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On the Physical Origin of the 1/4 Exact Exchange in Density Functional Theory

Bernardi, Marco (2018) On the Physical Origin of the 1/4 Exact Exchange in Density Functional Theory. , Pasadena, CA. (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20181112-071407515

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Abstract

We investigate the physical origin of the broadly used 1/4 fraction of exact exchange in density functional theory (DFT)'s hybrid functionals. We compare two models of the exchange energy of an electron pair in an unpolarized electron gas. One model treats the spin states of the electron pair as a statistical ensemble, while the other includes their quantum superposition. The quantum mechanical treatment is shown to possess an exchange energy equal to that of the statistical ensemble, plus an additional 1/4 exact exchange energy due to a spin-flip exchange interaction between electron pair states with antiparallel spin. This exchange interaction originates from the coupling between doubly-excited configurations, and is not explicitly included in semilocal DFT. By showing that the statistical ensemble contains 3/4 of the density-based exchange energy, we can attribute, for each pair of occupied orbitals, the 1/4 exact exchange used in hybrid DFT to the spin-flip exchange processes mentioned above. Practical and conceptual implications of our findings are outlined.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1810.02446arXivDiscussion Paper
Additional Information:M.B. thanks Nicola Marzari and Fernando Brandao for fruitful discussions. M.B. also thanks Megan Schill for discussion and for help with the initial stage of this project. This work was supported by the National Science Foundation under Grant CAREER no. CAREER-1750613.
Funders:
Funding AgencyGrant Number
NSFDMR-1750613
Record Number:CaltechAUTHORS:20181112-071407515
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181112-071407515
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90820
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Nov 2018 19:42
Last Modified:13 Nov 2018 19:42

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