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The optical response functions and band structures of LiCoO$_2$ are studiedat different levels of approximation, from density functional theory (DFT) inthe generalized gradient approximation (GGA) to quasiparticle self-consistentQS$GW$ (with $G$ for Green's function and $W$ for screened Coulomb interaction)without and with ladder diagrams (QS$G\hat W$) and the Bethe Salpeter Equation(BSE) approach. The QS$GW$ method is found to strongly overestimate the bandgap and electron-hole or excitonic effects are found to be important. Theylower the quasiparticle gap by only about 11~\% but the lowest energy peaks inabsorption are found to be excitonic in nature. The contributions fromdifferent band to band transitions and the relation of excitons to band-to-bandtransitions are analyzed. The excitons are found to be strongly localized. Acomparison to experimental data is presented.

Optical response and band structure of LiCoO2 including electron-hole interaction effects