Rare Events, Transition Pathways and Reaction Rates

 Introduction Zero-TemperatureString Method Finite-TemperatureString Method ModifiedString Method Reference

### Dynamics of String

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 . is a minimal energy path (MEP) if at each point on the path the force perpendicular to the path is zero. This means
 (1)

i.e.

 (2)

Here denotes projection to the hyperplane normal to .