Theory of Intersystem Crossing in Aromatic Hydrocarbons

The electronic matrix elements governing intersystem crossing in aromatic hydrocarbons are derived and evaluated. The derivation is equivalent to Fano's treatment of resonance scattering. It is shown that the best first-order description for crossings that show simple unimolecular behavior involves molecular states that are both spin contaminated and vibronically contaminated, but can be adequately represented by an expansion to second order in pure-spin adiabatic Born-Oppenheimer states. The corresponding first- and second-order matrix elements are expanded about a nuclear equilibrium configuration and the expansions are terminated through the application of a symmetry argument. This yields five different types of matrix elements with small or vanishing cross terms; these matrix elements are associated with five experimentally distinguishable mechanisms, namely (1) direct spin-orbit coupling, (2) vibronically induced spin-orbit coupling, (3) mixed vibronic and spin-orbit coupling, (4) resonant spin-orbit coupling, and (5) vibronically induced resonant spin-orbit coupling. To distinguish these mechanisms use is made of isotope effects, spin polarization and vibrational selection. The available experimental data on singlet-to-triplet crossing in naphthalene and anthracene are analyzed in detail and compared with qualitative and quantitative theoretical predictions. It is concluded that at low temperature singlet-to-triplet crossing in naphthalene is dominated by crossing to the third-lowest triplet state via the third mechanism. At high temperature the dominant process involves either resonant crossing to the fourth-lowest triplet state via the fifth mechanism or resonant crossing to the fifth-lowest triplet state via the fourth mechanism. In an appendix spin-rotational and orbital-rotational coupling are shown to be too small to contribute measurably to these crossings.