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Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 2 / Section E / 27 / d / Solution 2026-10-20

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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 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.

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.

Figure 1.
Original disconnectivity tree with two-unit superbasin thresholds and single-mode observation-time crossover
. **Details**.

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