A semiempirical generalized gradient approximation exchange-correlation functional.

We describe our attempts to improve upon the quality of the KT1 and KT2 generalized gradient approximation (GGA) exchange-correlation functionals [T. W. Keal and D. J. Tozer, J. Chem. Phys. 119, 3015 (2003)], through the introduction of additional gradient-corrected exchange and correlation terms. A GGA functional, denoted KT3, is presented, which maintains the high quality main-group nuclear magnetic resonance shielding constants obtained with KT1 and KT2; results are 2-3 times more accurate than conventional GGA and hybrid functionals. For the extensive range of systems considered in this study, KT3 also provides atomization energies, ionization potentials, electron affinities, proton affinities, bond angles, and electronic polarizabilities that are comparable to, or that surpass, those of the best present-day GGAs. Furthermore, it provides equilibrium molecular bond lengths and diatomic harmonic vibrational wave numbers that are as accurate as those from the best hybrid functionals. Further improvements are required in the description of classical chemical reaction barriers.

[1]  M. Kaupp,et al.  Construction of local hybrid exchange-correlation potentials and their evaluation for nuclear shielding constants , 2004 .

[2]  Donald G. Truhlar,et al.  Tests of second-generation and third-generation density functionals for thermochemical kineticsElectronic supplementary information (ESI) available: Mean errors for pure and hybrid DFT methods. See http://www.rsc.org/suppdata/cp/b3/b316260e/ , 2004 .

[3]  W. Hieringer,et al.  Density-functional calculations of NMR shielding constants using the localized Hartree–Fock method , 2004 .

[4]  A. M. Teale,et al.  Exchange representations in Kohn–Sham NMR shielding calculations , 2004 .

[5]  David J. Tozer,et al.  Relationship between long-range charge-transfer excitation energy error and integer discontinuity in Kohn–Sham theory , 2003 .

[6]  David J. Tozer,et al.  The exchange-correlation potential in Kohn–Sham nuclear magnetic resonance shielding calculations , 2003 .

[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]  V. Karasiev.  Local “hybrid” functionals based on exact-expression approximate exchange , 2003 .

[9]  J. Perdew,et al.  Simple iterative construction of the optimized effective potential for orbital functionals, including exact exchange. , 2002, Physical review letters.

[10]  David J. Tozer,et al.  Helium dimer dispersion forces and correlation potentials in density functional theory. , 2002 .

[11]  D. Tozer,et al.  Diatomic bond lengths and vibrational frequencies: assessment of recently developed exchange-correlation functionals , 2002 .

[12]  David J. Tozer,et al.  Hybrid exchange-correlation functional determined from thermochemical data and ab initio potentials , 2001 .

[13]  D. Tozer,et al.  NMR shielding constants from ab initio and Kohn-Sham electron densities , 2001 .

[14]  A. Daniel Boese,et al.  A new parametrization of exchange–correlation generalized gradient approximation functionals , 2001 .

[15]  N. Handy,et al.  Left-right correlation energy , 2001 .

[16]  Donald G. Truhlar,et al.  Adiabatic connection for kinetics , 2000 .

[17]  G. Scuseria,et al.  The meta-GGA functional: Thermochemistry with a kinetic energy density dependent exchange-correlation functional , 2000 .

[18]  N. Handy,et al.  Toward coupled-cluster accuracy in the prediction of nuclear shielding constants: a simple and efficient DFT approach , 1999 .

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

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

[21]  A. Daniel Boese,et al.  Predicting the binding energies of H-bonded complexes: A comparative DFT study , 1999 .

[22]  Fred A. Hamprecht,et al.  Development and assessment of new exchange-correlation functionals , 1998 .

[23]  Gustavo E. Scuseria,et al.  A novel form for the exchange-correlation energy functional , 1998 .

[24]  W. Thiel,et al.  Exchange-correlation density functional beyond the gradient approximation , 1998 .

[25]  A. Becke.  Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals , 1997 .

[26]  M. Spackman,et al.  An ab initio study of vibrational corrections to the electrical properties of the second-row hydrides , 1997 .

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

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

[29]  Dennis R. Salahub,et al.  NUCLEAR MAGNETIC RESONANCE SHIELDING TENSORS CALCULATED WITH A SUM-OVER-STATES DENSITY FUNCTIONAL PERTURBATION THEORY , 1994 .

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

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

[32]  A. J. Sadlej,et al.  Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties , 1991 .

[33]  Krishnan Raghavachari,et al.  Gaussian‐1 theory of molecular energies for second‐row compounds , 1990 .

[34]  L. Curtiss,et al.  Gaussian‐1 theory: A general procedure for prediction of molecular energies , 1989 .

[35]  A. Becke,et al.  Exchange holes in inhomogeneous systems: A coordinate-space model. , 1989, Physical review. A, General physics.

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

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

[38]  Axel D. Becke,et al.  Density Functional Calculations of Molecular Bond Energies , 1986 .

[39]  Aage E. Hansen,et al.  Localized orbital/local origin method for calculation and analysis of NMR shieldings. Applications to 13C shielding tensors , 1985 .

[40]  Marvin L. Cohen,et al.  Electronic structure of solids , 1984 .

[41]  R. Dreizler,et al.  Gradient expansion of the Coulomb exchange energy , 1981 .

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

[43]  A. Wachters,et al.  Gaussian Basis Set for Molecular Wavefunctions Containing Third‐Row Atoms , 1970 .

[44]  Frank Herman,et al.  Improved Statistical Exchange Approximation for Inhomogeneous Many-Electron Systems , 1969 .

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

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

[47]  P. Dirac.  Note on Exchange Phenomena in the Thomas Atom , 1930, Mathematical Proceedings of the Cambridge Philosophical Society.