Influence of spin-orbit interaction and self-consistency on quasiparticle electronic structure and exciton optical spectra beyond Tamm-Dancoff: The case of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>BaF</mml:mi> <mml

The electronic and optical properties of the fluorides ${\mathrm{BaF}}_{2}$ and ${\mathrm{SrF}}_{2}$ with heavy metal ions ${\mathrm{Ba}}^{++}$ and ${\mathrm{Sr}}^{++}$, respectively, are studied using advanced theoretical methods across a wide energy range. The single-quasi-particle effects are described within a self-consistent treatment of the exchange-correlation self-energy in the $\mathit{GW}$ approximation. Building on an improved starting point ${G}_{0}{W}_{0}$, where eigenfunctions and eigenvalues are obtained from a generalized Kohn-Sham scheme with the hybrid HSE06 functional, we iterate the eigenvalues in the Green's function ${G}_{n}$ and/or the screened Coulomb potential ${W}_{n}$ until convergence. Gaps are further opened in the self-consistent procedure. Spin-orbit interaction is taken into account. It particularly influences all interband transitions from the Ba $5p$ or Sr $4p$ valence bands into the lowest conduction bands in the photon energy region $15--24\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$. Excitonic effects are included in the calculation of optical spectra by solving the Bethe-Salpeter equation within the $\mathit{GW}$ framework. Moreover, to improve the results, we go beyond the Tamm-Dancoff approximation for the excitonic effects. The comparison with experimental spectra of the real and imaginary parts of the dielectric function shows that the combination of self-consistently treated quasiparticle effects, inclusion of spin-orbit coupling, and electron-hole interaction leads to excellent agreement with the measured spectra. Corrections beyond Tamm-Dancoff improve the spectra in the high-energy region.