ENERGY EXCHANGE IN PHOTOREACTIONS 43 



iiig are at the average distances calculated from concentrations or pre- 

 dicted by the very large cross sections for effective collision which would 

 result from the application of simple collision theory. It must be sug- 

 gested that the two types of molecules may form a weak complex pre- 

 ceding excitation. 



Watson and Livingston (1950) found that quanta absorbed by chloro- 

 phylls a and b could exchange electronic excitation energy over large 

 distances. Other experiments on such processes as the depolarization of 

 the fluorescence of dye molecules also point to electronic-energy migra- 

 tions over very large distances (Lewschin, 1924, 1935a, b; Pringsheim and 

 Wavilow, 1926). These phenomena are not to be confused with reemis- 

 sion and reabsorption of light (inner filter effect), which can, for geo- 

 metrical reasons, become important only at high dye concentrations. 

 The theories that have been applied to these and other observations 

 attribute the energy migration to the long-range coupling of dipole and 

 higher-moment electric and magnetic fields, thus producing the necessary 

 interaction energy for crossing of potential surfaces at large intermolecu- 

 lar distances. The phenomena may resemble the internal-conversion 

 process of nuclear physics in which coupling between the nuclear fields 

 and the field of external electrons allows excitation of the electron system 

 during nuclear decay. Arnold and Oppenheimer (1950) have employed 

 the comparison to calculate maximum distances for such coupling among 

 the photosynthetic pigments of Chroococcus. They find a distance 

 between 7 and 35 A. Other theories indicate larger distances. The 

 classical theory was given by J. Perrin (1924, 1927), and its quantum 

 analogue by F. Perrin (1932) and by Kallmann and London (1929). 

 Stueckelberg (1932) developed a general theory that includes the migra- 

 tion of electronic energy (see also Mott and Massey, 1949; Vavilov et at., 

 1949). The most complete treatment is that of Forster (1948). All 

 authors give primary consideration to dipole-dipole interaction, since this 

 is the most important type. Transfers dependent on this kind of coupling 

 correspond to excitation by electromagnetic fields and hence must satisfy 

 the same selection rules. Only those systems in which the fluorescence 

 band of the primarily excited molecule overlaps the absorption band of 

 the quencher experience efficient transfer. For example, the potential- 

 energy surface for chlorophyll a excited, chlorophyll b unexcited must 

 overlap that for the reverse distribution of excitation energy. The fur- 

 ther condition is that there must exist sufficient interaction through field 

 coupling to produce the actual conditions for crossing. The interactions 

 that are postulated are large at small intermolecular distances, analogous 

 to van der Waals' forces that depend on the same field components. 

 However, they fall off rapidly with distance, and it is surprising that 

 even the relatively long-range dipole fields can interact with any strength 

 at distances greater than a few kinetic-theory diameters. Ne\'ertheless 



