In classical and quantum dynamics for three-body systems with a rotating body frame, it has previously been assumed that for practical purposes the overall rotation and internal motion are decoupled and no geometric phase, e.g., Berry phase, is needed. However, this is not necessarily true for mass combinations other than the heavy-light-heavy combination (of, for example, the ArHCl van der Waals complex). Here, the condition of zero geometric phase produces the corresponding decoupled classical dynamics and decoupled quantum dynamics for arbitrary mass combinations beyond the special heavy-light-heavy combination. The classical dynamics obey Hamilton’s equations, and the quantum dynamics in the Born-Oppenheimer approximation proceed via traveling waves. For a three-body Hamiltonian, a decoupled rotating frame separates overall rotation and internal motion for arbitrary masses, including the heavy-heavy-light combination (of BrBr-He) and the heavy-heavy-heavy combination (of NO2). This model describes the decoupled rotating frame for dynamics observed in spectra of rare gas-diatomic molecule complexes with heavy-light-heavy mass combinations. This model also produces a decoupled rotating frame from a coupled rotating body frame for dynamics observed in triatomic photodissociation with heavy-heavy-heavy mass combinations. The dynamics within the decoupled rotating frame represent the relative dynamics, and their many applications include the internal dynamics of a reaction.

Using geometric phases to separate overall rotation and internal motions in classical and quantum three-body molecular dynamics

2019 Fall National Meeting

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