Interesting properties of Thomas–Fermi kinetic and Parr electron–electron‐repulsion DFT energy functional generated compact one‐electron density approximation for ground‐state electronic energy of molecular systems

Abstract

The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N-dimensions to a (nonlinear, approximate) density functional of three spatial dimension one-electron density for an N-electron system, which is tractable in the practice, is a long desired goal in electronic structure calculation. If the Thomas-Fermi kinetic energy ( approximately integralrho(5/3)dr(1)) and Parr electron-electron repulsion energy ( approximately integralrho(4/3)dr(1)) main-term functionals are accepted, and they should, the later described, compact one-electron density approximation for calculating ground state electronic energy from the 2nd Hohenberg-Kohn theorem is also noticeable, because it is a certain consequence of the aforementioned two basic functionals. Its two parameters have been fitted to neutral and ionic atoms, which are transferable to molecules when one uses it for estimating ground-state electronic energy. The convergence is proportional to the number of nuclei (M) needing low disc space usage and numerical integration. Its properties are discussed and compared with known ab initio methods, and for energy differences (here atomic ionization potentials) it is comparable or sometimes gives better result than those. It does not reach the chemical accuracy for total electronic energy, but beside its amusing simplicity, it is interesting in theoretical point of view, and can serve as generator function for more accurate one-electron density models.