Why does the B3LYP hybrid functional fail for metals?

The B3LYP hybrid functional has shown to successfully predict a wide range of molecular properties. For periodic systems, however, the failure to attain the exact homogeneous electron gas limit as well as the semiempirical construction turns out to be a major drawback of the functional. We rigorously assess the B3LYP functional for solids through calculations of lattice parameters, bulk moduli, and thermochemical properties (atomization energies and reaction energies). The theoretical lattice constants overestimate the experimental ones by approximately 1%, and hence behave similarly to the PBE gradient-corrected exchange-correlation functional. B3LYP atomization energies of solids are drastically worse than those of nonempirical hybrid Hartree-Fock/density functionals (HF/DFT) such as PBE0 and HSE03. These large errors can be traced back to the lack of a proper description of "free-electron-like" systems with a significant itinerant character (metals and small gap semiconductors). Similar calculations using the popular semiempirical B3PW91 hybrid functional, which fulfills the uniform electron gas limit, show a clear improvement over B3LYP regarding atomization energies. Finally, theoretical values for heats of formation for both the B3LYP as well as the B3PW91 functionals are presented. These document a most likely fortuitously good agreement with experiment for the B3LYP hybrid functional.

[1]  B. Lundqvist,et al.  Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism , 1976 .

[2]  Hermann Stoll,et al.  Results obtained with the correlation energy density functionals of becke and Lee, Yang and Parr , 1989 .

[3]  G. Baraff,et al.  Total energy of isolated point defects in solids , 1983 .

[4]  K. Burke,et al.  Rationale for mixing exact exchange with density functional approximations , 1996 .

[5]  Thom H. Dunning,et al.  Gaussian basis sets for use in correlated molecular calculations. V. Core-valence basis sets for boron through neon , 1995 .

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

[7]  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.

[8]  John P. Perdew,et al.  Erratum: Accurate Density Functional with Correct Formal Properties: A Step Beyond the Generalized Gradient Approximation [Phys. Rev. Lett. 82, 2544 (1999)] , 1999 .

[9]  Amir Karton,et al.  Comment on: “Estimating the Hartree–Fock limit from finite basis set calculations” [Jensen F (2005) Theor Chem Acc 113:267] , 2005, physics/0509216.

[10]  Axel D. Becke,et al.  Simulation of delocalized exchange by local density functionals , 2000 .

[11]  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.

[12]  C. Adamo,et al.  Density functional theory analysis of the structural and electronic properties of TiO2 rutile and anatase polytypes: performances of different exchange-correlation functionals. , 2007, The Journal of chemical physics.

[13]  Trygve Helgaker,et al.  Basis-set convergence of correlated calculations on water , 1997 .

[14]  Marvin L. Cohen,et al.  THEORY OF STATIC STRUCTURAL PROPERTIES, CRYSTAL STABILITY, AND PHASE TRANSFORMATIONS: APPLICATION TO Si AND Ge , 1982 .

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

[16]  Kirk A. Peterson,et al.  Accurate correlation consistent basis sets for molecular core–valence correlation effects: The second row atoms Al–Ar, and the first row atoms B–Ne revisited , 2002 .

[17]  T. Dunning,et al.  Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions , 1992 .

[18]  M. Ernzerhof,et al.  Construction of the adiabatic connection , 1996 .

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

[20]  Hafner,et al.  Ab initio molecular dynamics for open-shell transition metals. , 1993, Physical review. B, Condensed matter.

[21]  P. Gori-Giorgi,et al.  Uniform electron gas from the Colle-Salvetti functional: Missing long-range correlations , 2001 .

[22]  H. Monkhorst,et al.  SPECIAL POINTS FOR BRILLOUIN-ZONE INTEGRATIONS , 1976 .

[23]  David Feller,et al.  Application of systematic sequences of wave functions to the water dimer , 1992 .

[24]  Angela K. Wilson,et al.  Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited , 2001 .

[25]  Georg Kresse,et al.  Erratum: “Screened hybrid density functionals applied to solids” [J. Chem. Phys. 124, 154709 (2006)] , 2006 .

[26]  F. Murnaghan.  The Compressibility of Media under Extreme Pressures. , 1944, Proceedings of the National Academy of Sciences of the United States of America.

[27]  Davidson,et al.  Ground-state correlation energies for two- to ten-electron atomic ions. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[28]  R. Orlando,et al.  Ab Initio Quantum Simulation in Solid State Chemistry , 2005 .

[29]  Wang,et al.  Generalized gradient approximation for the exchange-correlation hole of a many-electron system. , 1996, Physical review. B, Condensed matter.

[30]  R. Dreizler,et al.  Density-Functional Theory , 1990 .

