There is a gap between 177.1-178.2 and between 181.5-182.6, where the QM optimization failed. Checking the plateau and either side of the plateau, what I find is that the plateau structures are all planar, whereas on either side of the plateau, some hydrogens come out of the plane (consistent on both sides of the plateau). For example, this is an overlay of two structures: blue = 178.2° = planar = higher energy. Red = 177.1° = nonplanar Hs = lower in energy. (front view and bottom side view)
Let's assume that the QM calculations are to be trusted (this was run using a few different levels of theory). A mere 1° causes this shift between planarity and nonplanarity. Intuitively, if we think about the ring system being the same in both cases, this makes no sense, as a planar molecule should be better conjugated and thus lower in energy, correct? What other factors might account for this phenomenon?