In a one-dimensional model system featuring a drop in dispersion energy, we can identify three possible scenarios, which are illustrated in Figure . In the first scenario, the sharp jump in dispersion energy occurs prior to the energetic minimum in a region with a large potential energy gradient. It is therefore nearly completely absorbed into this gradient and the smoothness of the resulting PES is hardly affected. This optimal case for dispersion energy jumps was observed for D4 in many chemically relevant systems with dispersion-dominated non-bonded interactions such as the T-shaped benzene dimer and the C 2v symmetric H 2 S-naphthalene complex. That will also naturally be the case for essentially all bonded interactions. The second possible scenario is that the drop in dispersion energy occurs close to the potential energy minimum. If the topology around the minimum is steep, the effect of the potential energy drop can be seen in the Hessian at the minimum as well as gradients in its neighborhood; if the minimum is relatively shallow, this drop may completely reshape the local PES, possibly even introducing additional, fictitious local minima and strongly affecting gradients and Hessians around the minimum energy geometry. It is important to note that in some cases where artificial minima were previously identified when using the D3 scheme, the dispersion energy step in D4 has been desirably shifted to the repulsive region of the PES. This adjustment eliminates the appearance of unphysical local minima, though it still introduces artificial curvature in the PES near the equilibrium geometry (Figure ). The last scenario (1c) occurs when the drop in dispersion energy happens well beyond the minimum. While equilibrium properties are again hardly affected, kinetic properties with respect to dissociation, which require accurate gradients in this regime, are significantly disturbed. If the potential energy surface levels off quickly in this region, the dispersion energy bump may also introduce artificial minima here. To explain our amendment to the standard D4 model, we will provide a short overview over its main components. For a more detailed explanation, the reader is referred to Ref. The total D4 dispersion energy E disp is calculated as the sum of the two-body dispersion energy E and the three-body dispersion energy E . The two-body contributions are generated as: