
	$9\ \to 8$	28023.5105(26)	7.40	−5.8948	94.52

Note. The spectroscopic data of the HC₄NC transitions corresponding to the three detected emission features are taken from the CDMS catalog (Müller et al. 2005) and the SPLATALOGUE spectroscopy database (https://www.splatalogue.online).

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3.1. Determinations of Column Density and Excitation Conditions

A total of 13 transitions of HC₄NC (see Appendix A) were used to rigorously determine the molecular abundance and excitation conditions using the Markov chain Monte Carlo (MCMC) fitting method described in Loomis et al. (2020). Each of the identified emission features consists of four individual velocity components (Loomis et al. 2020), indicating that TMC-1 is not quiescent and isotropic in terms of physical structure. This is supported by recent CCS and HC₃N observations performed with the 45 m telescope at the Nobeyama Radio Observatory (Dobashi et al. 2018).

A uniform excitation temperature (T_ex) and line width (ΔV) for each velocity component are assumed, while source velocity (V_lsr), source size, and column density (N_T) are variable among different velocity components. Therefore, there are 14 free parameters in total to be adjusted in the MCMC analysis. A forward model with 14 free parameters is used to iteratively generate model spectra which are compared with the observations. Posterior probability distributions for each parameter and their covariances are generated via several million of these parameter draws, populating the corner plot in Appendix A. The resulting best-fit parameters of each velocity component of HC₄NC are summarized in Table 3. As shown in Figure 1, if we take the noise level measured in each passband into account, the constructed profiles fit reasonably well with the observed spectra for the individual emission features. A total N_T of ${3.29}_{-1.20}^{+8.60}$ × 10¹¹ cm⁻² with a T_ex of ${6.7}_{-0.3}^{+0.3}\,{\rm{K}}$ is determined for HC₄NC.

Table 3.  HC₄NC Best-fit Parameters from the MCMC Analysis

Component	vlsr	Size	NTa	Tex	ΔV
	(km s−1)	('')	(1011 cm−2)	(K)	(km s−1)
C1	${5.628}_{-0.038}^{+0.045}$	${42}_{-9}^{+9}$	${0.30}_{-0.13}^{+0.19}$	${6.7}_{-0.3}^{+0.3}$	${0.120}_{-0.010}^{+0.012}$
C2	${5.745}_{-0.015}^{+0.021}$	${21}_{-8}^{+7}$	${1.35}_{-0.50}^{+1.38}$
C3	${5.907}_{-0.046}^{+0.038}$	${62}_{-20}^{+20}$	${0.23}_{-0.12}^{+0.12}$
C4	${6.009}_{-0.032}^{+0.044}$	${9}_{-6}^{+11}$	${1.40}_{-1.07}^{+8.48}$
NT (Total)b	${3.29}_{-1.20}^{+8.60}\times {10}^{11}$ cm−2

Notes. The quoted uncertainties represent the 16th and 84th percentile (1σ for a Gaussian distribution) uncertainties.

^aColumn density values are highly covariant with the derived source sizes. The marginalized uncertainties on the column densities are therefore dominated by the largely unconstrained nature of the source sizes, and not by the signal-to-noise of the observations. See Appendix A for a covariance plot, and Loomis et al. (2020) for a detailed explanation of the methods used to constrain these quantities and derive the uncertainties. ^bUncertainties derived by adding the uncertainties of the individual components in quadrature.

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The N_T per velocity components show variation on the order of a factor of a few but have consistency in the order of magnitude, unlike the case of HC₃N and CCS presented in Dobashi et al. (2018). The variation of N_T arises from the degeneracy between the N_T of each component and its source size, found by the MCMC analysis. Without any spatial information to constrain the source sizes, we cannot conclude much about their chemical properties.

