All electronic structure calculations were carried out using a local development version of Gaussian. Calculations using the AP model employed local implementations of analytic first-and second-derivative programs. The examination of J-coupling calculations used the test set reported by Peralta and Rudra. Calculations have been carried out using five different functionals: B3LYP, LC-ωPBE, CAM-B3LYP, 35 B3PW91 36 and ωB97XD. Previous studies have shown that B3LYP and LC-ωPBE yield the best J-couplings among several density functionals. All J-coupling calculations were performed with Ahlrich's all electron triple-ζ valence plus polarization for the metal centers and Ahlrich's double-ζ valence plus polarization basis sets for non-metal atoms. Broken symmetry solutions were generated by using a fragment guess approach to ensure spin-localized initial Kohn-Sham (KS) determinant guesses. All converged KS solutions were verified by stability analysis. To explore the impact of spin-projection on the types of calculations being explored here, we have chosen to use the AP method as a proxy for other spin-projection models (PAV, in particular). Indeed, recent work from our lab has demonstrated the conditions under which such approaches are rigorously equivalent and those cases for which such models are numerically equivalent. 11 AP calculations using self-consistent field based models, such as HF and DFT, require two converged determinants: (1) a spin-contaminated broken-symmetry state; and (2) a spin-pure high-spin state. Those two determinants are used to assemble an AP energy according to