  A global solution of the Schr\"odinger equation, obtained recently within the
wave operator formalism for explicitly time-dependent Hamiltonians [J. Phys. A:
Math. Theor. 48, 225205 (2015)], is generalized to take into account the case
of multidimensional active spaces. An iterative algorithm is derived to obtain
the Fourier series of the evolution operator issuing from a given
multidimensional active subspace and then the effective Hamiltonian
corresponding to the model space is computed and analysed as a measure of the
cyclic character of the dynamics. Studies of the laser controlled dynamics of
diatomic models clearly show that a multidimensional active space is required
if the wavefunction escapes too far from the initial subspace. A suitable
choice of the multidimensional active space, including the initial and target
states, increases the cyclic character and avoids divergences occuring when
one-dimensional active spaces are used. The method is also proven to be
efficient in describing dissipative processes such as photodissociation.
