Describing strong correlation with fractional-spin correction in density functional theory
Abstract
An effective fractional-spin correction is developed to describe static/strong correlation in density functional theory. Combined with the fractional-charge correction from recently developed localized orbital scaling correction (LOSC), a functional, the fractional-spin LOSC (FSLOSC), is proposed. FSLOSC, a correction to commonly used functional approximations, introduces the explicit derivative discontinuity and largely restores the flat-plane behavior of electronic energy at fractional charges and fractional spins. In addition to improving results from conventional functionals for the prediction of ionization potentials, electron affinities, quasiparticle spectra, and reaction barrier heights, FSLOSC properly describes the dissociation of ionic species, single bonds, and multiple bonds without breaking space or spin symmetry and corrects the spurious fractional-charge dissociation of heteroatom molecules of conventional functionals. Thus, FSLOSC demonstrates success in reducing delocalization error and including strong correlation, within low-cost density functional approximation.
- Authors:
-
- Department of Chemistry, Duke University, Durham, NC 27708,
- Department of Chemistry, Duke University, Durham, NC 27708,, Key Laboratory of Theoretical Chemistry of Environment, School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China
- Publication Date:
- Research Org.:
- Energy Frontier Research Centers (EFRC) (United States). Center for Complex Materials from First Principles (CCM); Temple Univ., Philadelphia, PA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1469268
- Alternate Identifier(s):
- OSTI ID: 1540302
- Grant/Contract Number:
- SC0012575
- Resource Type:
- Published Article
- Journal Name:
- Proceedings of the National Academy of Sciences of the United States of America
- Additional Journal Information:
- Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Volume: 115 Journal Issue: 39; Journal ID: ISSN 0027-8424
- Publisher:
- Proceedings of the National Academy of Sciences
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Citation Formats
Su, Neil Qiang, Li, Chen, and Yang, Weitao. Describing strong correlation with fractional-spin correction in density functional theory. United States: N. p., 2018.
Web. doi:10.1073/pnas.1807095115.
Su, Neil Qiang, Li, Chen, & Yang, Weitao. Describing strong correlation with fractional-spin correction in density functional theory. United States. https://doi.org/10.1073/pnas.1807095115
Su, Neil Qiang, Li, Chen, and Yang, Weitao. Mon .
"Describing strong correlation with fractional-spin correction in density functional theory". United States. https://doi.org/10.1073/pnas.1807095115.
@article{osti_1469268,
title = {Describing strong correlation with fractional-spin correction in density functional theory},
author = {Su, Neil Qiang and Li, Chen and Yang, Weitao},
abstractNote = {An effective fractional-spin correction is developed to describe static/strong correlation in density functional theory. Combined with the fractional-charge correction from recently developed localized orbital scaling correction (LOSC), a functional, the fractional-spin LOSC (FSLOSC), is proposed. FSLOSC, a correction to commonly used functional approximations, introduces the explicit derivative discontinuity and largely restores the flat-plane behavior of electronic energy at fractional charges and fractional spins. In addition to improving results from conventional functionals for the prediction of ionization potentials, electron affinities, quasiparticle spectra, and reaction barrier heights, FSLOSC properly describes the dissociation of ionic species, single bonds, and multiple bonds without breaking space or spin symmetry and corrects the spurious fractional-charge dissociation of heteroatom molecules of conventional functionals. Thus, FSLOSC demonstrates success in reducing delocalization error and including strong correlation, within low-cost density functional approximation.},
doi = {10.1073/pnas.1807095115},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 39,
volume = 115,
place = {United States},
year = {Mon Sep 10 00:00:00 EDT 2018},
month = {Mon Sep 10 00:00:00 EDT 2018}
}
https://doi.org/10.1073/pnas.1807095115
Web of Science
Works referenced in this record:
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
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
Improved Electronic Excitation Energies from Shape-Corrected Semilocal Kohn-Sham Potentials
journal, June 2012
- Gaiduk, Alex P.; Firaha, Dzmitry S.; Staroverov, Viktor N.
