Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Describing strong correlation with fractional-spin correction in density functional theory

Journal Article · · Proceedings of the National Academy of Sciences of the United States of America
 [1];  [1];  [2]
  1. Department of Chemistry, Duke University, Durham, NC 27708,
  2. 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
Significance

The static correlation error inherent in commonly used density functional approximations (DFAs) has seriously hindered the application of density functional theory (DFT) to strongly correlated systems. Here, an effective fractional-spin correction against the important issue of static/strong correlation in DFT is developed. With this, the flat-plane behavior of various DFAs is largely restored, and the potential energy curves of dissociation of ionic species, single bonds, and multiple bonds are properly described, which demonstrates great improvement in the treatment of strong correlation. This work should have a significant impact on the development and application of DFT.

Research Organization:
Energy Frontier Research Centers (EFRC) (United States). Center for Complex Materials from First Principles (CCM); Temple Univ., Philadelphia, PA (United States)
Sponsoring Organization:
USDOE Office of Science (SC); USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0012575
OSTI ID:
1469268
Alternate ID(s):
OSTI ID: 1540302
Journal Information:
Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Issue: 39 Vol. 115; ISSN 0027-8424
Publisher:
Proceedings of the National Academy of SciencesCopyright Statement
Country of Publication:
United States
Language:
English

References (86)

