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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]
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  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.
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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. https://doi.org/10.1063/1.5008981
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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. https://doi.org/10.1063/1.5008981. https://www.osti.gov/servlets/purl/1511169.
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@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 = {Tue Nov 21 00:00:00 EST 2017},
month = {Tue Nov 21 00:00:00 EST 2017}
}
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Publisher's Version of Record
https://doi.org/10.1063/1.5008981
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Cited by: 29 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 referenced in this record:

Assessment of a long-range corrected hybrid functional
journal, December 2006

  • Vydrov, Oleg A.; Scuseria, Gustavo E.
  • The Journal of Chemical Physics, Vol. 125, Issue 23
  • DOI: 10.1063/1.2409292

Development of exchange-correlation functionals with minimal many-electron self-interaction error
journal, May 2007

  • Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao
  • The Journal of Chemical Physics, Vol. 126, Issue 19
  • DOI: 10.1063/1.2741248

Communication: A density functional with accurate fractional-charge and fractional-spin behaviour for s -electrons
journal, August 2011

  • Johnson, Erin R.; Contreras-García, Julia
  • The Journal of Chemical Physics, Vol. 135, Issue 8
  • DOI: 10.1063/1.3630117

Density-Functional Theory of the Energy Gap
journal, November 1983

Simultaneous Determination of Structures, Vibrations, and Frontier Orbital Energies from a Self-Consistent Range-Separated Hybrid Functional
journal, July 2014

  • Tamblyn, Isaac; Refaely-Abramson, Sivan; Neaton, Jeffrey B.
  • The Journal of Physical Chemistry Letters, Vol. 5, Issue 15
  • DOI: 10.1021/jz5010939

Self-interaction error of local density functionals for alkali–halide dissociation
journal, April 2006

Extended DFT + U + V method with on-site and inter-site electronic interactions
journal, January 2010

Transition-metal dioxides: A case for the intersite term in Hubbard-model functionals
journal, March 2011

  • Kulik, Heather J.; Marzari, Nicola
  • The Journal of Chemical Physics, Vol. 134, Issue 9
  • DOI: 10.1063/1.3559452

Using optimally tuned range separated hybrid functionals in ground-state calculations: Consequences and caveats
journal, May 2013

  • Karolewski, Andreas; Kronik, Leeor; Kümmel, Stephan
  • The Journal of Chemical Physics, Vol. 138, Issue 20
  • DOI: 10.1063/1.4807325

Delocalization error of density-functional approximations: A distinct manifestation in hydrogen molecular chains
journal, December 2012

  • Zheng, Xiao; Liu, Min; Johnson, Erin R.
  • The Journal of Chemical Physics, Vol. 137, Issue 21
  • DOI: 10.1063/1.4768673

A density functional study of the simplest hydrogen abstraction reaction. Effect of self-interaction correction
journal, April 1994

Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities
journal, November 1983

Communication: Two types of flat-planes conditions in density functional theory
journal, July 2016

  • Yang, Xiaotian Derrick; Patel, Anand H. G.; Miranda-Quintana, Ramón Alain
  • The Journal of Chemical Physics, Vol. 145, Issue 3
  • DOI: 10.1063/1.4958636

Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy
journal, December 1982

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
journal, September 2009

  • Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola
  • Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502
  • DOI: 10.1088/0953-8984/21/39/395502

Density functionals for static, dynamical, and strong correlation
journal, February 2013

  • Becke, Axel D.
  • The Journal of Chemical Physics, Vol. 138, Issue 7
  • DOI: 10.1063/1.4790598

Deviations from piecewise linearity in the solid-state limit with approximate density functionals
journal, January 2015

  • Vlček, Vojtěch; Eisenberg, Helen R.; Steinle-Neumann, Gerd
  • The Journal of Chemical Physics, Vol. 142, Issue 3
  • DOI: 10.1063/1.4905236

Perspective: Treating electron over-delocalization with the DFT+U method
journal, June 2015

  • Kulik, Heather J.
  • The Journal of Chemical Physics, Vol. 142, Issue 24
  • DOI: 10.1063/1.4922693

