Identifying the Hamiltonian structure in linear response theory

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.