Can activation energy ever be negative in ordinary scenarios?
Absolutely not. Activation energy is defined as the energy INPUT needed to successfully carry out the reaction. The transition state is always higher in energy than the reactants, with
(Note: do not confuse
#DeltaG^(‡)#as a thermodynamic property; although it is proportional to the activation energy, a kinetic property, #DeltaG_(rxn)#is normally a thermodynamic property, relating the reactants to the products.)
Otherwise, there would exist a reaction that gets stuck in the transition state, which is quite unheard of. Transition states are notorious for being short-lived and thus difficult to detect by experiment.
On the other hand, it is possible that an intermediate is lower in energy than the reactants, but I've only seen that in a step in glycolysis.
At that point, one's body forms a LESS stable, thioester intermediate, to get the reaction to proceed.
However, that is NOT indicative of a negative activation energy. It just means the second activation energy is much larger than the first, both positive.