In this paper we show, based on symmetry considerations, that structural information cannot be obtained from the linear infrared dichroism of the dioxy vibrations of the phosphate group of nucleic acids. Consequently, the discrepancies between the results of x-ray structure measurements and linear dichroism measurements are not meaningful. The linear dichroism measurements are instead important for a calculation of transition dipole moments that involve both the vibrations of all the atoms of the nucleotide and their charges. Independent information on either the atomic displacements contributing to a given vibration or the atomic charges permits a refinement of the unknown quantities. Based on the molecular dynamics calculations of Prohofsky et al., atomic charges of DNA are calculated to reproduce the observed linear dichroism results. Some of the resulting charges are unexpected and may reflect the inadequacy of the molecular dynamic calculation.