The effect of localized modes on radiationless electronic transitions. I. Diatomic impurities in a crystal

The nonradiative relaxation of a diatomic homonuclear molecule dissolved in an infinite linear chain of inert host atoms is studied in the harmonic approximation. The coupling to the molecular vibration as well as to other local modes and the frequency-dependent coupling to the host vibrations are determined by only one parameter related to the bond length change of the diatomic under consideration. It is demonstrated that the saddle-point method as it is usually applied is not valid if the frequencies of the localized vibrations are sufficiently far above the continuum. An improved method is presented which treats only the coupling to the continuum by the stationary phase method. The calculated rates show a rich structure including strong nonmonotonous variations with the energy gap and activated behavior as a function of temperature with small activation energies even in the weak coupling limit. The limit in which one-phonon processes dominate is discussed. Applications to Cl₂ and O₂ in argon matrices are presented.