ENERGY EXCHANGE IN PHOTOREACTIONS 33 



sion are 



^ j\U-m + s- 1)! 

 ^ (i-m)!(i+.s - 1)! ^'^^^ 



and 



= (^y-" 



(1-25) 



the latter applying at large j, i. e., at classical conditions. Reaction 

 occurs when m or more quanta become localized in the bond. The 

 probability, summed for all m values greater than some critical value, 

 multiplied by the reciprocal of the average time for single-quantum trans- 

 fers gives the rate constant under reaction conditions such that the 

 velocity is limited by internal transfers of energy. The theory is not 

 especially satisfactory in either form because of the poor knowledge of 

 the average time for any large molecule. Similar limitations apply to 

 the calculation of the rate of dissipation of photoenergy absorbed and 

 converted to vibrational energy. In small molecules this energy may be 

 used efficiently because there are few degrees of freedom into which it 

 may be dissipated. In large molecules the energy will be greatly diluted 

 in the many degrees of freedom, so that quantum yields for photoreactions 

 can be expected to be low. For instance, photodenaturation of proteins 

 is usually an inefficient process with low quantum yields (McLaren and 

 Pearson, 1949; Katchman and McLaren, 1948; Kubowitz and Haas, 

 1933). 



A number of attempts have been made toward improving the Kassel- 

 Rice theory (Marcus, 1952; Slater, 1948; Benson, 1952). The problem 

 is very complicated in molecules even of small size because energy migra- 

 tion involves all atomic distances. Simplified potential surfaces are com- 

 pletely inadequate for the problem. Apart from a knowledge of the 

 complete surfaces, the absolute-rate theory for unimolecular processes is 

 reasonably complete (Glasstone et al., 1941, Chap. 5; Giddings and 

 Eyring, 1954; Magee, 1952). Giddings and coworkers have observed 

 that negative entropies of activation for unimolecular reactions are 

 impossible, and their apparent occurrence in unimolecular reactions must 

 be explained by small values of the transmission coefficient. They rea- 

 son that the reverse process, i.e., bimolecular combination of radicals, is 

 a poor process in that the activated complexes are reflected back to 

 reactants through their inability to dissipate energy sufficiently rapidly 

 among internal degrees of freedom. Since the transmission coefficient 

 must be the same independent of the direction of the reaction, it will 

 also be small for unimolecular decomposition. That is, the process by 

 which energy previously stockpiled in internal degrees of freedom is 

 delivered to the reacting bond is also poor. The ability of the internal 

 degrees to dilute the extra energy of the molecule varies with the amount 



