On the diagnostic value of (Ŝ2) in Kohn-Sham density functional theory

Abstract

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 Ŝ² is of interest, but is difficult to assess since the calculation of (Ŝ²) as the expectation value of a twoparticle operator is not possible within the single-determinant approach of DFT. A new way of determining (Ŝ²) from the UDFT (UHF or any other) spin magnetization density (SMD) m_s (r) = pα(r) −pβ(r) is described and applied to the stretched H₂ molecule and the singlet state of the para-didehydrobenzene biradical for a number of different functionals. Although (Ŝ²) 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.