Density functional theory is an indispensable theoretical method to study moderate to large systems due to its computational efficiency. Being physically sound, it relies on approximations since the explicit form of the density functional is not known. Most of the standard functionals available on the market have an inherent problem – electrons in the system experience spurious self-interaction. In many applications, this is not critical, but in some cases, it does matter.

A way to overcome it is to calculate exchange energy exactly. However, the perspective strategy is to add this “exact” correction only at long distances. The smooth function switching between short- and long-range behavior is density-dependent and thus varies for different systems. We use a purely first principles procedure on how to determine the parameters of the switching function for the particular system. As an end effect, we correct the orbital energies such that they become better estimates of ionization potentials which has immediate implication for the accuracy of the computed photoelectron spectra.

We have applied this procedure to the prediction of properties of charge-transfer states of photosensitizers and also to photoelectron spectroscopy before. In the recent publication

we systematically analyze the performance of a combination of optimally-tuned density functionals with Dyson orbital approach. Thus, this approach relies on two cornerstones: reliable prediction of ionization energies and more accurate treatment of intensities using Dyson orbital formalism together with TDDFT.

We critically discuss the advantages and disadvantages of this procedure. It should be advisable in cases when the system studied with photoelectron spectroscopy has a non-singlet ground state. In this case, one has two non-equivalent ionization spin-channels which are otherwise unsatisfactorily reproduced. Moreover, TDDFT with the Dyson approach even levels the error of conventional functionals, and the results are not much different from more accurate range-sepated functional. Another two issues which might be problematic for our approach are the stability of the ground state with respect to orbital variations and spin-contamination. The latter one is unavoidable as either a non-ionized or ionized system has open electronic shells and needs to be treated by the unrestricted variant of DFT which introduces this undesirable spin mixing.

The recommendations formulated in this publication should facilitate the practical application of the protocol. Some of the unsolved issues warrant further research.