Delocalization Errors in Density Functional Theory Are Essentially Quadratic in Fractional Occupation Number

Hait, Diptarka; Head-Gordon, Martin

doi:10.1021/acs.jpclett.8b02417

Title: Delocalization Errors in Density Functional Theory Are Essentially Quadratic in Fractional Occupation Number

Journal Article · 11 October 2018 · Journal of Physical Chemistry Letters

DOI: https://doi.org/10.1021/acs.jpclett.8b02417 · OSTI ID:1814748

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Univ. of California, Berkeley, CA (United States)
Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Approximate functionals used in practical density functional theory (DFT) deviate from the piecewise linear behavior of the exact functional for fractional charges. This deviation causes excess charge delocalization, which leads to incorrect densities, molecular properties, barrier heights, band gaps, and excitation energies. Here, we present a simple delocalization function for characterizing this error and find it to be almost perfectly linear vs the fractional electron number for systems spanning in size from the H atom to the C₁₂H₁₄ polyene. This causes the delocalization energy error to be a quadratic polynomial in the fractional electron number, which permits us to assess the comparative performance of 47 popular and recent functionals through the curvature. The quadratic form further suggests that information about a single fractional charge is sufficient to eliminate the principal source of delocalization error. Generalizing traditional two-point information like ionization potentials or electron affinities to account for a third, fractional charge-based data point could therefore permit fitting/tuning of functionals with lower delocalization error.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

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

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1814748

Journal Information:: Journal of Physical Chemistry Letters, Journal Name: Journal of Physical Chemistry Letters Journal Issue: 21 Vol. 9; ISSN 1948-7185

Publisher:: American Chemical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (110)