In addition to the HC₄NC analysis, we have also analyzed HCCNC and HC₆NC in these observations; the results of these analyses are presented in Appendices B and C. HCCNC is definitively detected with six emission features whereas there is no obvious emission detected for HC₆NC. The N_T for HCCNC is measured to be ${3.82}_{-0.53}^{+1.06}\times {10}^{12}\ {\mathrm{cm}}^{-2}$, while a 2σ upper limit of <4.04 × 10¹¹ cm⁻² for the HC₆NC column density is determined. HCCNC has been previously detected in TMC-1 with Nobeyama 45 m observations (Gratier et al. 2016), which reported N_T(HCCNC) to be ${8.51}_{-1.9}^{+8.87}\times {10}^{12}\,{\mathrm{cm}}^{-2}$, consistent with our GOTHAM result. The column densities listed in Table 4 are the sums of the four detected velocity components, where the column densities of HC₃N and HC₅N are from Loomis et al. (2020). The detection of HCCNC and HC₄NC in GOTHAM data gives column density ratios to their corresponding cyanide isomers of ${2.2}_{-0.4}^{+0.7} \%$ for HCCNC/HC₃N and ${0.49}_{-0.19}^{+1.32} \%$ HC₄NC/HC₅N toward TMC-1. The observed results are used to constrain the reaction rate coefficients and branching ratios of the formation routes of HC₄NC, as will be discussed in Section 4.2.

Table 4.  Column Densities and XNC/XCN Ratios

Species	NT	NT with the Nobeyama Observationsa	NT(XNC)/NT(XCN)
	(cm−2)	(cm−2)	Observation	High HC4NC BFb	Low HC4NC BFb
HCCCN	${1.75}_{-0.05}^{+0.05}\times {10}^{14}$ c	${2.34}_{-0.30}^{+0.82}\times {10}^{14}$
HCCNC	${3.82}_{-0.53}^{+1.06}\times {10}^{12}$	${8.51}_{-1.90}^{+8.87}\times {10}^{12}$	${2.2}_{-0.4}^{+0.7} \%$	3.0%	3.0%
HC4CN	${6.69}_{-0.13}^{+0.13}\times {10}^{13}$ c	${5.89}_{-1.10}^{+1.52}\times {10}^{13}$
HC4NC	${3.29}_{-1.20}^{+8.60}\times {10}^{11}$		${0.49}_{-0.19}^{+1.32} \%$	2.6%	0.34%
HC6CN	${3.65}_{-0.12}^{+0.13}\times {10}^{13}$ c	${4.57}_{-0.94}^{+1.74}\times {10}^{13}$
HC6NC	$\lt 4.04\times {10}^{11}$		<1.1%

Notes.

^aThe column density estimated by the Bayesian approach of the spectral survey performed with the Nobeyama 45 m dish (Gratier et al. 2016). ^b"High HC₄NC BF" corresponds to the model with a high branching fraction to form HC₄NC in the HC₅NH⁺ dissociative recombination, i.e., shown as solid lines in Figure 3, while "Low HC₄NC BF" is the modeled result with a low branching fraction shown as dashed lines in Figure 3. ^cLoomis et al. (2020) estimated the column densities of cyanopolyynes with similar MCMC analyses of the GOTHAM data, assuming the four velocity components are co-spatial.

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3.2. Visualization of the Detection

To better visualize the detection, and determine a minimum statistical significance, we constructed an intensity- and noise-weighted stacked composite spectrum using the GOTHAM data (Loomis et al. 2020). The spectral stacking was performed in velocity space using the 13 HC₄NC transitions covered by the survey. Another composite line profile using the best-fit parameters was constructed, and used as a matched filter to perform the cross-correlation and determine the statistical significance of the detection (Loomis et al. 2020). The results are shown in Figure 2, and indicate a minimum significance to the detection of HC₄NC of 10.5σ.

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4.1. Chemical Networks

A number of prior investigations have attempted to address the chemical origins of many of the cyanopolyynes observed in TMC-1 (Takano et al. 1998; Taniguchi et al. 2016; Burkhardt et al. 2018). For example, due to the significant abundance enhancement of HCC¹³CN relative to HC¹³CCN and H¹³CCCN, the formation of HC₃N was suggested to be dominated by the neutral–neutral reaction of C₂H₂ and the CN radical (Takano et al. 1998). On the other hand, HC₅N and HC₇N show no such enhancement for the analogous ¹³C position, implying that the primary formation route for HC₅N is the dissociative recombination (DR) reaction between the N-bearing hydrocarbon ions and electrons in cold environments (Burkhardt et al. 2018). Furthermore, Loison et al. (2014a) pointed out that the H₂CCN + C $\to$ HC₃N + H reaction is also involved in producing HC₃N.

