
Although the Born-Oppenheimer (adiabatic) approximation provides the most intuitive picture of molecular quantum dynamics in terms of densities/wavepackets moving along uncoupled(!) potential energy surfaces, many chemical reactions, most notably in photochemistry and photobiology are governed by non-adiabatic processes, i. e., they involve nuclear dynamics on (at least!) two different electronic states. This breakdown of the adiabatic approximation occurs most drastically where spectral gaps between electronic eigenstates become sufficiently small or vanish altogether. Prominent examples are (avoided) crossings of potential energy curves (in one dimension) and seams or conical intersections (in two or more dimensions).
Prototypical models
Molecular physics
Wiki: Demos.ConicalInter.Main
Wiki: Demos.CrossingBerlin.Main
Wiki: Demos.CrossingTully.Main
Wiki: Demos.ExcitonPhonon.Main
Wiki: Demos.FemtoChem.Main
Wiki: Demos.MolElectronic.Main