[31]  J. Paier,et al.  Screened hybrid density functionals applied to solids. , 2006, The Journal of chemical physics.

[32]  R O Jones,et al.  The surface energy of a bounded electron gas , 1974 .

[33]  D. Hamann,et al.  The electronic structure of solid surfaces , 1976 .

[34]  M. Alfredsson,et al.  The Performance of Hybrid Density Functionals in Solid State Chemistry , 2005 .

[35]  Singh,et al.  Erratum: Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation , 1993, Physical review. B, Condensed matter.

[36]  Jackson,et al.  Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. , 1992, Physical review. B, Condensed matter.

[37]  John P. Perdew,et al.  Molecular and solid‐state tests of density functional approximations: LSD, GGAs, and meta‐GGAs , 1999 .

[38]  K. Burke,et al.  Erratum: Generalized gradient approximation for the exchange-correlation hole of a many-electron system [Phys. Rev. B 54 , 16 533 (1996)] , 1998 .

[39]  John P. Perdew,et al.  Accurate Density Functional with Correct Formal Properties: A Step Beyond the Generalized Gradient Approximation , 1999 .

[40]  Teodora Todorova,et al.  Molecular dynamics simulation of liquid water: hybrid density functionals. , 2006, The journal of physical chemistry. B.

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

[42]  J. Perdew.  Local density and gradient-corrected functionals for short-range correlation: Antiparallel-spin and non-RPA contributions , 1993 .

[43]  James S. Harris,et al.  Adiabatic-connection approach to Kohn-Sham theory , 1984 .

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

[45]  R. O. Jones,et al.  The density functional formalism, its applications and prospects , 1989 .

[46]  Xiao-bing Feng.  Electronic structure of MnO and CoO from the B3LYP hybrid density functional method , 2004 .

[47]  Georg Kresse,et al.  The Perdew-Burke-Ernzerhof exchange-correlation functional applied to the G2-1 test set using a plane-wave basis set. , 2005, The Journal of chemical physics.

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

[49]  V. L. Moruzzi,et al.  Calculated electronic properties of metals , 1978 .

[50]  Yingkai Zhang,et al.  Comment on “Generalized Gradient Approximation Made Simple” , 1998 .

[51]  Frank Jensen,et al.  Polarization consistent basis sets. II. Estimating the Kohn-Sham basis set limit , 2002 .

[52]  E. Clementi,et al.  A comparative study of density functional models to estimate molecular atomization energies , 1990 .

[53]  M. Head‐Gordon,et al.  A fifth-order perturbation comparison of electron correlation theories , 1989 .

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

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

[56]  Thomas Bredow,et al.  Effect of exchange and correlation on bulk properties of MgO, NiO, and CoO , 2000 .

[57]  Blöchl,et al.  Improved tetrahedron method for Brillouin-zone integrations. , 1994, Physical review. B, Condensed matter.

[58]  Axel D. Becke,et al.  Density‐functional thermochemistry. IV. A new dynamical correlation functional and implications for exact‐exchange mixing , 1996 .

[59]  K. Burke,et al.  COUPLING-CONSTANT DEPENDENCE OF ATOMIZATION ENERGIES , 1997 .

[60]  L. Curtiss,et al.  Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation , 1997 .

[61]  M. W. Chase.  NIST-JANAF thermochemical tables , 1998 .

[62]  G. Kresse,et al.  Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set , 1996 .

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

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

[65]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[66]  J. Nørskov,et al.  Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals , 1999 .

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

[68]  I. Barin,et al.  Thermochemical properties of inorganic substances , 1973 .

[69]  B. Alder,et al.  THE GROUND STATE OF THE ELECTRON GAS BY A STOCHASTIC METHOD , 2010 .

[70]  N. Harrison,et al.  On the prediction of band gaps from hybrid functional theory , 2001 .

[71]  R. Bartlett,et al.  A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples , 1982 .

[72]  G. Kresse,et al.  From ultrasoft pseudopotentials to the projector augmented-wave method , 1999 .

[73]  Blöchl,et al.  Projector augmented-wave method. , 1994, Physical review. B, Condensed matter.

[74]  G. Scuseria,et al.  Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes , 2003 .

[75]  Kresse,et al.  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. , 1996, Physical review. B, Condensed matter.

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

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

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

[79]  R. O. Jones,et al.  Density Functional Calculations for Atoms, Molecules and Clusters , 1980 .

[80]  Axel D. Becke,et al.  A new inhomogeneity parameter in density-functional theory , 1998 .

[81]  G. Kresse,et al.  Relaxed core projector-augmented-wave method. , 2006, The Journal of chemical physics.