Time-resolved pump-probe spectroscopy to follow valence electronic motion in molecules: Theory

Anticipating the experimental realization of attosecond pulses with photon energies of a few hundred eV to 1 keV, we have developed a formalism that connects the evolution of a UV-pumped nonstationary electronic state to an x-ray probe signal, using the one-electron reduced density operator. The electronic states we wish to follow evolve on time scales of a few femtoseconds, and the valence occupancy structure of these states can be probed, resolved in both space and time, by taking advantage of the inherent locality of core-valence transitions and the comparatively short time scale on which they can be produced. The time-dependent reduced density operator is an intuitively simple quantity, representing the dynamic occupancy structure of the valence levels, but it is well defined for an arbitrary many-body state. This article outlines the connection between the complexities of many-body theory and an intuitive picture of dynamic local orbital occupancy.

Figure 1

Electronic excitation dynamics of $\pi$$\to$${\pi }^{*}$ excited 5-fluoro-pent-3-enoic acid (white: H; black: C; purple: F; red: O). At the center of the molecule is a C$=$C bond, where the initial excitation is localized, isolated by two CH${}_2$ linkers; this is a model for a sudden excitation on a chromophore group. The densities of the excited electron (particle) and resulting valence vacancy (hole) are shown evolving in time, using a logarithmic color scale (integrated in the out-of-page direction). The hole is quickly filled by an electron from the electron-rich F atom, oscillating back and forth on a $\sim$1 fs time scale. On a $\sim$3 fs time scale, the excited electron fills the empty space above the electron-deficient carboxylic C atom. At around 3 fs, the charges are maximally separated. (For theory and additional discussion, see [11, 18, 25].)