Electronic and nuclear flux dynamics at a conical intersection

Abstract

A combined electronic-nuclear wave packet motion is accompanied by temporal changes of probability flux densities. Using a two dimensional model, we study such densities in the vicinity of a conical intersection (CI) between the potential energy surfaces of two electronically excited states. When the dynamics is accompanied by an efficient population transfer, the electronic flux density behaves nearly time-independent although the nuclear flux does not. The second case involves a nuclear motion where the CI is surrounded. There, the nuclear wave packet undergoes a bifurcation, and the electronic density shows characteristics of a rotation. The electronic flux, however, exhibits a constant directional dynamics during the nuclear motion. The geometrical phase which appears in comparing the nuclear dynamics derived from the coupled motion and the Born-Oppenheimer calculation is also seen in the nuclear flux dynamics.

High-order geometric integrators for representation-free Ehrenfest dynamics

“…We use the four-dimensional extension [67][68][69] of the Shin-Metiu model 70,71 to demonstrate the geometric and convergence properties of the presented integrators. The system consists of an interacting electron and proton, both moving in two spatial dimensions and feeling an additional field of two fixed protons (all three protons are distinguishable).…”

“…II, that the high-order geometric integrators preserve almost all of the geometric properties of Ehrenfest dynamics, in Sec. III, we numerically demonstrate the efficiency and geometric properties of these integrators on a fourdimensional extension [67][68][69] of the Shin-Metiu model. 70,71 In this system, the first and second excited adiabatic states are coupled significantly due to a conical intersection.…”

Quantum flux densities for electronic–nuclear motion: exact versus Born–Oppenheimer dynamics

“…The flux density is a more sensible quantity than the probability density and it was studied, e.g. in the connection with pericyclic reactions [15,16], electronic ring currents [17,18] and in the vicinity of conical intersections [19]. The flux density was studied, e.g.…”

“…The flux density was studied, e.g. in the connection with pericyclic reactions [15,16], electronic ring currents [17,18] and in the vicinity of conical intersections [19]. Given the probability density, one is able to map a particle's location as a function of time.…”

“…This is more obvious in a configuration space with higher dimension, where the flux density is a vectorial quantity. As an example, it was shown that during the passage of an electron-nuclear wave packet through the position of a conical intersection, the electronic probability density does not exhibit any observable change, whereas the electronic flux density reveals circular motions characteristic for ring currents [19].…”