Time-dependent density functional theory for x-ray absorption spectra: Comparing the real-time approach to linear response

We examine the simulation of x-ray absorption spectra at elemental K-edges using time-dependent density functional theory, in both its conventional linear-response implementation and also its "real-time" formulation. Real-time simulations enable broadband x-ray spectra calculations without the need to invoke frozen occupied orbitals or "core/valence separation", but we find that the spectra are frequently contaminated by transitions to the continuum originating from lower-energy core and semi-core orbitals. This problem becomes acute in triple-zeta basis sets although it is sometimes bypassed serendipitously in lower-quality basis sets. Transitions to the continuum acquire surprisingly large dipole oscillator strengths, leading to spectra that are difficult or impossible to interpret. Meaningful spectra can be recovered by means of a filtering technique that decomposes the spectrum into contributions from individual occupied orbitals, and the same procedure can be used to separate L- and K-edge spectra. Nevertheless, the conventional linear-response approach is significantly more efficient even when hundreds of individual states are needed to reproduce near-edge absorption features, and even when Pade approximants are used to reduce the real-time simulations to less than 2 fs of time propagation. The real-time approach may be useful for examining the validity of core/valence separation, however.