On the other hand, the chemistry of the corresponding isocyanopolyynes (HC_2nNC) is less well known. Compared with neutral–neutral reactions, reaction schemes involving the DR process of protonated molecular ions such as HC₃NH⁺ and HC₂NCH⁺ are more likely to be the main production mechanisms for HCCNC (Kawaguchi et al. 1992; Gensheimer 1997; Osamura et al. 1999; Vastel et al. 2018). These protonated ions can be formed through ion–molecule reactions such as HCCH⁺ + HNC/HNC and CH₃CN + C⁺ (Takagi et al. 1999; Quénard et al. 2017). Even though the chemistry of HC₄NC is less well studied compared to HCCNC, both of them belong to the same homologous series. We therefore assumed analogous formation schemes of HCCNC and HC₄NC. In other words, HC₄NC would mainly form through the DR of the protonated cyanopolyynes HC₅NH⁺ and protonated isocyanopolyynes HC₄NCH⁺.

One of the most prevalent destruction mechanisms of cyano- and isocyanopolyynes is ion–molecule chemistry, particularly reactions with C⁺, H₃⁺, and HCO⁺ (Woon & Herbst 2009). In addition, as described in Loison et al. (2014b), reactions with carbon atoms are also efficient. Therefore, we extrapolate the mechanisms involving carbon atoms to isocyanopolyynes and propose that the main destruction mechanisms of HC₄NC are with the ions mentioned above, neutral carbon, and photons.

In this work, we adopted the chemical network of kida.uva.2014 (Wakelam et al. 2015), modified as described in McGuire et al. (2018), as the basis and added or updated the reactions related to HC₃N, HCCNC, HC₅N, and HC₄NC. Note that we introduce HC₄NC as the only isomer of HC₅N in the network. We neglected the other HC₅N isomers to avoid adding more new species of which we have even less knowledge. In the following sections, we will discuss the choices and estimations of the reaction rate coefficients of the formation and destruction pathways of the four molecules of interest. The production and destruction routes regarding HC₄NC are summarized in Table 5 with the corresponding rate coefficients.

Table 5.  Summary of the Proposed Dominant Reactions For HC₄NC

Reactions	α	β	γ	Formula Type	k (10 K)
Production Routes:
HC5NH+ + e− → HC4NC + H	4.400 × 10−8	−0.7	0	3	4.758 × 10−7a
HC4NCH+ + e− → HC4NC + Hb	4.000 × 10−7	−0.7	0	3	4.326 × 10−6c
Destruction Routes:
HC4NC + C+ → HC5N+ + C	0.2	2.334 × 10−9	3.499	4	4.554 × 10−9d
HC4NC + C+ → CNC+ + C4H	0.2	2.334 × 10−9	3.499	4	4.554 × 10−9d
HC4NC + C+ → C6N+ + H	0.2	2.334 × 10−9	3.499	4	4.554 × 10−9d
HC4NC + C+ → C5H+ + CN	0.2	2.334 × 10−9	3.499	4	4.554 × 10−9d
HC4NC + C+ → C4H+ + CCN	0.2	2.334 × 10−9	3.499	4	4.554 × 10−9d
HC4NC + ${{{\rm{H}}}_{3}}^{+}$ → HC4NCH+ + H2	1.0	4.420 × 10−9	3.499	4	4.312 × 10−8d
HC4NC + HCO+ → HC4NCH+ + CO	1.0	1.642 × 10−9	3.499	4	1.602 × 10−8d
HC4NC + H3O+ → HC4NCH+ + H2O	1.0	1.928 × 10−9	3.499	4	1.881 × 10−8d
HC4NC + H+ → CN + ${{\rm{C}}}_{4}{{{\rm{H}}}_{2}}^{+}$	0.333	$7.557\times {10}^{-9}$	3.499	4	2.455 × 10−8d
HC4NC + H+ → H2 + C5N+	0.333	7.557 × 10−9	3.499	4	2.455 × 10−8d
HC4NC + H+ → C + H2C4N+	0.333	7.557 × 10−9	3.499	4	2.455 × 10−8d
HC4NC + He+ → He + C4H + CN+	0.5	3.852 × 10−9	3.499	4	1.879 × 10−8d
HC4NC + He+ → He + C4H+ + CN	0.5	3.852 × 10−9	3.499	4	1.879 × 10−8d
HC4NC + C → C + HC5N	1.000 × 10−10	0	0	3	1.000 × 10−10e
HC4NC + CRPh → CN + C4H	3.450 × 103	0	0	1	4.485 × 10−14f
HC4NC + Photon → CN + C4H	9.540 × 10−10	0	1.830	2	1.076 × 10−17f

