EXCITATION OF POLYENES AND PORPHYRINS 117 



values are for the "one-electron approximation," neglecting the mixing 

 that has been postulated here between the one-electron Qx and B^ states 

 and between the one-electron Qy and By states. (The symbols Q and B 

 do not properly apply to one-electron wave functions but to the mixed 

 functions; we use them here only for brevity.) 



It is evident from the table that excitation from the ground state of 

 porphin to Qx involves electronic charge transfer principally within the 

 two rings that are on the H-H axis, from the nitrogen in those rings to 

 the external carbons. (This should excite strongly the corresponding 

 pyrrole vibration.) When Qx is mixed with Bx, charge will move from 

 the branch carbons to restore some of the nitrogen loss and will also build 

 up on the a positions. The total result in the mixed Qx state is acti- 

 vation of the a positions and of the external carbons on the H-H rings. 



Excitation from the ground state to Qy correspondingly produces acti- 

 vation of the external carbons on the other two rings, those perpendicular 

 to the H-H axis, and when Qy is mixed with the By state, excitation of 

 the a positions as well. 



In the Ux or Wx state, a nonbonding electron would go principally to 

 the a positions, to the end carbon atoms on the H-H axis, and to the 

 nitrogen atoms off it. In Table 2-4 tetrahydroporphin shows much the 

 same behavior, except that the Qy and By properties are interchanged. 

 The end carbon atoms on the H-H axis are activated in Qx excitation, 

 and the a positions also, when Bx is mixed in, with the branch carbon 

 atoms on the end rings losing charge. In Qy excitation, charge moves 

 from the branch carbon atoms to the a positions and the side nitrogens, 

 but mixing of Qy with By, since there are now no side rings to acquire 

 charge, tends to restore approximately the ground-state electron density. 



In the Ux or Wx state a nonbonding electron would go principally to 

 the a positions, the end carbon atoms, and the side nitrogen atoms. In 

 porphin, then, the singlet or triplet I \, Wx, or Qx (mixed) states should 

 favor proton addition at the carbon atoms in the rings on the H-H axis; 

 the Uy, Wy, or Qy states, in the rings off the axis. In tetrahydroporphin 

 the latter states would not be especially favorable to electrophilic addi- 

 tions except possibly at the a positions, but additions at these points 

 would separate the conjugated system into two less stable parts and so 

 might easily be lost again when the ground state was reached. The 

 singlet and triplet Ux, Wx, and Qx states have a high electron density 

 at the end carbon atoms and would attract two protons there, but again 

 the protons cannot stay, for this would produce a highly unstable 17-mem- 

 bered ring (with amino group attached) or, from another point of view, 

 a highly unstable 16-membered ring (with vinyl group attached). 



Photooxidation. In tetrahydroporphin, on the other hand. Table 2-4 

 shows that the x-electron density on the side rings is abnormally low, 

 particularly at the saturated carbon atoms and, in the Qy singlet and 



