Ionized, electron-attached, and excited states of molecular systems with spin-orbit coupling: Two-component GW and Bethe-Salpeter implementations.

We have implemented and applied the GW method and the static screened Bethe-Salpeter equation (BSE) for calculating linear-response properties for quasirelativistic molecular systems. Our ansatz is based on a two-component (2c) scheme that includes spin-orbit coupling as well as scalar relativistic effects. Efficient, state-of-the-art approaches including the analytic continuation (employing Padé approximants, scaling as N  with system size N ) and contour deformation schemes are presented to obtain the required 2c quasirelativistic GW quasiparticle energies. Screened exchange contributions are computed within the resolution-of-the-identity approximation, and working equations for the 2c GW/BSE method are given. The performance of the 2c GW/BSE method is assessed, and results are compared to other methods and experimental data. A robust iterative scheme for solving the eigenvalue problems occurring in the 2c GW/BSE and hybrid time-dependent density functional theories is presented.