Classical molecular dynamics (MD) is used to simulate atomic layer etching processes of silicon by alternating exposure to chlorine gas and argon ions. In order to validate our model, a rigorous comparison is done with ion beam experiments found in the literature [Park et al., Jpn. J. Appl. Phys. 44, 389 (2005)]. It is shown that the etch per cycle (EPC) as a function of argon ion energy from simulations is in quantitative agreement with experimental results if the correct argon ion fluence is used in the simulations. The EPC as a function of ion irradiation time and amount of chlorine exposure also show good agreement with the experiment. The MD simulations also show the formation of an amorphous silicon region with chlorine atoms mixed uniformly throughout following ion bombardment. Finally, the etch products during the ion irradiation step are analyzed and discussed.