Real-Time Core-Hole Dynamics in X-ray Spectroscopy

Abstract

While experimental developments have enabled the study of core-hole dynamics in X-ray spectroscopy, theoretical methods for dynamical effects are still underdeveloped. Additionally, traditional theoretical methods are in frequency space, in which the study of real-time dynamics does not come naturally. We develop a real-time formalism for calculating ordinary and time-dependent X-ray spectra. While we focus our calculations on ordinary (linear) XAS, we keep our methods sufficiently general that they are readily applied to pumped and nonlinear XAS. We combine DFT, TDDFT, and the Nozières-De Dominicis (ND) formalism to produce a real-time approach to model core-hole dynamics in X-ray spectroscopy. This method is based on a real-time time-correlation function. While the correlation function can be used alone, we also present a further approximation where we obtain the full Green’s function as a convolution of the single-particle photoelectron Green’s function calculated via the correlation function method, and the core-hole Green’s function calculated via a cumulant expansion based approach. The cumulant expansion is obtained from the density response of the valence electrons to the core hole. Calculations for diamond, C<span class="cmr-8">60</span>, and graphite are presented. Our calculations reproduce frequency space calculations based on the ND formalism. However, in our method the photoelectron interacts with dynamic valence electrons, unlike in frequency space methods.