  We show here that the Hamiltonian for an electronic system may be written
exactly in terms of fluctuation operators that transition constituent fragments
between internally correlated states, accounting rigorously for inter-fragment
electron exchange and charge transfer. Familiar electronic structure approaches
can be applied to the renormalized Hamiltonian. For efficiency, the basis for
each fragment can be truncated, removing high-energy local arrangements of
electrons from consideration, and effectively defining collective coordinates
for the fragments. For a large number of problems (especially for
non-covalently interacting fragments), this has the potential to fold the
majority of electron correlation into the effective Hamiltonian, and it should
provide a robust approach to incorporating difficult electronic structure
problems into large systems. The number of terms in the exactly transformed
Hamiltonian formally scales quartically with system size, but this can be
reduced to quadratic in the mesoscopic regime, to within an arbitrary error
tolerance. Finally, all but a linear-scaling number of these terms may be
efficiently decomposed in terms of electrostatic interactions between a
linear-scaling number of pre-computed transition densities. In a companion
article, this formalism is applied to an excitonic variant of coupled-cluster
theory.
