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We present a new model designed to simulate the process of energetic particle precipitation, a vital coupling mechanism from Earth's magnetosphere to its atmosphere. The atmospheric response, namely excess ionization in the upper and middle atmosphere, together with bremsstrahlung X-ray production, is calculated with kinetic particle simulations using the Geant4 Monte Carlo framework. Mono-energy and mono-pitch angle electron beams are simulated and combined using a Green's function approach to represent realistic electron spectra and pitch angle distributions. Results from this model include more accurate ionization profiles than previous analytical models, deeper photon penetration into the atmosphere than previous Monte Carlo model predictions, and predictions of backscatter fractions of loss cone electrons up to 40%. The model results are verified by comparison with previous precipitation modeling results, and validated using balloon X-ray measurements from the Balloon Array for RBSP Relativistic Electron Losses mission and backscattered electron energy and pitch angle measurements from the Electron Loss and Fields Investigation with a Spatio-Temporal Ambiguity-Resolving CubeSat mission. The model results and solution techniques are developed into a Python package for public use.