  An implementation of the generalized time-dependent generator coordinated
method (TD-GCM) is developed, that can be applied to the dynamics of small- and
large-amplitude collective motion of atomic nuclei. Both the generator states
and weight functions of the GCM correlated wave function depend on time. The
initial generator states are obtained as solutions of deformation-constrained
self-consistent mean-field equations, and are evolved in time by the standard
mean-field equations of nuclear density functional theory (TD-DFT). The TD-DFT
trajectories are used as a generally non-orthogonal and overcomplete basis in
which the TD-GCM wave function is expanded. The weights, expressed in terms of
a collective wave function, obey a TD-GCM (integral) equation. In this
explorative paper, the generalized TD-GCM is applied to the excitation energies
and spreading width of giant resonances, and to the dynamics of induced
fission. The necessity of including pairing correlations in the basis of TD-DFT
trajectories is demonstrated in the latter example.

Nuclear Theory