Temporally stable rotational coherent states for molecular simulations. I. Spherical and linear rotor cases

We reformulate a previous rotational coherent state (CS) to obtain temporally stable (TS) CSs for the spherical rotor (SR) and linear rotor (LR): TSSR and TSLR CSs, respectively. Being TS, the new CSs remain within their own classes during dynamics by evolving exclusively through their CS parameters. The new TS CSs are now appropriate to reconstruct quantum rotational properties from classical-mechanics simulations of chemical reactions. Following literature precedents, we enforce temporal stability by incorporating action-angle-related phase factors into the parameters of the original CS. In addition, to elucidate CS quantum reconstruction procedures, we derive one more rotational CS from a quantum electron nuclear dynamics description of a diatomic rotor (DR). The DR CS and the TSLR CS are not identical but display similar structures and properties. We rigorously demonstrate and examine the key properties of the three CSs: continuity, resolution of unity, temporal stability, action identity, minimum uncertainty relationships, and quasi-classical behavior. Finally, we present computer simulations of the CSs dynamics and an application of them to predict CO rotational excitation probabilities in the Li⁺ + CO reaction. CS results agree satisfactorily with experimental ones and encourage future applications in chemical dynamics, statistical mechanics, spectroscopy, nuclear physics, quantum coherence, and quantum computing.