= Solution
A <disconnectivity graph> joins minima when an energy threshold first permits a path between their basins. Taking thresholds in steps of 2 and admitting transition states with energy \b[at most] the threshold gives the following merges:
* $-18$: minima 8 and 9, whose exact connecting barrier is $-19$.
* $-14$: minima 6 and 7.
* $-8$: minima 2 and 3.
* $2$: minima 4 and 5, whose exact barrier is 0.25.
* $6$: the 2–3 and 4–5 groups join through the barrier of 5.
* $8$: the 6–7 group joins the 2–3–4–5 group.
* $10$: minimum 1 joins that group.
* $12$: the 8–9 group joins the rest.
\b[These eight merges connect all nine minima without duplicating a basin.] Minimum endpoints lie at their stated energies; branch heights are the discretized superbasin thresholds, not necessarily the exact saddle energies. If a strictly-less-than threshold convention is used, barriers exactly on a grid line join at the next grid level; the physical connectivity is unchanged.
\Image[/past-exam-of-the-chemistry-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2-disconnectivity.png]
{title=Original disconnectivity tree with two-unit superbasin thresholds and single-mode observation-time crossover}
Back to article page
