Emergence of the Molecular Geometric Phase from Exact Electron-Nuclear Dynamics

Geometric phases play a crucial role in diverse fields. In molecules, they appear when a reaction path encircles an intersection between adiabatic potential energy surfaces and the molecular wave function experiences quantum-mechanical interference effects. This intriguing effect, closely resembling the magnetic Aharonov-Bohm effect, crucially relies on the adiabatic description of the dynamics, and it is an open issue whether and how it persists in an exact quantum dynamical framework. Recent works suggest that the molecular geometric phase is an artifact of the adiabatic approximation, thereby challenging the entire concept. Here, building upon a recent investigation (Martinazzo, R.; Burghardt, I. Phys. Rev. Lett. 2024, 132, 243002), we address this issue using the exact factorization of the total wave function. We introduce instantaneous gauge-invariant phases separately for the electrons and nuclei and use them to monitor the phase difference between the trailing edges of a wavepacket encircling a conical intersection between adiabatic surfaces. The transition from the time-dependent open-path phase differences to the closed-path limit is examined, revealing how the phase differences in the electronic and nuclear subspaces compensate for each other upon path closure. In this way, we unambiguously demonstrate the role of the geometric phase in the interference process and shed light on its persistence beyond the adiabatic approximation.