- Physical Review Letters, Vol. 108, Issue 25
Full configuration interaction potential energy curves for breaking bonds to hydrogen: An assessment of single-reference correlation methods
journal, January 2003
- Dutta, Antara; Sherrill, C. David
- The Journal of Chemical Physics, Vol. 118, Issue 4
Quest for a universal density functional: the accuracy of density functionals across a broad spectrum of databases in chemistry and physics
journal, March 2014
- Peverati, Roberto; Truhlar, Donald G.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 372, Issue 2011
Quadratic configuration interaction. A general technique for determining electron correlation energies
journal, November 1987
- Pople, John A.; Head‐Gordon, Martin; Raghavachari, Krishnan
- The Journal of Chemical Physics, Vol. 87, Issue 10
Wave function methods for fractional electrons
journal, August 2013
- Steinmann, Stephan N.; Yang, Weitao
- The Journal of Chemical Physics, Vol. 139, Issue 7
Spin in density-functional theory
journal, August 2012
- Jacob, Christoph R.; Reiher, Markus
- International Journal of Quantum Chemistry, Vol. 112, Issue 23
Driven similarity renormalization group: Third-order multireference perturbation theory
journal, March 2017
- Li, Chenyang; Evangelista, Francesco A.
- The Journal of Chemical Physics, Vol. 146, Issue 12
Integration Approach at the Second-Order Perturbation Theory: Applications to Ionization Potential and Electron Affinity Calculations
journal, September 2015
- Su, Neil Qiang; Xu, Xin
- Journal of Chemical Theory and Computation, Vol. 11, Issue 10
Fractional Charge Behavior and Band Gap Predictions with the XYG3 Type of Doubly Hybrid Density Functionals
journal, June 2014
- Su, Neil Qiang; Yang, Weitao; Mori-Sánchez, Paula
- The Journal of Physical Chemistry A, Vol. 118, Issue 39
A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples
journal, February 1982
- Purvis, George D.; Bartlett, Rodney J.
- The Journal of Chemical Physics, Vol. 76, Issue 4
Density functionals for static, dynamical, and strong correlation
journal, February 2013
- Becke, Axel D.
- The Journal of Chemical Physics, Vol. 138, Issue 7
Improving Band Gap Prediction in Density Functional Theory from Molecules to Solids
journal, July 2011
- Zheng, Xiao; Cohen, Aron J.; Mori-Sánchez, Paula
- Physical Review Letters, Vol. 107, Issue 2
Failure of the random-phase-approximation correlation energy
journal, April 2012
- Mori-Sánchez, Paula; Cohen, Aron J.; Yang, Weitao
- Physical Review A, Vol. 85, Issue 4
Fractional-charge and fractional-spin errors in range-separated density-functional theory
journal, August 2016
- Mussard, Bastien; Toulouse, Julien
- Molecular Physics, Vol. 115, Issue 1-2
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
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
Theoretical study of spectroscopic and molecular properties of several low-lying electronic states of CO molecule
journal, February 2012
- Shi, De-Heng; Li, Wen-Tao; Sun, Jin-Feng
- International Journal of Quantum Chemistry, Vol. 113, Issue 7
Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy
journal, December 1982
- Perdew, John P.; Parr, Robert G.; Levy, Mel
- Physical Review Letters, Vol. 49, Issue 23
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
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
Fragment-based treatment of delocalization and static correlation errors in density-functional theory
journal, December 2015
- Nafziger, Jonathan; Wasserman, Adam
- The Journal of Chemical Physics, Vol. 143, Issue 23
Self-Interaction Error in Density Functional Theory: An Appraisal
journal, April 2018
- Bao, Junwei Lucas; Gagliardi, Laura; Truhlar, Donald G.
- The Journal of Physical Chemistry Letters, Vol. 9, Issue 9
Testing exchange–correlation functionals at fractional electron numbers
journal, September 2014
- Malek, Ali; Peng, Degao; Yang, Weitao
- Theoretical Chemistry Accounts, Vol. 133, Issue 10
Polaronic hole localization and multiple hole binding of acceptors in oxide wide-gap semiconductors
journal, August 2009
- Lany, Stephan; Zunger, Alex
- Physical Review B, Vol. 80, Issue 8
Density-Functional Theory of the Energy Gap
journal, November 1983
- Sham, L. J.; Schlüter, M.
- Physical Review Letters, Vol. 51, Issue 20
First-principles calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
journal, March 2011
- Blase, X.; Attaccalite, C.; Olevano, V.
- Physical Review B, Vol. 83, Issue 11
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
Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random-phase approximation
journal, September 2013
- van Aggelen, Helen; Yang, Yang; Yang, Weitao
- Physical Review A, Vol. 88, Issue 3
Generalized Valence Bond Description of the Ground States (X 1 Σ g + ) of Homonuclear Pnictogen Diatomic Molecules: N 2 , P 2 , and As 2
journal, May 2015
- Xu, Lu T.; Dunning, Thom H.
