1822 SPECTROSCOPY AND FLUORESCENCE OF PIGMENTS CHAP. 37C 



450-470 m/i peak; it thus increases the apparent absorption in the blue 

 component of the doublet much more strongly than in the violet one. 



The curves in Fig. 37C.16a-c were drawn so as to equalize the heights of the red 

 peaks. Estimates indicate that crystaUization causes no large change in the area 

 under the red band. The area under the blue-violet band, on the other hand, seems to 

 be substantially reduced by crystallization. (In the case of ethyl pheophorbide b, the 

 optical density in the peak of the blue band is seven times that in the peak of the red 

 band in solution, but about equal to it in small microcrystals!) 



In part, at least, the explanation may be the same as suggested above for mono- 

 layers: the light transmitted through thin plate-shaped crystals consists mainly of 

 beams that have passed through the crystals normally to their planes; the oscillation 

 dipole of the red band lies in this plane, while that of the "Soret band" is mainly (or 

 entirely) normal to it. 



Probably the formation of a high-density solid chlorophyll phase accounts for the 

 observations of Strain (1952). He dissolved chlorophyll (a, a', b, or b') in petroleum 

 ether + 5% methanol; upon extraction of methanol with water, the chlorophyll solution 

 in petroleum ether became "colloidal" and the red band moved to 710 m/* (in a and a') 

 and to 690 m/j, (in b and b'). 



A theoretical interpretation of the band shift in crystals and mono- 

 layers can be obtained (cf. Jacobs, Holt et al. 1954) by considering the 

 interaction of an orderly array of resonating "virtual" dipoles (which are 

 associated, in quantum theory, with the transition between two stationary 

 states, and determine the "oscillator strength" of the transition). Each 

 molecule in the array has the same average probability of being excited 

 by an incident light wave. Heller and Marcus (1951) showed that the 

 excitation energy of an infinite isotropic lattice of such virtual dipoles 

 differs from that of an individual dipole by a term equal to the "classical" 

 interaction energy of a system of actual oscillating dipoles of the same 



average magnitude, having a phase difference of e'""^ ^ (where k is the wave 



— > 



number vector of the incident wave, and R the distance vector between 



two lattice points). Jacobs applied Heller and Marcus' equations to a 



finite isotropic crystal, and obtained an expression for Er , the energy of 



the excited state as a function of the radius R of the crystal. Because 



of the mutual cancellation of the effects of dipoles with "unfavorable" 



phase differences, this function grows only very slowly, until the crystal 



dimensions reach the order of magnitude of a wave length, after which the 



increase becomes more rapid; in other words, the contribution to the 



interaction energy of spherical shells closest to the center is smaller than 



that of the shells \vith R > 100 m/n. 



The sigmoid-shaped 7?'^' = f{R) curve reaches saturation at 



(37C.1) E''' = Eo + ^E"' = Eo- {ATuVmi) 



