The threshold photodetachment spectra of the ArnI- (n=2-6) anions measured recently by Neumark and co-workers have been simulated semiclassically using the cellularized frozen Gaussian approximation of Walton and Manolopoulos. This is the first time that a semiclassical initial value method has been applied to a series of molecular problems with so many coupled degrees of freedom. It is found that the number of trajectories required for convergence and the absolute error in the semiclassical approximation both increase approximately linearly with the number of degrees of freedom. The simulated photodetachment spectra of the smaller anions Ar2I-, Ar3I-, and Ar4I- are in satisfactory agreement with experiment and the simulated spectra of the larger anions show that the corresponding experimental spectra are dominated by hot bands.