Linear-Response and Real-Time Time-Dependent Density Functional Theory Studies of Core-Level Near-Edge X-Ray Absorption.

We discuss our implementation and application of time-dependent density functional theory (TDDFT) to core-level near-edge absorption spectroscopy, using both linear-response (LR) and real-time (RT) approaches. We briefly describe our restricted window TDDFT (REWTDDFT) approach for core excitations which has also been reported by others groups. This is followed by a detailed discussion of real-time TDDFT techniques tailored to core excitations, including obtaining spectral information through delta-function excitation, post-processing time-dependent signals, and resonant excitation through quasi-monochromatic excitation. We present results for the oxygen K-edge of water and carbon dioxide; the carbon K-edge of carbon dioxide; the ruthenium L3-edge for the hexaamminerutheium(III) ion, including scalar relativistic corrections via the zeroth order regular approximation (ZORA); and the carbon and fluorine K-edges for a series of fluorobenzenes. In all cases, the calculated spectra are found to be in good agreement with experiment, requiring only a uniform shift on the order of a few percent. Real-time TDDFT visualization of excited state charge densities are used to visually examine the nature of each excitation, which gives insight into the effects of atoms bound to the absorbing center.