Semiempirical GGA-type density functional constructed with a long-range dispersion correction Grimme, Stefan Journal of Computational Chemistry, Vol. 27, Issue 15, p. 1787-1799 https://doi.org/10.1002/jcc.20495	journal	January 2006
What do the Kohn-Sham Orbital Energies Mean? How do Atoms Dissociate? Perdew, John P. https://doi.org/10.1007/978-1-4757-0818-9_10	book
The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals Zhao, Yan; Truhlar, Donald G. Theoretical Chemistry Accounts, Vol. 120, Issue 1-3 https://doi.org/10.1007/s00214-007-0310-x	journal	July 2007
The dependence on and continuity of the energy and other molecular properties with respect to the number of electrons Ayers, Paul W. Journal of Mathematical Chemistry, Vol. 43, Issue 1 https://doi.org/10.1007/s10910-006-9195-5	journal	December 2006
A standard grid for density functional calculations Gill, Peter M. W.; Johnson, Benny G.; Pople, John A. Chemical Physics Letters, Vol. 209, Issue 5-6 https://doi.org/10.1016/0009-2614(93)80125-9	journal	July 1993
A fifth-order perturbation comparison of electron correlation theories Raghavachari, Krishnan; Trucks, Gary W.; Pople, John A. Chemical Physics Letters, Vol. 157, Issue 6 https://doi.org/10.1016/S0009-2614(89)87395-6	journal	May 1989
A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) Yanai, Takeshi; Tew, David P.; Handy, Nicholas C. Chemical Physics Letters, Vol. 393, Issue 1-3, p. 51-57 https://doi.org/10.1016/j.cplett.2004.06.011	journal	July 2004
Self-interaction error of local density functionals for alkali–halide dissociation Dutoi, Anthony D.; Head-Gordon, Martin Chemical Physics Letters, Vol. 422, Issue 1-3 https://doi.org/10.1016/j.cplett.2006.02.025	journal	April 2006
Excited-State Geometry Optimization with the Density Matrix Renormalization Group, as Applied to Polyenes Hu, Weifeng; Chan, Garnet Kin-Lic Journal of Chemical Theory and Computation, Vol. 11, Issue 7 https://doi.org/10.1021/acs.jctc.5b00174	journal	June 2015
Reliable Prediction with Tuned Range-Separated Functionals of the Singlet–Triplet Gap in Organic Emitters for Thermally Activated Delayed Fluorescence Sun, Haitao; Zhong, Cheng; Brédas, Jean-Luc Journal of Chemical Theory and Computation, Vol. 11, Issue 8 https://doi.org/10.1021/acs.jctc.5b00431	journal	July 2015
Fractional Electron Loss in Approximate DFT and Hartree–Fock Theory Peach, Michael J. G.; Teale, Andrew M.; Helgaker, Trygve Journal of Chemical Theory and Computation, Vol. 11, Issue 11 https://doi.org/10.1021/acs.jctc.5b00804	journal	October 2015
MN15-L: A New Local Exchange-Correlation Functional for Kohn–Sham Density Functional Theory with Broad Accuracy for Atoms, Molecules, and Solids Yu, Haoyu S.; He, Xiao; Truhlar, Donald G. Journal of Chemical Theory and Computation, Vol. 12, Issue 3 https://doi.org/10.1021/acs.jctc.5b01082	journal	February 2016
Prediction of Excited-State Energies and Singlet–Triplet Gaps of Charge-Transfer States Using a Restricted Open-Shell Kohn–Sham Approach Hait, Diptarka; Zhu, Tianyu; McMahon, David P. Journal of Chemical Theory and Computation, Vol. 12, Issue 7 https://doi.org/10.1021/acs.jctc.6b00426	journal	June 2016
How Accurate Is Density Functional Theory at Predicting Dipole Moments? An Assessment Using a New Database of 200 Benchmark Values Hait, Diptarka; Head-Gordon, Martin Journal of Chemical Theory and Computation, Vol. 14, Issue 4 https://doi.org/10.1021/acs.jctc.7b01252	journal	March 2018
Single-Reference ab Initio Methods for the Calculation of Excited States of Large Molecules Dreuw, Andreas; Head-Gordon, Martin Chemical Reviews, Vol. 105, Issue 11 https://doi.org/10.1021/cr0505627	journal	November 2005
Describing Anions by Density Functional Theory: Fractional Electron Affinity Jensen, Frank Journal of Chemical Theory and Computation, Vol. 6, Issue 9 https://doi.org/10.1021/ct1003324	journal	August 2010
Improved Prediction of Properties of π-Conjugated Oligomers with Range-Separated Hybrid Density Functionals Salzner, Ulrike; Aydin, Aykut Journal of Chemical Theory and Computation, Vol. 7, Issue 8 https://doi.org/10.1021/ct2003447	journal	July 2011
Tuned Range-Separated Time-Dependent Density Functional Theory Applied to Optical Rotation Srebro, Monika; Autschbach, Jochen Journal of Chemical Theory and Computation, Vol. 8, Issue 1 https://doi.org/10.1021/ct200764g	journal	December 2011
Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals Kronik, Leeor; Stein, Tamar; Refaely-Abramson, Sivan Journal of Chemical Theory and Computation, Vol. 8, Issue 5 https://doi.org/10.1021/ct2009363	journal	April 2012
