Numerical self-consistent-field method to solve the Kohn-Sham equations in confined many-electron atoms

Abstract

A method to solve the Kohn-Sham equations numerically in confined many electron atoms is presented. The method combines a very efficient matrix approach to locate approximate orbital eigenvalues with a shooting method to integrate the radial equations, and an extrapolation to further refine the spin-orbital energies. The confinement is imposed on the atom by requiring that the electron density vanishes for distances greater than or equal to a confinement radius ${R}_{c}.$ The algorithm is tested with the confined hydrogen atom. The role of local and nonlocal exchange-only functionals in confined many-electron atoms is analyzed and compared with Hartree-Fock results.