100 RADIATION BIOLOGY 



push the B and Q states apart, with the Q lying lower (Hund rule) ; 

 triplets of each type will again lie below singlets of the same type. 



The important prediction that this trick of adding angular-momentum 

 vectors makes possible is that transitions from the ground state to the 

 low Q states will be comparatively weak because large changes of angular 

 momientum are forbidden, whereas the transition to the higher B states 

 will be strong and highly allowed. This is precisely the difference 

 between the porphin absorptions to the two lowest excited states, as 

 shown in Fig. 2-19. In the visible bands of porphin, near 18,000 cm ', 

 the observed molar extinction e^ax is about 10,000; in the violet or "Soret" 

 bands near 24,000 cm~i, it is about 200,000. This is a general result: 

 Comparatively weak long-wave-length transitions in 7r-electron spectra 

 are peculiar to molecules extended in two dimensions, especially sym- 

 metrical ones. 



Here the symbol Q has been given to the low state of high momentum, 

 instead of the symbol L that was used for the same kind of state in ben- 

 zene and the condensed-ring systems (Piatt, 1949), because the properties 

 of the Q state are very different, for instance, in its behavior with chemi- 

 cal substitution, as will be seen later. 



The prediction of weakness of the first transition by the vector model 

 is a result not easily obtained by the usual (one-electron) method, which 

 simply predicts that the first two transitions of porphin will be allowed. 

 Configuration interaction must be considered in such calculations before 

 any substantial difference is found in the predicted intensities of the first 

 two transitions. Simpson (1949) first made this prediction of weakness 

 for porphin by applying vector addition to a free-electron model, but he 

 oversimplified the problem unnecessarily by restricting his electrons to a 

 closed 18-atom loop, leaving out of consideration six other atoms in the 

 porphin conjugated system. When some of these atoms are actually 

 missing from the conjugated system, so that it is more similar to Simp- 

 son's model, the first transition loses its weakness, as will be seen later, 

 and no longer agrees w^ith Simpson's prediction. 



Summarizing, we identify the visible bands of square (Dih) porphin 

 from these theoretical considerations as the e^" ^A-eJg ^Q° transition, 

 degenerate and almost forbidden, and the Soret band near 4000 A as the 

 e-/- ^A-e^fg ^B° transition, degenerate and strongly allowed. 



STRUCTURE OF THE VISIBLE BANDS 



Configuration of Porphin. In neutral porphin the only parts that must 

 violate the Dih symmetry are the two central hydrogens. Discussion 

 raged for years about whether they were normally on opposite nitrogen 

 atoms or on adjacent nitrogen atoms or served as bridges between the 

 nitrogen atoms; or whether all these species were present in an equilibrium 

 mixture, with rapid transformation from one to the other. This problem 



