Many Monte Carlo simulations ignore coherent scattering events and utilise the Klein-Nishina free electron distribution, rather than the incoherent differential cross-section, for choosing the trajectories of incoherently scattered photons. The authors assess the accuracy of this model by comparing its results with those of the complete bound electron model (form factor approach), which simulates coherent scattering events, and uses the appropriate bound electron angular scattering distributions. Both analytic and Monte Carlo calculations demonstrate that use of the free electron scattering distributions significantly underestimates the angular distribution of scattered photon energy resulting from low and medium energy photons incident upon carbon, iron, and platinum barriers. In using the free electron approximations to calculate barrier transmission, significant errors occur only for primary photon energies below 100 keV. Implementation of the complete bound electron model reduces the computational efficiency of the authors' Monte Carlo code by only 10-25%.