Electronic properties and Raman spectra of rare-earth carbide halides investigated from first principles

${\mathrm{Y}}_2{\mathrm{C}}_2{X}_2$ $(X=\mathrm{Br},\mathrm{I})$ are layered metals, where superconductivity up to 11.6 K has been found. We have investigated these materials by means of first-principles calculations within the full-potential linearized augmented plane wave method based on density functional theory. In particular, we report electronic densities of states (DOS) and electronic band structures for the experimental geometry as well as for the geometry optimized structures. We discuss the peak in the DOS at the Fermi energy that has been suggested to be responsible for the $T_c$ variation in the ${\mathrm{Y}}_2{\mathrm{C}}_2(\mathrm{Br},\mathrm{I}{)}_2$ system when applying pressure or changing the bromine to iodine ratio. Moreover, we study in detail all Raman-active modes of ${\mathrm{Y}}_2{\mathrm{C}}_2{\mathrm{Br}}_2$ and ${\mathrm{Y}}_2{\mathrm{C}}_2{\mathrm{I}}_2,$ where the phonon frequencies are determined within the frozen-phonon approach by carrying out total-energy and atomic-force calculations. The excellent agreement of theoretical and experimental vibrational frequencies together with the calculated Raman intensities allow for a clear assignment of all measured Raman-active modes to $A_g$ and $B_g$ symmetry.