Density-functional theory (DFT) is a well-established and widely used approach to accurately describe many-electron systems, such as single atoms, molecules, crystalline solids and many more. Being exact in principle, DFT always bears an approximation for the exchange-correlation (xc) energy functional, which is responsible for a description of all the quantum interactions between the electrons in the system. The prediction of various physical properties crucially depends on the accuracy of the xc functional put to task.

Unfortunately, functionals that predict thermochemical properties well are known not to describe ionization and photoemission processes via the Kohn-Sham eigenvalues with a comparable quality, and vice versa. With the aim of achieving a reasonable description of thermochemistry and at the same time yielding physically interpretable eigenvalues, we designed an xc functional of the form of a local hybrid. The ansatz was constructed to satisfy exact constraints such as the freedom of self-interaction (SI) for one-electron systems and the correct scaling behavior. The functional, which contains one free parameter, was tested on a set of simple, yet representative systems. Its predictions for binding energies and ionization potentials (IP) according to the IP-theorem are, in dependence on the free parameter, compared to experimental data.