The Kinetic Energy Pauli Enhancement Factor and Its Role in Determining the Shell Structure of Atoms and Molecules

We deal with different representations of the noninteracting kinetic energy functional for the purpose of examining their effect upon the generation of shell structure in atoms. We decompose the noninteracting functional into a Weizsacker term plus a Pauli term where the latter is written as a product of the Thomas-Fermi rho 5/3(r) times the Pauli enhancement factor F-p[rho]. We examine the behavior of F-p[rho] when it is given in terms of a Hartree-Fock orbital representation, of density-dependent orbitals generated through local-scaling transformations, and of the Liu-Parr power series expansion. In the latter, we compare the cases when the expansion coefficients have been expanded in an all-shell vs a shell-by-shell procedure. We apply these approximations to the aluminum atom. In particular, for this case, we examine in these different approximations, the role of the Pauli enhancement factor for the production of shell structure.