Theoretical study of spectroscopic and molecular properties of several low-lying electronic states of CO molecule journal February 2012
Spin in density-functional theory journal August 2012
Hubbard-corrected DFT energy functionals: The LDA+U description of correlated systems journal July 2013
Spin-restricted ensemble-referenced Kohn-Sham method: basic principles and application to strongly correlated ground and excited states of molecules journal November 2014
Accurate ab initio potential energy curves and spectroscopic properties of the four lowest singlet states of C2 journal December 2013
Testing exchange–correlation functionals at fractional electron numbers journal September 2014
Perspective on "Density-functional theory for fractional particle number: derivative discontinuities of the energy" journal February 2000
Photoelectron spectroscopy of free fullerenes journal May 1996
Spin-restricted density functional approach to the open-shell problem journal May 1998
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
Integration Approach at the Second-Order Perturbation Theory: Applications to Ionization Potential and Electron Affinity Calculations journal September 2015
Density Functional Model for Nondynamic and Strong Correlation journal December 2015
Second-Order Perturbation Theory for Fractional Occupation Systems: Applications to Ionization Potential and Electron Affinity Calculations journal April 2016
Self-Interaction Error in Density Functional Theory: An Appraisal journal April 2018
Challenges for Density Functional Theory journal December 2011
Second-Order Perturbation Theory with Fractional Charges and Fractional Spins journal March 2009
Empirical Correction of Nondynamical Correlation Energy for Density Functionals journal September 2012
Fractional Charge Behavior and Band Gap Predictions with the XYG3 Type of Doubly Hybrid Density Functionals journal June 2014
Does a Molecule-Specific Density Functional Give an Accurate Electron Density? The Challenging Case of the CuCl Electric Field Gradient journal February 2012
Curvature and Frontier Orbital Energies in Density Functional Theory journal December 2012
Using Wannier functions to improve solid band gap predictions in density functional theory journal April 2016
Full configuration interaction potential energy curves for breaking bonds to hydrogen: An assessment of single-reference correlation methods journal January 2003
A real-space model of nondynamical correlation journal August 2003
Real-space post-Hartree–Fock correlation models journal February 2005
Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals journal November 2006
Many-electron self-interaction error in approximate density functionals journal November 2006
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
Tests of functionals for systems with fractional electron number journal April 2007
Development of exchange-correlation functionals with minimal many-electron self-interaction error journal May 2007
Fractional spins and static correlation error in density functional theory journal September 2008
Koopmans’ springs to life journal December 2009
Many-electron self-interaction and spin polarization errors in local hybrid density functionals journal October 2010
On Koopmans’ theorem in density functional theory journal November 2010
Communication: A density functional with accurate fractional-charge and fractional-spin behaviour for s -electrons journal August 2011
Correlation potentials for molecular bond dissociation within the self-consistent random phase approximation journal January 2012
A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples journal February 1982
Quadratic configuration interaction. A general technique for determining electron correlation energies journal November 1987
Perspective on density functional theory journal April 2012
Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation journal January 1997
A challenge for density functionals: Self-interaction error increases for systems with a noninteger number of electrons journal August 1998
Density functionals for static, dynamical, and strong correlation journal February 2013
Wave function methods for fractional electrons journal August 2013
A density functional for strong correlation in atoms journal August 2013
Communication: Self-interaction correction with unitary invariance in density functional theory journal March 2014
Perspective: Fifty years of density-functional theory in chemical physics journal May 2014
Fractional charge and spin errors in self-consistent Green’s function theory journal May 2015
Perspective: Treating electron over-delocalization with the DFT+U method journal June 2015
Fragment-based treatment of delocalization and static correlation errors in density-functional theory journal December 2015
Communication: Simple and accurate uniform electron gas correlation energy for the full range of densities journal July 2016
Driven similarity renormalization group: Third-order multireference perturbation theory journal March 2017
Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost journal November 2017
Fractional-charge and fractional-spin errors in range-separated density-functional theory journal August 2016
Localized orbital scaling correction for systematic elimination of delocalization error in density functional approximations journal September 2017
Quest for a universal density functional: the accuracy of density functionals across a broad spectrum of databases in chemistry and physics
  • Peverati, Roberto; Truhlar, Donald G.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 372, Issue 2011 https://doi.org/10.1098/rsta.2012.0476
journal March 2014
Inhomogeneous Electron Gas journal November 1964
Self-Consistent Equations Including Exchange and Correlation Effects journal November 1965
Density-functional exchange-energy approximation with correct asymptotic behavior journal September 1988
Exchange and correlation in open systems of fluctuating electron number journal October 2007
Failure of the random-phase-approximation correlation energy journal April 2012
Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random-phase approximation journal September 2013
Elimination of the asymptotic fractional dissociation problem in Kohn-Sham density-functional theory using the ensemble-generalization approach journal March 2015
Full self-consistency in the Fermi-orbital self-interaction correction journal May 2017
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density journal January 1988
Generalized Kohn-Sham schemes and the band-gap problem journal February 1996
Linear response approach to the calculation of the effective interaction parameters in the LDA + U method journal January 2005
Transition state method and Wannier functions journal August 2005
Polaronic hole localization and multiple hole binding of acceptors in oxide wide-gap semiconductors journal August 2009
Koopmans’ condition for density-functional theory journal September 2010
First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications journal March 2011
Static correlation and electron localization in molecular dimers from the self-consistent RPA and G W approximation journal April 2015
Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction journal April 2008
Discontinuous Nature of the Exchange-Correlation Functional in Strongly Correlated Systems journal February 2009
Improving Band Gap Prediction in Density Functional Theory from Molecules to Solids journal July 2011
Improved Electronic Excitation Energies from Shape-Corrected Semilocal Kohn-Sham Potentials journal June 2012
Quasiparticle Spectra from a Nonempirical Optimally Tuned Range-Separated Hybrid Density Functional journal November 2012
Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies journal March 2013
Local Scaling Correction for Reducing Delocalization Error in Density Functional Approximations journal February 2015
Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy journal December 1982
Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities journal November 1983
Density-Functional Theory of the Energy Gap journal November 1983
Degenerate Ground States and a Fractional Number of Electrons in Density and Reduced Density Matrix Functional Theory journal May 2000
Density Functional Theory in Transition-Metal Chemistry: A Self-Consistent Hubbard U Approach journal September 2006
Self-Consistent Field Theory for Open Shells of Electronic Systems journal April 1960
Canonical Configurational Interaction Procedure journal April 1960
Insights into Current Limitations of Density Functional Theory journal August 2008
Tuned Range-Separated Hybrids in Density Functional Theory journal March 2010

Similar Records

Multireference Density Functional Theory with Generalized Auxiliary Systems for Ground and Excited States
Journal Article · Wed Aug 30 20:00:00 EDT 2017 · Journal of Physical Chemistry Letters · OSTI ID:1469925