Many-electron self-interaction and spin polarization errors in local hybrid density functionals.

Errors for systems with noninteger occupation have been connected to common failures of density functionals. Previously, global hybrids and pure density functionals have been investigated for systems with noninteger charge and noninteger spin state. Local hybrids have not been investigated for either of those systems to the best of our knowledge. This study intends to close this gap. We investigate systems with noninteger charge to assess the many-electron self-interaction error and systems with noninteger spin state to assess the spin polarization error of recently proposed local hybrids and their range-separated variants. We find that long-range correction is very important to correct for many-electron self-interaction error in cations, whereas most full-range local hybrids seem to be sufficient for anions, where long-range-corrected density functionals tend to overcorrect. On the other hand, while all hitherto proposed long-range-corrected density functionals show large spin polarization errors, the Perdew-Staroverov-Tao-Scuseria (PSTS) functional performs best of all local hybrids in this case and shows an outstanding behavior for the dependence of the energy on the spin polarization.

[1]  Benjamin G. Janesko,et al.  Assessment of a density functional with full exact exchange and balanced non-locality of correlation , 2009 .

[2]  G. Scuseria,et al.  A simple method to selectively scale down the self-interaction correction. , 2006, Journal of Chemical Physics.

[3]  Weitao Yang,et al.  Fractional charge perspective on the band gap in density-functional theory , 2007, 0708.3175.

[4]  A. Zunger,et al.  Self-interaction correction to density-functional approximations for many-electron systems , 1981 .

[5]  G. Scuseria,et al.  The importance of middle-range Hartree-Fock-type exchange for hybrid density functionals. , 2007, The Journal of chemical physics.

[6]  M. Kaupp,et al.  Local hybrid exchange-correlation functionals based on the dimensionless density gradient , 2007 .

[7]  M. Kaupp,et al.  Local hybrid functionals: an assessment for thermochemical kinetics. , 2007, The Journal of chemical physics.

[8]  M. Head‐Gordon,et al.  Self-interaction Error of Local Density Functionals for Alkali-halide Dissociation , 2006 .

[9]  G. Scuseria,et al.  Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids. , 2003, Physical review letters.

[10]  Gustavo E. Scuseria,et al.  Local hybrid functionals , 2003 .

[11]  Gustavo E Scuseria,et al.  Effect of the Perdew-Zunger self-interaction correction on the thermochemical performance of approximate density functionals. , 2004, The Journal of chemical physics.

[12]  David Feller.  The role of databases in support of computational chemistry calculations , 1996 .

[13]  Thomas M Henderson,et al.  Screened hybrid density functionals for solid-state chemistry and physics. , 2009, Physical chemistry chemical physics : PCCP.

[14]  Local hybrid functionals with an explicit dependence on spin polarization. , 2009, The journal of physical chemistry. A.

[15]  Weitao Yang,et al.  Fractional spins and static correlation error in density functional theory. , 2008, The Journal of chemical physics.

[16]  Benjamin G. Janesko,et al.  Self-consistent generalized Kohn-Sham local hybrid functionals of screened exchange: Combining local and range-separated hybridization. , 2008, The Journal of chemical physics.

[17]  V. Barone,et al.  Toward reliable density functional methods without adjustable parameters: The PBE0 model , 1999 .

[18]  Benjamin G. Janesko,et al.  Generalized gradient approximation model exchange holes for range-separated hybrids. , 2008, The Journal of chemical physics.

[19]  Gustavo E Scuseria,et al.  Ionization potentials and electron affinities in the Perdew-Zunger self-interaction corrected density-functional theory. , 2005, The Journal of chemical physics.

[20]  Weitao Yang,et al.  Localization and delocalization errors in density functional theory and implications for band-gap prediction. , 2007, Physical review letters.

[21]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[22]  G. Scuseria,et al.  Hybrid functionals based on a screened Coulomb potential , 2003 .

[23]  C. J. Umrigar,et al.  A critical assessment of the Self-Interaction Corrected Local Density Functional method and its algorithmic implementation , 1996 .

