Molecular Modes of Attosecond Charge Migration

First-principles calculations are employed to elucidate the modes of attosecond charge migration (CM) in halogenated hydrocarbon chains. We use constrained density functional theory (DFT) to emulate the creation of a localized hole on the halogen and follow the subsequent dynamics via time-dependent DFT. We find low-frequency CM modes ($\sim 1\mathrm{eV}$) that propagate across the molecule and study their dependence on length, bond order, and halogenation. We observe that the CM speed ($\sim 4\AA /\mathrm{fs}$) is largely independent of molecule length, but is lower for triple-bonded versus double-bonded molecules. Additionally, as the halogen mass increases, the hole travels in a more particlelike manner as it moves across the molecule. These heuristics will be useful in identifying molecules and optimal CM detection methods for future experiments, especially for halogenated hydrocarbons which are promising targets for ionization-triggered CM.

Figure 1

The effect of molecule length on charge migration in the linear alkyne family. (a)–(d) The time-dependent hole density in (bromoacetylene, bromobutadiyne, bromohexatriyne, and bromooctatetrayne) following sudden ionization from the Br atom. (e)–(h) The intensity of the Fourier transforms of the hole densities. We show the positive part of the hole density integrated over the directions perpendicular to the molecular axis. The inset in (h) shows the computed CM speeds for linear poly-ynes $\mathrm{Br}-{\mathrm{C}}_n\mathrm{H}$, where $n=2$, 4, 6, 8, 10, 12.

Figure 2

Time-dependent perpendicular-integrated hole densities in linear halohydrocarbons as a function of bond order and halogen atomic number ($Z$) following sudden ionization from the halogen. Top left-hand inset: lineout of the hole densities in bromobutadiyne at two extrema of the CM ($A$, hole on terminal $\mathrm{C}\equiv \mathrm{C}$; $B$, hole on Br).