Systematically Improvable Excitonic Hamiltonians for Electronic Structure Theory

TL;DR

This paper introduces a rigorous method to reformulate electronic Hamiltonians using fluctuation operators for fragments, enabling efficient and scalable electronic structure calculations especially for large, non-covalently bonded systems.

Contribution

It presents a novel exact Hamiltonian transformation based on fluctuation operators, allowing efficient truncation and decomposition for large-scale electronic structure problems.

Findings

Hamiltonian can be exactly expressed with fluctuation operators.

Basis truncation reduces computational complexity.

Decomposition into electrostatic interactions enables linear scaling.

Abstract

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.