Localized intrinsic bond orbitals decode correlated charge migration dynamics

Abstract

For decades, scientists have studied the intricate charge migration dynamics, where after ionization a localized charge distribution ("hole") migrates across the molecule on a femtosecond timescale. This has the potential for controlling electrons in molecules, yet a comprehensive understanding of the many aspects of charge migration is still missing. In this work, we analyze charge migration using an extension of localized intrinsic bond orbitals (IBOs). These orbitals lead to a compact representation of the dynamics and map the complex, correlated many-electron charge migration to chemical concepts such as curly arrows and orbital-orbital interactions. By analyzing multiple challenging scenarios, we show how IBOs enable us to identify key mechanisms in charge migration. For example, we show that different mechanisms are responsible for converting a $π$-shaped hole to a $σ$-shaped hole and vice versa. We explain these in terms of hyperconjugation interactions and configurations that couple orbitals with different symmetries. We further demonstrate how IBOs can be used to find molecules with high charge migration efficiency. We carry out all simulations using an efficient set up of the time-dependent density matrix renormalization group (TDDMRG), correlating as many as 45 electrons in 50 orbitals. We believe that our results will be useful to design future experiments. The proposed IBO analysis is applicable to other types of real-time electron dynamics and spectroscopy.

Figures (8)

• Figure 1: Comparison of global and local symmetries. (a, b) Venn-diagram illustrations of the relationship between the global and local symmetries for the IBOs localized around the C=O bond in furfural. (c) The two mirror planes that define the global ($M_1$) and local ($M_2$) symmetries illustrated in the Venn diagrams. The local symmetries are labeled as $a'(x)$ and $a"(x)$, respectively, where $x$ arbitrarily enumerates them.
• Figure 2: Charge migration analysis of chloroacetylene. (a) Hole density snapshots. Regions with positive (negative) density are shown as green (purple) lobes. (b) Hole density snapshots obtained by projecting the density from (a) to the space of the two dominant IBOs. (c) Hole occupancies of the two IBOs that dominate the hole dynamics. The IBOs are shown on the graph. The times at which the snapshots in (a) are taken are indicated with dashed vertical lines. (d) Absolute value of the autocorrelation function (dark green curve) in comparison to a two-state model (cyan curve). (e)-(i) Orbital densities of the three most dominant (largest absolute eigenvalues) natural charge orbitals at the times of the snapshots in (a). (j) Mapping of IBOs to cationic Lewis structures. (k) Curly-arrow representation of the periodic hole oscillations.
• Figure 3: Charge migration analysis of chlorobutadiyne. (a) Hole density snapshots. The color code is the same as that in \ref{['fig:draft-chloro']}(a). The arrows signify the quasiparticle-like characteristics of the dynamics within the first 2fs. (b) Snapshots of the hole density in (a) projected into the space of the three most dominant IBOs. (c) Sum of hole occupancies within the subspaces of the three dominant IBOs, IBOs, IBOs $\oplus$ cIBOs, and IBOs $\oplus$ cIBOs $\oplus$ oIBOs. (d) Shapes and hole occupancies of the three dominant IBOs. (e) Absolute value of autocorrelation function (dark green) in comparison to a 3-state model (cyan).
• Figure 4: Charge migration analysis of phenylacetaldehyde. (a)-(c) Hole density snapshots for the $\sigma$, $\pi$, and $p$ dynamics, respectively. The color code is the same as that in \ref{['fig:draft-chloro']}(a). (d) Hole occupancies of IBOs localized in the 2-oxoethyl group during the three dynamics. The IBO associated with each hole occupancy and its irrep label are shown in each panel. (e) Hole occupancies of selected $\sigma$ and $\pi$ IBOs localized at the phenyl group. Note that the ordinate range differs from that in (d). (f, g) summed hole occupancies of IBOs within the phenyl ring having $\sigma$ and $\pi$ local symmetries, respectively. This includes IBOs localized at the H atoms and those shown in (e).
• Figure 5: Main IBOs taking part in the hyperconjugation interactions in phenylacetaldehyde. (a) $\pi$, (b) $p$, and (c) $\sigma$ dynamics. The interactions lead to ring $\sigma$ holes in the first and ring $\pi$ holes in the last two dynamics, respectively. The arrows indicate the interactions.