[24]  D. Hartree.  The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part I. Theory and Methods , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[25]  K. Burke,et al.  Unambiguous exchange-correlation energy density , 1998 .

[26]  Benjamin G. Janesko.  A simple nonlocal model for exchange. , 2009, The Journal of chemical physics.

[27]  D. Cremer,et al.  The impact of the self-interaction error on the density functional theory description of dissociating radical cations: ionic and covalent dissociation limits. , 2004, The Journal of chemical physics.

[28]  Görling,et al.  Correlation-energy functional and its high-density limit obtained from a coupling-constant perturbation expansion. , 1993, Physical review. B, Condensed matter.

[29]  Adrienn Ruzsinszky,et al.  Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H2+, He2+, LiH+, and Ne2+. , 2007, The Journal of chemical physics.

[30]  J. Perdew,et al.  Two avenues to self-interaction correction within Kohn—Sham theory: unitary invariance is the shortcut , 2003, physics/0301039.

[31]  Benjamin G. Janesko,et al.  Local hybrids as a perturbation to global hybrid functionals. , 2009, The Journal of chemical physics.

[32]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[33]  Vogl,et al.  Generalized Kohn-Sham schemes and the band-gap problem. , 1996, Physical review. B, Condensed matter.

[34]  Richard L. Martin,et al.  Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional. , 2005, The Journal of chemical physics.

[35]  Eric J. Bylaska,et al.  New development of self-interaction corrected DFT for extended systems applied to the calculation of native defects in 3C–SiC , 2006 .

[36]  A. Savin,et al.  On degeneracy, near-degeneracy and density functional theory , 1996 .

[37]  Weitao Yang,et al.  A challenge for density functionals: Self-interaction error increases for systems with a noninteger number of electrons , 1998 .

[38]  G. Scuseria,et al.  Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional , 1999 .

[39]  A. Savin,et al.  A Systematic Failing of Current Density Functionals: Overestimation of Two-Center Three-Electron Bonding Energies , 1998 .

[40]  R. Parr.  Density-functional theory of atoms and molecules , 1989 .

[41]  Weitao Yang,et al.  Development of exchange-correlation functionals with minimal many-electron self-interaction error. , 2007, The Journal of chemical physics.

[42]  John P. Perdew,et al.  A self-interaction corrected approach to many-electron systems: Beyond the local spin density approximation , 1980 .

[43]  Gustavo E Scuseria,et al.  Efficient hybrid density functional calculations in solids: assessment of the Heyd-Scuseria-Ernzerhof screened Coulomb hybrid functional. , 2004, The Journal of chemical physics.

[44]  J. Perdew,et al.  Simplified self-interaction correction applied to the energy bands of neon and sodium chloride , 1983 .

[45]  Jianmin Tao,et al.  Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction , 2008, 0808.2523.

[46]  S. Patchkovskii,et al.  Improving ``difficult'' reaction barriers with self-interaction corrected density functional theory , 2002 .

[47]  G. Scuseria,et al.  Importance of short-range versus long-range Hartree-Fock exchange for the performance of hybrid density functionals. , 2006, The Journal of chemical physics.

[48]  Gustavo E. Scuseria,et al.  Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)] , 2006 .

[49]  John P. Perdew,et al.  Generalized gradient approximation to the angle- and system-averaged exchange hole , 1998 .

[50]  Benny G. Johnson,et al.  A density functional study of the simplest hydrogen abstraction reaction. Effect of self-interaction correction , 1994 .

[51]  Gábor I. Csonka,et al.  Understanding and correcting the self-interaction error in the electrical response of hydrogen chains , 2008 .

[52]  V. Fock,et al.  Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems , 1930 .

[53]  M. Kaupp,et al.  A thermochemically competitive local hybrid functional without gradient corrections. , 2007, The Journal of chemical physics.

[54]  Jianmin Tao,et al.  Exchange and correlation in open systems of fluctuating electron number , 2007 .

[55]  E J Baerends,et al.  Exact exchange-correlation treatment of dissociated H(2) in density functional theory. , 2001, Physical review letters.

