Assessing the role of the Kohn-Sham density in the calculation of the low-lying Bethe-Salpeter excitation energies

We adopt the GW many-body perturbation theory in conjunction with the Bethe-Salpeter equation (BSE) to compute 57 excitation energies of a set of 37 molecules in order to shed light on the dependence on the initial Kohn-Sham (KS) density functional. By using the PBEh global hybrid and a self-consistent scheme on the eigenvalue, our calculations show a weak correlation between the change in the BSE energies upon variation of the exact exchange fraction (α) and the change in the GW quasiparticle energy of the corresponding electronic levels, pointing to the critical role of the KS electronic density. In order to address the arbitrariness in the mean field choice, we adopt an orbital-tuning scheme where the amount of exact exchange is tuned to fulfill the ionization potential theorem in DFT. The performance of the proposed scheme is found to be similar to M06-2X and PBEh with α=75%, consistent with tuned-values of α ranging between 60% and 80%. Interestingly, the best performers yield systematically smaller errors for n → π∗ excitations than for π → π∗.