Spin-Orbit Interactions in Ultrafast Molecular Processes

We investigate spin-orbit interactions in ultrafast molecular processes employing the exact factorization of the electron-nuclear wave function. We revisit the original derivation by including spin-orbit coupling, and show how the dynamics driven by the time-dependent potential energy surface alleviates inconsistencies arising from different electronic representations. We propose a novel trajectory-based scheme to simulate spin-forbidden non-radiative processes, and we show its performance in the treatment of excited-state dynamics where spin-orbit effects couple different spin multiplets.

Figure 1

Singlet and triplet energy curves (black lines) compared with ${\epsilon }_{\mathrm{GI}}(R,t)$ at $t=0$, 129, 248 fs (colored dots). The nuclear densities—divided by 10—at the same times are shown as colored lines. $R_{\sigma }=8.0$ bohr is the position where the SO coupling changes sign.

Figure 2

Left: Singlet and triplet potential curves (black lines) compared to the spin-adiabatic curves (colored lines) for different strengths of the SO coupling. Right: Exact (gray lines) and CT-MQC-SO (colored lines) populations of the singlet (blue) and triplet (light-blue) states.

Figure 3

Spin-adiabatic populations from exact (gray) and CT-MQC-SO (red and orange) calculations for two values of $R_{\sigma }$. Final populations of the singlet ($S$, blue) and triplet ($T$, cyan) states are indicated by the arrows.

Figure 4

Singlet and triplet potential curves (black lines) compared with the exact ${\epsilon }_{\mathrm{GI}}(R,t)$ (purple lines) and with ${\epsilon }_{\mathrm{GI}}^{(\alpha )}(t)$ calculated at the positions of the trajectories (dots) at $t=0$, 129, 248 fs. Colored dots refer to spin-adiabatic results, and gray dots to spin-diabatic results.