Density functionals for exchange and correlation energies: Exact conditions and comparison of approximations

A set of exact conditions is compiled for the purpose of developing and testing approximations for the exchange-correlation energy as a functional of the electron density. Special emphasis is placed upon recently developed density-scaling relationships. Commonly used generalized gradient approximations are compared against several of these conditions. A direct tabular comparison of these functionals (not of calculated properties) with one another is also made. © 1994 John Wiley & Sons, Inc.

[1]  M. Rasolt.  Exchange and correlation energy in a nonuniform fermion fluid. , 1986, Physical review. B, Condensed matter.

[2]  A new functional with homogeneous coordinate scaling in density functional theory: F [ ρ,λ] , 1985 .

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

[4]  P. Löwdin.  Quantum theory of cohesive properties of solids , 2001 .

[5]  Perdew,et al.  Low-density limit of the correlation energy in the random-phase approximation for charged particles of arbitrary statistics. , 1992, Physical review. B, Condensed matter.

[6]  J. Perdew,et al.  Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation. , 1986, Physical review. B, Condensed matter.

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

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

[9]  Lévy,et al.  Density-functional exchange correlation through coordinate scaling in adiabatic connection and correlation hole. , 1991, Physical review. A, Atomic, molecular, and optical physics.

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

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

[12]  A. Becke.  Density-functional thermochemistry. II: The effect of the Perdew-Wang generalized-gradient correlation correction , 1992 .

[13]  Perdew,et al.  Expectation values in density-functional theory, and kinetic contribution to the exchange-correlation energy. , 1993, Physical review. B, Condensed matter.

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

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

[16]  John P. Perdew,et al.  Density-functional theory of the correlation energy in atoms and ions: A simple analytic model and a challenge , 1981 .

[17]  Lévy,et al.  Nonuniform coordinate scaling requirements for exchange-correlation energy. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[18]  Görling,et al.  Requirements for correlation energy density functionals from coordinate transformations. , 1992, Physical review. A, Atomic, molecular, and optical physics.

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

[20]  A. Savin,et al.  Singly ionized first‐row dimers and hydrides calculated with the fully‐numerical density‐functional program numol , 1992 .

[21]  D. Langreth,et al.  Beyond the local-density approximation in calculations of ground-state electronic properties , 1983 .

[22]  J. Perdew.  Generalized gradient approximation for the fermion kinetic energy as a functional of the density , 1992 .

[23]  J. Perdew,et al.  Hellmann-Feynman, virial, and scaling requisites for the exact universal density functionals. Shape of the correlation potential and diamagnetic susceptibility for atoms. , 1985, Physical review. A, General physics.

[24]  E. Lieb,et al.  Improved Lower Bound on the Indirect Coulomb Energy , 1981 .

[25]  D. Lacks,et al.  Pair interactions of rare-gas atoms as a test of exchange-energy-density functionals in regions of large density gradients. , 1993, Physical review. A, Atomic, molecular, and optical physics.