Frenkel excitons in LiCoO₂: QSGW calculations including ladder diagrams and BSE approach

While rhombohedral (R-3m) LiCoO₂ has been widely studied in the context of its battery applications, the relation between its band structure and optical properties is not yet clear. The basic understanding is that a gap exists between t_2g filled and e_g empty Co-d states of the octahedral environment and gives rise to optical transitions near 2 eV and with an onset near 1.4 eV, which at first seems reasonably close to the LDA gap of 1.2 eV found in the literature. However, we show that in the much more reliable quasiparticle self-consistent (QS) GW method, the gap is as high as 4.125 eV. In this work, we apply a recently developed QSGW method including ladder-diagram  (electron-hole) corrections to the screening of W, implemented in the linearized muffin-tin orbital basis set. Even this gives a gap or 3.76 eV. However, when the optical dielectric function is calculated at the Bethe Salpeter equation (BSE) level, we find a huge change in the optical response  with exciton binding energies  in excesss of 2 eV. The density of states of BSE eigenvalues as a whole is shifted rigidly from the one-particle joint density of states. The lowest exciton state is found to be dark but several bright peaks exist. The optical spectrum should thus be interpreted in terms of excitons instead of interband transitions. The exciton wavefunctions are found to be very delocalized in  k-space and hence localized in real space and can thus be labeled Frenkel excitons. A systematic study of the dielectric function at different levels of theory is presented.