The development of new exchange-correlation functionals

A procedure is presented for the possible systematic development of exchange-correlation functionals using ab initio electron densities and accurate total energies. For a training set of first row open- and closed-shell systems, densities are computed and are used to determine asymptotically vanishing exchange-correlation potentials. The new functional is then written as an expansion in products of the density and its gradient, and optimum expansion parameters are determined through a least squares fit involving both these potentials and accurate exchange-correlation energies. Unlike conventional functionals, the potential of the fitted functional approaches a non-zero value asymptotically, and this is achieved by introducing a self-consistently computed system-dependent shift into the fitting procedure. This shift represents the influence of the integer derivative discontinuity in the exact energy. The method has been used to determine a 21 term spin-polarized exchange-correlation functional using Brueck...

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

[2]  Engel,et al.  Exact exchange-only potentials and the virial relation as microscopic criteria for generalized gradient approximations. , 1993, Physical review. B, Condensed matter.

[3]  Nicholas C. Handy,et al.  Exchange functionals and potentials , 1996 .

[4]  N. Handy,et al.  Towards accurate exchange-correlation potentials for molecules , 1996 .

[5]  D. Tozer.  EXACT HYDROGENIC DENSITY FUNCTIONALS , 1997 .

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

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

[8]  N. Handy,et al.  Large basis set calculations using Brueckner theory , 1994 .

[9]  William H. Green,et al.  Exchange-correlation functionals from ab initio electron densities , 1997 .

[10]  D. J. L. Roy,et al.  Kinetics of the Reaction H+p‐H2=o‐H2+H , 1965 .

[11]  Kieron Burke,et al.  Comparison shopping for a gradient-corrected density functional , 1996 .

[12]  John P. Perdew,et al.  Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities , 1983 .

[13]  Parr,et al.  From electron densities to Kohn-Sham kinetic energies, orbital energies, exchange-correlation potentials, and exchange-correlation energies. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[14]  D L Diedrich,et al.  An Accurate Quantum Monte Carlo Calculation of the Barrier Height for the Reaction H + H2 → H2 + H , 1992, Science.

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

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

[17]  J. Janak,et al.  Proof that ? E /? n i =e in density-functional theory , 1978 .

[18]  Density-functional theory using an optimized exchange-correlation potential , 1995, chem-ph/9504004.

[19]  Benny G. Johnson,et al.  A density functional study of the simplest hydrogen abstraction reaction. Effect of self-interaction correction , 1994 .

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

[21]  Parr,et al.  Toward understanding the exchange-correlation energy and total-energy density functionals. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[22]  Nicholas C. Handy,et al.  Exchange‐correlation potentials , 1996 .

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