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.