A new method for approximate solution of the time-dependent vibrational
Schrodinger equation, applicable to extended molecular systems, is presented. 
The new method is essentially an approximate time-dependent quantization
of classical dynamics. A molecular dynamics simulation is used to obtain
a separable, effective time-dependent potential for each mode, that implicitly
includes also the effects of all the other modes on this degree of freedom.
A time-dependent wave packet is then propagated separately for each mode, using
the corresponding effective potential. The new approximation is valid for
short time scale processes only, but easily applicable to large realistic
systems. Test calculations against exact quantum and time-dependent self-
consistent field (TDSCF) results are carried out for two examples: photodissociation
of HI in the collinear Xe...HI cluster, and electron photodetachment from
the collinear Ar...I-...Ar cluster. For illustration, the new scheme is
also applied to photodetachment from large linear clusters Arn...I-...Arn
(n=2-8) and the results are discussed. For the test systems, the results of
the new method are virtually identical to those following from the computationally
much more demanding TDSCF approach, and they are in excellent agreement with the
exact results.