GW-BSE X-ray absorption spectra of small molecules: benchmarking approximations and basis sets

The present thesis investigates the calculation of valence and core-level photoabsorption spectra of small molecules within many-body perturbation theory, with a particular focus on the GW approximation and the Bethe-Salpeter equation (BSE). The purpose of this work is to assess the reliability and accuracy of selected computational choices and approximations commonly involved in the description of excited-state properties. The study is carried out on H2O, CH4 and C2H4 using the MOLGW code on the Leonardo supercomputer hosted by CINECA. Starting from a Density Functional Theory description of the electronic structure, quasiparticle energies are computed within the GW approximation for both valence and core levels. Valence spectra are first analysed within the RPA@DFT approximation, in which the screened electron-hole attraction is neglected, and are subsequently compared with full BSE calculations. This comparison highlights the essential role of the attractive electron-hole interaction in determining neutral excitation energies. The convergence of the results and their dependence on the exchange-correlation functional, Gaussian basis set, number of virtual states and treatment of quasiparticle corrections are systematically discussed. The analysis highlights the importance of diffuse basis functions for an accurate description of unoccupied states and shows that the lowest bound excitations converge well with respect to basis-set size. The Tamm-Dancoff and scissor approximations are also examined and compared with the full BSE. The comparison shows that the Tamm-Dancoff approximation closely reproduces the full BSE spectra for the systems considered, whereas a rigid scissor correction provides a more limited description of state-dependent quasiparticle effects. Overall, this work provides a benchmark of GW-BSE calculations for optical and near-edge X-ray absorption spectra of finite molecular systems.