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. By using the PBEh global hybrid functional and a self-consistent scheme on the eigenvalues in GW, we show a strong dependence of the BSE energy on the starting Kohn-Sham (KS) density functional. This arises from both the quasiparticle energies and the spatial localization of the frozen KS orbitals employed to compute the BSE. In order to address the arbitrariness in the mean field choice, we adopt an orbital-tuning scheme where the amount of Fock exchange, alpha, is tuned to impose that the KS HOMO matches the GW quasiparticle eigenvalue, thus fulfilling the ionization potential theorem in DFT. The performance of the proposed scheme yields excellent results and it is similar to M06-2X and PBEh with alpha = 75%, consistent with tuned values of alpha ranging between 60% and 80%.