Exploiting the flexibility of intermediate effective Hamiltonians

This paper both recalls and takes a fresh look into the reasons which led to the introduction of the intermediate effective Hamiltonian concept, as well as the degrees of freedom that they leave, and which result in different dressings of the Hamiltonian matrix in the model space. A few types of minimal dressings are discussed. A special attention is paid to state-specific intermediate Hamiltonians, in particular the so-called partitioning technique. The transcriptions of single-reference or multi-reference coupled electron pairs or coupled cluster methods in terms of configuration interaction matrix dressings are reviewed. It is shown that perturbation theory is a relevant guide to decide where to put the effects of the outer space as dressings of the matrix elements of the model space Hamiltonian.