Measuring the Kernel of Time-Dependent Density Functional Theory with X-Ray Absorption Spectroscopy of $3d$ Transition Metals

The $2p\mathrm{\text{−}}3d$ core-hole interaction in the $L_{2,3}$ absorption spectra of the $3d$ transition metals is treated within time-dependent density functional theory. A simple three-level model explains the origin of the strong deviations from the one-particle branching ratio and yields matrix elements of the unknown exchange-correlation kernel directly from experiment.

Figure 1

Schematic illustration of the DPA model. The model describes the shifts of the excitation energies (uncorrelated ${\omega }_i$ and correlated ${\Omega }_i$) and the changes in corresponding oscillator strengths $f_i$ in the presence of an excited core hole.

Figure 2

The experimental isotropic absorption spectra (solid line) at the $L_{2,3}$ edges are shown for the early $3d$ TMs Ti, V, and Cr versus Fe. The edge jumps are normalized to unity for direct comparison. The continuum in the experimental spectrum is simulated by a two-step function as shown for Fe (dashed-dotted line). The treatment of the core hole redshifts the independent particle spectrum (dotted line) and changes the statistical branching ratio in the correlated spectrum (dashed line) as revealed by the DPA model.