Background:
Some quantum chemistry papers explore potential energy surfaces by characterizing critical points with an ab initio method. Reactants, products, intermediates, and transition states are found through optimization calculations, and then confirmed using frequency calculations. Intermediates connected by a transition state can be confirmed by intrinsic reaction coordinate (IRC) or some other minimal energy path (MEP) calculation. Here's an example potential energy surface from a paper online:
Question:
For any given intermediate and reactant/product pair, how does one confirm (1) a barrierless connection or (2) a lack of connection? A connection with a barrier is simple: a transition state must exist and connect back to the two species. That's like TS3 connecting H + SO$_2$ and HSO$_2$ above. But it's not clear how something like SO--HO and OH + SO can be confirmed, or the lack of connection between HOSO and OH + SO can be confirmed.
My thoughts:
(1) Intuitively, an optimization that does very small steps and always goes downhill from the reactant/product to the intermediate of interest may be sufficient to confirm the barrierless connection. At the same time, this feels like a bit of a slippery slope.. If there is a downhill route going from OH+SO to TS', then this could be used to confirm that OH+SO can barrierlessly form HOSO (see crude cyan-drawn path below).
(2) Intuitively, confirming a lack of connection would require some sort of constrained optimization starting from the intermediate which shows that all possible degrees of freedom lead to other intermediates or products.
((Here, I am just assuming we stay on a single, simple, adiabatic potential energy surface. Here is a similar question with smaller scope: What is a barrier-less reaction in Quantum Chemistry?))