  In the present work, the electronic and vibrational properties of both
pristine V$_2$C and fully-terminated V$_2$CT$_2$ (where T = F, O, OH) 2D
monolayers are investigated using density functional theory. Firstly, the
atomic structures of V$_2$C-based MXene phases are optimized and their
respective dynamical stabilities are discussed. Secondly, electronic band
structures are computed indicating that V$_2$C is metallic as well as all the
corresponding functionalized systems. Thirdly, the vibrational properties
(phonon frequencies and spectra) of V$_2$C-based MXenes are computed thanks to
density functional perturbation theory and reported for the first time. Both
Raman (E$_g$, A$_{1g}$) and infrared active (E$_u$, A$_{2u}$) vibrational modes
are predicted \textit{ab initio} with the aim to correlate the experimental
Raman peaks with the calculated vibrational modes and to assign them with
specific atomic motions. The effect of the terminal groups on the vibrational
properties is emphasized as well as on the presence and position of the
corresponding Raman peaks. Our results provide new insights for the
identification and characterization of V$_2$C-based samples using Raman
spectroscopy.
