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.