Spin–Orbit Coupling in Aromatic Hydrocarbons. Calculation of the Radiative Triplet Lifetimes of Naphthalene, Anthracene, and Phenanthrene

A formalism is developed to calculate spin–orbit interactions in aromatic hydrocarbons. The theory is based on $\mathrm{\sigma \pi }$ interactions and involves singlet and triplet $\mathrm{\sigma \pi *}$ and $\mathrm{\pi \sigma *}$ states and their interactions with both the ground and lowest triplet states. CH and CC $\sigma$ electrons are treated separately, and their wavefunctions are written as linear combinations of bonding and antibonding CH and CC orbitals. An estimate is made of the σ‐state energies on the basis of spectroscopic and theoretical data. The calculations are restricted to one‐center, one‐electron terms in the matrix elements of the spin–orbit Hamiltonian. Radiative lifetimes obtained for naphthalene, anthracene and phenanthrene are in reasonable agreement with experiment. The calculations show the importance of including all of the mixing mechanisms considered here in any calculation of spin–orbit coupling in these molecules.