We calculate differential and integrated cross sections for the Compton interaction as well as mass attenuation (μ/ρ), mass energy-transfer (μ/ρ), and mass energy-absorption (μ/ρ) coefficients, within the relativistic impulse approximation (RIA) using Compton profiles (CPs) obtained from unrestricted Hartree--Fock electron densities. We investigate the impact of using molecular as opposed to atomic CPs on dosimetric photon interaction coefficients for air, water and graphite, and compare our cross sections to the simpler Waller--Hartree (WH) and Klein--Nishina (KN) formalisms. We find that differences in μ/ρ and μ/ρ resulting from the choice of CPs within the RIA are small relative to the differences between the RIA, WH, and KN calculations. Surprisingly, although the WH binding corrections seem accurate when considering μ/ρ, there are significant discrepancies between the WH and RIA results when we look at μ/ρ. The WH theory can differ substantially from the predictions of KN and the RIA in the tens of keV range (e.g., 6-10% at 20 keV), when Compton scattering becomes the dominant interaction mechanism. For lower energies, the disagreement further grows to about one order of magnitude at 1 keV. However, since the photoelectric effect transfers more energy than the Compton interaction in the tens of keV range and below, the differences in the total μ/ρ values resulting from the choice of Compton models (KN, WH, or RIA) are not larger than 0.4%, and the differences between WH and the other two theories are no longer prominent.