All-Electron BSE@ GW Method for K -Edge Core Electron Excitation Energies.

We present an accurate computational approach to calculate absolute K -edge core electron excitation energies as measured by X-ray absorption spectroscopy. Our approach employs an all-electron Bethe-Salpeter equation (BSE) formalism based on GW quasiparticle energies (BSE@ GW ) using numeric atom-centered orbitals (NAOs). The BSE@ GW method has become an increasingly popular method for the computation of neutral valence excitation energies of molecules. However, it was so far not applied to molecular K -edge excitation energies. We discuss the influence of different numerical approximations on the BSE@ GW calculation and employ in our final setup (i) exact numeric algorithms for the frequency integration of the GW self-energy, (ii) G 0 W 0 and BSE starting points with ∼50% of exact exchange, (iii) the Tamm-Dancoff approximation and (iv) relativistic corrections. We study the basis set dependence and convergence with common Gaussian-type orbital and NAO basis sets. We identify the importance of additional spatially confined basis functions as well as of diffuse augmenting basis functions. The accuracy of our BSE@ GW method is assessed for a benchmark set of small organic molecules, previously used for benchmarking the equation-of-motion coupled cluster method [Peng et al., J. Chem. Theory Comput. , 2015 , 11 , 4146], as well as the medium-sized dibenzothiophene (DBT) molecule. Our BSE@ GW results for absolute excitation energies are in excellent agreement with the experiment, with a mean average error of only 0.63 eV for the benchmark set and with errors <1 eV for the DBT molecule.