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Reduced Density Matrix Cumulants: The Combinatorics of Size-Consistency and Generalized Normal Ordering

preprint
submitted on 26.04.2020 and posted on 27.04.2020 by Jonathon Misiewicz, Justin Turney, Henry Schaefer
Reduced density matrix cumulants play key roles in the theory of both reduced density matrices and multiconfigurational normal ordering, but the underlying formalism has remained mysterious. We present a new, simpler generating function for reduced density matrix cumulants that is formally identical to equating the coupled cluster and configuration interaction ansätze. This is shown to be a general mechanism to convert between a multiplicatively separable quantity and an additively separable quantity, as defined by a set of axioms. It is shown that both the cumulants of probability theory and reduced density matrices are entirely combinatorial constructions, where the differences can be associated to changes in the notion of "multiplicative separability'' for expectation values of random variables compared to reduced density matrices. We compare our generating function to that of previous works and criticize previous claims of probabilistic significance of the reduced density matrix cumulants. Finally, we present the simplest proof to date of the Generalized Normal Ordering formalism to explore the role of reduced density matrix cumulants therein.

Funding

Molecular Electronic Structure Theory: Methods and Applications

Directorate for Mathematical & Physical Sciences

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History

Email Address of Submitting Author

jm16657@uga.edu

Institution

University of Georgia

Country

United States

ORCID For Submitting Author

0000-0002-6425-9551

Declaration of Conflict of Interest

no conflict of interest

Version Notes

Initial submission.

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in Journal of Chemical Theory and Computation

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