On the diagnostic value of (S)over-cap2 in Kohn-Sham density functional theory

Unrestricted density functional theory (UDFT) is, in addition to its application to high spin multiplet systems, an efficient method for describing singlet 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 cap (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 to the stretched H-2 molecule and the singlet state of the para-didehydrobenzene biradical for a number of different functionals. Although [(S) over cap (2)] as calculated from the Kohn-Sham determinant is found to differ significantly from the corresponding value obtained with the help of the SMD in the case of singlet biradicals, the former result is a diagnostic value and can be used to assess spin contamination of the UDFT description on a qualitative basis.