The equilibrium geometry, the Raman and IR vibrational spectra at the Γ point, TO–LO splitting, IR intensities, Born and dielectric tensors of magnesite MgCO3, dolomite MgCa(CO3)2 and calcite CaCO3 have been calculated with the periodic ab initio program CRYSTAL, by using an all-electron gaussian type basis set and the B3LYP hamiltonian. LO (longitudinal-optical) modes are computed by correcting the dynamical matrix through Born charges and high frequency dielectric tensors obtained from well localized Wannier functions and a saw-tooth computational scheme. The mean absolute difference between calculated and experimental frequencies (IR TO and LO and RAMAN) is as small as 6.9 cm−1 for magnesite, 7.7 cm−1 for dolomite and 8.5 cm−1 for calcite. Calculated IR intensities are in semiquantitative agreement with experiment. The modes of the three compounds are compared through graphical animation available on the CRYSTAL web-site.