Modeling L 2,3 -edge X-ray absorption spectroscopy with linear response exact two-component relativistic time-dependent density functional theory

X-ray absorption spectroscopy (XAS) is a powerful tool that can provide physical insights into element-specific chemical processes and reactivities. Although relativistic time-dependent density functional theory (TDDFT) has been previously applied to model the L-edge region in XAS, there has not been a more comprehensive study of the choices of basis sets and density functional kernels available for variational relativistic excited state methods. In this work, we introduce the implementation of the generalized preconditioned locally harmonic residual algorithm to solve the complex-valued relativistic TDDFT for modeling the L-edge X-ray absorption spectra. We investigate the L -edge spectra of a series of molecular complexes using relativistic linear response TDDFT with a hybrid iterative diagonalization algorithm. A systematic error analysis was carried out with a focus on the energetics, intensities, and magnitude of L -L splitting compared to experiments. Additionally, the results from relativistic TDDFT calculations are compared to those computed using other theoretical methods, and the multideterminantal effects on the L-edge XAS were investigated.