  The propagation of general electronic quantum states provides information of
the interaction of molecular systems with external driving fields. These can
also offer understandings regarding non-adiabatic quantum phenomena. Well
established methods focus mainly on propagating a quantum system that is
initially described exclusively by the ground state wavefunction. In this work,
we expand a previously developed size-extensive formalism within coupled
cluster theory, called second response theory, so it propagates quantum systems
that are initially described by a general linear combination of different
states, which can include the ground state, and show how with a special set of
time-dependent cluster operators such propagations are performed. Our theory
shows strong consistency with numerically exact results for the determination
of quantum mechanical observables, probabilities, and coherences. We discuss
unperturbed non-stationary states within second response theory and their
ability to predict matrix elements that agree with those found in linear and
quadratic response theories. This work also discusses an approximate
regularized methodology to treat systems with potential instabilities in their
ground-state cluster amplitudes, and compares such approximations with respect
to reference results from standard unitary theory.
