EXCITATION OF POLYENES AND PORPHYRINS 103 



being mixed with the wave functions of nearby allowed transitions that 

 have strong 0-0 absorption peaks. Probably these are the KA-^B° tran- 

 sitions. We shall show how the peak intensities can be predicted in 

 bands I and III, which grow from essentially zero values in D4h porphin. 



The available theory of the vector directions of the moments has not 

 been rigorously justified, but it suggests that the directions of positive 

 moments at different positions on porphin might be related as indicated 

 in Fig. 2-20a for the two components of ^A~^Q°. In each diagram the 

 dashed line shows the position of the essential nodal plane of the wave 

 function. The polarization of the transition should be formally perpen- 

 dicular to this plane. The positions of the central hydrogen atoms and 

 the assignment of the observed bands to these electronic components 

 were not given by the theory. How they were determined we shall see. 



Note that in each component, for positive substituents at exactly 

 opposite points on the ring system, the vector directions are parallel. 

 Their moments will add. Such disubstitution at opposite points will 

 produce double the moment and four times the intensity change pro- 

 duced by monosubstitution. This general prediction is more soundly 

 based than the special vector-moment directions in Fig. 2-20a, since it 

 must be true for every even-odd transition in centrally symmetric mole- 

 cules (Piatt, 1951c). In even-even transitions the moments from 

 opposed disubstitutions must cancel. This will be a useful test in the 

 classification of transitions. In Fig. 2-22 it is seen that both bands I 

 and III grow with increasing alkyl substitution up to octaalkyl porphin 

 (compound 7) ; there is no evidence of cancellation of moments. Conse- 

 cjuently the predicted even-odd character of the visible transitions is 

 confirmed. Disubstitution does not give so much as four times the inten- 

 sity of monosubstitution, but this was true also in benzene and is presum- 

 ably due to the deficiencies of the simple first-order theory. 



The more detailed predictions of Fig. 2-20a require more examination. 

 In principle, if (1) accurate data on enough different porphyrins were 

 available, if (2) the theory were valid to a few per cent, and if (3) the 

 peak molar extinction e,nax were strictly proportional to the squared 

 transition-moment integral, then we could determine the following quan- 

 tities for each electronic transition: 



1. From different substitutions at a single position, the spectroscopic 

 moment of each substituent; 



2. From a single substituent placed at different positions, the value of 

 its moment as a function of position, which is not necessarily constant 

 (three different values being possible, as at positions 2, a, and 3, plus the 

 central nitrogen atom), and so the values of all moments as functions of 

 position, since their ratios should be constant in a first-order theory; 



3. From di- and polysubstitution with one substituent, the exact direc- 

 tion of the vectors at every position (three different directions to be deter- 



