Quantum reflection is a pure wave phenomena that predicts reflection of a particle at a changing potential for cases where complete transmission occurs classically. For a chemical bond, we find that this effect can lead to non-classical vibrational turning points and bound states at extremely large interatomic distances. Only recently has the existence of such ultralong-range Rydberg molecules been demonstrated experimentally. Here, we identify a broad range of molecular lines, most of which are shown to originate from two different novel sources: a single-photon associated triatomic molecule formed by a Rydberg atom and two ground state atoms and a series of excited dimer states that are bound by a so far unexplored mechanism based on internal quantum reflection at a steep potential drop. The properties of the Rydberg molecules identified in this work qualify them as prototypes for a new type of chemistry at ultracold temperatures.
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