ENERGY TRANSFER IN PHOTOCHEMICAL SYSTEMS 49 



lisions between excited and unexcited molecules. The energy levels of 

 the molecules will, in general, be significantly perturbed by such 

 collisions, and thus the absorption and emission spectra of the com- 

 ponents may be changed. If, on occasion, only a small amount of the 

 excitation energy is removed, this being transformed into vibrational 

 energy of the acceptor molecule, the excited molecule may be brought 

 into the triplet state (Pringsheim, 1949, pp. 99-100). Such a process 

 may occur with particularly high probability if the acceptor molecule 

 contains an atom of high atomic number or is paramagnetic (Kasha, 

 1952; Kasha and McGlynn, 1956). The close collision mechanism is 

 believed to be the most important one in the fluorescence of liquid 

 organic solutions induced by high-energy radiation (Furst and Kail- 

 man, 1954). It has been shown to be unimportant in some UV- 

 induced energy transfer phenomena (Hardwick, 1957). 



3. The transfer of electronic excitation energy through collisions 

 over a distance of several molecular diameters (resonance transfer) 

 (Kallman and London, 1928; Forster, 1948, 1951; Vavilov, 1943). 

 The main quantitative theory of resonance transfer is due to Forster 

 (1951) and is based on a calculation of a mutually induced dipole 

 interaction between donor and acceptor molecules, both of which are 

 capable of being excited to the same energy level. The theory predicts 

 that the probability of transfer is proportional to the extent of the 

 overlap between the emission spectrum of the donor and the absorption 

 spectrum of the acceptor, and also to the intensity of these transitions. 

 This phenomenon may be thought of as being analogous to the prop- 

 erty of resonance in organic molecules, inasmuch as, during the actual 

 collision, the interaction between the molecules makes it impossible to 

 consider the excitation energy as belonging to only one of the partners, 

 but rather to both of them simultaneously. Thus, on subsequent sepa- 

 ration of the colliding molecules, the energy has a definite calculable 

 probability of being found in the previously unexcited molecule. 

 Forster estimated that, for typical dye molecules (i.e., molecules with 

 intense transitions in the visible region), the probability of energy 

 transfer during an excited state lifetime of 10~'- sec will become equal 

 to the probability of fluorescence when the colliding molecules come 

 within about 100 A of each other, i.e., about 10 times their ordinary 

 kinetic collision diameter. The probability of transfer, and thus the 