Does a Molecule-Specific Density Functional Give an Accurate Electron Density? The Challenging Case of the CuCl Electric Field Gradient
journal, February 2012

  • Srebro, Monika; Autschbach, Jochen
  • The Journal of Physical Chemistry Letters, Vol. 3, Issue 5
  • DOI: 10.1021/jz201685r

Curvature and Frontier Orbital Energies in Density Functional Theory
journal, December 2012

  • Stein, Tamar; Autschbach, Jochen; Govind, Niranjan
  • The Journal of Physical Chemistry Letters, Vol. 3, Issue 24
  • DOI: 10.1021/jz3015937

Fractional spins and static correlation error in density functional theory
journal, September 2008

  • Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao
  • The Journal of Chemical Physics, Vol. 129, Issue 12
  • DOI: 10.1063/1.2987202

Orbital energies and negative electron affinities from density functional theory: Insight from the integer discontinuity
journal, July 2008

  • Teale, Andrew M.; De Proft, Frank; Tozer, David J.
  • The Journal of Chemical Physics, Vol. 129, Issue 4
  • DOI: 10.1063/1.2961035

Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H2+, He2+, LiH+, and Ne2+
journal, March 2007

  • Ruzsinszky, Adrienn; Perdew, John P.; Csonka, Gábor I.
  • The Journal of Chemical Physics, Vol. 126, Issue 10
  • DOI: 10.1063/1.2566637

Incorrect Dissociation Behavior of Radical Ions in Density Functional Calculations
journal, October 1997

  • Bally, Thomas; Sastry, G. Narahari
  • The Journal of Physical Chemistry A, Vol. 101, Issue 43
  • DOI: 10.1021/jp972378y

Density-functional errors in ionization potential with increasing system size
journal, May 2015

  • Whittleton, Sarah R.; Sosa Vazquez, Xochitl A.; Isborn, Christine M.
  • The Journal of Chemical Physics, Vol. 142, Issue 18
  • DOI: 10.1063/1.4920947

Insights into Current Limitations of Density Functional Theory
journal, August 2008

Where Does the Density Localize? Convergent Behavior for Global Hybrids, Range Separation, and DFT+U
journal, November 2016

  • Gani, Terry Z. H.; Kulik, Heather J.
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 12
  • DOI: 10.1021/acs.jctc.6b00937

Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals
journal, November 2006

  • Ruzsinszky, Adrienn; Perdew, John P.; Csonka, Gábor I.
  • The Journal of Chemical Physics, Vol. 125, Issue 19
  • DOI: 10.1063/1.2387954

Computation of the Hardness and the Problem of Negative Electron Affinities in Density Functional Theory
journal, October 2005

  • Tozer, David J.; De Proft, Frank
  • The Journal of Physical Chemistry A, Vol. 109, Issue 39
  • DOI: 10.1021/jp053504y

Valence electronic structure of cobalt phthalocyanine from an optimally tuned range-separated hybrid functional
journal, July 2017

  • Brumboiu, Iulia Emilia; Prokopiou, Georgia; Kronik, Leeor
  • The Journal of Chemical Physics, Vol. 147, Issue 4
  • DOI: 10.1063/1.4993623

A long-range correction scheme for generalized-gradient-approximation exchange functionals
journal, August 2001

  • Iikura, Hisayoshi; Tsuneda, Takao; Yanai, Takeshi
  • The Journal of Chemical Physics, Vol. 115, Issue 8
  • DOI: 10.1063/1.1383587

Challenges for Density Functional Theory
journal, December 2011

  • Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr200107z

On Koopmans’ theorem in density functional theory
journal, November 2010

  • Tsuneda, Takao; Song, Jong-Won; Suzuki, Satoshi
  • The Journal of Chemical Physics, Vol. 133, Issue 17
  • DOI: 10.1063/1.3491272

Many-electron self-interaction error in approximate density functionals
journal, November 2006

  • Mori-Sánchez, Paula; Cohen, Aron J.; Yang, Weitao
  • The Journal of Chemical Physics, Vol. 125, Issue 20
  • DOI: 10.1063/1.2403848

Many-electron self-interaction and spin polarization errors in local hybrid density functionals
journal, October 2010