Notes. Definitions of α, β, and γ can be found on the KIDA online database (http://kida.astrophy.u-bordeaux.fr/help.html). Formulae of type 1 and 2 are k = αζ and $k=\alpha {e}^{-\gamma {A}_{\nu }}$, where k is in s⁻¹, and formulae of type 3 and 4 are $k(T)=\alpha {\left(T/300\right)}^{\beta }{e}^{-\gamma /T}$ and $k(T)=\alpha \beta \left(0.62+0.4767\gamma {\left(300/T\right)}^{0.5}\right)$, where k is in cm³ s⁻¹ and T is in K.

^aThe total reaction coefficient of the HC₅NH⁺ DR is 2.0 × 10⁻⁶ (T/300)^−0.7 cm³ s⁻¹ followed as suggested in kida.uva.2014 while the branching ratio leading to HC₄NC is assumed to be 1/20 of that leading to HC₅N, which is based on the branching fractions for producing HC₃N and HCCNC of the HC₃NH⁺ DR (Vastel et al. 2019). ^bHC₄NCH⁺ is mainly produced through the reaction between CH₃C₃N and the C⁺ ion. ^cThe reaction coefficient of the HC₄NCH⁺ DR is assumed to have the same rate coefficient as that of HC₅NH⁺: 2.0 × 10⁻⁶ (T/300)^−0.7 cm³ s⁻¹, while the branching ratio is assumed to be similar to that of HC₂NCH⁺, which is included in kida.uva.2014. ^dRate coefficient estimated from Equation (1) with μ of 3.24 D and α of 10.3501 ų. ^eRate coefficient same as the family reacting with atomic carbon (Loison et al. 2014b). ^fRate coefficient same as that of the HCCNC + CRPh and HCCNC + photon reactions in kida.uva.2014 respectively.

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4.1.1. Formation Mechanisms: The Dissociative Recombination Reactions

The estimation of the branching ratios and rate coefficients of the HC₃NH⁺ DR are constrained by the laboratory measurements of the DR of DC₃ND⁺ and the consideration of isomerization among the products (Vastel et al. 2019 and references therein). We adopt their values in this paper.

Since HC₃N and HCCNC are both products of the HC₃NH⁺ DR reactions, the HC₅NH⁺ DR, originally included in the kida.uva.2014 network, is amended to include HC₄NC as another product:

$$\begin{eqnarray*}\begin{array}{rcl}{\mathrm{HC}}_{5}{\mathrm{NH}}^{+}\ +\ {e}^{-}\ & \to \ {{\rm{C}}}_{4}{\rm{H}}\ +\ \mathrm{HCN} & \quad 22 \% \\ & \to {{\rm{C}}}_{4}{\rm{H}}+\mathrm{HNC} & \quad 22 \% \\ & \to \mathrm{CCH}\ +\ {\mathrm{HC}}_{3}{\rm{N}} & \quad 6 \% \\ & \to {{\rm{C}}}_{5}{\rm{N}}\ +\ {{\rm{H}}}_{2} & \quad 4 \% \\ & \to {\mathrm{HC}}_{5}{\rm{N}}\ +\ {\rm{H}} & \quad 43.8 \% \\ & \to {\mathrm{HC}}_{4}\mathrm{NC}\ +\ {\rm{H}} & \quad 2.2 \% .\end{array}\end{eqnarray*}$$

The particular choice of the branching ratio is explained below.

