1296 THE PIGMENT FACTOR CHAP. 32 



the energy of a molecule in the center dechnes with the square of the radius. 

 If the ring of nearest neighbors contributes the interaction energy AE, the 

 second ring will contribute (approximately) AE/4, the third one, AE/9, 

 and so on, the total for an infinite number of rings being (7rV6)A£;. The 

 contribution of rings beyond the Nth. one will be 



/ 1 1 



or <5% for A^ = 12, and <1% for A^ > 60. The interaction energy of the 

 layer should thus be >99% saturated— and the band shift should practi- 

 cally cease— when the radius of the layer has grown to sixty molecular 

 diameters; the shift will reach the limit of rehabihty of our present meas- 

 urements at 12-15 molecular diameters. 



The crystals for which band shift saturation was observed, according 

 to figure 37C.16, contained about 10^ molecules; even if correction is made 

 for scattering, and the true shift assumed to end at about 730 mfx, this 

 limit still corresponds to crystals containing as many as 10^ molecules each. 

 Assuming equal development in three dimensions (which is admissible for 

 the "small", as contrasted to the "large" microcrystals ; cf. fig. 37B.8), 

 such crystals consist, roughly, of 100 layers of 100 X 100 molecules each- 

 somewhat in excess of the dimensions over which the interaction energy 

 should be 99% saturated in a single two-dimensional layer. However, as 

 the distance from the central molecule grows, the role of the crystal layer 

 to which this molecule belongs becomes less dominant, and this should 

 cause the energy saturation to be approached more slowly. 



Spectral effects similar to those observed in chlorophyll derivatives must occur also 

 in other molecular crystals, if the absorption bands of the molecules are intense enough 

 to cause strong interaction. This subject was analyzed theoretically by Davydov 

 (1948), specially in appUcation to hydrocarbons (anthracene, naphthalene, etc.), whose 

 absorption spectra have been described by Obreimov, Prikhodko and co-workers (cf. 

 Prikhodko 1949). Similar to the chlorophyllide crystals, naphthalene crystals are thin, 

 monochnic sheets. Their absorption spectrum (for light falling normally to the sheets) 

 depends on polarization, since electric oscillations can be excited parallel to one or the 

 other of the two crystallographic axes located in the plane of the sheets. Some bands 

 occur with only one (or predominantly one) polarization; others wdth both of them. 

 Two of the latter can be correlated with known bands of naphthalene vapor, shifted 

 toward the longer waves (by 500 and 2000 cm.-', respectively). Their vibrational 

 structure is similar to that of the vapor bands. Bands leading to three other excited 

 levels observed in crystals have no parallel in the vapor spectrum. One of them is 

 about equally strong with both polarizations, the other two are strongly polarized. 

 These three electronic levels, considered as "crystal levels," rather than "molecular 

 levels," combine with a set of vibrational quanta not encountered in vapor, which must 

 be attributed to the lattice as a whole. 



