Relativistic fully self-consistent GW for molecules: Total energies and ionization potentials

The fully self-consistent GW (scGW) method with the iterative solution of Dyson equation provides a consistent approach for describing the ground and excited states without any dependence on the mean-field reference. In this work, we present a relativistic version of scGW for molecules containing heavy element using the exact two-component (X2C) Coulomb approximation. We benchmark dataset containing closed shell heavy elements for the first ionization potential using the fully self-consistent GW as well as one-shot GW. The self-consistent GW provides superior result compared to G_0W_0 with PBE reference and comparable to G_0W_0 with PBE0 while also removing the starting point dependence. The photoelectron spectra obtained at the X2C level demonstrate very good agreement with experimental spectra. We also observe that scGW provides very good estimation of ionization potential for the inner d shell orbitals. Additionally, using the well conserved total energy, we investigate the equilibrium bond length and harmonic frequencies of few halogen dimers using scGW. Overall, our findings demonstrate the applicability of the fully self-consistent GW method for accurate ionization potential, photoelectron spectra and total energies in finite systems with heavy elements with a reasonable computational scaling.