Based on the potential energy surface of the various HC₃N isomers, Vastel et al. (2019) suggested the branching fraction for the HC₃NH⁺ DR forming HC₃N to be 20 times greater than that for the process forming HCCNC (J. Loison 2020, private communication). The energy difference between HC₄NC and HC₅N is calculated to be ∼114.5 kJ mol⁻¹ (or 13,771 K) with the W1BD thermochemical method, which is similar to the difference between HCCNC and HC₃N, ∼113.1 kJ mol⁻¹ (or 13,603 K). Because of the lack of a laboratory measurement of the branching ratio in the HC₅NH⁺ DR, we assume a fiducial ratio between the branching fractions for the HC₅N isomers to be 20, analogous to that of the HC₃N isomers. The total rate coefficient for the HC₅NH⁺ DR, $2.0\times {10}^{-6}{(T/300)}^{-0.7}\,{\mathrm{cm}}^{3}\,{{\rm{s}}}^{-1}$, and the branching ratios for the other product species are followed as suggested in kida.uva.2014.

The DR of HC₂NCH⁺ is another important pathway leading to HCCNC (Botschwina et al. 1993). In kida.uva.2014, the rate coefficient for the DR of HC₂NCH⁺ is $6.0\,\times {10}^{-7}{(T/300)}^{-0.5}\,{\mathrm{cm}}^{3}\,{{\rm{s}}}^{-1}$, which seems to be underestimated compared with the experimentally measured rate coefficient for the DR of DC₃ND⁺, $1.5\times {10}^{-6}{(T/300)}^{-0.7}\,{\mathrm{cm}}^{3}\,{{\rm{s}}}^{-1}$ (Geppert et al. 2004; Vigren et al. 2012). We expect these rate coefficients to be similar because rate coefficients for DR tend to increase with complexity (Larsson et al. 2012), and because the two cations are of similar complexity. Considering that, we modified the total rate coefficient for the HC₂NCH⁺ DR to be analogous with that of DC₃ND⁺.

Furthermore, we also added HC₄NCH⁺ as a secondary precursor of HC₄NC. For the HC₄NCH⁺ DR, we assume the total rate coefficient to be consistent with the HC₅NH⁺ DR rate coefficient of 2.0 × 10⁻⁶ (T/300)^−0.7 cm³ s⁻¹. The channels and branching ratios of the DR of HC₄NCH⁺ are assumed to be equal to that of HC₂NCH⁺ in the kida.uva.2014 network:

$$\begin{eqnarray*}\begin{array}{rcl}{\mathrm{HC}}_{4}{\mathrm{NCH}}^{+}\ +\ {e}^{-} & \to \ {{\rm{C}}}_{4}{\rm{H}}\ +\ \mathrm{HCN} & \quad 38 \% \\ & \to \ {{\rm{C}}}_{4}{{\rm{H}}}_{2}\ +\ \mathrm{CN} & \quad 38 \% \\ & \to \ {\mathrm{HC}}_{5}{\rm{N}}\ +\ {\rm{H}} & \quad 4 \% \\ & \to \ {\mathrm{HC}}_{4}\mathrm{NC}\ +\ {\rm{H}} & \quad 20 \% .\end{array}\end{eqnarray*}$$

Note that, while HC₄NC can be protonated to form HC₄NCH⁺, the formation of HC₄NCH⁺ is dominated by the proposed reaction between CH₃C₃N and the C⁺ ion. Thus, consecutive protonation and de-protonation of HC₄NC, resulting in a zero net abundance change, is avoided.

Since the barrierless DR reactions contribute dominantly to the formation of isocyanopolyynes, we emphasize that the determination of the branching ratios are usually more crucial than those of the overall rate coefficients for the case of DR in astronomical environments (Larsson et al. 2012). Nonetheless, although the branching ratios of the related DR reactions are mostly estimated and relatively arbitrary due to the lack of experimental measurement other than for DC₃ND⁺ (Geppert et al. 2004), we believe that the values we estimated are reasonable, as supported by the reproduction of observed values discussed below.

