More on the multidimensional surface intersection problem and classical trajectory surface hopping

We respond to the previous Comment by Mead and Truhlar pointing out a circularity in our published analysis of a trajectory passing through a locally avoided intersection of potential energy surfaces in a two state system. We did not distinguish clearly in that analysis between properties of the physical system and those of our model for it. Our ''reduction'' to a one-dimensional problem is rather a ''mapping'' onto a one-dimensional model. We present a clearer description of the actual procedures we used to demonstrate that our method is valid for the types of systems to which we have applied it