Highly Accurate\nand Robust Constraint-Based Orbital-Optimized\nCore Excitations

We adapt our recently developed constraint-based orbital-optimized\nexcited-state method (COOX) for the computation of core excitations.\nCOOX is a constrained density functional theory (cDFT) approach based\non excitation amplitudes from linear-response time-dependent DFT (LR-TDDFT),\nand has been shown to provide accurate excitation energies and excited-state\nproperties for valence excitations within a spin-restricted formalism.\nTo extend COOX to core-excited states, we introduce a spin-unrestricted\nvariant which allows us to obtain orbital-optimized core excitations\nwith a single constraint. Using a triplet purification scheme in combination\nwith the constrained unrestricted Hartree–Fock formalism, scalar-relativistic\nzero-order regular approximation corrections, and a semiempirical\ntreatment of spin–orbit coupling, COOX is shown to produce\nhighly accurate results for K- and L-edge excitations of second- and\nthird-period atoms with subelectronvolt errors despite being based\non LR-TDDFT, for which core excitations pose a well-known challenge.\nL- and M-edge excitations of heavier atoms up to uranium are also\ncomputationally feasible and numerically stable, but may require more\nadvanced treatment of relativistic effects. Furthermore, COOX is shown\nto perform on par with or better than the popular ΔSCF approach\nwhile exhibiting more robust convergence, highlighting it as a promising\ntool for inexpensive and accurate simulations of X-ray absorption\nspectra.