Using the first-principles Hartree-Fock procedure, the nuclear quadrupole interaction parameters for N-14 nuclei in the ring nitrogens of the RDX molecule are found to have the values 5.671, 5.808, and 5.839 MHz for the quadrupole coupling constants and 0.542, 0.557, and 0.562 for the asymmetry parameters, in good quantitative agreement with the corresponding experimental values 5.735, 5.799, and 5.604 MHz and 0.6215, 0.6146, and 0.6024, respectively, from nuclear quadrupole resonance measurements in the single crystal. Possible reasons for the small but significant difference in trend in the theoretical and experimental nuclear quadrupole interaction parameters over the three ring nitrogen atoms are discussed. The calculated nuclear quadrupole parameters for the N-14 nuclei of the three nitrogens of the three nitro groups and O-17 and H-2 nuclei at the oxygen and hydrogen sites are also presented, with the anticipation that they will be obtained experimentally in the future for comparison with theory to obtain a more complete understanding of the electron distribution over the whole molecule than is presently possible with ring nitrogen data.