ENERGY MIGRATION AND THE PHOTOSYNTHETIC UNIT 1295 



large resonating system, not only by a residual coupling with inter- or 

 intramolecular vibrations, but also by an efficient quenching of fluorescence 

 by a relatively small number of molecules of an impurity — a "trapping" of 

 electronic excitation in a "potential hole," in which it can then be dissi- 

 pated in the usual way by conversion into vibrations. 



Of some relevance here are the experiments on the absorption spectra 

 and fluorescence of certain pigments (particularly chlorophyllides) in the 

 crystalline state, described in chapter 37C, section 3. 



These experiments showed that, in chlorophyllide crystals and mono- 

 layers, the red absorption band is shifted by as much as 80 m/x (up to 2000 

 cm.~^; cf. table 37C.II) toward the longer waves. Theoretical calcula- 

 tions, using the actual density of the chromophores in the crystal, indicated 

 that a shift of approximately this extent is to be expected in consequence 

 of the interaction between closely packed chromophores (Kromhout 1952; 

 Jacobs, Holt, Kromhout and Rabinowitch 1954; cj. also Heller and Marcus 

 1951). 



In contrast to calculations of Forster et at., in which only the energy 

 exchange between two molecules was considered, these estimates were 

 based on simultaneous consideration of "virtual dipole" interactions be- 

 tween all pairs of molecules in a cubic lattice. 



The calculations were carried out for an isotropic three-dimensional 

 lattice. The chlorophyllide crystals have, however, a layered structure 

 (illustrated by fig. 37B.9) ; and molecular interaction can be expected 

 to be much stronger within each layer than between them. (A difference 

 is likely also between two directions within each layer.) This expectation is 

 confirmed by the observation that the spectra of monomolecular layers of 

 chlorophyllide show almost as wide a red shift as those of crystals. The 

 predominantly two-dimensional interaction must lead to a more rapid 

 saturation of interaction energy with distance than in a three-dimensional 

 system (since the integration of the resonance energies has to be carried 

 out over circular belts, rdr, instead of spherical shells, rHr). Con- 

 sequently, the relative contribution of the nearest neighbors to the total 

 resonance energy of a molecule is greater in the layered structure than 

 in an isotropic three-dimensional system. This has a bearing on the ob- 

 servations — described in chapter 37C — of the saturation of the band shift 

 with increasing size of the microcrystals. Obviously, as a crystal begins to 

 grow, the interaction effect must at first increase with the number of mole- 

 cules in it; saturation will be reached when new molecules, added on the 

 surface, are so far from an average molecule inside the crystal that they 

 do not contribute significantly to its excitation energy. For an energy de- 

 creasing with inverse third power of distance (such as the mutual energy of 

 two dipoles), the contribution of circular belts of increasing diameter to 



