A recipe for geometry optimization of diradicalar singlet states from broken-symmetry calculations

The equilibrium geometries of the singlet and triplet states of diradicals may be somewhat different, which may have an influence on their magnetic properties. The single-determinantal methods, such as Hartree-Fock or Kohn-Sham density functional theory, in general rely on broken-symmetry solutions to approach the singlet-state energy and geometry. An approximate spin decontamination is rather easy for the energy of this state but is rarely performed for its geometry optimization. We suggest simple procedures to estimate the optimized geometry and energy of a spin-decontaminated singlet, the accuracies of which are tested on a few organic diradicals. This technique can be generalized to interactions between higher-spin units or to multispin systems.