- Journal of Chemical Theory and Computation, Vol. 11, Issue 6
Degenerate Ground States and a Fractional Number of Electrons in Density and Reduced Density Matrix Functional Theory
journal, May 2000
- Yang, Weitao; Zhang, Yingkai; Ayers, Paul W.
- Physical Review Letters, Vol. 84, Issue 22
Koopmans’ condition for density-functional theory
journal, September 2010
- Dabo, Ismaila; Ferretti, Andrea; Poilvert, Nicolas
- Physical Review B, Vol. 82, Issue 11
Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
journal, March 2013
- Kraisler, Eli; Kronik, Leeor
- Physical Review Letters, Vol. 110, Issue 12
Insights into Current Limitations of Density Functional Theory
journal, August 2008
- Cohen, A. J.; Mori-Sanchez, P.; Yang, W.
- Science, Vol. 321, Issue 5890
A density functional for strong correlation in atoms
journal, August 2013
- Johnson, Erin R.
- The Journal of Chemical Physics, Vol. 139, Issue 7
Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities
journal, November 1983
- Perdew, John P.; Levy, Mel
- Physical Review Letters, Vol. 51, Issue 20
Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965
- Kohn, W.; Sham, L. J.
- Physical Review, Vol. 140, Issue 4A, p. A1133-A1138
Linear response approach to the calculation of the effective interaction parameters in the method
journal, January 2005
- Cococcioni, Matteo; de Gironcoli, Stefano
- Physical Review B, Vol. 71, Issue 3
Hubbard-corrected DFT energy functionals: The LDA+U description of correlated systems
journal, July 2013
- Himmetoglu, Burak; Floris, Andrea; de Gironcoli, Stefano
- International Journal of Quantum Chemistry, Vol. 114, Issue 1
Using Wannier functions to improve solid band gap predictions in density functional theory
journal, April 2016
- Ma, Jie; Wang, Lin-Wang
- Scientific Reports, Vol. 6, Issue 1
Fractional charge and spin errors in self-consistent Green’s function theory
journal, May 2015
- Phillips, Jordan J.; Kananenka, Alexei A.; Zgid, Dominika
- The Journal of Chemical Physics, Vol. 142, Issue 19
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
Generalized Kohn-Sham schemes and the band-gap problem
journal, February 1996
- Seidl, A.; Görling, A.; Vogl, P.
- Physical Review B, Vol. 53, Issue 7
Challenges for Density Functional Theory
journal, December 2011
- Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao
- Chemical Reviews, Vol. 112, Issue 1
Tests of functionals for systems with fractional electron number
journal, April 2007
- Vydrov, Oleg A.; Scuseria, Gustavo E.; Perdew, John P.
- The Journal of Chemical Physics, Vol. 126, Issue 15
Real-space post-Hartree–Fock correlation models
journal, February 2005
- Becke, Axel D.
- The Journal of Chemical Physics, Vol. 122, Issue 6
Spin-restricted ensemble-referenced Kohn-Sham method: basic principles and application to strongly correlated ground and excited states of molecules
journal, November 2014
- Filatov, Michael
- Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 5, Issue 1
Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost
journal, November 2017
- Bajaj, Akash; Janet, Jon Paul; Kulik, Heather J.
- The Journal of Chemical Physics, Vol. 147, Issue 19
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
Static correlation and electron localization in molecular dimers from the self-consistent RPA and approximation
journal, April 2015
- Hellgren, Maria; Caruso, Fabio; Rohr, Daniel R.
- Physical Review B, Vol. 91, Issue 16
A real-space model of nondynamical correlation
journal, August 2003
- Becke, Axel D.
- The Journal of Chemical Physics, Vol. 119, Issue 6
Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction
journal, April 2008
- Mori-Sánchez, Paula; Cohen, Aron J.; Yang, Weitao
- Physical Review Letters, Vol. 100, Issue 14
Perspective: Fifty years of density-functional theory in chemical physics
journal, May 2014
- Becke, Axel D.
