Role of molecular distortions in the spin–orbit coupling between the singlet and triplet states of the 4π electron systems C4H4, C5H5+, and C3H3−

How molecular distortions enhance the strength of spin–orbit coupling (SOC) between the singlet and triplet states of cyclobutadiene, cyclopentadienyl cation, and cyclopropenyl anion is described. The crossing region of the two potential energy surfaces of cyclobutadiene is characterized by a Jahn–Teller active vibrational mode that can connect the singlet and triplet structures. The spin inversion from triplet to singlet occurs in cyclobutadiene with a structural change from D4h to D2h, but the in-plane distortion along the Jahn–Teller mode cannot directly enhance the strength of SOC. Molecular distortions along some C–H out-of-plane bending modes significantly strengthen the SOC in cyclobutadiene. Also in cyclopentadienyl cation, C–H out-of-plane distortions play an essential role in enhancing the strength of SOC. The out-of-plane motions destroy the planarity of cyclobutadiene and cyclopentadienyl cation, leading to rehybridization of their σ and π orbitals. This is a main reason that the strength of SOC is enhanced by the C–H out-of-plane bending distortions in these planar molecules. On the other hand, in cyclopropenyl anion the carbon-ring distortion that can connect the triplet and singlet structures is a main factor that dominates the transition between the two states, due to its nonplanarity.