The Liu-Parr power series expansion of the Pauli kinetic energy functional with the incorporation of shell-inducing traits: Atoms

An approximate expression for the Pauli kinetic energy functional T-p is advanced in terms of the Liu-Parr expansion [S. Liu, R.G. Parr, Phys. Rev. A1997, 55, 1792] which involves a power series of the one-electron density. We use this explicit functional for T-p to compute the value of the noninteracting kinetic energy functional T-s of 34 atoms, from Li to Kr (and their positive and negative monoions). In particular, we examine the effect that a shell-by-shell mean-square optimization of the expansion coefficients has on the kinetic energy values and explore the effect that the size of the expansion, given by the parameter n, has on the accuracy of the approximation. The results yield a mean absolute percent error abs=(1/N)for 34 neutral atoms of 0.15, 0.08, 0.04, 0.03, and 0.01 for expansions with n=3, 4, 5, 6, and 7, respectively (where i)). We show that these results, which are the most accurate ones obtained to date for the representation of the noninteracting kinetic energy functional, stem from the imposition of shell-inducing traits. We also compare these Liu-Parr functionals with the exact but nonexplicit functional generated in the local-scaling transformation version of DFT.