The crystallographic structure of switchable mirror material YD₃ is still under debate. Aiming at a final structure assessment, currently considered structure models of P-3c1 , P63cm and P63 symmetry are studied by means of ab initio methods. The relative stability of these candidate structures is investigated by a comparison of total energies, where the structural parameters are derived from experiments, and in addition are calculated by geometry optimization. The P63 structure is found to yield the lowest energy, followed, in this order, by the P63cm and P-3c1 structures. The energy differences between these structures, however, are as small as 0.01 eV per unit cell of six formula units and are thus too small for definitive structure assignments. In addition, electric-field gradients for the D and Y atoms were calculated for the three structures applying the optimized structural parameters, and are compared to experimental data obtained recently by deuteron magnetic resonance for YD₂.₉₈ as well as substitutions for the Y nucleus. Best agreement is observed for the structure with P63cm symmetry. For the P63cm structure we also calculated the band structure and the optical transitions on the basis of the screened-exchange local-density approximation, and obtained a medium-band-gap semiconductor. The relative position of valence and conduction band edge states as well as other states close to the Fermi level seem to be in agreement with available experimental data.