[56]  G. Scuseria,et al.  Scaling down the Perdew-Zunger self-interaction correction in many-electron regions. , 2006, The Journal of chemical physics.

[57]  D. Cremer,et al.  Effect of the self-interaction error for three-electron bonds: On the development of new exchange-correlation functionals , 2004 .

[58]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[59]  Robin Haunschild,et al.  Range-separated local hybrids. , 2010, The Journal of chemical physics.

[60]  A. Becke.  A real-space model of nondynamical correlation , 2003 .

[61]  A. Becke.  A New Mixing of Hartree-Fock and Local Density-Functional Theories , 1993 .

[62]  Weitao Yang,et al.  Discontinuous nature of the exchange-correlation functional in strongly correlated systems. , 2008, Physical review letters.

[63]  Benjamin G. Janesko,et al.  Locally range‐separated hybrids as linear combinations of range‐separated local hybrids , 2009 .

[64]  G. Scuseria,et al.  Assessment of a long-range corrected hybrid functional. , 2006, The Journal of chemical physics.

[65]  T. Bally,et al.  INCORRECT DISSOCIATION BEHAVIOR OF RADICAL IONS IN DENSITY FUNCTIONAL CALCULATIONS , 1997 .

[66]  Giovanni Scalmani,et al.  Can short-range hybrids describe long-range-dependent properties? , 2009, The Journal of chemical physics.

[67]  Artur F Izmaylov,et al.  Influence of the exchange screening parameter on the performance of screened hybrid functionals. , 2006, The Journal of chemical physics.

[68]  Weitao Yang,et al.  Second-Order Perturbation Theory with Fractional Charges and Fractional Spins. , 2009, Journal of chemical theory and computation.

[69]  Andreas Savin,et al.  Hybrid functionals with local range separation. , 2008, The Journal of chemical physics.

[70]  M. Grüning,et al.  The failure of generalized gradient approximations (GGAs) and meta-GGAs for the two-center three-electron bonds in He-2(+), (H2O)(2)(+), and (NH3)(2)(+) , 2001 .

[71]  G. Scuseria,et al.  Prescription for the design and selection of density functional approximations: more constraint satisfaction with fewer fits. , 2005, The Journal of chemical physics.

[72]  R. Baer,et al.  A well-tempered density functional theory of electrons in molecules. , 2007, Physical chemistry chemical physics : PCCP.

[73]  Weitao Yang,et al.  Many-electron self-interaction error in approximate density functionals. , 2006, The Journal of chemical physics.

[74]  Adrienn Ruzsinszky,et al.  Spurious fractional charge on dissociated atoms: pervasive and resilient self-interaction error of common density functionals. , 2006, The Journal of chemical physics.

[75]  Wolfram Koch,et al.  A Chemist's Guide to Density Functional Theory , 2000 .

[76]  J. Ángyán,et al.  Hybrid functional with separated range , 2005 .

[77]  Adrienn Ruzsinszky,et al.  Diminished gradient dependence of density functionals: constraint satisfaction and self-interaction correction. , 2007, The Journal of chemical physics.

[78]  Weitao Yang,et al.  Insights into Current Limitations of Density Functional Theory , 2008, Science.

[79]  D. R. Hartree,et al.  The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part II. Some Results and Discussion , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[80]  Weitao Yang,et al.  Delocalization errors in density functionals and implications for main-group thermochemistry. , 2008, The Journal of chemical physics.

[81]  T. Koopmans,et al.  Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den Einzelnen Elektronen Eines Atoms , 1934 .

[82]  J. Perdew.  Orbital functional for exchange and correlation: self-interaction correction to the local density approximation☆ , 1979 .

[83]  Benny G. Johnson,et al.  Inclusion of exact exchange for self-interaction corrected H3 density functional potential energy surface , 1998 .

[84]  G. Scuseria,et al.  Tests of functionals for systems with fractional electron number. , 2007, The Journal of chemical physics.

[85]  J. Perdew,et al.  Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy , 1982 .

[86]  F. E. Jorge,et al.  Accurate universal Gaussian basis set for all atoms of the Periodic Table , 1998 .