26 LIGHT AND LIFE 



different energy may occur only if energy can be radiated or absorbed. 

 Only in a few special cases is this a very probable process compared 

 with others which may occur when an environment is present. The 

 case of a molecule in a collisionless environment is important only 

 in the sparse density of interstellar space. Normally, radiationless 

 energy transfer takes place without the above energy restrictions, since 

 units of energy may be transferred rapidly to or from translational, 

 rotational, vibrational, or electronic states of the environment. 



Criteria for non-radiative energy transfer. For a non-radiative transi- 

 tion to take place between two electronic states of a polyatomic mole- 

 cule, a number of considerations should be especially stressed. Assume 

 that the environment acts only as an energy reservoir. Experiments 

 have shown that rapid transfer of energy to the environment can take 

 place only if the energy spacing in the environment is approximately 

 of the same magnitude as the units of energy which are to be lost by 

 the molecule. In other words, many near resonances should occur 

 between environmental energy levels and the molecular ones. Be- 

 cause of this condition, large molecules, with many closely spaced vi- 

 brational levels, nearly always lose excess vibrational energy to an 

 environment in a time short compared with radiative deactivation 

 or chemical processes. For very small molecules such is often not the 

 case. As a corollary to the above, transfer of a large unit of elec- 

 tronic energy to the closely spaced vibrational levels of the environ- 

 ment is an improbable process. 



A second condition important for cross-over from one electronic 

 state to another is that potential energy surfaces correspoyiding to 

 the two electroyiic states in question should have an available region 

 of mutual "intersection." This means in particidar that non-radiative 

 processes between excited states and the ground state of a molecule 

 have relatively small prolmbility, since these states do not in general 

 cross. The precise meaning of the term "intersection" is important, 

 and it will be discussed more fully in the next paragraph. 



A third, and very important criterion for non-radiative transfer 

 of energy between electronic states deals with the question of perturba- 

 tions. Even though an environmental energy reservoir is available, 

 some perturbation must be present to "mix" the two states between 

 which energy transfer is to take place. It is known from quantum 

 mechanical jicrturijation theory that a ])erturbation of this kind 

 is most important in the region where the two states have nearly 

 the same energy and geometry, i.e., in the region of potential surface 

 intersection. Perturbation theory also shows that the interaction be- 



