All-electron BSE@GW method for K-edge Core Electron Excitation Energy

We present an accurate computational approach to calculate K-edge core electron excitation energies, achieved by combining all-electron GW and Bethe-Salpeter equation (BSE) methods. We assess the BSE@GW approach for calculating K-edge X-ray absorption spectra using a set of small organic molecules and also a medium-sized sulfur-containing molecule, which was used in a past benchmark of an equation-of-motion coupled cluster (EOM-CC) method by Peng and coworkers [Peng et al., J. Chem. Theory Comput., 11, 4146 (2015)]. We present the influence of different numerical approximations on the BSE@GW calculations, including the frequency integration scheme for GW, the Tamm-Dancoff approximation for BSE, and a relativistic correction scheme. We assess the basis set dependence and convergence with the Gaussian type of Dunning's basis sets and numerical atomic-centered basis sets. We identify the importance of core-correlation basis functions as well as the augmenting basis functions. As a result, compared to the experimental values of the absolute core excitation energies, the predicted mean absolute error by BSE@GW is as low as 0.6-0.7 eV.