Perhaps the most interesting such case is ozone (O 3 ), which has a vast number of important properties, a very rich history of study 1 , and unlike the relatively simple water molecule, a profound quantum-mechanical complexity . Structurally, while we think of ozone as having two distinct kinds of oxygen atoms (and an NMR experiment would reveal that), the full molecular Hamiltonian does not distinguish between them. Rather, it yields the three equivalent structures separated by a barrier that lies tantalizingly close to the O 3 → O 2 + O dissociation threshold (102.4 kJ/mol) , as shown in Fig. . In reality, the energy levels of ozone all have a near triple (e + a) degeneracy, albeit with a tunneling splitting so small that it can be ignored, along with a semi-infinite lifetime (despite opposing opinion ). More than a half century ago, this intriguing aspect of the ozone molecule was first discussed by Berry . Beyond the structural aspects of ozone, other mysteries surround this curious molecule.