Application of the String Method to Determine the Ambimodal Nature of Transition States in Bifurcation Reactions

Abstract

Recent quantum chemical studies have revealed that a wide range of organic reactions exhibit post-transition-state bifurcation (PTSB), in which a single transition state (TS) leads directly to two or more distinct products along barrierless downhill pathways. Such TSs are commonly referred to as ambimodal TSs. In contrast, conventional intrinsic reaction coordinate (IRC) calculations typically connect the TS to only one of the possible products and therefore fail to identify alternative non-IRC products. To assess the ambimodal character of TSs in PTSB reactions, we analyzed relaxed pathways connecting a TS directly to a non-IRC product using the double-ended string method. Application of this approach to a total of 33 reaction systems, including pericyclic reactions (among them two trifurcation systems) and non-pericyclic reactions, enabled unambiguous classification of TS-product connections as either a static downhill connection or a static small-barrier connection, depending on whether an energy maximum exists below the TS. The proposed method provides a practical and robust tool for the static topological analysis of PTSB reactions and serves as an effective complement to on-the-fly dynamical trajectory simulations.