Polynomial and Pad� Representations for the Kinetic ComponentTc[?] of the Correlation Energy Density Functional

Abstract

Polynomial and Padé representations of the kinetic energy component Tc[ρ] of the correlation energy density functional Ec[ρ] are presented in this article. Two approximate local formulas similar to the Wigner form for Ec[ρ] are investigated for Tc[ρ]. Applications of these formulas along with their two polynomial counterparts are carried out for atoms, ions, and a few simple molecules. Numerical predictions of Tc values are made for these species. Both Hartree–Fock and self-consistent-field densities are used in their evaluations. Recommended at this time is the two-parameter Padé [0, 1] formula Tc[ρ]=∫a0ρ/(1+b0ρ−1/3) dr, with a0=0.1658 and b0=6.102 (atomic units). © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 513–522, 1998