$CaF_{2}$ have been determined within a GW approximation, using a PW-PP scheme.[@shirley] On the other hand the imaginary part $Im ~\varepsilon (\omega)$ of the dielectric function has been calculated for $CaF_{2}$ after an iterative procedure using an effective Hamiltonian,[@benedict] within a PW-PP scheme considering a screened interaction for electron-hole (*e-h*) coupling, and using localized orbitals.[@rohlfing]

In this paper the electronic excitations and optical spectra of $CdF_2$ are calculated up to 40 eV employing state-of-the-art techniques based on density functional theory (DFT) and many-body perturbation theory (MBPT). We use the GW scheme proposed by Hedin[@hedin] for the exchange-correlation (XC) self-energy, employing an Heyd-Scuseria-Ernzerhof (HSE)[@hse03] hybrid functional as starting point for the electronic quasiparticle structure to calculate single-particle excitation properties as the energy bands and the DOS. The DOS near the gap region and the energy-band structure are compared with existing data from literature; we show and discuss the comparison with them. The role of many-body effects turns out to be fundamental for these single-particle properties. Moreover, we demonstrate that a simple one-shot GW ($G_{0}W_{0}$) is not sufficient to obtain the correct band gaps. For optical properties excitonic effects, treated within the Bethe-Salpeter equation (BSE)[@onidarubioreining] framework, are crucial to allow a reasonable 