  Density functional calculations on atoms are often used for determining
accurate initial guesses as well as generating various types of pseudopotential
approximations and efficient atomic-orbital basis sets for polyatomic
calculations. To reach the best accuracy for these purposes, the atomic
calculations should employ the same density functional as the polyatomic
calculation. Atomic density functional calculations are typically carried out
employing spherically symmetric densities, corresponding to the use of
fractional orbital occupations. We have described their implementation for
density functional approximations (DFAs) belonging to the local density
approximation (LDA) and generalized gradient approximation (GGA) levels of
theory as well as Hartree-Fock (HF) and range-separated exact exchange [S.
Lehtola, Phys. Rev. A 2020, 101, 012516]. In this work, we describe the
extension to meta-GGA functionals using the generalized Kohn-Sham scheme, in
which the energy is minimized with respect to the orbitals, which in turn are
expanded in the finite element formalism with high-order numerical basis
functions. Furnished with the new implementation, we continue our recent work
on the numerical well-behavedness of recent meta-GGA functionals [S. Lehtola
and M. A. L. Marques, J. Chem. Phys. 2022, 157, 174114]. We pursue complete
basis set (CBS) limit energies for recent density functionals, and find many to
be ill-behaved for the Li and Na atoms. We report basis set truncation errors
(BSTEs) of some commonly used Gaussian basis sets for these density functionals
and find the BSTEs to be strongly functional dependent. We also discuss the
importance of density thresholding in DFAs and find that all of the functionals
studied in this work yield total energies converged to $0.1\ \mu E_{h}$ when
densities smaller than $10^{-11}a_{0}^{-3}$ are screened out.
