The process of electron photodetachment in the I-Ar₂ cluster is chosen for testing new approximate quantum dynamical methods - the Classical Separable Potential (CSP) approach and its Configuration Interaction (CI-CSP) extension. The results are encouraging in the sense of a quantitative agreement between the CSP and the established Time-Dependent Self-Consistent Field schemes, and in the fact that inclusion of correlations via the CI-CSP approach brings the results significantly closer to numerically exact ones. These findings justify applying the new methods to fast dynamical processes in moderately quantal large polyatomic systems, where other approaches become computationally extremely demanding or unfeasible.