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

International Journal of Quantum Chemistry

5 years ago

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

Darío E. Arroyo, Eduardo V. Ludeña, Mauricio H. Cornejo, Valentin V. Karasiev, Edison X. Salazar

An approximate expression for the Pauli kinetic energy functional Tp is advanced in terms of the Liu-Parr expansion [S. Liu, R.G. Parr, Phys. Rev. A 1997, 55, 1792] which involves a power series of the one-electron density. We use this explicit functional for Tp to compute the value of the noninteracting kinetic energy functional Ts 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 Δabs=(1/N)∑i=1NΔi 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 Δi=100|Tsapp(i)−TsHF(i)|/TsHF(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. The effect of a shell-by-shell optimization of the expansion coefficients of the Liu-Parr expansion of the Pauli kinetic energy functional leads to striking improvements in the mean absolute error of the non-interacting kinetic energy functional. The results are the most accurate ones obtained to date for the representation of the non-interacting kinetic energy functional.

Publisher URL: http://onlinelibrary.wiley.com/resolve/doi

DOI: 10.1002/qua.25601