Direct orbital-free calculations using DFT and one-electron Greenʹs functions: applications to atoms

A method based on density functional theory which utilizes the numerical calculation of one-electron Greenʹs function instead of the diagonalization of the Kohn-Sham Hamiltonian is presented. The method is applied to atoms employing the approximation of spherically averaged electron density. The use of rectangular non-uniformly spaced basis functions for the representation of the radial part of the Hamiltonian provides a favourable dependence of the results on numerical parameters and a simple implementation scheme with the computational cost scaling linearly with the number of electrons. The all-electron SCF calculation within the generalized gradient approximation leads to encouraging results for the total and first ionization energies.