Identifying Barrierless Mechanisms For Benzene Formation In The Interstellar Medium Using Permutationally Invariant Reaction Discovery

Complex chemical reaction environments, such as those found in combustion engines, the upper atmosphere, or the interstellar medium, can contain large numbers of different reactive species participating in similarly large numbers of different chemical reactions. In such settings, identifying the most-likely multistep reaction mechanisms which lead to the production of a particular defined product species is an extremely challenging problem, requiring search and evaluation over a large number of different possible candidate mechanisms while also addressing the permutational challenges posed when considering a large number of reaction routes available to sets of identical molecular species. In this article, the problem of generating candidate reaction mechanisms which form a defined product from a diverse set of reactive molecules is cast as a discrete optimization of a permutationally invariant cost function describing similarity between the target product and the product generated by a trial reaction mechanism. This approach is demonstrated by generating 2230 candidate reaction mechanisms which form benzene from diverse sets of reactive molecules which have been experimentally identified in the interstellar medium. By screening this set of autogenerated mechanisms, using dispersion-corrected DFT to evaluate reaction energies and activation barriers, we identify several candidate barrierless reaction mechanisms (both previously proposed and new) for benzene formation which may operate in the low temperatures found in the interstellar medium and could be investigated further to supplement existing microkinetic models.