Exchange–Correlation Functional with Good Accuracy for Both Structural and Energetic Properties while Depending Only on the Density and Its Gradient Peverati, Roberto; Truhlar, Donald G. Journal of Chemical Theory and Computation, Vol. 8, Issue 7 https://doi.org/10.1021/ct3002656	journal	June 2012
Reliable Prediction of Charge Transfer Excitations in Molecular Complexes Using Time-Dependent Density Functional Theory Stein, Tamar; Kronik, Leeor; Baer, Roi Journal of the American Chemical Society, Vol. 131, Issue 8 https://doi.org/10.1021/ja8087482	journal	March 2009
Adiabatic Connection for Kinetics Lynch, Benjamin J.; Fast, Patton L.; Harris, Maegan The Journal of Physical Chemistry A, Vol. 104, Issue 21 https://doi.org/10.1021/jp000497z	journal	June 2000
Design of Density Functionals That Are Broadly Accurate for Thermochemistry, Thermochemical Kinetics, and Nonbonded Interactions Zhao, Yan; Truhlar, Donald G. The Journal of Physical Chemistry A, Vol. 109, Issue 25 https://doi.org/10.1021/jp050536c	journal	June 2005
Density Functional for Spectroscopy: No Long-Range Self-Interaction Error, Good Performance for Rydberg and Charge-Transfer States, and Better Performance on Average than B3LYP for Ground States Zhao, Yan; Truhlar, Donald G. The Journal of Physical Chemistry A, Vol. 110, Issue 49 https://doi.org/10.1021/jp066479k	journal	December 2006
Polarization Consistent Basis Sets. 4: The Elements He, Li, Be, B, Ne, Na, Mg, Al, and Ar ^† Jensen, Frank The Journal of Physical Chemistry A, Vol. 111, Issue 44 https://doi.org/10.1021/jp068677h	journal	November 2007
Generalized Gradient Approximation That Recovers the Second-Order Density-Gradient Expansion with Optimized Across-the-Board Performance Peverati, Roberto; Zhao, Yan; Truhlar, Donald G. The Journal of Physical Chemistry Letters, Vol. 2, Issue 16 https://doi.org/10.1021/jz200616w	journal	July 2011
Improving the Accuracy of Hybrid Meta-GGA Density Functionals by Range Separation Peverati, Roberto; Truhlar, Donald G. The Journal of Physical Chemistry Letters, Vol. 2, Issue 21 https://doi.org/10.1021/jz201170d	journal	October 2011
M11-L: A Local Density Functional That Provides Improved Accuracy for Electronic Structure Calculations in Chemistry and Physics Peverati, Roberto; Truhlar, Donald G. The Journal of Physical Chemistry Letters, Vol. 3, Issue 1 https://doi.org/10.1021/jz201525m	journal	December 2011
Does a Molecule-Specific Density Functional Give an Accurate Electron Density? The Challenging Case of the CuCl Electric Field Gradient Srebro, Monika; Autschbach, Jochen The Journal of Physical Chemistry Letters, Vol. 3, Issue 5 https://doi.org/10.1021/jz201685r	journal	February 2012
Curvature and Frontier Orbital Energies in Density Functional Theory Stein, Tamar; Autschbach, Jochen; Govind, Niranjan The Journal of Physical Chemistry Letters, Vol. 3, Issue 24 https://doi.org/10.1021/jz3015937	journal	December 2012
MN15: A Kohn–Sham global-hybrid exchange–correlation density functional with broad accuracy for multi-reference and single-reference systems and noncovalent interactions Yu, Haoyu S.; He, Xiao; Li, Shaohong L. Chemical Science, Vol. 7, Issue 8 https://doi.org/10.1039/C6SC00705H	journal	January 2016
How accurate are static polarizability predictions from density functional theory? An assessment over 132 species at equilibrium geometry Hait, Diptarka; Head-Gordon, Martin Physical Chemistry Chemical Physics, Vol. 20, Issue 30 https://doi.org/10.1039/C8CP03569E	journal	January 2018
Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections Chai, Jeng-Da; Head-Gordon, Martin Physical Chemistry Chemical Physics, Vol. 10, Issue 44 https://doi.org/10.1039/b810189b	journal	January 2008
An improved and broadly accurate local approximation to the exchange–correlation density functional: The MN12-L functional for electronic structure calculations in chemistry and physics Peverati, Roberto; Truhlar, Donald G. Physical Chemistry Chemical Physics, Vol. 14, Issue 38 https://doi.org/10.1039/c2cp42025b	journal	January 2012
Screened-exchange density functionals with broad accuracy for chemistry and solid-state physics Peverati, Roberto; Truhlar, Donald G. Physical Chemistry Chemical Physics, Vol. 14, Issue 47 https://doi.org/10.1039/c2cp42576a	journal	January 2012
ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy Mardirossian, Narbe; Head-Gordon, Martin Physical Chemistry Chemical Physics, Vol. 16, Issue 21 https://doi.org/10.1039/c3cp54374a	journal	January 2014
Hybrid exchange-correlation functional determined from thermochemical data and ab initio potentials Wilson, Philip J.; Bradley, Thomas J.; Tozer, David J. The Journal of Chemical Physics, Vol. 115, Issue 20 https://doi.org/10.1063/1.1412605	journal	November 2001
Polarization consistent basis sets: Principles Jensen, Frank The Journal of Chemical Physics, Vol. 115, Issue 20 https://doi.org/10.1063/1.1413524	journal	November 2001
Polarization consistent basis sets. II. Estimating the Kohn–Sham basis set limit Jensen, Frank The Journal of Chemical Physics, Vol. 116, Issue 17 https://doi.org/10.1063/1.1465405	journal	May 2002
Improving “difficult” reaction barriers with self-interaction corrected density functional theory Patchkovskii, Serguei; Ziegler, Tom The Journal of Chemical Physics, Vol. 116, Issue 18 https://doi.org/10.1063/1.1468640	journal	May 2002
Polarization consistent basis sets. III. The importance of diffuse functions Jensen, Frank The Journal of Chemical Physics, Vol. 117, Issue 20 https://doi.org/10.1063/1.1515484	journal	November 2002
Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange Dreuw, Andreas; Weisman, Jennifer L.; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 119, Issue 6 https://doi.org/10.1063/1.1590951	journal	August 2003
Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes Staroverov, Viktor N.; Scuseria, Gustavo E.; Tao, Jianmin The Journal of Chemical Physics, Vol. 119, Issue 23 https://doi.org/10.1063/1.1626543	journal	December 2003
The impact of the self-interaction error on the density functional theory description of dissociating radical cations: Ionic and covalent dissociation limits Gräfenstein, Jürgen; Kraka, Elfi; Cremer, Dieter The Journal of Chemical Physics, Vol. 120, Issue 2 https://doi.org/10.1063/1.1630017	journal	January 2004
Polarization consistent basis sets. V. The elements Si–Cl Jensen, Frank; Helgaker, Trygve The Journal of Chemical Physics, Vol. 121, Issue 8 https://doi.org/10.1063/1.1756866	journal	August 2004
Development of density functionals for thermochemical kinetics Boese, A. Daniel; Martin, Jan M. L. The Journal of Chemical Physics, Vol. 121, Issue 8 https://doi.org/10.1063/1.1774975	journal	August 2004
Quantifying the effects of the self-interaction error in DFT: When do the delocalized states appear? Lundberg, Marcus; Siegbahn, Per E. M. The Journal of Chemical Physics, Vol. 122, Issue 22 https://doi.org/10.1063/1.1926277	journal	June 2005
Exchange-correlation functional with broad accuracy for metallic and nonmetallic compounds, kinetics, and noncovalent interactions Zhao, Yan; Schultz, Nathan E.; Truhlar, D. G. The Journal of Chemical Physics, Vol. 123, Issue 16 https://doi.org/10.1063/1.2126975	journal	October 2005
Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group Hachmann, Johannes; Cardoen, Wim; Chan, Garnet Kin-Lic The Journal of Chemical Physics, Vol. 125, Issue 14 https://doi.org/10.1063/1.2345196	journal	October 2006
A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions Zhao, Yan; Truhlar, Donald G. The Journal of Chemical Physics, Vol. 125, Issue 19, Article No. 194101 https://doi.org/10.1063/1.2370993	journal	November 2006
Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals Ruzsinszky, Adrienn; Perdew, John P.; Csonka, Gábor I. The Journal of Chemical Physics, Vol. 125, Issue 19 https://doi.org/10.1063/1.2387954	journal	November 2006
Many-electron self-interaction error in approximate density functionals Mori-Sánchez, Paula; Cohen, Aron J.; Yang, Weitao The Journal of Chemical Physics, Vol. 125, Issue 20 https://doi.org/10.1063/1.2403848	journal	November 2006
Influence of the exchange screening parameter on the performance of screened hybrid functionals Krukau, Aliaksandr V.; Vydrov, Oleg A.; Izmaylov, Artur F. The Journal of Chemical Physics, Vol. 125, Issue 22 https://doi.org/10.1063/1.2404663	journal	December 2006
Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H2+, He2+, LiH+, and Ne2+ Ruzsinszky, Adrienn; Perdew, John P.; Csonka, Gábor I. The Journal of Chemical Physics, Vol. 126, Issue 10 https://doi.org/10.1063/1.2566637	journal	March 2007
Tests of functionals for systems with fractional electron number Vydrov, Oleg A.; Scuseria, Gustavo E.; Perdew, John P. The Journal of Chemical Physics, Vol. 126, Issue 15 https://doi.org/10.1063/1.2723119	journal	April 2007
