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Title: Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost

Abstract

The flat-plane condition is the union of two exact constraints in electronic structure theory: (i) energetic piecewise linearity with fractional electron removal or addition and (ii) invariant energetics with change in electron spin in a half filled orbital. Semi-local density functional theory (DFT) fails to recover the flat plane, exhibiting convex fractional charge errors (FCE) and concave fractional spin errors (FSE) that are related to delocalization and static correlation errors. We previously showed that DFT+U eliminates FCE but now demonstrate that, like other widely employed corrections (i.e., Hartree-Fock exchange), it worsens FSE. To find an alternative strategy, we examine the shape of semi-local DFT deviations from the exact flat plane and we find this shape to be remarkably consistent across ions and molecules. We introduce the judiciously modified DFT (jmDFT) approach, wherein corrections are constructed from few-parameter, low-order functional forms that fit the shape of semi-local DFT errors. Here we select one such physically intuitive form and incorporate it self-consistently to correct semi-local DFT. We demonstrate on model systems that jmDFT represents the first easy-to-implement, no-overhead approach to recovering the flat plane from semi-local DFT.

Authors:
 [1];  [1]; ORCiD logo [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1511169
Alternate Identifier(s):
OSTI ID: 1409703
Grant/Contract Number:  
SC0018096
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 147; Journal Issue: 19; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats

Bajaj, Akash, Janet, Jon Paul, and Kulik, Heather J. Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost. United States: N. p., 2017. Web. doi:10.1063/1.5008981.
Bajaj, Akash, Janet, Jon Paul, & Kulik, Heather J. Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost. United States. doi:10.1063/1.5008981.
Bajaj, Akash, Janet, Jon Paul, and Kulik, Heather J. Tue . "Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost". United States. doi:10.1063/1.5008981. https://www.osti.gov/servlets/purl/1511169.
@article{osti_1511169,
title = {Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost},
author = {Bajaj, Akash and Janet, Jon Paul and Kulik, Heather J.},
abstractNote = {The flat-plane condition is the union of two exact constraints in electronic structure theory: (i) energetic piecewise linearity with fractional electron removal or addition and (ii) invariant energetics with change in electron spin in a half filled orbital. Semi-local density functional theory (DFT) fails to recover the flat plane, exhibiting convex fractional charge errors (FCE) and concave fractional spin errors (FSE) that are related to delocalization and static correlation errors. We previously showed that DFT+U eliminates FCE but now demonstrate that, like other widely employed corrections (i.e., Hartree-Fock exchange), it worsens FSE. To find an alternative strategy, we examine the shape of semi-local DFT deviations from the exact flat plane and we find this shape to be remarkably consistent across ions and molecules. We introduce the judiciously modified DFT (jmDFT) approach, wherein corrections are constructed from few-parameter, low-order functional forms that fit the shape of semi-local DFT errors. Here we select one such physically intuitive form and incorporate it self-consistently to correct semi-local DFT. We demonstrate on model systems that jmDFT represents the first easy-to-implement, no-overhead approach to recovering the flat plane from semi-local DFT.},
doi = {10.1063/1.5008981},
journal = {Journal of Chemical Physics},
number = 19,
volume = 147,
place = {United States},
year = {2017},
month = {11}
}

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Cited by: 5 works
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Figures / Tables:

FIG. 1 FIG. 1: Deviation from linearity (left) and relative FSL energy (right) of PBE (gray squares) and with Ueff = 16 eV (blue circles) for the He+ to He line. The maximum deviation of PBE is annotated. Lines correspond to interpolation of the explicitly calculated points.

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    Works referencing / citing this record:

    Non-empirical, low-cost recovery of exact conditions with model-Hamiltonian inspired expressions in jmDFT
    journal, April 2019

    • Bajaj, Akash; Liu, Fang; Kulik, Heather J.
    • The Journal of Chemical Physics, Vol. 150, Issue 15
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