EXCITATION OF POLYENES AND PORPHYRINS 107 



tetra- and octaalkyl data, we see further that either the 1,2,5,6 moments 

 are less than one-fourth as large as the 3,4,7,8 moments if the position-1 

 and -2 vector directions of Fig. 2-20a are correct, or these tentative vector 

 directions are in error by at least 45° if the moments at all positions are 

 taken equal. Examination of the meta-directing 6-substituents given in 

 Fig. 2-22 (compounds 9-15) showed that the predicted 3-vector and with 

 it the ct-vector must also be in error by about 45° or by about 135° ; this 

 conclusion did not depend on the equality of different positions. The 

 best agreement with the theoretical predictions is obtained if we choose 

 the 45° error. 



Such an error is not unreasonable if we remember that the theoretical 

 directions were derived for a Dih porphin with all bonds equal. The 

 directions depend on the phase of the wave functions at the substituted 

 atom. In an upper state with effective angular momentum 9, the phase 

 will change by about 180° in one bond distance. Alternations in bond 

 length, plus the change to a strongly D-2h structure, may therefore easily 

 produce changes in moment directions of many degrees. 



With the directions so altered, the data can now be fitted taking the 

 moments equal at all external positions. This assumption in turn fixes 

 the vector directions more accurately. Within an uncertainty of about 

 20°, they are as given in Fig. 2-205 and c. Surprisingly enough, they are 

 almost perpendicular or parallel to the essential nodal plane in ever}^ case 

 and may be taken exactly so for convenience in intensity computations. 



We may call the polarizations of Fig. 2-206 "porphyrin polarizations" 

 and those of Fig. 2-20c "chlorin polarizations." 



Determination of Moments. Once the vector directions are established, 

 we can find the values of the moments from the intensity data. The 

 values adopted in Table 2-3 fit the data fairly well. They are given in 

 units such that the square of their vector sum will be numerically equal 

 to the peak molar extinction. 



They are uncertain by about 20 per cent. Some of the uncertainties 

 are interdependent; an increase of one value would require lowering or 

 raising another to maintain the fit with the data. A change in the vector 

 directions would also entail adjustments in the values. The fit with the 

 data, as shown in Fig. 2-22, is therefore somewhat better than the accu- 

 racy of the individual moments. 



The spectroscopic moments of four of these substituents had been 

 determined previously for the benzene 2600 A bands: alkyl ( + 6, +7), 

 nitrile (-19), acid (-28), imino (-38) (Piatt, 1951b). The moments 

 in porphin are roughly proportional to these, but about two or three 

 times as large. The difference is partly due to a difference in the way 

 the data were smoothed in benzene, and partly due to our application 

 of the theory to e,nax. A quantity of more theoretical significance would 

 be the contribution Q of a substituent to the transition-moment integral, 



