Consistent Spin Decontamination of Broken-Symmetry Calculations of Diradicals

Broken-symmetry calculations of diradicals exploit the mean-field energies of determinants that are not eigenfunctions of the Ŝ2 operator, the mean value of which is close to 1 for the ms = 0 solution. This spin contamination must be corrected. Two different contributions affect ⟨Ŝ2⟩, namely, the mixing between neutral and ionic valence bond components, the so-called kinetic exchange, which decreases ⟨Ŝ2⟩, and the spin polarization of the supposedly closed shell orbitals, which increases ⟨Ŝ2⟩. The popular Yamaguchi formula is valid for the first effect but irrelevant for the second one. From a few constrained broken-symmetry calculations, one may treat separately the two contributions and apply their specific spin decontamination correction. This work proposes a consistent spin-decontaminated procedure for the evaluation of singlet–triplet gaps in diradicals.