We present a unifying framework for linear response eigenvalue equations that encompasses both
variational Hartree-Fock and Kohn-Sham density functional theory as well as non-variational
coupled-cluster theory. The joint description is rooted in the so-called Hamiltonian structure of the
response kernel matrices, whose properties permit an immediate identification of the well-known
paired eigenvalue spectrum describing a molecule in the isolated state. Recognizing the Hamiltonian
structure underlying the equations further enables a generalization to the case of a polarizableembedded
molecule treated in variational and, in particular, in non-variational theories.
