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The propagation of general electronic quantum states provides information ofthe interaction of molecular systems with external driving fields. These canalso offer understandings regarding non-adiabatic quantum phenomena. Wellestablished methods focus mainly on propagating a quantum system that isinitially described exclusively by the ground state wavefunction. In this work,we expand a previously developed size-extensive formalism within coupledcluster theory, called second response theory, so it propagates quantum systemsthat are initially described by a general linear combination of differentstates, which can include the ground state, and show how with a special set oftime-dependent cluster operators such propagations are performed. Our theoryshows strong consistency with numerically exact results for the determinationof quantum mechanical observables, probabilities, and coherences. We discussunperturbed non-stationary states within second response theory and theirability to predict matrix elements that agree with those found in linear andquadratic response theories. This work also discusses an approximateregularized methodology to treat systems with potential instabilities in theirground-state cluster amplitudes, and compares such approximations with respectto reference results from standard unitary theory.

Second Response Theory: A Theoretical Formalism for the Propagation of Quantum Superpositions