Correlation-driven charge migration following double ionization and attosecond transient absorption spectroscopy

We theoretically investigate charge migration following prompt double ionization. Thereby, we extend the concept of correlation-driven charge migration, which was introduced by Cederbaum and coworkers for single ionization [Chem. Phys. Lett. 307, 205 (1999)], to doubly ionized molecules. This allows us to demonstrate that compared to singly ionized molecules, in multiply ionized molecules, electron dynamics originating from electronic relaxation and correlation are particularly prominent. In addition, we also discuss how these correlation-driven electron dynamics might be evidenced and traced experimentally using attosecond transient absorption spectroscopy. For this purpose, we determine the time-resolved absorption cross section and find that the correlated electron dynamics discussed are reflected in it with exceptionally great detail. Strikingly, we find that features in the cross section can be traced back to electron hole populations and time-dependent partial charges and hence, can be interpreted with surprising ease. By taking advantage of element-specific core-to-valence transitions even atomic spatial resolution can be achieved. Thus, with the theoretical considerations presented, not only do we predict particularly diverse and correlated electron dynamics in molecules to follow prompt multiple ionization but we also identify a promising route towards their experimental investigation.

Figure 1

(a), (b) Spectral decomposition (thick, red bars) of the 2H configuration, in which both holes are in the HOMO orbital, within the respective approximation. (a) Only the subspace spanned by the 2H configurations is considered. (b) The 3H1P configurations are included in the calculation. Thin, gray bars represent the weight of 2H configurations in the dicationic eigenstates. (d), (e) Isosurfaces of the molecular orbitals most prominently involved in the dynamics.

Figure 2

The time-resolved absorption cross section for the situation where at $t=0$, the 2H configuration is prepared in which both holes are in the HOMO. (a) In the calculation, only the subspace spanned by the 2H configurations is taken into account. (b) 3H1P configurations are included in the calculation.

Figure 3

The time-dependent partial charges (dashed lines) obtained by Löwdin population analysis [37] in units of the elementary positive charge and the cross section $\sigma$ in arbitrary units integrated over selected spectral regions (solid lines with markers) perfectly reflecting the hole charge dynamics (see text).

Figure 4

The time-dependent difference iodine partial charge $\mathrm{\Delta }Q$ $[\mathrm{\Delta }Q=Q(t)-Q(t=0)$; $Q$ denotes here the iodine partial charge determined by Löwdin population analysis] obtained from the 3H1P component (dashed, green curve) and, respectively, the 2H component (solid, blue curve) of the coherent superposition of the two dicationic eigenstates that are predominantly populated when the 2H configuration is prepared in which both holes are in the HOMO-5 orbital.

Figure 5

(a) Spectral decomposition (thick, red bars) of the spin-adapted two-hole configuration in which both electron holes are in the HOMO-5 orbital ($|\text{HOMO}-5,\text{HOMO-5}\rangle$) and the weight of the 2H configurations in the dicationic singlet eigenstates (thin, gray bars). (b) The time-dependent populations of Hartree-Fock orbitals by electron holes following the preparation of the state $|\text{HOMO}-5,\text{HOMO-5}\rangle$. (c)–(f) The isosurfaces of the molecular orbitals most prominently populated by electron holes in the course of these dynamics, cf. (b).

Figure 6

The time-resolved absorption cross section for the situation where at $t=0$, the two-hole configuration is prepared in which both holes are in the HOMO-5. Particle-hole excitations are taken into account. Black bars at the right side of the panel reflect the weight of the transitions involved.

Figure 7

The time-resolved absorption cross section $\sigma$ in arbitrary units (see Fig. 6) integrated over selected spectral regions (blue, solid curve) and time-dependent hole populations (red, dotted curves) for the situation where at $t=0$, the two-hole configuration is prepared in which both holes are in the HOMO-5. The time-dependent populations of Hartree-Fock orbitals by electron holes are reflected in the piecewise integrated absorption cross section (see text).

Figure 8

The time-resolved absorption cross section in dependence of the number of virtual orbitals (VO) that are included in the calculation. Here, the situations are considered where (a) two electrons are removed from the HOMO and (b) two electrons are removed from the HOMO-5. Already by inclusion of two virtual orbitals, the features discussed arise. In the paper, we showed the time-resolved absorption cross section obtained from calculations in which four virtual orbitals were included.