Development of exchange-correlation functionals with minimal many-electron self-interaction error Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao The Journal of Chemical Physics, Vol. 126, Issue 19 https://doi.org/10.1063/1.2741248	journal	May 2007
Simultaneous benchmarking of ground- and excited-state properties with long-range-corrected density functional theory Rohrdanz, Mary A.; Herbert, John M. The Journal of Chemical Physics, Vol. 129, Issue 3 https://doi.org/10.1063/1.2954017	journal	July 2008
A long-range-corrected density functional that performs well for both ground-state properties and time-dependent density functional theory excitation energies, including charge-transfer excited states Rohrdanz, Mary A.; Martins, Katie M.; Herbert, John M. The Journal of Chemical Physics, Vol. 130, Issue 5 https://doi.org/10.1063/1.3073302	journal	February 2009
On Koopmans’ theorem in density functional theory Tsuneda, Takao; Song, Jong-Won; Suzuki, Satoshi The Journal of Chemical Physics, Vol. 133, Issue 17 https://doi.org/10.1063/1.3491272	journal	November 2010
Nonlocal van der Waals density functional: The simpler the better Vydrov, Oleg A.; Van Voorhis, Troy The Journal of Chemical Physics, Vol. 133, Issue 24 https://doi.org/10.1063/1.3521275	journal	December 2010
Communication: A global hybrid generalized gradient approximation to the exchange-correlation functional that satisfies the second-order density-gradient constraint and has broad applicability in chemistry Peverati, Roberto; Truhlar, Donald G. The Journal of Chemical Physics, Vol. 135, Issue 19 https://doi.org/10.1063/1.3663871	journal	November 2011
Density‐functional thermochemistry. III. The role of exact exchange Becke, Axel D. The Journal of Chemical Physics, Vol. 98, Issue 7, p. 5648-5652 https://doi.org/10.1063/1.464913	journal	April 1993
Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties Woon, David E.; Dunning, Thom H. The Journal of Chemical Physics, Vol. 100, Issue 4 https://doi.org/10.1063/1.466439	journal	February 1994
Long-range corrected hybrid meta-generalized-gradient approximations with dispersion corrections Lin, You-Sheng; Tsai, Chen-Wei; Li, Guan-De The Journal of Chemical Physics, Vol. 136, Issue 15 https://doi.org/10.1063/1.4704370	journal	April 2012
Gaussian basis sets for use in correlated molecular calculations. V. Core‐valence basis sets for boron through neon Woon, David E.; Dunning, Thom H. The Journal of Chemical Physics, Vol. 103, Issue 11 https://doi.org/10.1063/1.470645	journal	September 1995
Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals Becke, Axel D. The Journal of Chemical Physics, Vol. 107, Issue 20 https://doi.org/10.1063/1.475007	journal	November 1997
A challenge for density functionals: Self-interaction error increases for systems with a noninteger number of electrons Zhang, Yingkai; Yang, Weitao The Journal of Chemical Physics, Vol. 109, Issue 7 https://doi.org/10.1063/1.476859	journal	August 1998
Toward reliable density functional methods without adjustable parameters: The PBE0 model Adamo, Carlo; Barone, Vincenzo The Journal of Chemical Physics, Vol. 110, Issue 13 https://doi.org/10.1063/1.478522	journal	April 1999
Semilocal and hybrid meta-generalized gradient approximations based on the understanding of the kinetic-energy-density dependence Sun, Jianwei; Haunschild, Robin; Xiao, Bing The Journal of Chemical Physics, Vol. 138, Issue 4 https://doi.org/10.1063/1.4789414	journal	January 2013
Perspective: Fifty years of density-functional theory in chemical physics Becke, Axel D. The Journal of Chemical Physics, Vol. 140, Issue 18 https://doi.org/10.1063/1.4869598	journal	May 2014
mBEEF: An accurate semi-local Bayesian error estimation density functional Wellendorff, Jess; Lundgaard, Keld T.; Jacobsen, Karsten W. The Journal of Chemical Physics, Vol. 140, Issue 14 https://doi.org/10.1063/1.4870397	journal	April 2014
Increasing the applicability of density functional theory. IV. Consequences of ionization-potential improved exchange-correlation potentials Verma, Prakash; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 140, Issue 18 https://doi.org/10.1063/1.4871409	journal	May 2014
Mapping the genome of meta-generalized gradient approximation density functionals: The search for B97M-V Mardirossian, Narbe; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 142, Issue 7 https://doi.org/10.1063/1.4907719	journal	February 2015
