Orbital interactions expressed in resonance structures: An approach to compute stabilisation of cyclobutanediyl diradicals

Ab initio valence bond (VB) calculations give direct evidence for the stabilisation and closed-shell character formation of formal diradicals by neighbouring group interactions. By allowing the singly occupied p-orbitals to delocalise during the orbital optimisation, neighbouring group effects are implicitly included in the wavefunction. By constraining the orbitals in the wavefunction to remain strictly atomic, through-bond effects are excluded from the wavefunction. These effects can then be included in the wavefunction by expanding the wavefunction using more valence bond structures. The choice of these structures used to built the wavefunction determines which interactions will be accounted for. For the compounds considered here, 2,4-dioxo-1,3-cyclobutanediyl (1), 2,4-bis(methylene)-1,3-cyclobutanediyl (2), 1,3-cyclobutanediyl (3), and 1,1,3,3-tetrahydro-1,3,2,4-diphosphadiboretane-1,3-diyl (4), the calculations show that the most important VB structures for mediating interactions between the opposing radical centres are those that withdraw electrons from the ring, thereby creating an aromatic, 2π-electron four-membered ring. For the 1,3-cyclobutanediyl analogues (3 and 4), the PH2 group functions similar to the CO group, and is a better electron-accepting substituent than the CH2 group. The energy differences between the strictly atomic and delocal orbital optimisation models show that the molecules with less diradical character are stabilised more by through-bond orbital interactions.