Steepest descent path SDP

Because of the Boltzmann distribution the potential energy minima are most important, mainly low-energy ones.  

In a moment we will note a certain disadvantage of the SDP, which causes us to prefer another definition of the reaction path (see p. 781). 

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An alternative approach to MD for modeling kinetics of molecular systems is based on (a) statistical theories of the rate and (b) the concept of a reaction coordinate [2]. The latter is usually identified as the steepest descent path (SDP). The SDP is a curve with a low-energy barrier connecting two minima, a reactant and a product. It provides a qualitative view of the progress of the reaction, along with useful input to theories of rate such as the transition state theory [3]. 

The question we address in the present section is the asymptotic behavior of a trajectory when the step becomes quite large. We are unable to answer that question in a useful way for the SDET algorithm however, an intriguing result is obtained for SDEL. In the present section we will show a connection between SDEL trajectories and the usual definition of the reaction coordinate, the steepest descent path (SDP). 

Equation (4) generates a path in which the force is minimized in all directions but the direction of the path. This is one of the definitions of the Steepest Descent Path (SDP) [57]. This suggests that SDEL provides a physically meaningful result even at low resolution (large step sizes). 

The algorithm produces an interpolation between the steepest descent path (SDP) and a true classical trajectory. Hence, even trajectories with low-resolution can be useful in reaction path studies. 

We define the center of the tube with the help of (1) a guiding trajectory, (2) a steepest descent path (SDP) calculation, (3) and a flexible choice of collective variables. 

Potential Energy Minima and Saddle Points Distinguished Reaction Cowdinate (DRO Steepest Descent Path (SDP)... 

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