Evaluation of ⟨Ŝ2⟩ in density functional theory

The evaluation of ⟨S^̂2⟩ in density functional theory (DFT) is considered. Wang et al. [J. Chem. Phys. 102, 3477 (1995)] have derived an approximate, local density expression for ⟨S^̂2⟩ and in the present study their formula is evaluated using densities from unrestricted Hartree-Fock (UHF) and a range of DFT exchange-correlation functionals. The results are compared with those obtained by evaluating the conventional UHF expression using the Kohn-Sham orbitals, which is appropriate for the noninteracting system. A generalized gradient approximation for ⟨S^̂2⟩ is then proposed and investigated.