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

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... and the presence of low frequency polar modes, the static dielectric constant is very large and highly anisotropic.