ENERGY MIGRATION AND THE PHOTOSYNTHETIC UNIT 1283 



begin fluctuating back and forth between the two atoms. The frequency, 

 V, with which this fluctuation occurs, determines the interaction energy, E, 

 according to the quantum-mechanical equation relating energy to fre- 

 quency: 

 (32.4) E = hv 



If 1/v is small compared with the duration of the collision (which, for 

 average thermal velocities of the molecules, is of the order of 10~^^ second) 

 a large number of energy exchanges will occur during a single coUision, and, 

 when the atoms separate after the collision, the chance of finding the exci- 

 tation energy associated with the formerly unexcited helium atom will be 

 equal to that of finding it in the originally excited particle. 



When identical molecules are present in close mutual proximity in a 

 concentrated solution, a pure liquid or a crystal, the probability of excita- 

 tion energy exchanges can be so high that the energy quantum will change 

 its location several times before it is re-emitted as fluorescence, dissipated 

 as heat or utilized for a photochemical transformation. This phenomenon 

 of energy migration includes two extreme cases (and all transitions between 

 them). In the one extreme, the frequency of intermolecular exchanges is 

 much higher than that of intramolecular vibrations. In this case, the ex- 

 citation energy migrates from molecule to molecule without tarrying in any 

 one of them long enough to warrant the application of the Franck-Condon 

 principle; in other words, the electronic excitation energy is in and out of 

 the molecule before the sluggish nuclei can adjust themselves to its pres- 

 ence. The excited state then belongs to the system of many identical 

 molecules as a whole, rather than to any individual molecule; the excita- 

 tion energy "package" is in a condition reminiscent of that of an electron 

 in the "conductivity band" of a metal (or a "pi electron" in the benzene 

 ring). 



In the other extreme case, the excitation energy stays with each mole- 

 cule long enough for intramolecular vibrations to be acquired (or lost) in 

 accordance with the Franck-Condon principle. At each given moment, 

 then, the excitation energy belongs to a definite molecule. It moves from 

 one molecule to another by a diffusion mechanism reminiscent of the 

 Brownian movement of material particles. 



There is some confusion in the terminology used to describe the different cases of 

 resonance migration of energy. The term "exciton" was first proposed by the Russian 

 theoretical physicist Frenkel in a discussion of the "fast" propagation mechanism, and it 

 has been suggested that this term should be reserved for this case (although Frenkel him- 

 self has used it later also in referring to "slow" migration). The first phenomenon could 

 also be described as "non-localized" or "communal" absorption of light quanta by a 

 system of coupled resonators; while the second is reminiscent of repeated "collisions of 

 the second kind," such as are responsible for sensitized fluorescence in gases; it has been 



