Geometrical picture of the electron–electron correlation at the large-D limit

Ghosh, Kumar B.; Kais, Sabre; Herschbach, Dudley R.

doi:10.1039/d2cp00438k

Title: Geometrical picture of the electron–electron correlation at the large-D limit

Journal Article · Wed Mar 30 04:00:00 UTC 2022 · Physical Chemistry Chemical Physics. PCCP

DOI: https://doi.org/10.1039/d2cp00438k · OSTI ID:1871196

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E.ON Digital Technology GmbH, Essen (Germany); Purdue Univ., West Lafayette, IN (United States); Chemistry Department, Purdue University, West Lafayette, IN (United States)
Purdue Univ., West Lafayette, IN (United States)
Harvard Univ., Cambridge, MA (United States)

In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schrödinger equation. Such an error in the different calculations is not directly observable as there is no simple quantum mechanical operator, apart from correlation functions, that correspond to such quantity. Here, we use the dimensional scaling approach, in which the electrons are localized at the large-dimensional scaled space, to describe a geometric picture of the electronic correlation. Both, the mean field, and the exact solutions at the large-D limit have distinct geometries. Thus, the difference might be used to describe the correlation effect. Moreover, correlations can be also described and quantified by the entanglement between the electrons, which is a strong correlation without a classical analog. Entanglement is directly observable and it is one of the most striking properties of quantum mechanics and bounded by the area law for local gapped Hamiltonians of interacting many-body systems. This study opens up the possibility of presenting a geometrical picture of the electron–electron correlations and might give a bound on the correlation energy. Furthermore, the results at the large-D limit and at D = 3 indicate the feasibility of using the geometrical picture to get a bound on the electron–electron correlations.

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Research Organization:: Purdue Univ., West Lafayette, IN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0019215

OSTI ID:: 1871196

Journal Information:: Physical Chemistry Chemical Physics. PCCP, Journal Name: Physical Chemistry Chemical Physics. PCCP Journal Issue: 16 Vol. 24; ISSN 1463-9076

Publisher:: Royal Society of ChemistryCopyright Statement

Country of Publication:: United States

Language:: English

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