$\alpha \text{−}{\mathrm{Li}}_x{\mathrm{V}}_2{\mathrm{O}}_5$ is obtained by intercalating Li between the layers of ${\mathrm{V}}_2{\mathrm{O}}_5$. The partial filling of the split-off conduction band by electron donation from Li leads to significant changes in optical properties. Here we study the electronic band structure of $\alpha \text{−}{\mathrm{LiV}}_2{\mathrm{O}}_5$ using quasiparticle self-consistent (QS) $GW$ calculations and the optical dielectric function by means of the Bethe-Salpeter equation (BSE). The half filling of the narrow split-off band leads to a spin splitting and formation of magnetic moments of $0.5{\mu }_B$ per V which order antiferromagnetically along the chain or $b$ direction. The imaginary part of the dielectric function shows a very strong optical absorption band near 2 eV for polarization along the $a$ direction already in the independent particle approximation but redshifted in the BSE. It is about ten times stronger in intensity than the lowest exciton peaks in pure ${\mathrm{V}}_2{\mathrm{O}}_5$ or than the $b$ direction. This absorption stems from a localized transition between the occupied V-$d_{xy}$ derived band, which is odd with respect to the $a$-mirror plane to the higher lying empty band formed from the same V-$d_{xy}$ orbitals but even with respect to that mirror plane, which explains its polarization and large oscillator strength. It is found both for the ferromagnetic and antiferromagnetic arrangement of the spins along the $b$ direction. We relate our main finding to a recent experimental study of cathodoluminescence (CL) in which a suppression of the lowest CL peak was observed upon addition of Li. Based on our and literature results, we present a different interpretation of the CL peaks from that study, which was based on the orbital character in a band-to-band picture. The lowest CL peak near 1.8 eV, which lies well below the indirect absorption onset of ${\mathrm{V}}_2{\mathrm{O}}_5$, is proposed to be related to recombination of a self-trapped electron polaron, resulting from oxygen vacancies, with a hole at the valence band maximum and is suppressed in ${\mathrm{LiV}}_2{\mathrm{O}}_5$ by the strong self-absorption from the Li induced occupied band to the higher empty bands at about the same energy.

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• Electronic structure
• Luminescence
• Optical conductivity
• GW method