Figure 14.

Alanine dipeptide ring integration. Left panel: Extended structure minimum: 30 rounds of reverse (coarse Euler) ring integration (number of ring nodes N=12) with scaled effective potential steps. Note that the scaled steps correspond to constant steps in free energy only if the effective diffusion tensor is diagonal with identical, constant entries, which appears to be a good approximation here. Eigenvectors corresponding to positive eigenvalues for candidate saddle points determined from ring integration are shown (long red arrows). Right panel: Downhill runs initialized at transition regions suggested by the reverse ring integration from the extended structure minimum. Initial conditions (black dots) are generated by umbrella sampling at a target coarse point selected by perturbation along the unstable eigenvector at the saddle. Final conditions for these downhill runs (red dots) suggest starting points for new rounds of reverse integration from adjacent minima. (1k_BT contour lines used in both plots). Note that both wells are plotted rotated by 90° relative to Fig. 13.