What is a barrier-less reaction in Quantum Chemistry? After finding a reaction "Transitional State" by GAMESS, and finding Hessian Eigenvalues, my project instructor said:


  seems your imaginary frequency (negative eigenvalue) is not that big (it is around -13.01), which means your reaction is barrier-less.


As I am a beginner in Quantum Chemistry, I could not figure out what is the relation between a small imaginary frequency and being barrier-less. 

As I remember from the Arrhenius equation, being barrier-less has something to do with higher temperature leading to a slower reaction, but I could not understand its relation to imaginary frequencies.
Usually, in the reactions with a barrier, the saddle point with one imaginary frequency is taken as TS. However, many unimolecular dissociation reactions are barrierless: the reaction path on potential surface, connecting (minimum of) reactant with (minima of) products, is such that the energy along the path does not have a local maximum. Kinetic treatments of such reactions are more difficult: it is still possible to assign a TS, but it no longer a saddle point. In order to find it, one can use variational TST, but it is somewhat expensive. 

A general recommendation after location of a saddle point: run reaction path calculation to see that this saddle point indeed connects the products and reactants that you expect. 

About this small eigenvalue: this eigenvalue can easily pop up instead of zero eigenvalues of rotations and translations. Even if your calculation explicitly projects them out, numerical noise can be this order of magnitude (as pointed out above).