|Rare Events, Transition Pathways and Reaction Rates|
|Consider two local minima A and B on the
multi-dimensional potential energy landscape. A can be taken as the initial
state (in the configuration space) and B be the final state (the algorithm actually
works fine as long as B is on the other side of the line dividing the two basins).
Let be the potential which characterizes
the PES and be a path in
configuration space that connects A and B. This path is parameterized by which can be the
position of the system in the multidimentional as is diffusion PES or size of loop for
a nucleation process. The unit tangent vector is denote by
minimal energy path (MEP)
if at each point on the path the force perpendicular to the path is zero. This means
Here denotes projection to the hyperplane normal to .