A shortcoming of presently available fragment-based methods is that electron correlation (if included) is described at the level of individual electrons, resulting in many
redundant evaluations of the electronic relaxations associated with any given fluctuation.
A generalized variant of coupled-cluster (CC) theory is described, wherein the degrees of
freedom are fluctuations of fragments between internally correlated states. The effects of
intra-fragment correlation on the inter-fragment interaction is pre-computed and permanently folded into the effective Hamiltonian. This article provides a high-level description
of the CC variant, establishing some useful notation, and it demonstrates the advantage
of the proposed paradigm numerically on model systems. A companion article shows that
the electronic Hamiltonian of real systems may always be cast in the form demanded.
This framework opens a promising path to build finely tunable systematically improvable
methods to capture precise properties of systems interacting with a large number of other