An approximate quantum dynamical simulation of a large polyatomic system employing a non-empirical potential, which is calculated 'on-the-fly' using a Kohn-Sham approach within the local density approximation is presented. A mean-field calculation based on the classical separable potential (CSP) method for 41 coupled vibrational modes allows for a detailed analysis of the fast dynamics following electron photodetachment in the buckminsterfullerene anion and provides a vibrationally resolved photoelectron spectrum that is in good agreement with experiment.