  The quantum-to-classical correspondence is often quantified in dynamics by a
quantity referred to as the out-of-time-order correlator (OTOC). In chaotic
systems, the OTOC is expected to grow exponentially at early time,
characteristic of a Lyapunov exponent, however, exponential growth can also
occur for integrable systems. Here we investigate the OTOC for realistic
diatomic molecular potentials in one degree of freedom, finding that the OTOC
can grow exponentially near the dissociation energy of the moelcule. Further,
this dynamics is tied to the classical dynamics of the atoms at the outer
classical turning point of the potential. These results should serve to guide
and interpret dynamical chaos in more complex molecules.
