Intersystem Crossing in Gaseous Molecules

The theory of electronic relaxation in the solid phase is discussed in terms of gaseous molecules. Two limits are examined—the ``small-molecule limit'' (α limit), where electronic relaxation cannot occur in the free molecule, and the ``big-molecule limit'' (ω limit), where electronic relaxation at a rate virtually identical with that in the solid can take place in the absence of any external perturbation. An ``intermediate case'' (μ case) is described where no relaxation can occur in the completely free molecule, but where only extremely minute perturbations are required to induce such a process. Intersystem crossing B2u1→B1u3 in benzene is close to the borderline between the ω limit and the μ case. Although the concepts are somewhat inexact quantitatively because of the difficulty in estimating matrix elements and the vibrational density-of-state function, the theory does indicate that the zero-point level of the 1B2u state could behave like a μ case, while the excited vibrational levels of this electronic state, those mainly reached in past experiments, may lie in the ω limit. Available experimental data support the idea that the higher vibrational levels of the 1B2u state of benzene very likely lie in the ω limit, but cannot shed light on the behavior of the zero-point level. Theoretical expressions for the rate of intersystem crossing, the fluorescence lifetime, and the fluorescence yield as functions of pressure are worked out. Theory shows that in both the α limit and in the μ case the absolute fluorescence yield approaches unity in the limit of zero pressure. For the ω limit, the absolute fluorescence yield can very well be less than unity even for a molecule in free space. Some new experiments are suggested by the theoretical conclusions.