Time-dependent Schrödinger equation for molecular core-hole dynamics

X-ray spectroscopy is an important tool for the investigation of matter. X rays primarily interact with inner-shell electrons, creating core (inner-shell) holes that will decay on the time scale of attoseconds to a few femtoseconds through electron relaxations involving the emission of a photon or an electron. The advent of femtosecond x-ray pulses expands x-ray spectroscopy to the time domain and will eventually allow the control of core-hole population on time scales comparable to core-vacancy lifetimes. For both cases, a theoretical approach that accounts for the x-ray interaction while the electron relaxations occur is required. Here we describe a time-dependent framework, based on solving the time-dependent Schrödinger equation, that is suitable for describing the induced electron and nuclear dynamics.

Figure 1

X-ray absorption spectrum for CO in the energy range of the O $1s\to {\pi }^{*}$ resonance. The TDSE-IS was solved for 50-fs x-ray pulses at different photon energies with ${10}^{13}$ W/${\mathrm{cm}}^2$ peak intensity. The vibrational states of the electronic $1s^{-1}{\pi }^{*}$ level is resolved. The experimental data are taken from Ref. [53].

Figure 2

Auger electron spectrum for CO excited at 534.5 eV in the O $1s\to {\pi }^{*}$ resonance. The TDSE-IS was solved for a 50-fs x-ray pulse with ${10}^{13}$ W/${\mathrm{cm}}^2$ peak intensity. The experimental data are taken from Ref. [56].