  • Haunschild, Robin; Henderson, Thomas M.; Jiménez-Hoyos, Carlos A.
  • The Journal of Chemical Physics, Vol. 133, Issue 13
  • DOI: 10.1063/1.3478534

Delocalization Error and “Functional Tuning” in Kohn–Sham Calculations of Molecular Properties
journal, June 2014

  • Autschbach, Jochen; Srebro, Monika
  • Accounts of Chemical Research, Vol. 47, Issue 8
  • DOI: 10.1021/ar500171t

Fractional charge perspective on the band gap in density-functional theory
journal, March 2008

Long-range corrected hybrid functionals for π-conjugated systems: Dependence of the range-separation parameter on conjugation length
journal, November 2011

  • Körzdörfer, Thomas; Sears, John S.; Sutton, Christopher
  • The Journal of Chemical Physics, Vol. 135, Issue 20
  • DOI: 10.1063/1.3663856

Range-Separation Parameter in Tuned Exchange–Correlation Functionals: Successive Ionizations and the Fukui Function
journal, September 2016

  • Gledhill, Jonathan D.; De Proft, Frank; Tozer, David J.
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 10
  • DOI: 10.1021/acs.jctc.6b00709

One- and many-electron self-interaction error in local and global hybrid functionals
journal, April 2016

Fundamental and excitation gaps in molecules of relevance for organic photovoltaics from an optimally tuned range-separated hybrid functional
journal, August 2011

Electron correlations in narrow energy bands
journal, November 1963

  • Hubbard, J.
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 276, Issue 1365, p. 238-257
  • DOI: 10.1098/rspa.1963.0204

Impact of the Kohn–Sham Delocalization Error on the 4f Shell Localization and Population in Lanthanide Complexes
journal, June 2016

  • Duignan, Thomas J.; Autschbach, Jochen
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 7
  • DOI: 10.1021/acs.jctc.6b00238

A challenge for density functionals: Self-interaction error increases for systems with a noninteger number of electrons
journal, August 1998

  • Zhang, Yingkai; Yang, Weitao
  • The Journal of Chemical Physics, Vol. 109, Issue 7
  • DOI: 10.1063/1.476859

Extreme density-driven delocalization error for a model solvated-electron system
journal, November 2013

  • Johnson, Erin R.; Otero-de-la-Roza, A.; Dale, Stephen G.
  • The Journal of Chemical Physics, Vol. 139, Issue 18
  • DOI: 10.1063/1.4829642

Global and local curvature in density functional theory
journal, August 2016

  • Zhao, Qing; Ioannidis, Efthymios I.; Kulik, Heather J.
  • The Journal of Chemical Physics, Vol. 145, Issue 5
  • DOI: 10.1063/1.4959882

Accurate potential energy surfaces with a DFT+U(R) approach
journal, November 2011

  • Kulik, Heather J.; Marzari, Nicola
  • The Journal of Chemical Physics, Vol. 135, Issue 19
  • DOI: 10.1063/1.3660353

Organic Electronic Materials: Recent Advances in the DFT Description of the Ground and Excited States Using Tuned Range-Separated Hybrid Functionals
journal, April 2014

  • Körzdörfer, Thomas; Brédas, Jean-Luc
  • Accounts of Chemical Research, Vol. 47, Issue 11
  • DOI: 10.1021/ar500021t

Fractional Electron Loss in Approximate DFT and Hartree–Fock Theory
journal, October 2015

  • Peach, Michael J. G.; Teale, Andrew M.; Helgaker, Trygve
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 11
  • DOI: 10.1021/acs.jctc.5b00804
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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
    • DOI: 10.1063/1.5091563

    Describing strong correlation with fractional-spin correction in density functional theory
    journal, September 2018

    • Su, Neil Qiang; Li, Chen; Yang, Weitao
    • Proceedings of the National Academy of Sciences, Vol. 115, Issue 39
    • DOI: 10.1073/pnas.1807095115

    Stable Surfaces That Bind Too Tightly: Can Range-Separated Hybrids or DFT+U Improve Paradoxical Descriptions of Surface Chemistry?
    journal, August 2019

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