4.1.2. Destruction Mechanisms

As previously mentioned, the destruction of the cyano- and isocyanopolyynes is dominated by ion–molecule reactions and reactions with atomic carbon. The reaction coefficient of the related ion–molecule reactions are estimated from Equation (3) from Woon & Herbst (2009), which can be rewritten as

$$\begin{eqnarray}&&{k}_{{\rm{D}}}=0.4767\displaystyle \frac{2\pi e{\mu }_{{\rm{D}}}}{\sqrt{2{kT}\mu }}+0.62\times 2\pi e\sqrt{\displaystyle \frac{\alpha }{\mu }},\end{eqnarray} \tag{ 1 }$$

where μ_D and α are the dipole moment and the average dipole polarizability of the neutral molecule, respectively, and μ is the reduced mass of the reactants. In addition to adding the new destruction routes proposed for HC₄NC, we also updated the ion–molecule reaction rate coefficients of HCCNC, HC₅N, and CH₃C₃N from the kida.uva.2014 network with this formula and the dipole moments and polarizabilities listed in Table 5. The reaction rate coefficients for the reactions of isocyanopolyynes with carbon atoms are estimated to be the same as those of the cyanopolyynes (Loison et al. 2014b), while the reaction coefficients for the UV photon dissociation and cosmic-ray ionization reactions of HC₄NC are assumed to be the same as those of HCCNC in kida.uva.2014 respectively.

4.2. Chemical Modeling

We used the three-phase gas-grain astrochemical model NAUTILUS 1.1 (Ruaud et al. 2016) together with our updated network to attempt to reproduce the abundances of HC₄NC and the related species. Physical conditions are assumed to follow typical cold dense cloud conditions, i.e., a gas and dust temperature of 10 K, a gas density n_H of 2 × 10⁴ cm⁻³, a visual extinction (A_v) of 10, and a cosmic ray ionization rate (ζ) of 1.3 × 10⁻¹⁷ s⁻¹ (Ruaud et al. 2016). We adopted assumed initial elemental abundances in TMC-1 CP as described in Hincelin et al. (2011) with the exception of atomic oxygen. The resulting abundances, with respect to the ${N}_{{\rm{T}},({{\rm{H}}}_{2})}$ ∼ 10²² cm⁻² (Gratier et al. 2016), were converted to column densities and compared with the observed values.

We found that both cyano- and isocyanopolyynes are highly sensitive to the initial oxygen elemental abundance. A higher oxygen abundance would result in lower abundances of the HC₃N, HCCNC, HC₅N, and HC₄NC molecules because the majority of C is being locked into CO while reacting with the abundant O. In Figure 3, we present the results of the chemical modeling with an initial C/O ratio of 1.1, in which the model at an age of ∼3.5 × 10⁵ yr gives satisfactory agreement with the observations for HC₃N, HCCNC, and HC₅N. The initial physical conditions and elemental abundances are all homogeneous among the current series of GOTHAM papers (Burkhardt et al. 2020; Loomis et al. 2020; McCarthy et al. 2020; McGuire et al. 2020b; this work) and have reproduced the observed abundances of the other cyanopolyynes species HC₇N, HC₉N, and HC₁₁N well. Compared with previous astrochemical modeling on TMC-1, the modeled results produce a similar agreement. For example, in Loison et al. (2014b), when assuming the C/O ratio to be 0.95, the peak abundances for HC₃N and HC₅N are ∼4 × 10⁻⁸ and ∼7 × 10⁻⁹ respectively and occur at ∼3 × 10⁵ yr, which are consistent with our results.

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The overproduction of HC₄NC could be explained by the defects in the chemical network. Concerning destruction, there could be secondary destruction mechanisms that we have not accounted for, while concerning production, the branching ratios in the related DR processes could be inaccurate. First, the ratio between the branching fraction for forming HC₅N and that for forming HC₄NC in the HC₅NH⁺ DR was assumed to be an analogous value of 20 from the HC₃NH⁺ DR, which could be underestimated. We conducted additional models by varying this ratio and found that increasing it would result in a significant decrease in the simulated abundance of HC₄NC while the increase in HC₅N is less significant, as shown in Figure 3. When this ratio is set to be 200, the modeled abundance ratio for HC₄NC/HC₅N can reach 0.34%, which matches well with the observed value, ${0.49}_{-0.19}^{+1.32} \%$. Therefore, as constrained by the observed abundances, this ratio is suggested to fall within a range of 20–200. Second, neglecting other possible HC₅N isomers in the DR processes would also lead to an overestimation of the branching fractions for forming HC₄NC and HC₅N in the HC₄NCH⁺ DR. A reduction in the branching ratio could easily reduce the simulated HC₄NC abundance. Experimental studies on the formation and destruction pathways of this molecule are rare, and its detection in TMC-1 therefore highlights the need for more experimental and theoretical work.

