Electron Dynamics upon Ionization of Polyatomic Molecules: Coupling to Quantum Nuclear Motion and Decoherence

Knowledge about the electronic motion in molecules is essential for our understanding of chemical reactions and biological processes. The advent of attosecond techniques opens up the possibility to induce electronic motion, observe it in real time, and potentially steer it. A fundamental question remains the factors influencing electronic decoherence and the role played by nuclear motion in this process. Here, we simulate the dynamics upon ionization of the polyatomic molecules paraxylene and modified bismethylene-adamantane, with a quantum mechanical treatment of both electron and nuclear dynamics using the direct dynamics variational multiconfigurational Gaussian method. Our simulations give new important physical insights about the expected decoherence process. We have shown that the decoherence of electron dynamics happens on the time scale of a few femtoseconds, with the interplay of different mechanisms: the dephasing is responsible for the fast decoherence while the nuclear overlap decay may actually help maintain it and is responsible for small revivals.

Figure 1

Structures of (a) paraxylene and (b) BMA[5,5] molecules. BMA[5,5] is a modified bismethylene-adamantane where the cage consists of four connected cyclopentane (instead of cyclohexane) rings [19].

Figure 2

Electron dynamics in paraxylene cation (at a single fixed nuclear geometry, the equilibrium geometry of the neutral species). (a) The initial electronic wave packet, $1/\sqrt{2}({\varphi }_{s1}+{\varphi }_{s2})$, corresponding to $C=1$ [Eq. (5)], leads to a hole on one side of the phenyl ring. (b) At $t=5.2\mathrm{fs}$, the time-dependent electronic wave packet becomes $1/\sqrt{2}({\varphi }_{s1}-{\varphi }_{s2})$, corresponding to $C=-1$, and leads to a hole on the other side of the phenyl ring. Figure adapted from Ref. [16].

Figure 3

Same as Fig. 2 in BMA[5,5] cation. (a) The initial electronic wave packet, $1/\sqrt{2}({\varphi }_{s1}+{\varphi }_{s2})$, corresponding to $C=1$ [Eq. (5)], leads to a hole on the left carbon double bond. (b) At $t=2.4\mathrm{fs}$, the time-dependent electronic wave packet becomes $1/\sqrt{2}({\varphi }_{s1}-{\varphi }_{s2})$, corresponding to $C=-1$, and leads to a hole on the right carbon double bond. Figure adapted from Ref. [19].

Figure 4

Electron dynamics coupled with quantum nuclear motion in paraxylene cation. (a) The summed electronic coherence $C^{(s_1{s}_2)}$ in the diabatic basis, in simulations with 1 GBF (dashed line) and 17 GBF (solid line). (b) Degree of electronic coherence with $M_{\mathrm{coh}}$ (solid line), where $S$ is set to 1 (dashed line) and $2P^{(s_1)}{P}^{(s_2)}$ (dotted line). The initial electronic wave packet is $1/\sqrt{2}({\varphi }_{s_1}+{\varphi }_{s_2})$. The initial nuclear wave packet is the vibrational ground state of the neutral species.

Figure 5

Same as Fig. 4 in BMA[5,5] cation. The dotted line plotting $2P^{(s_1)}{P}^{(s_2)}$ in (b) stays mostly equal to 0.5.