We note that computing S 2 using the Kohn-Sham determinant gives the value for the non-interacting system. Obtaining S 2 for the fully interacting system requires use of the-two particle density matrix, which significantly complicates the implementation of such models. This has been shown to give slightly larger S 2 values than the non-interacting system. In this way, the projection models used in this paper are not as well defined in a formal sense as in wave function theories. However, in practical terms, experience suggests that the approximate and more tractable form of S 2 obtained from the Kohn-Sham determinant is acceptable in the types of calculations being carried out here. For each approximate density functional, three different geometries were used for calculating J-couplings. The first approach, and perhaps most widely used methodology in similar benchmark studies, determines the J value using published crystal structures. The second source of geometries was the minimum energy structures on the HS or broken-symmetry PESs. The third set of geometries used minimum energy structures located on the AP PESs.