cQTP25: A New Exchange-Correlation Functional for Core-Electron Ionization Energy

We present a new exchange-correlation (XC) functional inspired by Correlated Orbital Theory (COT), and designed to enhance the accuracy of core-electron ionization energy predictions as measured by X-ray photoelectron spectroscopy (XPS). This functional, referred to as cQTP25, differs from other Quantum Theory Project (QTP) functionals by optimizing the range-separation parameters through a targeted restriction of the orbital space to core 1s electrons only. We benchmarked cQTP25 against a diverse set of XC functionals spanning multiple rungs of Jacob's ladder in Density Functional Theory (DFT). Performance was evaluated primarily using the relation $IP_{1s} = -\varepsilon_{1s}$, but for completeness, we also computed core ionization potentials using the $\Delta$DFT method. All calculations accounted for both non-relativistic and relativistic corrections. In general, regardless of the computational approach or test set, the results consistently show the same trend: cQTP25 delivers the best performance, followed closely by QTP00 and then QTP17.