Spectral element solution of the Kohn-Sham atom

Electronic structure calculations of atoms are important in nuclear physics, and are necessary input for most methods to construct first-principles effective potentials (i.e., pseudopotentials and projector augmented wave potentials). The standard method to solve the atomic problem within Kohn-Sham density functional theory is the shooting method. In this work, the more robust spectral element method is applied to the 1D atomic radial equation. The spectral element method provides a strict, upper-bound on the absolute error in the Kohn-Sham eigenvalues and wavefunctions enabling the solution to be converged to a well controlled accuracy. The results of this method are compared to the extensive ``NIST Atomic Reference Data for Electronic Structure Calculations'' database for elements H to U, providing a more rigourous assessment of this dataset than previously available.