Many-electron self-interaction error in approximate density functionals.

One of the most important challenges in density functional theory (DFT) is the proper description of fractional charge systems relating to the self-interaction error (SIE). Traditionally, the SIE has been formulated as a one-electron problem, which has been addressed in several recent functionals. However, these recent one-electron SIE-free functionals, while greatly improving the description of thermochemistry and reaction barriers in general, still exhibit many of the difficulties associated with SIE. Thus we emphasize the need to surpass this limit and shed light on the many-electron SIE. After identifying the sufficient condition for functionals to be free from SIE, we focus on the symptoms and investigate the performance of most popular functionals. We show that these functionals suffer from many-electron SIE. Finally, we give a SIE classification of density functionals.

[1]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[2]  R. Dreizler,et al.  Density Functional Methods In Physics , 1985 .

[3]  Yang,et al.  Degenerate ground states and a fractional number of electrons in density and reduced density matrix functional theory , 2000, Physical review letters.

[4]  Benoît Champagne,et al.  Electric field dependence of the exchange-correlation potential in molecular chains , 1999 .

[5]  J. Perdew.  What do the Kohn-Sham Orbital Energies Mean? How do Atoms Dissociate? , 1985 .

[6]  Qin Wu,et al.  Direct method for optimized effective potentials in density-functional theory. , 2002, Physical review letters.

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

[8]  K. Hirao,et al.  A long-range correction scheme for generalized-gradient-approximation exchange functionals , 2001 .

[9]  Weitao Yang,et al.  Self-interaction-free exchange-correlation functional for thermochemistry and kinetics. , 2006, The Journal of chemical physics.

[10]  Wang,et al.  Accurate and simple analytic representation of the electron-gas correlation energy. , 1992, Physical review. B, Condensed matter.

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

[12]  A. Becke.  Real-space post-Hartree-Fock correlation models. , 2005, The Journal of chemical physics.

[13]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

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

[15]  Qin Wu,et al.  Accurate polymer polarizabilities with exact exchange density-functional theory , 2003 .

[16]  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.

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

[18]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[19]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

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

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

[22]  N. Handy,et al.  A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) , 2004 .

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