4.3. CN/NC Formation Chemistry

In this paper, we report the astronomical detection of HC₄NC for the first time in the interstellar medium using the GOTHAM survey at a minimum significance of 10.5σ. Three emission features above the noise level of the observations are assigned to HC₄NC. Our analysis indicates a total of four distinct velocity components contribute to the emission signal observed for this species. The observed ratio between HC₄NC and its cyanopolyyne counterpart HC₅N is $\sim {0.49}_{-0.19}^{+1.32} \%$ while the observed relative abundance ratio between HCCNC and HC₃N is $\sim {2.2}_{-0.4}^{+0.7} \%$.

The synthesis of the HC₄NC molecule is linked to the chemistry of the protonated cyanides and isocyanides. We attempted to reproduce the observed abundances of the selected cyano- and isocyanopolyynes with the inclusion of DR as major formation routes and ion–molecule reactions, as well as reactions with atomic carbon as dominant destruction routes. We are aware that HC₃N and HC₅N have different dominant formation pathways whereas the chemical network of HC₄NC in the current study is assumed to be analogous to that of HCCNC. The similar molecular structure of the two isocyanopolyynes makes it the best assumption we can posit.

The chemical modeling presented reproduces the observed abundance of HC₄NC within an order of magnitude. The result of the chemical modeling suggests that the considered formation and destruction routes are reasonable and relevant for HC₄NC and has enabled us to constrain the reaction rate coefficients to some extent. With the increasing number of detected cyano- and isocyanopolyynes in astronomical environments, accurate laboratory measurements of the rate coefficients and branching ratios for reactions of interest would certainly help to better reproduce the observed results.

A.M.B. acknowledges support from the Smithsonian Institution as a Submillimeter Array (SMA) Fellow. M.C.M and K.L.K.L. acknowledge financial support from NSF grants AST-1908576, AST-1615847, and NASA grant 80NSSC18K0396. Support for B.A.M. was provided by NASA through Hubble Fellowship grant #HST-HF2-51396 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. C.N.S. thanks the Alexander von Humboldt Stiftung/Foundation for their generous support, as well as V. Wakelam for use of the NAUTILUS v1.1 code. C.X. is a Grote Reber Fellow, and support for this work was provided by the NSF through the Grote Reber Fellowship Program administered by Associated Universities, Inc./National Radio Astronomy Observatory and the Virginia Space Grant Consortium. E.H. thanks the National Science Foundation for support through grant AST 1906489. S.B.C. and M.A.C. were supported by the NASA Astrobiology Institute through the Goddard Center for Astrobiology. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. The Green Bank Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

A total of 13 transitions (including hyperfine components) of HC₄NC were covered by GOTHAM observations at the time of analysis and were above the predicted flux threshold of 5%, as discussed in Loomis et al. (2020). Of these transitions, none was coincident with interfering transitions of other species, and thus a total of 13 transitions were considered. Observational data windowed around these transitions, spectroscopic properties of each transition, and the partition function used in the MCMC analysis are provided in the Harvard Dataverse repository (GOTHAM Collaboration 2020). A corner plot of the parameter covariances and their distribution for the HC₄NC MCMC fit is shown in Figure A1. Worth noting are the strong covariances between the column density and the source size for sources #2 and #4. The poor constraint on these source sizes leads to a large uncertainty in the total column density. Future detections of lines at lower or higher frequencies to anchor the source size fit (through measured beam dilution) would greatly enhance the precision of the column density measurement.

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An identical analysis to that for HC₄NC was carried out for HCCNC. Six emission features contributed by the nine rotational transitions (including hyperfine components) of HCCNC are well detected above the noise, as shown in Figure B1. The top three panels are the three hyperfine components of the 1–0 transition respectively while the bottom panel shows all the hyperfine components of the 3–2 transition. The spectroscopic properties of the nine transitions are summarized in Table B1.

