A new gradient-corrected exchange functional

A new gradient-corrected exchange functional (G96) is introduced. While similar to Becke's B88 functional, it is much simpler and its potential in finite systems is asymptotically unbounded. The mean absolute deviations of the B88 and G96 exchange energies from the corresponding Hartree-Fock values for the atoms H to Ar are 12⋅5 and 8⋅5 mE h, respectively. In combination with the LYP correlation functional, it yields a density functional (G-LYP) that performs similarly to B-LYP on the standard G2 benchmark and we infer that the usefulness of a functional for molecular calculations does not depend critically on its asymptotic behaviour.

[1]  Benny G. Johnson,et al.  The performance of a family of density functional methods , 1993 .

[2]  Benny G. Johnson,et al.  Kohn—Sham density-functional theory within a finite basis set , 1992 .

[3]  R. D. Adamson,et al.  Density Functional Partitions , 1996 .

[4]  Krishnan Raghavachari,et al.  Gaussian-2 theory for molecular energies of first- and second-row compounds , 1991 .

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

[6]  Gill,et al.  Exact exchange functional for the hydrogen atom. , 1993, Physical review. A, Atomic, molecular, and optical physics.

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

[8]  Nicholas C. Handy,et al.  A study of O3, S3, CH2, and Be2 using Kohn–Sham theory with accurate quadrature and large basis sets , 1993 .

[9]  J. Perdew,et al.  Density-functional approximation for the correlation energy of the inhomogeneous electron gas. , 1986, Physical review. B, Condensed matter.

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

[11]  John C. Slater,et al.  Quantum Theory of Molecules and Solids Vol. 4: The Self‐Consistent Field for Molecules and Solids , 1974 .

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

[13]  Erich Wimmer,et al.  Density functional Gaussian‐type‐orbital approach to molecular geometries, vibrations, and reaction energies , 1992 .

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

[15]  L. Kleinman,et al.  Kohn-Sham exchange potential exact to first order in rho (K , 1985, Physical review. B, Condensed matter.

[16]  J. Pople,et al.  Self‐consistent molecular orbital methods. XX. A basis set for correlated wave functions , 1980 .

[17]  Wilson,et al.  Nonlocal Wigner-like correlation-energy density functional through coordinate scaling. , 1990, Physical review. B, Condensed matter.

[18]  Benny G. Johnson,et al.  A standard grid for density functional calculations , 1993 .

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

[20]  A. D. McLean,et al.  Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, Z=11–18 , 1980 .

[21]  John C. Slater,et al.  Quantum Theory of Molecules and Solids , 1951 .

[22]  Eugene P. Wigner,et al.  Effects of the Electron Interaction on the Energy Levels of Electrons in Metals , 1938 .

[23]  Nicholas C. Handy,et al.  A general purpose exchange-correlation energy functional , 1993 .

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

[25]  Peter M. W. Gill,et al.  Becke–Wigner : a simple but powerful density functional , 1995 .

[26]  Axel D. Becke,et al.  Density-functional thermochemistry. I. The effect of the exchange-only gradient correction , 1992 .

[27]  A. Becke.  Correlation energy of an inhomogeneous electron gas: A coordinate‐space model , 1988 .

[28]  Parr,et al.  Phase-space approach to the exchange-energy functional of density-functional theory. , 1986, Physical review. A, General physics.

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