  The structural, dielectric and dynamical properties of the low temperature
antiferromagnetic orthorhombic phase of CaMnO$_3$ have been computed from first
principles using a density functional theory approach within the local spin
density approximation. The theoretical structural parameters are in good
agreement with experiment. The full set of infrared and Raman zone-center
phonons is reported and compared to experimental data. It is shown that
coherently with the anomalous Born effective charges and the presence of low
frequency polar modes, the static dielectric constant is very large and highly
anisotropic.
