  The formulation of the time-dependent Schrodinger equation in terms of
coupled-cluster theory is outlined, with emphasis on the bivariational
framework and its classical Hamiltonian structure. An indefinite inner product
is introduced, inducing physical interpretation of coupled-cluster states in
the form of transition probabilities, autocorrelation functions, and explicitly
real values for observables, solving interpretation issues which are present in
time-dependent coupled-cluster theory and in ground-state calculations of
molecular systems under influence of external magnetic fields. The problem of
the numerical integration of the equations of motion is considered, and a
critial evaluation of the standard fourth-order Runge--Kutta scheme and the
symplectic Gauss integrator of variable order is given, including several
illustrative numerical experiments. While the Gauss integrator is stable even
for laser pulses well above the perturbation limit, our experiments indicate
that a system-dependent upper limit exists for the external field strengths.
Above this limit, time-dependent coupled-cluster calculations become very
challenging numerically, even in the full configuration interaction limit. The
source of these numerical instabilities is shown to be rapid increases of the
amplitudes as ultrashort high-intensity laser pulses pump the system out of the
ground state into states that are virtually orthogonal to the static
Hartree-Fock reference determinant.
