A novel method is presented for time dependent quantum-mechanical
simulations of systems having many degrees of freedom. The method
uses classical Molecular Dynamics as a first step, from which
separable effective single-mode potentials are computed for each
degree of freedom. Single-mode wavepackets ("nuclear orbitals") are
calculated from the effective potential, and the full multidimensional
wavefunction is then constructed from the time-dependent orbitals.
In the present applications the method is not exact, but an
approximation of good accuracy for large realistic systems.
The method was applied to study the dynamics following S->P excitation
of Ba atoms in B(Ar)n clusters. The P states are nearly degenerate in 
this system, and we compute timescales of electronic relaxation, the
electronic orbital reorientation (depolarization), and other aspects of 
the coupled electronic-nuclear dynamics. Results are obtained for clusters
up to n=20, including all degrees of freedom in in 3D geometry. 
Nonadiabatic electronic transitions in the P-state manifold are found to 
become significant around t=1 ps. For the larger clusters (n=20) electronic
relaxation is far more efficient than evaporation of Ba atoms from the
cluster. For the smaller clusters (n=10) the opposite is true. The
semiclassical surface hopping method of Tully is tested against our
quantum calculations: This method is found to be semiquantitatively
very satisfactory, but electronic state populations are off by a factor
of ~2 for t=1.5 ps. The semiclassical method yields good results for the
evolution in time of the structures of the cluster, but is significantly
in error for time-dependent spectroscopic properties.