Is the Inversion of Phosphorus Trihalides (PF₃, PCl₃, PBr₃, and PI₃) a Diradical Process?

This work explores possible reaction paths for the inversion of a series of trigonal pyramidal phosphorus trihalides, PF₃, PCl₃, PBr₃, and PI₃, and it especially addresses the question of whether and when the bonding of the lowest-energy species along the inversion paths should be described as a hyper-open-shell diradical. The various paths for inversion are calculated using a single-reference method within the framework of Kohn-Sham density functional theory and also with multireference wave function methods. Our calculated results using both kinds of methods show that, for all the halogens studied (F, Cl, Br, and I), the lowest-energy singlet path for the inversion occurs by the formation of a C_{2 v} transition structure rather than a D_{3 h} transition structure. This geometrical preference agrees with what has been inferred previously based on closed-shell singlet calculations. But in the present study, we examined not only closed-shell singlet transition states but also open-shell singlet states and triplet states for calculating stationary points and inversion paths, and for some of the phosphorus trihalides, we found that paths involving open-shell configurations are lower in energy than those restricted to closed-shell configurations. We analyzed the changes along the paths in terms of hybridization and orientation of the frontier orbitals and in terms of locally avoided crossings, and the extent of the diradical character was quantified by calculating the effective number of unpaired electrons. Even for the singlet inversion path that goes via a D_{3 h} structure, the barrier for PF₃, PCl₃, and PBr₃ is higher for a closed-shell singlet spin state than for the open-shell singlet configuration. Furthermore, the energy of the triplet D_{3 h} structure is below even that of the open-shell D_{3 h} singlet for PCl₃, PBr₃, and PI₃. This necessitates rethinking the role of open-shell states in nominally closed-shell processes.