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.A.P. is grateful to C. Bostedt for inspiring this project, scientific discussions, and his support. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division and supported by the Argonne group under Contract No. DE-AC02-06CH11357. A.P. also acknowledges support from the European Union’s Horizon 2020 research and innovation program under Marie Sklodowska-Curie Grant Agreement No. 702565