Determining the Ambimodality of Transition State Structures by the Exploration of Dimensionality-Reduced Potential Energy Surfaces

Ambimodal reaction pathways are characterized by a post transition state bifurcation (PTSB) on the potential energy surface (PES), which could therefore lead to multiple products from a single and common transition state, without intermediate formation or additional activation barrier. Ambimodality has been widely found in pericyclic reactions and functional group migrations, among other reactions. Currently, it is primarily characterized using ab initio molecular dynamics simulations to explore the PES. However, this approach is computationally expensive and may introduce errors, since downhill trajectories can surpass small energy barriers, leading to spurious identification of ambimodality. Here, a dimensionality-reduced optimization (DRO) strategy based on performing sequential geometric optimizations within a tailored lower-dimensional PES is proposed to determine the ambimodal character of transition states via efficient PES exploration. In the DRO protocol, the dimensionality of the PES is systematically reduced by hindering access to the product identified from the previous intrinsic reaction coordinate (IRC) calculation. Subsequently, alternative downhill pathways are explored. Only when an alternative non-IRC product can be reached downhill in a barrierless manner can the transition state be characterized as ambimodal within the DRO protocol. This approach has been validated against different cycloaddition reactions and represents a significant advancement in the study of ambimodal reactions, providing a static, computationally inexpensive, and effective method for characterizing complex reaction pathways directly from transition state structures.