An approximate quantum dynamical simulation of a large polyatomic
system employing a non-empirical potential, which is calculated
``on the fly'' using an approximate Kohn--Sham approach within
the local density approximation is presented. A mean-field 
calculation based on the Classical Separable Potential 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 in a very good agreement with experiment.