Kinetic energy density dependent approximations to the exchange energy

Two nonempirical kinetic energy density dependent approximations are introduced. First, the local tau approximation (LTA) is proposed in which the exchange energy E-x depends only on a kinetic energy density tau. This LTA scheme appears to be complementary to the local spin density (LSD) approximation in the sense that its exchange contribution to the atomization energy Delta E-x=E-x(atoms)-E-x(molecule) is fairly accurate for systems where LSD fails. On the other hand, in cases where LSD works well LTA results for Delta E-x are worse. Secondly, the tau PBE approximation to E-x is developed which combines some of the advantages of LTA and of the Perdew-Burke-Ernzerhof (PBE) exchange functional. Like the PBE exchange functional, tau PBE is free of empirical parameters. Furthermore, it yields improved atomization energies compared to the PBE approximation. (C) 1999 American Institute of Physics. [S0021-9606(99)30126-4].