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Table B1.  Spectroscopic Properties of the HCCNC Lines

Transitions		Frequency	Eup	${\mathrm{log}}_{10}\tfrac{{A}_{{ul}}}{{{\rm{s}}}^{-1}}$	Sijμ2
$J^{\prime} \ \to J^{\prime\prime}$	$F^{\prime} \ \to F^{\prime\prime}$	(MHz)	(K)		(Debye2)
$1\ \to 0$	$0\ \to 1$	9935.2000(150)	0.48	−7.4859	2.86
$1\ \to 0$	$2\ \to 1$	9935.6270(150)	0.48	−7.4859	14.31
$1\ \to 0$	$1\ \to 1$	9935.9100(150)	0.48	−7.4858	8.59
$3\ \to 2$	$2\ \to 2$	29806.5354(122)	2.86	−6.7535	2.86
	$2\ \to 3$	29806.8398(39)	2.86	−8.2976	0.08
	$4\ \to 3$	29806.9503(20)	2.86	−5.9454	33.11
	$3\ \to 2$	29806.9615(20)	2.86	−5.9965	22.89
	$2\ \to 1$	29807.0089(25)	2.86	−6.0211	15.45
	$3\ \to 3$	29807.2660(89)	2.86	−6.8996	2.86

Note. The spectroscopic data of the HCCNC transitions corresponding to the six detected lines are taken from the JPL catalog (https://spec.jpl.nasa.gov) and the SPLATALOGUE spectroscopy database, which are based on the FTMW and millimeter-wave measurements of Guarnieri et al. (1992) and Kruger et al. (1993).

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Of these transitions, six are above the 5% threshold, which was uniformly applied to the whole GOTHAM data set, and were therefore considered for the MCMC fitting and spectral stacking process, the data used in which are available in GOTHAM Collaboration (2020). The resulting best-fit parameters are given in Table B2. The noise level of the ${1}_{0}\ \to {0}_{1}$ spectrum is ∼3 mK, which accounts for the apparent difference seen between the constructed and observed profiles. The stacked spectrum and matched filter results are shown in Figure B2, while a corner plot of the parameter covariances for the HCCNC MCMC fit is shown in Figure B3.

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Table B2.  HCCNC Best-fit Parameters from the MCMC Analysis

Component	vlsr	Size	${N}_{T}^{\dagger }$	Tex	ΔV
	(km s−1)	('')	(1012 cm−2)	(K)	(km s−1)
C1	${5.622}_{-0.011}^{+0.016}$	${140}_{-27}^{+34}$	${0.97}_{-0.16}^{+0.18}$	${6.9}_{-0.3}^{+0.3}$	${0.166}_{-0.014}^{+0.017}$
C2	${5.756}_{-0.020}^{+0.022}$	${117}_{-25}^{+38}$	${1.04}_{-0.16}^{+0.15}$
C3	${5.926}_{-0.017}^{+0.015}$	${110}_{-23}^{+40}$	${1.06}_{-0.19}^{+0.16}$
C4	${6.051}_{-0.045}^{+0.066}$	${17}_{-9}^{+26}$	${0.75}_{-0.44}^{+1.02}$
NT (Total)††	${3.82}_{-0.53}^{+1.06}\times {10}^{12}$ cm−2

Note. The quoted uncertainties represent the 16th and 84th percentile (1σ for a Gaussian distribution) uncertainties, which are derived with the same methods mentioned in Table 3. See Figure B3 for a covariance plot.

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Following the similar line-selection process with HC₄NC, a total of 10 transitions (including hyperfine components) of HC₆NC were considered and the data are again available in GOTHAM Collaboration (2020). In our observation, no signal beyond a 1σ detection limit can be assigned to HC₆NC. Column density upper limits are therefore constrained using the modified fitting process described in Loomis et al. (2020), the results of which are given in Table C1. A corner plot of the parameter covariances for the HC₆NC MCMC fit is shown in Figure C1.

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Table C1.  HC₆NC Derived Upper Limit Column Densities from the MCMC Analysis

Component	vlsr	Size	${N}_{T}^{\dagger }$	Tex	ΔV
	(km s−1)	('')	(1011 cm−2)	(K)	(km s−1)
C1	[5.624]	[33]	<0.65	[6.5]	[0.117]
C2	[5.790]	[22]	<0.64
C3	[5.910]	[50]	<0.35
C4	[6.033]	[18]	<2.39
NT (Total)††	<4.04 × 1011 cm−2

Note. Upper limits are given as the 97.8th percentile (2σ) value. Parameters in brackets were held fixed to the 50th percentile value. See Figure C1 for a covariance plot.

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