The electronic band structure of ${\mathrm{CaSnN}}_2$ in the wurtzite-based $Pna{2}_1$ structure is calculated using the quasiparticle self-consistent$G{W}^{\mathrm{BSE}}$ method, including ladder diagrams in the screened Coulomb interaction $W^{\mathrm{BSE}}$ and is found to have a direct gap of 2.59 eV at $\mathrm{\Gamma }$, which corresponds to blue light wavelength of 478 nm and makes it an attractive candidate for sustainable blue light-emitting diodes, avoiding Ga and In. The valence band splitting is analyzed in terms of symmetry labeling and the effective mass tensor is calculated for several bands at $\mathrm{\Gamma }$. The valence band maximum has $a_1$ symmetry and gives allowed transitions to the conduction band minimum (also of $a_1$ symmetry) for light polarized along the c direction. While this is unfavorable for light emission with transverse electric or $s$ polarization from the basal plane, this would not be an impediment if another surface than the basal plane is used. Furthermore, the crystal field splitting between the $a_1$ and $b_1$ states, corresponding to polarizations along c and a respectively, reverses under an applied uniaxial tensile strain of 3.7% along the c direction, which might occur under biaxial compressive strain in the basal plane. The optical dielectric function including electron-hole interaction effects is also reported and the excitons are analyzed, including several dark excitons.

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• Dielectric properties
• Excitons
• LEDs
• First-principles calculations