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On the assumptions underlying milestoning
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View: Figures


Image of FIG. 1.
FIG. 1.

Schematic of a piece of a long ergodic trajectory crossing a set of three milestones: , , and . In this example, , , , and . The part of the trajectory highlighted in bold contributes to one event counted in and the time contributes to the statistics of . The figure also shows the previous transition event from to , which contributes to with the time contributing to , and the next one from to , which contributes to with the time contributing to .

Image of FIG. 2.
FIG. 2.

Contour plot of the potential (23) with the three milestones , , and ( and are the boundaries of the reactant set and product set where and , respectively, and is the isocommittor surface for this reaction). The minimum energy path is also shown (dot-dashed line). The gray dots are snapshots every along trajectories starting from points distributed on according to Eq. (10), and the predicted density (10) of first hitting points on (thick black line) is compared to the equilibrium density on (dashed line).

Image of FIG. 3.
FIG. 3.

Comparison of the probability density of first hitting points obtained by binning the location where trajectories started from points in distributed according to Eq. (10) hit (black solid curve) with the density [Eq. (10)] (black dashed curve) and with the equilibrium density (gray dot-dashed curve). We also computed the first hitting point density using a long unbiased trajectory and, up to statistical errors, it coincides with the solid curve shown in the figure.

Image of FIG. 4.
FIG. 4.

Contour plot of the potential (23) with superimposed isocommittor surfaces used as milestones: from left to right, these surfaces are , , , , , , , , and .

Image of FIG. 5.
FIG. 5.

Comparison of the probability density (10) (solid line) on the four milestones shown as thick lines in Fig. 4 with the equilibrium probability density (dashed line). The probability densities are plotted as functions of the arc length along the milestones.

Image of FIG. 6.
FIG. 6.

Contour plot of the three-hole potential. We use three milestones, shown as vertical lines and corresponding to (from left to right) , , and . The density (10) (thick solid line) on the surface shows that the lower channel is the preferred one, even though the equilibrium density (thick dashed line) is peaked in the upper channel.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: On the assumptions underlying milestoning