The advancement in next-generation synchrotrons, 1,2 X-ray free-electron lasers, and tabletop coherent X-ray resources 5 have positioned X-ray spectroscopy at the forefront of characterizing chemical, material, and biological sciences. 6-8 X-ray photoelectron spectroscopy (XPS) is crucial in investigating element-and site-specific geometric and electronic properties. The analysis of XPS relies significantly on determining core-electron binding energies or core-ionization energies. In this regard, ab initio calculations are essential for predicting core-ionization energy and interpreting experimental data. Consequently, a wide variety of methods have been developed and applied in recent years to calculate core-binding energies. The theoretical treatment of core-level spectra poses significant challenges. First, creating a core-hole induces orbital relaxations and polarization effects. Second, core electrons are tightly bound by the nucleus. Therefore, a proper treatment of relativistic effects is necessary, scalar relativistic effects are essential for addressing the K-edge, and spin-orbit coupling for the L-edge. The ∆SCF method is commonly used to determine core ionization energy, calculated as the energy difference between the ground state and the core-ionized states. This approach encounters challenges such as variational collapse and becomes cumbersome for extended and periodic systems. Additionally, calculating transition properties poses difficulties. Timedependent density functional theory (TD-DFT) frequently exhibits significant deviations from experimental values due to the absence of orbital relaxation effects. GW methods and orbital-optimized DFT (OO-DFT) are also used to calculate core excitation or ionization. However, they have shortcomings, such as functional dependence and the need for multiplestate optimization.