10.26434/chemrxiv.5330794.v2
Anthony Dutoi
Yuhong Liu
Excitonic Coupled-cluster Theory: Part II, Electronic Hamiltonian
2017
ChemRxiv
electronic structure theory
large systems
coupled cluster
excitons
electron exchange
Chemistry
2017-08-28 15:09:29
article
https://chemrxiv.org/articles/Excitonic_Coupled-cluster_Theory_Part_II_Electronic_Hamiltonian/5330794
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<div>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.
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