A new perspective on transition states: χ1 separatrix.

We present a new definition of the transition state for chemical reactions, named the χ(1) separatrix. In contrast to previous transition state definitions which depend on the choice of reaction coordinates, the χ(1) separatrix is defined by choosing a time scale for observation and is connected to exact rate constants in the high friction limit. We demonstrate that this separatrix appears in the isomerization of alanine dipeptide as a stationary population in quasi-equilibrium, without assuming a particular coordinate system or reactant and product surfaces.