GW-BSE approach on S₁ vertical transition energy of large charge transfer compounds: A performance assessment

In this work, we apply many-body perturbation theory (MBPT) on large critical charge transfer (CT) complexes to assess its performance on the S₁ excitation energy. Since the S₁ energy of CT compounds is heavily dependent on the Hartree-Fock (HF) exchange fraction in the reference density functional, MBPT opens a new way for reliable prediction of CT S₁ energy without explicit knowledge of suitable amount of HF-exchange, in contrary to the time-dependent density functional theory (TD-DFT), where depending on various functionals, large errors can arise. Thus, simply by starting from a (semi-)local reference functional and performing update of Kohn-Sham (KS) energies in the Green's function G while keeping dynamical screened interaction (W(ω)) frozen to the mean-field level, we obtain impressingly highly accurate S₁ energy at slightly higher computational cost in comparison to TD-DFT. However, this energy-only updating mechanism in G fails to work if the initial guess contains a fraction or 100% HF-exchange, and hence considerably inaccurate S₁ energy is predicted. Furthermore, eigenvalue updating both in G and W(ω) overshoots the S₁ energy due to enhanced underscreening of W(ω), independent of the (hybrid-)DFT starting orbitals. A full energy-update on top of HF orbitals even further overestimates the S₁ energy. An additional update of KS wave functions within the Quasi-Particle Self-Consistent GW (QSGW) deteriorates results, in stark contrast to the good results obtained from QSGW for periodic systems. For the sake of transferability, we further present data of small critical non-charge transfer systems, confirming the outcomes of the CT-systems.