cQTP25: A new exchange–correlation functional for core-electron ionization energy

We present a new exchange-correlation (XC) functional inspired by correlated orbital theory and designed to enhance the accuracy of core-electron ionization energy predictions as measured by x-ray photoelectron spectroscopy. 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). The performance was evaluated primarily using the relation IP1s = -ɛ1s, but for completeness, we also computed core ionization potentials using the ΔDFT method. All calculations accounted for both non-relativistic and relativistic corrections. Overall, within Koopmans's framework, the QTP functionals perform best, and specifically cQTP25. The exception is the ΔDFT analysis, where M11, ωB97X, and BHandHLYP are more accurate and cQTP25 ranks fourth.