A non-separable method for time-dependent quantum simulations
of large polyatomic systems is presented and applied to the dynamics
of the I2Ar17 cluster, following electronic excitation of the
iodine molecule. The new method is an extension of the 
Classical Separable Potential (CSP) approximation, in which the evolution of
each mode is governed by a time-dependent mean potential due to the other 
modes and the total wavepacket is a product of single mode wavefunctions.
The computational effectiveness of the CSP approach stems from the use
of classical Molecular Dynamics (MD) trajectories, carried out at the outset
of the procedure, for obtaining the effective single-mode potentials.
The present method generalizes the CSP scheme by a Configuration Interaction
(CI) treatment, in which the total wavepacket is represented as a linear
combination of separable terms, with coefficients determined from the
time-dependent Schrodinger equation. The single mode wavefunctions for
each configuration are propagated along effective potentials that are
generated using individual classical trajectories. The classical MD
simulation is also used for simplifying the dynamical equations for the CI
coefficients. Thus, the selection of correlations that are included
quantum mechanically is guided by classical mechanics, which is the
basis for the computational efficiency of this approach.
The CI wavepacket for the I2Ar17 system with 51 vibrational degrees
of freedom was propagated for 500 fs following I2(B<-X)
excitation. About 1500 configurations proved sufficient for convergence
of the CI series. The separable approximation to the wavefunction holds for
60 fs and begins to break down upon the first collision of the iodine
atoms with argons. After the second iodine-argon collision 
this breakdown is almost complete, and at t=500 fs the CSP term represents
less than 5 % of the correlated wavepacket. Both absorption and
resonance Raman spectra are, however, well described by the separable
CSP method, since they are dermined within the first 60 fs.
The CI-CSP method offers very good accuracy due to inclusion of important
correlation effects between different modes, while remaining computationally
feasible for systems up to a hundred degrees of freedom and more.