The chemical pathways linking the small organic molecules commonly observed in molecular clouds to the large, complex, polycyclic species long-suspected to be carriers of the ubiquitous unidentified infrared emission bands remain unclear. To investigate whether the formation of mono- and poly-cyclic molecules observed in cold cores could form via the bottom-up reaction of ubiquitous carbon-chain species with, e.g. atomic hydrogen, a search is made for possible intermediates in data taken as part of the GOTHAM (GBT Observations of TMC-1 Hunting for Aromatic Molecules) project. Markov-Chain Monte Carlo (MCMC) Source Models were run to obtain column densities and excitation temperatures. Astrochemical models were run to examine possible formation routes, including a novel grain-surface pathway involving the hydrogenation of C$_6$N and HC$_6$N, as well as purely gas-phase reactions between C$_3$N and both propyne (CH$_3$CCH) and allene (CH$_2$CCH$_2$), as well as via the reaction CN + H$_2$CCCHCCH. We report the first detection of cyanoacetyleneallene (H$_2$CCCHC$_3$N) in space toward the TMC-1 cold cloud using the Robert C. Byrd 100 m Green Bank Telescope (GBT). Cyanoacetyleneallene may represent an intermediate between less-saturated carbon-chains, such as the cyanopolyynes, that are characteristic of cold cores and the more recently-discovered cyclic species like cyanocyclopentadiene. Results from our models show that the gas-phase allene-based formation route in particular produces abundances of H$_2$CCCHC$_3$N that match the column density of $2times10^{11}$ cm$^{-2}$ obtained from the MCMC Source Model, and that the grain-surface route yields large abundances on ices that could potentially be important as precursors for cyclic molecules.
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