Kinetic energy density dependent approximations to the exchange energy

Abstract

Two nonempirical kinetic energy density dependent approximations are introduced. First, the local τ approximation (LTA) is proposed in which the exchange energy E x depends only on a kinetic energy density τ. 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 ΔE 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 ΔE x are worse. Secondly, the τPBE 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, τPBE is free of empirical parameters. Furthermore, it yields improved atomization energies compared to the PBE approximation.