Correlated three-dimensional electron-nuclear motion: Adiabatic dynamics vs passage of conical intersections

We study the three-dimensional correlated motion of an electron and a proton. In one situation, the dynamics is restricted to the electronic ground state and is, thus, well described within the Born-Oppenheimer (BO) approximation. The probability and flux densities yield information about the coupled dynamics. Because the electronic flux density vanishes if determined from the BO wave function, another flux density is regarded, which provides insight into the directional motion of the electron. This flux density can be calculated within the BO approximation and agrees numerically well with the one derived from the full-dimensional calculation. Starting in the first excited electronic state at a similar geometry as chosen for the ground state dynamics results in a short-time dynamics that takes place in the same regions of the configuration space. Adopting the picture that evolves from the adiabatic expansion of the wave function, the nuclear wave packet motion in the two coupled adiabatic electronic states proceeds through a ring of conical intersections (CIs), which is accompanied by an effective population transfer. Nevertheless, the total nuclear probability and flux densities resemble very much those obtained for the ground state dynamics. While passing the CI, the electronic densities remain nearly constant, as expected for a diabatic dynamics. This confirms the conclusions obtained from our former two-dimensional study, namely, that also in three-dimensional space the wave packet dynamics does not exhibit features of the non-adiabatic dynamics.