All stationary point are local minimum, if any parameters changed the energy should be increase. There is no way for a stationary point that energy go straight down to reach another.
I was told that radical reaction have no transition state, but why? What kind of reaction also do not have transition state? Is there any way to confirm there is no transition state using quantum chemical calculation method?
There is nothing special in having an activation barrier between reactants and products although, obviously, very many reactions do. But some reactions, such as electron transfer, are observed experimentally to have no barrier which happens when the product potential crosses that of the reactant at its minimum (i.e. between the 'normal' and 'inverted' regions). In fact electron transfer is an interesting case as it is possible to control the barrier height by changing the redox potential. Some atom diatom reactions such as H+F2 also have very very small barriers. Whether you want to call the crossing point a transition state when it has a zero barrier is a moot point. The behaviour is more like water going over a waterfall, so limited by the transport of the wavepacket along the reaction path, rather than sometimes being reflected at the barrier and sometimes crossing.
