The time-dependent Schrödinger equation for a time-periodic perturbation is recasted into a Hermitian eigenvalue equation, where the quasi-energy is an eigenvalue and the time-periodic regular wave function an eigenstate. From this Hermitian eigenvalue equation, a rigorous and transparent formulation of response function theory is developed where (i) molecular properties are defined as derivatives of the quasi-energy with respect to perturbation strengths, (ii) the quasi-energy can be determined from the time-periodic regular wave function using a variational principle or via projection, and (iii) the parametrization of the unperturbed state can differ from the parametrization of the time evolution of this state. This development brings the definition of molecular properties and their determination on par for static and time-periodic perturbations and removes inaccuracies and inconsistencies of previous response function theory formulations. The development where the parametrization of the unperturbed state and its time evolution may differ also extends the range of the wave function models for which response functions can be determined. The simplicity and universality of the presented formulation is illustrated by applying it to the configuration interaction (CI) and the coupled cluster (CC) wave function models and by introducing a new model-the coupled cluster configuration interaction (CC-CI) model-where a coupled cluster exponential parametrization is used for the unperturbed state and a linear parametrization for its time evolution. For static perturbations, the CC-CI response functions are shown to be the analytical analogues of the static molecular properties obtained from finite field equation-of-motion coupled cluster (EOMCC) energy calculations. The structural similarities and differences between the CI, CC, and CC-CI response functions are also discussed with emphasis on linear versus non-linear parametrizations and the size-extensivity of the obtained molecular properties.