102 RADIATION BIOLOGY 



where Q^ and Qy are polarized in mutually perpendicular directions, whose 

 relations to the H-H axis of the central protons has yet to be determined. 



EFFECT OF SUBSTITUTIONS 



The effect of substituents on forbidden transitions is easier and more 

 entertaining to compute than the effects on allowed transitions. In the 

 porphyrin visible bands, the intensity changes with substitution are espe- 

 cially interesting. Several "types" of spectra have been distinguished 

 (Stern and Wenderlein, 1936, V; Rabinowitch, 1944) according to the 

 relative intensities of the different band maxima and have been roughly 

 correlated with the presence or absence of certain kinds of substitutions. 

 The spectra are different enough to be used for following reactions, for 

 identification, and for analysis. 



Spedroscopic-moment Vectors. The theory of intensity changes in the 

 forbidden 2600 A bands of benzene on substitution was given by Sklar 

 (1942) and Forster (1947). Substituents cannot decrease the native 

 (vibrational) intensity of a forbidden transition, but can only increase it 

 by destroying the symmetry that makes it forbidden and by mixing 

 the excited-state wave function with the wave function of an allowed 

 transition. 



Briefly, the result of the theory is that the increase of intensity over 

 the unsubstituted compound is proportional to the square of a vector, 

 the transition-moment integral of Eq. (2-12), or rather that part of it 

 induced by the presence of the substituents. This induced vector is the 

 sum of vector components, one for each substituent. The magnitude of 

 each component, or its "spectroscopic moment," which may be either 

 positive or negative, is a parameter that depends only on the substituent; 

 its direction depends only on the position of substitution. (See Fig. 2-20 

 for typical vector directions as functions of position of substitution, and 

 Fig. 2-21 for typical vector sums with several substituents. The spectro- 

 scopic-moment vector must not be confused with the angular-momentum 

 vectors described earlier.) 



This theory was applied to a determination of the moments of 25 ben- 

 zene substituents from the observed spectral intensities of the 2600 A 

 bands (Piatt, 1951b). It was shown that the moments were roughly 

 proportional to the chemical "directing power" of the substituents, with 

 ortho-para-directing substituents having positive moments, and meta- 

 directing substituents, negative ones. 



Application to Porphyrins. This theory can be adapted to interpret 

 the changes in the visible bands of the porphyrins. The reasoning is as 

 follows: 



Substitution in porphins usually seems to strengthen the I and III, or 

 0-0, bands, of the two electronic components, leaving almost unchanged 

 the II and IV, or 0-1, bands. Therefore the 'A-Hf wave functions are 



