The local-spin-density approximation (LSD) is a generalization of the LDA in which the spin-degree of freedom is treated in a nontrivial way [10,11].
For atoms, it is sufficient to pick an arbitrary spin-polarization direction,
and to consider the local-spin-density,
.
Our choice of functional is that of Vosko, Wilk, and Nusair (1980)
[4], as described
above.
In general, the local-spin density approximation requires consideration
of the spin-density matrix,
,
where 
and 
represent spin up or spin down. This leads to
consideration of a potential of the form, 
.
This additional generality is not required in the present work.