Density functional theory for core-level X-ray absorption

Abstract: We establish a rigorous density functional theory (DFT) framework for core-level X-ray absorption spectroscopy (XAS) by formulating a constrained search for core-excited states based on the Gunnarsson-Lundqvist theorem. Within this framework, the explicit-core Delta SCF scheme enables shift-free absolute edge alignment and a consistent treatment of L/M edges with spin-orbit-resolved projectors. In addition, by exploiting dipole selection rules, we recast the evaluation of the dipole matrix elements, which otherwise requires many independent Slater determinant calculations, into a compact single determinant form. This reduces the computational scaling from $\mathcal{O}(N^4)$ to $\mathcal{O}(N^3)$, where $N$ is the number of electrons, without introducing additional approximations. Across representative C, B, O, and Li K-edge benchmarks in molecules and solids, the method reproduces line shapes, polarization anisotropies, and absolute onsets without empirical shifts, providing a robust and scalable route to quantitatively reliable XAS simulations within DFT.