- The Journal of Chemical Physics, Vol. 140, Issue 18
Discontinuous Nature of the Exchange-Correlation Functional in Strongly Correlated Systems
journal, February 2009
- Mori-Sánchez, Paula; Cohen, Aron J.; Yang, Weitao
- Physical Review Letters, Vol. 102, Issue 6
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
Second-Order Perturbation Theory with Fractional Charges and Fractional Spins
journal, March 2009
- Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao
- Journal of Chemical Theory and Computation, Vol. 5, Issue 4
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
Inhomogeneous Electron Gas
journal, November 1964
- Hohenberg, P.; Kohn, W.
- Physical Review, Vol. 136, Issue 3B, p. B864-B871
Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation
journal, January 1997
- Curtiss, Larry A.; Raghavachari, Krishnan; Redfern, Paul C.
- The Journal of Chemical Physics, Vol. 106, Issue 3
Accurate ab initio potential energy curves and spectroscopic properties of the four lowest singlet states of C2
journal, December 2013
- Boschen, Jeffery S.; Theis, Daniel; Ruedenberg, Klaus
- Theoretical Chemistry Accounts, Vol. 133, Issue 2
Transition state method and Wannier functions
journal, August 2005
- Anisimov, V. I.; Kozhevnikov, A. V.
- Physical Review B, Vol. 72, Issue 7
Photoelectron spectroscopy of free fullerenes
journal, May 1996
- Liebsch, T.; Plotzke, O.; Hentges, R.
- Journal of Electron Spectroscopy and Related Phenomena, Vol. 79
Second-Order Perturbation Theory for Fractional Occupation Systems: Applications to Ionization Potential and Electron Affinity Calculations
journal, April 2016
- Su, Neil Qiang; Xu, Xin
- Journal of Chemical Theory and Computation, Vol. 12, Issue 5
Elimination of the asymptotic fractional dissociation problem in Kohn-Sham density-functional theory using the ensemble-generalization approach
journal, March 2015
- Kraisler, Eli; Kronik, Leeor
- Physical Review A, Vol. 91, Issue 3
Tuned Range-Separated Hybrids in Density Functional Theory
journal, March 2010
- Baer, Roi; Livshits, Ester; Salzner, Ulrike
- Annual Review of Physical Chemistry, Vol. 61, Issue 1
Communication: Simple and accurate uniform electron gas correlation energy for the full range of densities
journal, July 2016
- Chachiyo, Teepanis
- The Journal of Chemical Physics, Vol. 145, Issue 2
Localized orbital scaling correction for systematic elimination of delocalization error in density functional approximations
journal, September 2017
- Li, Chen; Zheng, Xiao; Su, Neil Qiang
- National Science Review, Vol. 5, Issue 2
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
Local Scaling Correction for Reducing Delocalization Error in Density Functional Approximations
journal, February 2015
- Li, Chen; Zheng, Xiao; Cohen, Aron J.
- Physical Review Letters, Vol. 114, Issue 5
Perspective on "Density-functional theory for fractional particle number: derivative discontinuities of the energy"
journal, February 2000
- Zhang, Yingkai; Yang, Weitao
- Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 103, Issue 3-4
Empirical Correction of Nondynamical Correlation Energy for Density Functionals
journal, September 2012
- Jiang, Wanyi; Jeffrey, Chris C.; Wilson, Angela K.
- The Journal of Physical Chemistry A, Vol. 116, Issue 40
Density Functional Model for Nondynamic and Strong Correlation
journal, December 2015
- Kong, Jing; Proynov, Emil
- Journal of Chemical Theory and Computation, Vol. 12, Issue 1
Perspective on density functional theory
journal, April 2012
- Burke, Kieron
- The Journal of Chemical Physics, Vol. 136, Issue 15
Correlation potentials for molecular bond dissociation within the self-consistent random phase approximation
journal, January 2012
- Hellgren, Maria; Rohr, Daniel R.; Gross, E. K. U.
- The Journal of Chemical Physics, Vol. 136, Issue 3
Density Functional Theory in Transition-Metal Chemistry: A Self-Consistent Hubbard Approach
journal, September 2006
- Kulik, Heather J.; Cococcioni, Matteo; Scherlis, Damian A.
- Physical Review Letters, Vol. 97, Issue 10
Koopmans’ springs to life
journal, December 2009
- Salzner, Ulrike; Baer, Roi
- The Journal of Chemical Physics, Vol. 131, Issue 23
Communication: Self-interaction correction with unitary invariance in density functional theory
journal, March 2014
- Pederson, Mark R.; Ruzsinszky, Adrienn; Perdew, John P.
- The Journal of Chemical Physics, Vol. 140, Issue 12