Comparison of Theoretical Methods for Predicting Tunneling Rates: The Alanine + Hydrogen Atom Reactions at Low Temperatures

Hydrogen-atom-abstraction reactions play a central role in astrochemistry, where the low temperature of the interstellar medium makes tunneling an important reaction mechanism. The reliability of theoretical methods in predicting reaction rate constants under these conditions is not obvious. In this paper, ring-polymer instanton rate theory, known to provide accurate rates for tunneling-driven reactions, is compared with classical transition state theory (TST) and semiclassical transition state theory (SCTST) for the H- and D-atom-abstraction reactions of the astrochemically relevant molecule alanine. Classical TST, in line with expectations, fails completely, underestimating the rates by several orders of magnitude unless tunneling corrections are included. SCTST, in contrast, yields rate constants in surprisingly good agreement with instanton theory over a broad temperature range, even within the deep-tunneling regime. However, at very low temperatures, SCTST increasingly deviates from instanton rates. A comparison of the quantum-chemical potential energy surface used in ring polymer evaluation and that used for the vibrational energy levels within VPT2 in SCTST shows that the latter does not adequately describe the regions that dominate at low temperatures. These findings clarify the origins of the limitations of SCTST and eventually can be used to create possible strategies to improve its applicability.