Excitonic Coupled-cluster Theory: Part II, Electronic Hamiltonian

Generic equations were presented in a companion article for a variant of coupled-cluster theory that operates directly on fragment excitation coordinates (excitonic CC), and its promise was illustrated on model systems. Three conditions were asserted for the excitonic CC framework to be valid and practicable; these concerned (1) the existence of an appropriate fragment-decomposed complete basis, (2) the existence of single-fragment fluctuation operators referencing that basis, and (3) the existence and complexity of the Hamiltonian resolved in terms of strings of those operators. In this article, we take on these assertions specificially for fragment-decomposed electronic systems, proceeding ultimately to explicit recipes for resolving the Hamiltonian in a systematically improvable manner. Though framed in the context of excitonic CC theory, the derivations here are applicable to the general inter-fragment electron-exchange problem. The number of terms in the exactly transformed Hamiltonian formally scales quartically, but this can be reduced to quadratic within an arbitrary error tolerance. The vast majority of these terms are outside of exchange range and may be decomposed efficiently in terms of single-fragment information.