The exact forces on classical nuclei in non-adiabatic charge transfer

TL;DR

This paper demonstrates that classical nuclear trajectories on the exact time-dependent potential can closely replicate quantum dynamics in non-adiabatic charge transfer, highlighting the importance of specific features in the potential for accurate wave packet splitting.

Contribution

It shows that classical trajectories on the exact potential can reproduce quantum results and analyzes the potential's features critical for non-adiabatic dynamics.

Findings

Classical trajectories match quantum dynamics in a model non-adiabatic charge transfer.

Step and bump features in the potential are crucial for wave packet splitting.

Preliminary insights into trajectory surface hopping and decoherence effects.

Abstract

The decomposition of electronic and nuclear motion presented in~[A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces, and analyze their structure. Lastly, an analysis of the exact potentials in the context of trajectory surface hopping procedure is presented, including preliminary investigations of velocity-adjustment, and the force-induced decoherence effect.