Spin-orbit coupling in aromatic molecules

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Abstract
A calculation is presented of the radiative lifetimes of the ππ′ phosphorescent state of quinoxaline and a number of aromatic hydrocarbons. For the matrix elements of the spin-orbit hamiltonian an ‘atoms in molecules’ approach is used and only the one-electron one-centre terms in the expansion of these matrix elements in integrals over AO's are retained. This approach is similar to that used by Goodman and Krishna for the nπ′ states of some aza-aromatics. For quinoxaline a lifetime τ=0·33 s is obtained. For aromatic hydrocarbons the phosphorescence is attributed to ‘intensity stealing’ from π→σ′ and σ→π′ transitions in which an electron is transferred between the σ and π system, in agreement with the out-of-plane polarization of phosphorescence observed experimentally. It is found that interactions involving the sigma orbitals of the C-C bonds are an order of magnitude more effective than those involving C-H orbitals. The calculated radiative lifetimes are: benzene 23·2 s (77 s), naphthalene 3·3 s (11 s), phenanthrene 1·5 s (5 s), anthracene 25·4 s (85 s), azulene 35·3 s (118 s), phenalenylium 2·7 s (9 s); the values first quoted are increased to those in parentheses when the transition moments of the σ↔π excitations which enter the calculation are scaled according to Mulliken.