Spin in density-functional theory

The accurate description of open-shell molecules, in particular of transition metal complexes and clusters, is still an important challenge for quantum chemistry. Although density-functional theory (DFT) is widely applied in this area, the sometimes severe limitations of its currently available approximate realizations often preclude its application as a predictive theory. Here, we review the foundations of DFT applied to open-shell systems, both within the nonrelativistic and the relativistic framework. In particular, we provide an in-depth discussion of the exact theory, with a focus on the role of the spin density and possibilities for targeting specific spin states. It turns out that different options exist for setting up KohnSham DFT schemes for open-shell systems, which imply different definitions of the exchangecorrelation energy functional and lead to different exact conditions on this functional. Finally, we suggest possible directions for future developments. (C) 2012 Wiley Periodicals, Inc.