SCAN-based hybrid and double-hybrid density functionals from models without fitted parameters Hui, Kerwin; Chai, Jeng-Da The Journal of Chemical Physics, Vol. 144, Issue 4 https://doi.org/10.1063/1.4940734	journal	January 2016
ω B97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation Mardirossian, Narbe; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 144, Issue 21 https://doi.org/10.1063/1.4952647	journal	June 2016
The QTP family of consistent functionals and potentials in Kohn-Sham density functional theory Jin, Yifan; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 145, Issue 3 https://doi.org/10.1063/1.4955497	journal	July 2016
Global and local curvature in density functional theory Zhao, Qing; Ioannidis, Efthymios I.; Kulik, Heather J. The Journal of Chemical Physics, Vol. 145, Issue 5 https://doi.org/10.1063/1.4959882	journal	August 2016
Cost-effective description of strong correlation: Efficient implementations of the perfect quadruples and perfect hextuples models Lehtola, Susi; Parkhill, John; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 145, Issue 13 https://doi.org/10.1063/1.4964317	journal	October 2016
On the piecewise convex or concave nature of ground state energy as a function of fractional number of electrons for approximate density functionals Li, Chen; Yang, Weitao The Journal of Chemical Physics, Vol. 146, Issue 7 https://doi.org/10.1063/1.4974988	journal	February 2017
Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost Bajaj, Akash; Janet, Jon Paul; Kulik, Heather J. The Journal of Chemical Physics, Vol. 147, Issue 19 https://doi.org/10.1063/1.5008981	journal	November 2017
Communication: xDH double hybrid functionals can be qualitatively incorrect for non-equilibrium geometries: Dipole moment inversion and barriers to radical-radical association using XYG3 and XYGJ-OS Hait, Diptarka; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 148, Issue 17 https://doi.org/10.1063/1.5031027	journal	May 2018
Revised M06-L functional for improved accuracy on chemical reaction barrier heights, noncovalent interactions, and solid-state physics Wang, Ying; Jin, Xinsheng; Yu, Haoyu S. Proceedings of the National Academy of Sciences, Vol. 114, Issue 32 https://doi.org/10.1073/pnas.1705670114	journal	July 2017
Advances in molecular quantum chemistry contained in the Q-Chem 4 program package Shao, Yihan; Gan, Zhengting; Epifanovsky, Evgeny Molecular Physics, Vol. 113, Issue 2 https://doi.org/10.1080/00268976.2014.952696	journal	September 2014
Fractional-charge and fractional-spin errors in range-separated density-functional theory Mussard, Bastien; Toulouse, Julien Molecular Physics, Vol. 115, Issue 1-2 https://doi.org/10.1080/00268976.2016.1213910	journal	August 2016
Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals Mardirossian, Narbe; Head-Gordon, Martin Molecular Physics, Vol. 115, Issue 19 https://doi.org/10.1080/00268976.2017.1333644	journal	April 2017
Molecular excited states from the SCAN functional Tozer, David J.; Peach, Michael J. G. Molecular Physics, Vol. 116, Issue 11 https://doi.org/10.1080/00268976.2018.1453094	journal	November 2017
Localized orbital scaling correction for systematic elimination of delocalization error in density functional approximations Li, Chen; Zheng, Xiao; Su, Neil Qiang National Science Review, Vol. 5, Issue 2 https://doi.org/10.1093/nsr/nwx111	journal	September 2017
Quantised Singularities in the Electromagnetic Field Dirac, P. A. M. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 133, Issue 821 https://doi.org/10.1098/rspa.1931.0130	journal	September 1931
Inhomogeneous Electron Gas Hohenberg, P.; Kohn, W. Physical Review, Vol. 136, Issue 3B, p. B864-B871 https://doi.org/10.1103/PhysRev.136.B864	journal	November 1964
Self-Consistent Equations Including Exchange and Correlation Effects Kohn, W.; Sham, L. J. Physical Review, Vol. 140, Issue 4A, p. A1133-A1138 https://doi.org/10.1103/PhysRev.140.A1133	journal	November 1965
Density-functional exchange-energy approximation with correct asymptotic behavior Becke, A. D. Physical Review A, Vol. 38, Issue 6 https://doi.org/10.1103/PhysRevA.38.3098	journal	September 1988
Proof that ∂ E ∂ n i = ε in density-functional theory Janak, J. F. Physical Review B, Vol. 18, Issue 12 https://doi.org/10.1103/PhysRevB.18.7165	journal	December 1978
Self-interaction correction to density-functional approximations for many-electron systems Perdew, J. P.; Zunger, Alex Physical Review B, Vol. 23, Issue 10, p. 5048-5079 https://doi.org/10.1103/PhysRevB.23.5048	journal	May 1981
