I teach physics, and I'm looking for simple, easy examples from chemistry to use in order to illustrate basic ideas about quantum mechanics for my students. A conceptually simple example is the $\text{He}^-$ ion, which has a metastable state with a mean lifetime of 0.36 ms. This is for the totally isolated ion, i.e., we're not talking about a gas or plasma in which there can be collisions or reactions. (How would chemists refer to this? "In vacuo?") This is easy to relate to in chemical terms (a noble gas needs an electron like a fish needs a bicycle) and provides a simple example of quantum mechanical concepts like exponential decay.
What would be more fun for my purposes would be an example of a metastable molecule or molecular ion that would spontaneously break up in two different ways. I would imagine that for the ions, one could measure the half-life and branching ratios by storing them in a circular accelerator. So we could have something like the decay channel
$$\text{XYZ}^+ \rightarrow \text{XY}^+ + \text{Z}$$
competing with, say,
$$\text{XYZ}^+ \rightarrow \text{X}^+ + \text{YZ}.$$
We can then discuss things like the probabilities (branching ratios) and the fact that if the ion starts out in a well-defined state, presumably its ground state, then we can only predict these probabilities, not the actual outcome.
Part of what's making it hard for me to find examples is that I don't know the terminology to google on. Is this "autodetachment," or is that only used for the loss of an electron? "Autodissociation?"
Note: I really am looking for the process described above, not something else like breakup induced by a collision, nuclear decay, electromagnetic decay of an electronic excitation, electron emission, or chemical reactions that require two reactants to come in contact. Those other examples might be fine for some educational purposes, but they're not what this question is about.