An impurity molecule located as a solute in a condensed solvent, a solid matrix or a liquid, when put in an excited vibrational state will loose its excess energy due to its interaction with the surrounding solvent molecules. Vibrational energy accumulation is a precursor to all thermal chemical reactions. Its release by vibrational relaxation following a reactive barrier crossing or optically induced reaction defines the formation of a product state. The direct observation of this process by, for example, infrared emission or more often laser induced fluorescence teaches us about its characteristic timescales and their energetic (i.e. couplings and frequencies) origin. These issues are discussed in this chapter. Before turning to our main task, which is constructing and analyzing a model for vibrational relaxation in condensed phases, we make some general observations about this process. In particular we will contrast condensed phase relaxation with its gas phase counterpart and will comment on the different relaxation pathways taken by diatomic and polyatomic molecules. First, vibrational relaxation takes place also in low density gases. Collisions involving the vibrationally excited molecule may result in transfer of the excess vibrational energy to rotational and translational degrees of freedom of the overall system. Analysis based on collision theory, with the intermolecular interaction potential as input, then leads to the cross-section for inelastic collisions in which vibrational and translational/rotational energies are exchanged. If C∗ is the concentration of vibrationally excited molecules and ρ is the overall gas density, the relaxation rate coefficient kgas is defined from the bimolecular rate law When comparing this relaxation to its condensed phase counterpart one should note a technical difference between the ways relaxation rates are defined in the two phases.
The Sommerfeld ground-wave limit for a molecule adsorbed at a surface
