Offset-corrected $\mathrm{\Delta }$-Kohn-Sham scheme for semiempirical prediction of absolute x-ray photoelectron energies in molecules and solids

Absolute binding energies of core electrons in molecules and bulk materials can be efficiently calculated by spin paired density-function theory employing a $\mathrm{\Delta }$-Kohn-Sham $\left(\mathrm{\Delta }\mathrm{KS}\right)$ scheme corrected by offsets that are highly transferable. These offsets depend on core level and atomic species and can be determined by comparing $\mathrm{\Delta }\mathrm{KS}$ energies to experimental molecular x-ray photoelectron spectra. We demonstrate the correct prediction of absolute and relative binding energies on a wide range of molecules, metals, and insulators.

Figure 1

Schematic presentation of x-ray photoelectron spectroscopy and the relevant energy levels in core hole ionization. The core electron binding energy $\text{CEBE}=-E_B$ for molecules and $\text{CEBE}=-E_B^F$ for solids.

Figure 2

Core electron binding energies obtained with the PBE functional compared to experimental values for molecules in the gas phase. The constant offset $\delta$ for each element corresponding to the straight line is given (see text). The exact numbers are listed in the Supplemental Material [36].

Figure 3

(a) Difference between experimental $E_B^{F,\mathrm{expt}}$ and calculated $E_B^{F,\mathrm{calc}}-\delta$ for various solids. The numbers quoted and the shaded area give the PBE band gaps of the respective material. (b) Differences of relative shifts between pairs of elements for a certain compound. Multiple points indicate individual experimental results.