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density Lee, Chengteh; Yang, Weitao; Parr, Robert G. Physical Review B, Vol. 37, Issue 2 https://doi.org/10.1103/PhysRevB.37.785	journal	January 1988
Accurate and simple analytic representation of the electron-gas correlation energy Perdew, John P.; Wang, Yue Physical Review B, Vol. 45, Issue 23, p. 13244-13249 https://doi.org/10.1103/PhysRevB.45.13244	journal	June 1992
Linear response approach to the calculation of the effective interaction parameters in the LDA + U method Cococcioni, Matteo; de Gironcoli, Stefano Physical Review B, Vol. 71, Issue 3 https://doi.org/10.1103/PhysRevB.71.035105	journal	January 2005
Fractional charge perspective on the band gap in density-functional theory Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao Physical Review B, Vol. 77, Issue 11 https://doi.org/10.1103/PhysRevB.77.115123	journal	March 2008
Koopmans’ condition for density-functional theory Dabo, Ismaila; Ferretti, Andrea; Poilvert, Nicolas Physical Review B, Vol. 82, Issue 11 https://doi.org/10.1103/PhysRevB.82.115121	journal	September 2010
Comparative first-principles studies of prototypical ferroelectric materials by LDA, GGA, and SCAN meta-GGA Zhang, Yubo; Sun, Jianwei; Perdew, John P. Physical Review B, Vol. 96, Issue 3 https://doi.org/10.1103/PhysRevB.96.035143	journal	July 2017
Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction Mori-Sánchez, Paula; Cohen, Aron J.; Yang, Weitao Physical Review Letters, Vol. 100, Issue 14 https://doi.org/10.1103/PhysRevLett.100.146401	journal	April 2008
Improving Band Gap Prediction in Density Functional Theory from Molecules to Solids Zheng, Xiao; Cohen, Aron J.; Mori-Sánchez, Paula Physical Review Letters, Vol. 107, Issue 2 https://doi.org/10.1103/PhysRevLett.107.026403	journal	July 2011
Local Scaling Correction for Reducing Delocalization Error in Density Functional Approximations Li, Chen; Zheng, Xiao; Cohen, Aron J. Physical Review Letters, Vol. 114, Issue 5 https://doi.org/10.1103/PhysRevLett.114.053001	journal	February 2015
Strongly Constrained and Appropriately Normed Semilocal Density Functional Sun, Jianwei; Ruzsinszky, Adrienn; Perdew, John P. Physical Review Letters, Vol. 115, Issue 3 https://doi.org/10.1103/PhysRevLett.115.036402	journal	July 2015
Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy Perdew, John P.; Parr, Robert G.; Levy, Mel Physical Review Letters, Vol. 49, Issue 23 https://doi.org/10.1103/PhysRevLett.49.1691	journal	December 1982
Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/PhysRevLett.77.3865	journal	October 1996
Degenerate Ground States and a Fractional Number of Electrons in Density and Reduced Density Matrix Functional Theory Yang, Weitao; Zhang, Yingkai; Ayers, Paul W. Physical Review Letters, Vol. 84, Issue 22 https://doi.org/10.1103/PhysRevLett.84.5172	journal	May 2000
Climbing the Density Functional Ladder: Nonempirical Meta–Generalized Gradient Approximation Designed for Molecules and Solids Tao, Jianmin; Perdew, John P.; Staroverov, Viktor N. Physical Review Letters, Vol. 91, Issue 14 https://doi.org/10.1103/PhysRevLett.91.146401	journal	September 2003
Density functional theory: Its origins, rise to prominence, and future Jones, R. O. Reviews of Modern Physics, Vol. 87, Issue 3 https://doi.org/10.1103/RevModPhys.87.897	journal	August 2015
Tuned Range-Separated Hybrids in Density Functional Theory Baer, Roi; Livshits, Ester; Salzner, Ulrike Annual Review of Physical Chemistry, Vol. 61, Issue 1 https://doi.org/10.1146/annurev.physchem.012809.103321	journal	March 2010
Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals [Supplemental Data] Head-Gordon, Martin; Mardirossian, Narbe figshare-Supplementary information for journal article at DOI: 10.1080/00268976.2017.1333644, 10 files https://doi.org/10.6084/m9.figshare.5132923	fileset	June 2017

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Well-behaved versus ill-behaved density functionals for single bond dissociation: Separating success from disaster functional by functional for stretched H$_2$ Hait, Diptarka; Rettig, Adam; Head-Gordon, Martin arXiv https://doi.org/10.48550/arxiv.1810.09083	text	January 2018
Beyond the Coulson-Fischer point: Characterizing single excitation CI and TDDFT for excited states in single bond dissociations Hait, Diptarka; Rettig, Adam; Head-Gordon, Martin arXiv https://doi.org/10.48550/arxiv.1908.07081	text	January 2019

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