On the diagnostic value of (S)over-cap(2) in Kohn-Sham density functional theory

Unrestricted density functional theory (UDFT) is, in addition to its applic ation to high spin multiplet systems, an efficient method for describing si nglet biradical states. In this connection, spin contamination of the UDFT description as measured by the expectation values of (S) over cap (2) is of interest, but is difficult to assess since the calculation of [(S) over ca p (2)] as the expectation value of a two-particle operator is not possible within the single-determinant approach of DFT. A new way of determining [(S ) over cap (2)] from the UDFT (UHF or any other) spin magnetization density (SMD) m(s) (r) = rho (alpha)(r) - rho (beta)(r) is described and applied t o the stretched H-2 molecule and the singlet state of the para-didehydroben zene biradical for a number of different functionals. Although [(S) over ca p (2)] as calculated from the Kohn-Sham determinant is found to differ sign ificantly from the corresponding value obtained with the help of the SMD in the case of singlet biradicals, the former result is a diagnostic value an d can be used to assess spin contamination of the UDFT description on a qua litative basis.